text: away galaxies, they produce additional γ-rays in their interactions with the local interstellar medium; or microwaves from synchrotron emission; providing additional possible signals of Wino annihilations. These energetic CRs can even impact the CMB at the recombination epoch. In this setup the higher order corrections are crucial for making robust predictions for the indirect detection. It is especially important, because this is the only feasible way of excluding (or detecting) Wino DM, at least in the near future. Monochromatic γ-rays, potentially giving a smoking-gun signature of DM annihilation, can only be produced at the loop level. Additionally, three body ﬁnal −→ − − −→ − −→ − − state processes χχ W+W γ, W+W Z and χχ χ+χ W+W γ, W+W Z have to be included, as they modify the ﬁnal spectra and total annihilation cross section. Wino dark matter has been studied on its indirect detection prospects already in the past, see e.g. [6–10]. Most of these works were interested in the low mass region, at most a few hundreds of GeV. The reason is that at a tree level such Wino can have large cross sections possibly giving interesting signals. On the other hand, when one goes beyond tree level approximation, and in particular includes the Sommerfeld eﬀect, also TeV scale Wino starts to have an interesting phenomenology. Sommerfeld (cid:29) ∼ − eﬀects become important for m m enhancing the current epoch (at 10 3c velocities) annihi- χ W lation cross section and modifying the ﬁnal annihilation products injection spectra. This was already noticed in [11], where positron and antiproton signals were discussed, especially inspired by the HEAT cosmic ray results. After PAMELA reported the positron fraction rise people were suggesting heavy DM as a possible explanation and this model was also advocated as one of the possibilities [12, 13]. However, none of these works considered electroweak corrections and all concentrated on only one or two detection channels. In this work we discuss all possible channels, which is essential for making robust claims on the exclusion or detection. More speciﬁcally, in section we present the eﬀects of the Sommerfeld enhancement and the electroweak corrections on the CR, neutrino and γ-ray spectra produced from the DM annihilations, as well as our general methodology for calculating the end product signals (after galactic propagation of CRs). In section , we show our results for a variety of indirect detection probes, that can provide more or less strong limits on Wino DM with masses anywhere between 0.5 and 3.2 TeV. We study the impact that DM annihilations can have on CR antiprotons and positrons, galactic and extragalactic diﬀuse γ-rays, in γ-ray signals from nearby dwarf spheroidal galaxies and from galaxy clusters. We also include current limits from observations of the CMB angular temperature and polarization power spectra and also future perspectives from neutrinos from the galactic center and from antideuterons. For each of these indirect detection probes, we study not just a reference case, but include the most important astrophysical uncertainties that can impact the strength of the derived limits. Those uncertainties can be related to the background production and propagation assumptions of the CRs (for the CR probes), to the local DM density, to the DM density proﬁle of our Galaxy, to the impact of the DM substructures, or to the target selection (see more details in the individual subsections of section ). Such a study allows us a comparison on the strength between the various indirect detection methods. Finally, in section we discuss on the combination of these indirect detection probes and conclude. 2 The Sommerfeld eﬀect and Wino DM The Sommerfeld enhancement is a non-relativistic eﬀect, resulting in correcting the annihilation cross section due to presence of some “long range force” between the particles in the incoming state. It can be described as an eﬀect of distorting the initial wave function of the incoming two-particle state by a non-relativistic potential. This potential is taken to be Yukawa or Coulomb, as the force arises due to exchange of massive or massless boson.1 For a review of this eﬀect in the dark matter context we refer the Reader to e.g. [14, 15] and references therein. Here, we would only like to stress the main implications of this eﬀect for the Wino DM model. At the tree level and in the leading order Born approximation, which in the following we will simply refer to as the ”tree”, the annihilation cross section for pure Wino is given by: 1In the cosmological setting in reality the potentials are always Yukawa type, since in the thermal background due to the plasma screening there are no strictly massless modes. – 2 – ##LTLine##

text: away

label: paragraph

text: galaxies,

text: they

text: produce

text: additional

text: γ-rays

text: in

text: their

text: interactions

text: with

text: the

text: local

text: interstellar

text: medium;

text: or

text: microwaves

text: from

text: synchrotron

text: emission;

text: providing

text: additional

text: possible

text: signals

text: of

text: Wino

text: annihilations.

text: These

text: energetic

text: CRs

text: can

text: even

text: impact

text: the

text: CMB

text: at

text: the

text: recombination

text: epoch.

text: In

text: this

text: setup

text: the

text: higher

text: order

text: corrections

text: are

text: crucial

text: for

text: making

text: robust

text: predictions

text: for

text: the

text: indirect

text: detection.

text: It

text: is

text: especially

text: important,

text: because

text: this

text: is

text: the

text: only

text: feasible

text: way

text: of

text: excluding

text: (or

text: detecting)

text: Wino

text: DM,

text: at

text: least

text: in

text: the

text: near

text: future.

text: Monochromatic

text: γ-rays,

text: potentially

text: giving

text: a

text: smoking-gun

text: signature

text: of

text: DM

text: annihilation,

text: can

text: only

text: be

text: produced

text: at

text: the

text: loop

text: level.

text: Additionally,

text: three

text: body

text: ﬁnal

text: state

text: processes

text: χχ

text: W+W

text: γ,

text: W+W

text: Z

text: and

text: χχ

text: χ+χ

text: W+W

text: γ,

text: W+W

text: Z

text: have

text: to

text: be

text: included,

text: as

text: they

text: modify

text: the

text: ﬁnal

text: spectra

text: and

text: total

text: annihilation

text: cross

text: section.

text: Wino

text: dark

text: matter

text: has

text: been

text: studied

text: on

text: its

text: indirect

text: detection

text: prospects

text: already

text: in

text: the

text: past,

text: see

text: e.g.

text: Most

text: of

text: these

text: works

text: were

text: interested

text: in

text: the

text: low

text: mass

text: region,

text: at

text: most

text: a

text: few

text: hundreds

text: of

text: GeV.

text: The

text: reason

text: is

text: that

text: at

text: a

text: tree

text: level

text: such

text: Wino

text: can

text: have

text: large

text: cross

text: sections

text: possibly

text: giving

text: interesting

text: signals.

text: On

text: the

text: other

text: hand,

text: when

text: one

text: goes

text: beyond

text: tree

text: level

text: approximation,

text: and

text: in

text: particular

text: includes

text: the

text: Sommerfeld

text: eﬀect,

text: also

text: TeV

text: scale

text: Wino

text: starts

text: to

text: have

text: an

text: interesting

text: phenomenology.

text: Sommerfeld

text: eﬀects

text: become

text: important

text: for

text: m

text: m

text: enhancing

text: the

text: current

text: epoch

text: (at

text: velocities)

text: annihi-

text: χ

text: W

text: lation

text: cross

text: section

text: and

text: modifying

text: the

text: ﬁnal

text: annihilation

text: products

text: injection

text: spectra.

text: This

text: was

text: already

text: noticed

text: in

text: where

text: positron

text: and

text: antiproton

text: signals

text: were

text: discussed,

text: especially

text: inspired

text: by

text: the

text: HEAT

text: cosmic

text: ray

text: results.

text: After

text: PAMELA

text: reported

text: the

text: positron

text: fraction

text: rise

text: people

text: were

text: suggesting

text: heavy

text: DM

text: as

text: a

text: possible

text: explanation

text: and

text: this

text: model

text: was

text: also

text: advocated

text: as

text: one

text: of

text: the

text: possibilities

text: However,

text: of

text: these

text: works

text: considered

text: electroweak

text: corrections

text: and

text: all

text: concentrated

text: on

text: only

text: one

text: or

text: two

text: detection

text: channels.

text: In

text: this

text: work

text: we

text: discuss

text: all

text: possible

text: channels,

text: which

text: is

text: essential

text: for

text: making

text: robust

text: claims

text: on

text: the

text: exclusion

text: or

text: detection.

text: More

text: speciﬁcally,

text: in

text: section

text: we

text: present

text: the

text: eﬀects

text: of

text: the

text: Sommerfeld

text: enhancement

text: and

text: the

text: electroweak

text: corrections

text: on

text: the

text: CR,

text: neutrino

text: and

text: γ-ray

text: spectra

text: produced

text: from

text: the

text: DM

text: annihilations,

text: as

text: well

text: as

text: our

text: general

text: methodology

text: for

text: calculating

text: the

text: end

text: product

text: signals

text: (after

text: galactic

text: propagation

text: of

text: CRs).

text: In

text: section

text: we

text: show

text: our

text: results

text: for

text: a

text: variety

text: of

text: indirect

text: detection

text: probes,

text: that

text: can

text: provide

text: more

text: or

text: less

text: strong

text: limits

text: on

text: Wino

text: DM

text: with

text: masses

text: anywhere

text: between

text: and

text: TeV.

text: We

text: study

text: the

text: impact

text: that

text: DM

text: annihilations

text: can

text: have

text: on

text: CR

text: antiprotons

text: and

text: positrons,

text: galactic

text: and

text: extragalactic

text: diﬀuse

text: γ-rays,

text: in

text: γ-ray

text: signals

text: from

text: nearby

text: dwarf

text: spheroidal

text: galaxies

text: and

text: from

text: galaxy

text: clusters.

text: We

text: also

text: include

text: current

text: limits

text: from

text: observations

text: of

text: the

text: CMB

text: angular

text: temperature

text: and

text: polarization

text: power

text: spectra

text: and

text: also

text: future

text: perspectives

text: from

text: neutrinos

text: from

text: the

text: galactic

text: center

text: and

text: from

text: antideuterons.

text: For

text: each

text: of

text: these

text: indirect

text: detection

text: probes,

text: we

text: study

text: not

text: just

text: a

text: reference

text: case,

text: but

text: include

text: the

text: most

text: important

text: astrophysical

text: uncertainties

text: that

text: can

text: impact

text: the

text: strength

text: of

text: the

text: derived

text: limits.

text: Those

text: uncertainties

text: can

text: be

text: related

text: to

text: the

text: background

text: production

text: and

text: propagation

text: assumptions

text: of

text: the

text: CRs

text: (for

text: the

text: CR

text: probes),

text: to

text: the

text: local

text: DM

text: density,

text: to

text: the

text: DM

text: density

text: proﬁle

text: of

text: our

text: Galaxy,

text: to

text: the

text: impact

text: of

text: the

text: DM

text: substructures,

text: or

text: to

text: the

text: target

text: selection

text: (see

text: more

text: details

text: in

text: the

text: individual

text: subsections

text: of

text: section

text: Such

text: a

text: study

text: allows

text: us

text: a

text: comparison

text: on

text: the

text: strength

text: between

text: the

text: various

text: indirect

text: detection

text: methods.

text: Finally,

text: in

text: section

text: we

text: discuss

text: on

text: the

text: combination

text: of

text: these

text: indirect

text: detection

text: probes

text: and

text: conclude.

text: The

text: Sommerfeld

text: eﬀect

text: and

text: Wino

text: DM

text: The

text: Sommerfeld

text: enhancement

text: is

text: a

text: non-relativistic

text: eﬀect,

text: resulting

text: in

text: correcting

text: the

text: annihilation

text: cross

text: section

text: due

text: to

text: presence

text: of

text: some

text: “long

text: range

text: force”

text: between

text: the

text: particles

text: in

text: the

text: incoming

text: state.

text: It

text: can

text: be

text: described

text: as

text: an

text: eﬀect

text: of

text: distorting

text: the

text: initial

text: wave

text: function

text: of

text: the

text: incoming

text: two-particle

text: state

text: by

text: a

text: non-relativistic

text: potential.

text: This

text: potential

text: is

text: taken

text: to

text: be

text: Yukawa

text: or

text: Coulomb,

text: as

text: the

text: force

text: arises

text: due

text: to

text: exchange

text: of

text: massive

text: or

text: massless

text: For

text: a

text: review

text: of

text: this

text: eﬀect

text: in

text: the

text: dark

text: matter

text: context

text: we

text: refer

text: the

text: Reader

text: to

text: e.g.

text: and

text: references

text: therein.

text: Here,

text: we

text: would

text: only

text: like

text: to

text: stress

text: the

text: main

text: implications

text: of

text: this

text: eﬀect

text: for

text: the

text: Wino

text: DM

text: model.

text: At

text: the

text: tree

text: level

text: and

text: in

text: the

text: leading

text: order

text: Born

text: approximation,

text: which

text: in

text: the

text: following

text: we

text: will

text: simply

text: refer

text: to

text: as

text: the

text: ”tree”,

text: the

text: annihilation

text: cross

text: section

text: for

text: pure

text: Wino

text: is

text: given

text: by:

text: the

text: cosmological

text: setting

text: in

text: reality

text: the

text: potentials

text: are

text: always

text: Yukawa

text: type,

text: since

text: in

text: the

text: thermal

text: background

text: due

text: to

text: the

text: plasma

text: screening

text: there

text: are

text: no

text: strictly

text: massless

text: modes.

text: ##LTLine##


text: Ursa Minor Sextans Mass [GeV] 90% CL 95% CL 99.9% CL 90% CL 95% CL 99.9% CL 500 0.66 0.94 2.13 1.52 2.02 4.02 1000 3.19 4.77 11.8 7.17 9.67 19.7 2360 0.020 0.031 0.079 0.043 0.059 0.123 2400 0.033 0.051 0.132 0.071 0.097 0.203 2500 0.55 0.83 2.14 1.16 1.59 3.31 2700 3.69 5.61 14.46 7.84 10.7 22.4 3200 14.7 22.4 58.0 30.4 41.9 87.9 Table 3. The upper limits on the boost factors coming from two dSphs: Ursa Minor and Sextans. Values of BFs smaller than one suggest the model is excluded. 10(cid:45)21 excluded by dSphs at 95 CL (cid:37) 10(cid:45)22 (cid:144)(cid:68)3ms 10(cid:45)23 Sextans (cid:64)c UrsaMinor (cid:62) vΣ 10(cid:45)24 (cid:60) 10(cid:45)25 10(cid:45)26 500 1000 1500 2000 2500 3000 (cid:64) (cid:68) m GeV Figure 11. 95% CL upper limits on the total annihilation cross-section. The limits are derived individually from Ursa Minor and from Sextans dwarf spheroidal galaxies, using the Fermi-LAT data (see text for details). analyses (including ours) treat Ursa Minor as a spherically symmetric system. This is a simpliﬁcation on the DM proﬁle, for which the accurate triaxial treatment, we leave for future work. The method for obtaining the limits is the same as in [105], from where we adopted also the values for the J- factors, deﬁnitions of regions of interest which are used for estimating the signal and the treatment of subtracting the galactic foreground and extragalactic background. Referring for all the details to this paper, here we will just give the results for the Wino model. After computing the γ-ray ﬂux for a given mass of the Wino, we confront it with the data collected by Fermi-LAT between August 2008 and December 2013, with energies between 1 and 100 GeV. From this we compute what is the additional boost factor (BF) i.e. the multiplication factor on the cross section for each model, that is allowed by the observed residual γ-ray spectrum at the given conﬁdence levels (CL). Our results are summarized in Tab. 3, where three diﬀerent conﬁdence levels are presented; and in Fig. 11 where we show the 95 % CL from Ursa Minor and Sextans. Again the results show that only masses very close to the resonance, m = 2.4 TeV, can be ruled out. When χ moving a bit further from the resonance the allowed boost factors are getting close to 1, and eﬀectively all other masses are not constrained in any way by this search channel. Note, that the biggest uncertainty here comes from the evaluation of the J-factor. The Fermi collaboration itself following diﬀerent assumptions on the uncertainties of the J-factors and the mod- eling of the background+foreground emission has provided limits on several ”standard” channels of annihilation by doing a stacked and a source by source analysis [103, 104]. For such an analysis our ∼ limits would be for the individual Ursa Minor dSph a factor of 3 weaker than those of Tab. 3. With a joint likelihood analysis though the limits are a factor of 2 stronger, thus conﬁning also the cases of 0.5 and 2.5 TeV mass. Also the authors of [117] using a diﬀerent joint analysis strategy for the Milky Way dSphs, have shown the signiﬁcance in the uncertainties of the J-factors with their weaker limits – 23 – ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: Ursa

label: table

text: Minor

text: Sextans

text: Mass

text: [GeV]

text: CL

text: CL

text: CL

text: CL

text: CL

text: CL

text: Table

text: The

label: caption

text: upper

text: limits

text: on

text: the

text: boost

text: factors

text: coming

text: from

text: two

text: dSphs:

text: Ursa

text: Minor

text: and

text: Sextans.

text: Values

text: of

text: BFs

text: smaller

text: than

text: one

text: suggest

text: the

text: model

text: is

text: excluded.

font: default

text: excluded

text: by

text: dSphs

text: at

text: CL

text: Sextans

text: UrsaMinor

text: vΣ

text: m

text: GeV

text: Figure

text: CL

text: upper

text: limits

text: on

text: the

text: total

text: annihilation

text: cross-section.

text: The

text: limits

text: are

text: derived

text: individually

text: from

text: Ursa

text: Minor

text: and

text: from

text: Sextans

text: dwarf

text: spheroidal

text: galaxies,

text: using

text: the

text: Fermi-LAT

text: data

text: (see

text: text

text: for

text: details).

text: analyses

text: (including

text: ours)

text: treat

text: Ursa

text: Minor

text: as

text: a

text: spherically

text: symmetric

text: system.

text: This

text: is

text: a

text: simpliﬁcation

text: on

text: the

text: DM

text: proﬁle,

text: for

text: which

text: the

text: accurate

text: triaxial

text: treatment,

text: we

text: leave

text: for

text: future

text: work.

text: The

text: method

text: for

text: obtaining

text: the

text: limits

text: is

text: the

text: same

text: as

text: in

text: from

text: where

text: we

text: adopted

text: also

text: the

text: values

text: for

text: the

text: J-

text: factors,

text: deﬁnitions

text: of

text: regions

text: of

text: interest

text: which

text: are

text: used

text: for

text: estimating

text: the

text: signal

text: and

text: the

text: treatment

text: of

text: subtracting

text: the

text: galactic

text: foreground

text: and

text: extragalactic

text: background.

text: Referring

text: for

text: all

text: the

text: details

text: to

text: this

text: paper,

text: here

text: we

text: will

text: just

text: give

text: the

text: results

text: for

text: the

text: Wino

text: model.

text: After

text: computing

text: the

text: γ-ray

text: ﬂux

text: for

text: a

text: given

text: mass

text: of

text: the

text: Wino,

text: we

text: confront

text: it

text: with

text: the

text: data

text: collected

text: by

text: Fermi-LAT

text: between

text: August

text: and

text: December

text: with

text: energies

text: between

text: and

text: GeV.

text: From

text: this

text: we

text: compute

text: what

text: is

text: the

text: additional

text: boost

text: factor

text: (BF)

text: i.e.

text: the

text: multiplication

text: factor

text: on

text: the

text: cross

text: section

text: for

text: each

text: model,

text: that

text: is

text: allowed

text: by

text: the

text: observed

text: residual

text: γ-ray

text: spectrum

text: at

text: the

text: given

text: conﬁdence

text: levels

text: (CL).

text: Our

text: results

text: are

text: summarized

text: in

text: Tab.

text: where

text: three

text: diﬀerent

text: conﬁdence

text: levels

text: are

text: presented;

text: and

text: in

text: Fig.

text: where

text: we

text: show

text: the

text: CL

text: from

text: Ursa

text: Minor

text: and

text: Sextans.

text: Again

text: the

text: results

text: show

text: that

text: only

text: masses

text: very

text: close

text: to

text: the

text: resonance,

text: m

text: TeV,

text: can

text: be

text: ruled

text: out.

text: When

text: χ

text: moving

text: a

text: bit

text: further

text: from

text: the

text: resonance

text: the

text: allowed

text: boost

text: factors

text: are

text: getting

text: close

text: to

text: and

text: eﬀectively

text: all

text: other

text: masses

text: are

text: not

text: constrained

text: in

text: any

text: way

text: by

text: this

text: search

text: channel.

text: Note,

text: that

text: the

text: biggest

text: uncertainty

text: here

text: comes

text: from

text: the

text: evaluation

text: of

text: the

text: J-factor.

text: The

text: Fermi

text: collaboration

text: itself

text: following

text: diﬀerent

text: assumptions

text: on

text: the

text: uncertainties

text: of

text: the

text: J-factors

text: and

text: the

text: mod-

text: eling

text: of

text: the

text: background+foreground

text: emission

text: has

text: provided

text: limits

text: on

text: several

text: ”standard”

text: channels

text: of

text: annihilation

text: by

text: doing

text: a

text: stacked

text: and

text: a

text: source

text: by

text: source

text: analysis

text: For

text: such

text: an

text: analysis

text: our

text: limits

text: would

text: be

text: for

text: the

text: individual

text: Ursa

text: Minor

text: dSph

text: a

text: factor

text: of

text: weaker

text: than

text: those

text: of

text: Tab.

text: With

text: a

text: joint

text: likelihood

text: analysis

text: though

text: the

text: limits

text: are

text: a

text: factor

text: of

text: stronger,

text: thus

text: conﬁning

text: also

text: the

text: cases

text: of

text: and

text: TeV

text: mass.

text: Also

text: the

text: authors

text: of

text: using

text: a

text: diﬀerent

text: joint

text: analysis

text: strategy

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text: the

text: Milky

text: Way

text: dSphs,

text: have

text: shown

text: the

text: signiﬁcance

text: in

text: the

text: uncertainties

text: of

text: the

text: J-factors

text: with

text: their

text: weaker

text: limits

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text: excluded by HESS Γ(cid:45)line searches at 95(cid:37) CL 10(cid:45)22 Burk10 (cid:144)(cid:68)3ms 10(cid:45)24 (cid:64)vc(cid:62) EENiinnF00W1272 Σ (cid:60) 10(cid:45)26 Burk05 10(cid:45)28 500 1000 1500 2000 2500 3000 (cid:64) (cid:68) m GeV Figure 12. 95 % CL upper limits on the total annihilation cross-section. The limits are based on Wino −→ annihilations giving monochromatic γ-rays: χχ γγ, γZ and γ-rays from internal bremsstrahlung. We use the data from HESS [120] and show ﬁve diﬀerent DM proﬁles; from top to bottom: Burkert with R = 10 B kpc, Einasto with α = 0.22, NFW, Einasto with α = 0.17 and Burkert with R = 0.5 kpc (see text for B details). being a factor of 5 weaker than those of Tab. 3. 3.7 Limits from a γ-ray line feature A smocking gun signature in γ-rays, from DM annihilations in the Galaxy is the presence of a line feature toward the galactic center (see [118] for a recent review). Both Fermi and HESS have recently searched for such an excess and published upper limits on monochromatic γ-ray ﬂuxes [119, 120]. As can be indicated from Fig. 2, all the Wino mass range has a branching ratio to monochromatic γ-rays at the high energy end of the spectrum, allowing for such a search mode. For the case at hand, since we are mostly interested in the masses at the TeV scale, the data of interest are those from HESS. [121, 122], have recently suggested that the absence of any evident γ-ray line feature in the HESS data, can place very strong limits on the Wino DM models in most of the mass range. In Fig. 12, using ﬁve diﬀerent DM proﬁles for the smooth halo, we show the 95% CL upper limits on the total −→ −→ annihilation cross-section coming from the χχ γγ and χχ γZ partial cross-sections and also the internal bremsstrahlung. Given that the HESS energy resolution in the energy range of interest, (cid:39) is 15%, the three components can not be discriminated. 13 (cid:18) (cid:19) The ﬁve DM halo proﬁles that we use, are the standard NFW proﬁle (3.1) with R = 20 kpc, c the Einasto DM proﬁle [123]: − − 2 rα R(cid:12)α ρ(r) = ρ exp , (3.6) 0 α Rα c with a slope α of 0.22 and 0.17, and R = 10 kpc (R(cid:12) = 8.5 kpc is the Sun’s galacto-centric distance) c and the Burkert DM proﬁle [124]: 1 1 ρ(r) = ρ , (3.7) B (1 + r/R ) (1 + (r/R )2) B B with R = 10 and 0.5 kpc. The normalizations ρ , ρ and ρ are taken such that in all cases the B 0 NFW B local DM density is 0.4 GeV/cm3. The two Burkert cases are shown only for direct comparison with the work of [121]. Both of them either over-predict or under-predict the included DM mass in the inner 8 kpc of the Milky Way. Especially the case of R = 0.5 kpc, grossly violates bounds from local B dynamical measurements, as well as of the inner and outer rotation curve. Moreover, the Burkert ∝ − case with R = 0.5 kpc core radius is not a cored proﬁle, but in fact a proﬁle with ρ(r) r 3; thus B the term ”Burkert” is slightly deceiving. For these reasons we only present it in Fig. 12 for reference and we disregard it in our ﬁnal conclusions. Instead, the NFW and the two Einasto proﬁles are representative of the DM density in the Galaxy. 13We consider a 15% energy resolution for the entire mass range of 0.5 to 3.2 TeV. – 24 – ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: excluded

text: by

text: HESS

text: searches

text: at

text: CL

text: Σ

text: m

text: GeV

text: Figure

text: CL

text: upper

text: limits

text: on

text: the

text: total

text: annihilation

text: cross-section.

text: The

text: limits

text: are

text: based

text: on

text: Wino

text: annihilations

text: giving

text: monochromatic

text: γ-rays:

text: χχ

text: γγ,

text: γZ

text: and

text: γ-rays

text: from

text: internal

text: bremsstrahlung.

text: We

text: use

text: the

text: data

text: from

text: HESS

text: and

text: show

text: ﬁve

text: diﬀerent

text: DM

text: proﬁles;

text: from

text: top

text: to

text: bottom:

text: Burkert

text: with

text: R

text: B

text: kpc,

text: Einasto

text: with

text: α

text: NFW,

text: Einasto

text: with

text: α

text: and

text: Burkert

text: with

text: R

text: kpc

text: (see

text: text

text: for

text: B

text: details).

text: being

text: a

text: factor

text: of

text: weaker

text: than

text: those

text: of

text: Tab.

text: Limits

text: from

text: a

text: γ-ray

text: line

text: feature

text: A

text: smocking

text: gun

text: signature

text: in

text: γ-rays,

text: from

text: DM

text: annihilations

text: in

text: the

text: Galaxy

text: is

text: the

text: presence

text: of

text: a

text: line

text: feature

text: toward

text: the

text: galactic

text: center

text: (see

text: for

text: a

text: recent

text: review).

text: Both

text: Fermi

text: and

text: HESS

text: have

text: recently

text: searched

text: for

text: such

text: an

text: excess

text: and

text: published

text: upper

text: limits

text: on

text: monochromatic

text: γ-ray

text: ﬂuxes

text: As

text: can

text: be

text: indicated

text: from

text: Fig.

text: all

text: the

text: Wino

text: mass

text: range

text: has

text: a

text: branching

text: ratio

text: to

text: monochromatic

text: γ-rays

text: at

text: the

text: high

text: energy

text: end

text: of

text: the

text: spectrum,

text: allowing

text: for

text: such

text: a

text: search

text: mode.

text: For

text: the

text: case

text: at

text: hand,

text: since

text: we

text: are

text: mostly

text: interested

text: in

text: the

text: masses

text: at

text: the

text: TeV

text: scale,

text: the

text: data

text: of

text: interest

text: are

text: those

text: from

text: HESS.

text: have

text: recently

text: suggested

text: that

text: the

text: absence

text: of

text: any

text: evident

text: γ-ray

text: line

text: feature

text: in

text: the

text: HESS

text: data,

text: can

text: place

text: very

text: strong

text: limits

text: on

text: the

text: Wino

text: DM

text: models

text: in

text: most

text: of

text: the

text: mass

text: range.

text: In

text: Fig.

text: using

text: ﬁve

text: diﬀerent

text: DM

text: proﬁles

text: for

text: the

text: smooth

text: halo,

text: we

text: show

text: the

text: CL

text: upper

text: limits

text: on

text: the

text: total

text: annihilation

text: cross-section

text: coming

text: from

text: the

text: χχ

text: γγ

text: and

text: χχ

text: γZ

text: partial

text: cross-sections

text: and

text: also

text: the

text: internal

text: bremsstrahlung.

text: Given

text: that

text: the

text: HESS

text: energy

text: resolution

text: in

text: the

text: energy

text: range

text: of

text: interest,

text: is

text: the

text: three

text: components

text: can

text: not

text: be

text: discriminated.

text: The

text: ﬁve

text: DM

text: halo

text: proﬁles

text: that

text: we

text: use,

text: are

text: the

text: standard

text: NFW

text: proﬁle

text: with

text: R

text: kpc,

text: c

text: the

text: Einasto

text: DM

text: proﬁle

text: rα

text: ρ(r)

text: ρ

text: exp

text: α

text: Rα

text: c

text: with

text: a

text: slope

text: α

text: of

text: and

text: and

text: R

text: kpc

text: kpc

text: is

text: the

text: Sun’s

text: galacto-centric

text: distance)

text: c

text: and

text: the

text: Burkert

text: DM

text: proﬁle

text: ρ(r)

text: ρ

text: B

text: r/R

text: (r/R

text: B

text: B

text: with

text: R

text: and

text: kpc.

text: The

text: normalizations

text: ρ

text: ρ

text: and

text: ρ

text: are

text: taken

text: such

text: that

text: in

text: all

text: cases

text: the

text: B

text: NFW

text: B

text: local

text: DM

text: density

text: is

text: The

text: two

text: Burkert

text: cases

text: are

text: shown

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text: for

text: direct

text: comparison

text: with

text: the

text: work

text: of

text: Both

text: of

text: them

text: either

text: over-predict

text: or

text: under-predict

text: the

text: included

text: DM

text: mass

text: in

text: the

text: inner

text: kpc

text: of

text: the

text: Milky

text: Way.

text: Especially

text: the

text: case

text: of

text: R

text: kpc,

text: grossly

text: violates

text: bounds

text: from

text: local

text: B

text: dynamical

text: measurements,

text: as

text: well

text: as

text: of

text: the

text: inner

text: and

text: outer

text: rotation

text: curve.

text: Moreover,

text: the

text: Burkert

text: case

text: with

text: R

text: kpc

text: core

text: radius

text: is

text: not

text: a

text: cored

text: proﬁle,

text: but

text: in

text: fact

text: a

text: proﬁle

text: with

text: ρ(r)

text: r

text: thus

text: B

text: the

text: term

text: ”Burkert”

text: is

text: slightly

text: deceiving.

text: For

text: these

text: reasons

text: we

text: only

text: present

text: it

text: in

text: Fig.

text: for

text: reference

text: and

text: we

text: disregard

text: it

text: in

text: our

text: ﬁnal

text: conclusions.

text: Instead,

text: the

text: NFW

text: and

text: the

text: two

text: Einasto

text: proﬁles

text: are

text: representative

text: of

text: the

text: DM

text: density

text: in

text: the

text: Galaxy.

text: consider

text: a

text: energy

text: resolution

text: for

text: the

text: entire

text: mass

text: range

text: of

text: to

text: TeV.

text: ##LTFigure##

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text: 5´10-4 mΧ=1000GeV mΧ=2400GeV mΧ=3200GeV 1´10-4 LogxHL 5´10-5 Nd(cid:144) d 1´10-5 5´10-6 10-5 10-4 0.001 0.01 0.1 1 x=Ek(cid:144)mΧ Figure 14. Antideuteron spectra from Wino annihilation for masses m = 1, 2.4, 3.2 TeV. Dotted lines show χ the tree level results, while solid the Sommerfeld enhanced ones. of 3-dim sphere in momentum space with radius p . The d¯ yield is given by 0 dN 4πp3 dN dN γ d = 0 γ n γ p , (3.9) d d3k 3 n d3k p d3k d n p ≈ ≈ where the Lorenz factors are approximately equal γd (cid:112)γn γp. We have also E (cid:112) d3kX = 4πkX2 dkX = 4πkX2 E2 X− m2 dEX, (3.10) X X − where k = E2 m2 . In order for d¯ to form, the diﬀerence in momentum of p¯ and n¯ has to be X (cid:28) X X less then p k , k . Thus, the momenta approximately satisfy the relation: 0 n p k ≈ ≈ ≡ d k k k , (3.11) 2 p n ≈ ≡ (cid:18) (cid:19) and thus also E E E. Finally, the antideuteron spectrum can be computed from the proton p n (cid:113) one via:18 dN 4p3 γ dN 2 d = 0 p p . (3.12) − dE 3 dE d E E2 m2 p Apart from the update in value of p there is another, much more important diﬀerence in the 0 newer works [142–145] from the older ones: although they rely on the coalescence model they do not make the spherical approximation, but run a dedicated Monte Carlo codes to compute the d¯ yields. The authors argue, that this is correct way to proceed, in contrary to previous works of [138, 140, 141], which they claim to be oversimpliﬁed. The important phenomenological diﬀerence, is the behavior − of the ﬂux for higher dark matter masses, where the spherical approximation gives m 2 dependence, χ while Monte Carlo gives a more ﬂat distribution. The physical reason why the spherical coalescence model is not suﬃcient is that after dark matter annihilates, ﬁnal states are very energetic and go in back-to-back jets, rather than distributed over all 4π. Therefore, the p¯ and n¯ are typically produced with much smaller separation angle. This is especially pronounced for high m and explains why the in this regime the diﬀerence is the largest. χ In our work we adopted the results from the Monte Carlo approach of Ref. [142], which is publicly available via the PPPC 4 DM ID code. However, as before, for the electroweak corrections we used our computation and also incorporated the Sommerfeld eﬀect. 18This is based on the assumption that the spectra of antiprotons and antineutrons in a single annihilation are approximately equal. For a more reﬁned approach see [144]. – 27 – ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: LogxHL

text: d

text: Figure

text: Antideuteron

text: spectra

text: from

text: Wino

text: annihilation

text: for

text: masses

text: m

text: TeV.

text: Dotted

text: lines

text: show

text: χ

text: the

text: tree

text: level

text: results,

text: while

text: solid

text: the

text: Sommerfeld

text: enhanced

text: ones.

text: of

text: sphere

text: in

text: momentum

text: space

text: with

text: radius

text: p

text: The

text: d¯

text: yield

text: is

text: given

text: by

text: dN

text: dN

text: dN

text: γ

text: d

text: γ

text: n

text: γ

text: p

text: d

text: n

text: p

text: d

text: n

text: p

text: where

text: the

text: Lorenz

text: factors

text: are

text: approximately

text: equal

text: γd

text: γp.

text: We

text: have

text: also

text: E

text: dkX

text: X−

text: dEX,

text: X

text: X

text: where

text: k

text: In

text: order

text: for

text: d¯

text: to

text: form,

text: the

text: diﬀerence

text: in

text: momentum

text: of

text: p¯

text: and

text: n¯

text: has

text: to

text: be

text: X

text: X

text: X

text: less

text: then

text: p

text: k

text: k

text: Thus,

text: the

text: momenta

text: approximately

text: satisfy

text: the

text: relation:

text: n

text: p

text: k

text: d

text: k

text: k

text: k

text: p

text: n

text: and

text: thus

text: also

text: E

text: E

text: E.

text: Finally,

text: the

text: antideuteron

text: spectrum

text: can

text: be

text: computed

text: from

text: the

text: proton

text: p

text: n

text: one

text: dN

text: γ

text: dN

text: d

text: p

text: p

text: dE

text: dE

text: d

text: E

text: p

text: Apart

text: from

text: the

text: update

text: in

text: value

text: of

text: p

text: there

text: is

text: another,

text: much

text: more

text: important

text: diﬀerence

text: in

text: the

text: newer

text: works

text: from

text: the

text: older

text: ones:

text: although

text: they

text: rely

text: on

text: the

text: coalescence

text: model

text: they

text: do

text: not

text: make

text: the

text: spherical

text: approximation,

text: but

text: run

text: a

text: dedicated

text: Monte

text: Carlo

text: codes

text: to

text: compute

text: the

text: d¯

text: yields.

text: The

text: authors

text: argue,

text: that

text: this

text: is

text: correct

text: way

text: to

text: proceed,

text: in

text: contrary

text: to

text: previous

text: works

text: of

text: which

text: they

text: claim

text: to

text: be

text: oversimpliﬁed.

text: The

text: important

text: phenomenological

text: diﬀerence,

text: is

text: the

text: behavior

text: of

text: the

text: ﬂux

text: for

text: higher

text: dark

text: matter

text: masses,

text: where

text: the

text: spherical

text: approximation

text: gives

text: m

text: dependence,

text: χ

text: while

text: Monte

text: Carlo

text: gives

text: a

text: more

text: ﬂat

text: distribution.

text: The

text: physical

text: reason

text: why

text: the

text: spherical

text: coalescence

text: model

text: is

text: not

text: suﬃcient

text: is

text: that

text: after

text: dark

text: matter

text: annihilates,

text: ﬁnal

text: states

text: are

text: very

text: energetic

text: and

text: go

text: in

text: back-to-back

text: jets,

text: rather

text: than

text: distributed

text: over

text: all

text: Therefore,

text: the

text: p¯

text: and

text: n¯

text: are

text: typically

text: produced

text: with

text: much

text: smaller

text: separation

text: angle.

text: This

text: is

text: especially

text: pronounced

text: for

text: high

text: m

text: and

text: explains

text: why

text: the

text: in

text: this

text: regime

text: the

text: diﬀerence

text: is

text: the

text: largest.

text: χ

text: In

text: our

text: work

text: we

text: adopted

text: the

text: results

text: from

text: the

text: Monte

text: Carlo

text: approach

text: of

text: Ref.

text: which

text: is

text: publicly

text: available

text: via

text: the

text: PPPC

text: DM

text: ID

text: code.

text: However,

text: as

text: before,

text: for

text: the

text: electroweak

text: corrections

text: we

text: used

text: our

text: computation

text: and

text: also

text: incorporated

text: the

text: Sommerfeld

text: eﬀect.

text: is

text: based

text: on

text: the

text: assumption

text: that

text: the

text: spectra

text: of

text: antiprotons

text: and

text: antineutrons

text: in

text: a

text: single

text: annihilation

text: are

text: approximately

text: equal.

text: For

text: a

text: more

text: reﬁned

text: approach

text: see

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text: Next we determine a set of benchmark propagation models, whose parameters are ﬁtted to the available CR data (see Sec. ). This allows for predictions of the CR background. Using this propagation models, we compute the expected signal of the Wino in antiprotons, antiproton to proton ratio, positrons and antideuterons, from which we derive the limits on the cross section for a given Wino mass. Then we study the diﬀuse γ-rays in the galactic halo, whose predicted backgrounds are determined based on the previously obtained CR lepton ﬂuxes. We compare with the high and low latitude Fermi data to rule out the very thin propagation models, which in result make the constraints from antiprotons stronger, and in addition place strong limits themselves on the DM component. Additionally, we calculate the limits from dwarf spheroidal galaxies and a monochromatic γ-ray line feature from the Galactic Center. We also discuss the diﬀuse emission close to the GC, galaxy clusters and CMB constraints. Finally, we derive the prospects for neutrino and antideuteron searches. The ﬁnal set of limits for the Wino DM model is presented on Fig. 16. All the channels give limits around the resonance and most of them also in the low mass range, which allow to exclude these parameter regions with high level of conﬁdence. The precise constraints depend on various assumptions, which we have analysed in detail. For every search channel one can single out one physical quantity that has the strongest impact on the derived limits. To show the impact in a given channel, of the uncertainty on the leading quantity, we calculate the 95% CL upper limits under diﬀerent choices/assumptions on that leading quantity. This is shown on Fig.. 16 with diﬀerent color shading. For the case of antiprotons, the largest impact comes from the diﬀusion zone scale height assump- tion and therefore we parametrize its eﬀect by varying the diﬀusion zone height z from 1 to 20 kpc d (see Sec. ). Cosmic ray leptons, are very local and as we have shown, propagation has a very minor inﬂuence. On the other hand, the energy losses and even more importantly the local DM density can signiﬁcantly change the predicted ﬂuxes. The former can be parametrized by the local energy density of the ISRF and the magnetic ﬁeld, which we vary in the range 1.2-2.6 eV/cm3, while the uncertainty on the latter, we probe by assuming ρ between 0.25 and 0.7 GeV/cm3 (see Sec. ). From γ-ray ob- servations we derive limits from the GC, from low and high latitudes and from observations toward known dwarf spheroidal galaxies. The low latitude γ-ray limits, mainly depend on assumptions on the radiation ﬁeld in the inner galaxy and on assumptions on the interstellar gas (see Sec. ). The high latitude γ-rays contain mostly the extragalactic component, for which the biggest uncertainty comes from the knowledge of the DM substructures on distant galaxies and galaxy clusters (see Sec. ). For the dSphs, the main limiting factor is the uncertainty related to the J-factor and the foreground emission, which varies between targets (see Sec. ). The constraints from the γ-line toward the GC ◦ are limited by the knowledge of the DM proﬁle in the inner 1 . Depending whether a cored or a cuspy proﬁle is assumed the limits change by a few orders of magnitude, nevertheless for quite a wide range of DM proﬁles, the Wino DM is severely constrained (see Sec. ). Finally, the CMB constraints depend on the diﬀerent combinations of data sets used (see Sec. ). On the plot we do not include galaxy clusters because the uncertainties are too large to infer any unchallenged limits (see discussion in Sec. ). Additionally, on Fig. 17 we show how the limits change when Wino is constituting only a fraction of the whole dark matter. For every channel we take the most stringent limits and reduce the Wino abundance from 100% (lighter shaded regions) to 10% (darker shaded regions) in steps of 10%. Apart from the above limits, we also determined future prospects for the neutrinos and an- tideuteron searches. In the former, only the KM3NeT experiment could be able to probe the vicinity of the resonance, a region excluded by all the above discussed channels. The antideuterons on the other hand constitute also a quite promising channel for the low mass region, however masses below around 400 GeV (500 GeV) are already ruled out (constrained) by antiprotons, dSphs and leptons. Moreover, this channel has very large uncertainties related to both propagation and antideuterons’ production. More promising prospects, can be expected in the high latitude γ-rays, where the 10 yr Fermi data will have the potential to probe the entire (cosmologically relevant) Wino mass range discussed, if the extragalactic DM substructures are included (see [81]). Finally the CMB limits from ∼ Planck are expected to be a factor 5 tighter than the current ones after the polarization data are released. – 30 –

text: Next

text: we

text: determine

text: a

text: set

text: of

text: benchmark

text: propagation

text: models,

text: whose

text: parameters

text: are

text: ﬁtted

text: to

text: the

text: available

text: CR

text: data

text: (see

text: Sec.

text: This

text: allows

text: for

text: predictions

text: of

text: the

text: CR

text: background.

text: Using

text: this

text: propagation

text: models,

text: we

text: compute

text: the

text: expected

text: signal

text: of

text: the

text: Wino

text: in

text: antiprotons,

text: antiproton

text: to

text: proton

text: ratio,

text: positrons

text: and

text: antideuterons,

text: from

text: which

text: we

text: derive

text: the

text: limits

text: on

text: the

text: cross

text: section

text: for

text: a

text: given

text: Wino

text: mass.

text: Then

text: we

text: study

text: the

text: diﬀuse

text: γ-rays

text: in

text: the

text: galactic

text: halo,

text: whose

text: predicted

text: backgrounds

text: are

text: determined

text: based

text: on

text: the

text: previously

text: obtained

text: CR

text: lepton

text: ﬂuxes.

text: We

text: compare

text: with

text: the

text: high

text: and

text: low

text: latitude

text: Fermi

text: data

text: to

text: rule

text: out

text: the

text: very

text: thin

text: propagation

text: models,

text: which

text: in

text: result

text: make

text: the

text: constraints

text: from

text: antiprotons

text: stronger,

text: and

text: in

text: addition

text: place

text: strong

text: limits

text: themselves

text: on

text: the

text: DM

text: component.

text: Additionally,

text: we

text: calculate

text: the

text: limits

text: from

text: dwarf

text: spheroidal

text: galaxies

text: and

text: a

text: monochromatic

text: γ-ray

text: line

text: feature

text: from

text: the

text: Galactic

text: Center.

text: We

text: also

text: discuss

text: the

text: diﬀuse

text: emission

text: close

text: to

text: the

text: GC,

text: galaxy

text: clusters

text: and

text: CMB

text: constraints.

text: Finally,

text: we

text: derive

text: the

text: prospects

text: for

text: neutrino

text: and

text: antideuteron

text: searches.

text: The

text: ﬁnal

text: set

text: of

text: limits

text: for

text: the

text: Wino

text: DM

text: model

text: is

text: presented

text: on

text: Fig.

text: All

text: the

text: channels

text: give

text: limits

text: around

text: the

text: resonance

text: and

text: most

text: of

text: them

text: also

text: in

text: the

text: low

text: mass

text: range,

text: which

text: allow

text: to

text: exclude

text: these

text: parameter

text: regions

text: with

text: high

text: level

text: of

text: conﬁdence.

text: The

text: precise

text: constraints

text: depend

text: on

text: various

text: assumptions,

text: which

text: we

text: have

text: analysed

text: in

text: detail.

text: For

text: every

text: search

text: channel

text: one

text: can

text: single

text: out

text: one

text: physical

text: quantity

text: that

text: has

text: the

text: strongest

text: impact

text: on

text: the

text: derived

text: limits.

text: To

text: show

text: the

text: impact

text: in

text: a

text: given

text: channel,

text: of

text: the

text: uncertainty

text: on

text: the

text: leading

text: quantity,

text: we

text: calculate

text: the

text: CL

text: upper

text: limits

text: under

text: diﬀerent

text: choices/assumptions

text: on

text: that

text: leading

text: quantity.

text: This

text: is

text: shown

text: on

text: Fig..

text: with

text: diﬀerent

text: color

text: shading.

text: For

text: the

text: case

text: of

text: antiprotons,

text: the

text: largest

text: impact

text: comes

text: from

text: the

text: diﬀusion

text: zone

text: scale

text: height

text: assump-

text: tion

text: and

text: therefore

text: we

text: parametrize

text: its

text: eﬀect

text: by

text: varying

text: the

text: diﬀusion

text: zone

text: height

text: z

text: from

text: to

text: kpc

text: d

text: (see

text: Sec.

text: Cosmic

text: ray

text: leptons,

text: are

text: very

text: local

text: and

text: as

text: we

text: have

text: shown,

text: propagation

text: has

text: a

text: very

text: minor

text: inﬂuence.

text: On

text: the

text: other

text: hand,

text: the

text: energy

text: losses

text: and

text: even

text: more

text: importantly

text: the

text: local

text: DM

text: density

text: can

text: signiﬁcantly

text: change

text: the

text: predicted

text: ﬂuxes.

text: The

text: former

text: can

text: be

text: parametrized

text: by

text: the

text: local

text: energy

text: density

text: of

text: the

text: ISRF

text: and

text: the

text: magnetic

text: ﬁeld,

text: which

text: we

text: vary

text: in

text: the

text: range

text: while

text: the

text: uncertainty

text: on

text: the

text: latter,

text: we

text: probe

text: by

text: assuming

text: ρ

text: between

text: and

text: (see

text: Sec.

text: From

text: γ-ray

text: ob-

text: servations

text: we

text: derive

text: limits

text: from

text: the

text: GC,

text: from

text: low

text: and

text: high

text: latitudes

text: and

text: from

text: observations

text: toward

text: known

text: dwarf

text: spheroidal

text: galaxies.

text: The

text: low

text: latitude

text: γ-ray

text: limits,

text: mainly

text: depend

text: on

text: assumptions

text: on

text: the

text: radiation

text: ﬁeld

text: in

text: the

text: inner

text: galaxy

text: and

text: on

text: assumptions

text: on

text: the

text: interstellar

text: gas

text: (see

text: Sec.

text: The

text: high

text: latitude

text: γ-rays

text: contain

text: mostly

text: the

text: extragalactic

text: component,

text: for

text: which

text: the

text: biggest

text: uncertainty

text: comes

text: from

text: the

text: knowledge

text: of

text: the

text: DM

text: substructures

text: on

text: distant

text: galaxies

text: and

text: galaxy

text: clusters

text: (see

text: Sec.

text: For

text: the

text: dSphs,

text: the

text: main

text: limiting

text: factor

text: is

text: the

text: uncertainty

text: related

text: to

text: the

text: J-factor

text: and

text: the

text: foreground

text: emission,

text: which

text: varies

text: between

text: targets

text: (see

text: Sec.

text: The

text: constraints

text: from

text: the

text: γ-line

text: toward

text: the

text: GC

text: are

text: limited

text: by

text: the

text: knowledge

text: of

text: the

text: DM

text: proﬁle

text: in

text: the

text: inner

text: Depending

text: whether

text: a

text: cored

text: or

text: a

text: cuspy

text: proﬁle

text: is

text: assumed

text: the

text: limits

text: change

text: by

text: a

text: few

text: orders

text: of

text: magnitude,

text: nevertheless

text: for

text: quite

text: a

text: wide

text: range

text: of

text: DM

text: proﬁles,

text: the

text: Wino

text: DM

text: is

text: severely

text: constrained

text: (see

text: Sec.

text: Finally,

text: the

text: CMB

text: constraints

text: depend

text: on

text: the

text: diﬀerent

text: combinations

text: of

text: data

text: sets

text: used

text: (see

text: Sec.

text: On

text: the

text: plot

text: we

text: do

text: not

text: include

text: galaxy

text: clusters

text: because

text: the

text: uncertainties

text: are

text: too

text: large

text: to

text: infer

text: any

text: unchallenged

text: limits

text: (see

text: discussion

text: in

text: Sec.

text: Additionally,

text: on

text: Fig.

text: we

text: show

text: how

text: the

text: limits

text: change

text: when

text: Wino

text: is

text: constituting

text: only

text: a

text: fraction

text: of

text: the

text: whole

text: dark

text: matter.

text: For

text: every

text: channel

text: we

text: take

text: the

text: most

text: stringent

text: limits

text: and

text: reduce

text: the

text: Wino

text: abundance

text: from

text: (lighter

text: shaded

text: regions)

text: to

text: (darker

text: shaded

text: regions)

text: in

text: steps

text: of

text: Apart

text: from

text: the

text: above

text: limits,

text: we

text: also

text: determined

text: future

text: prospects

text: for

text: the

text: neutrinos

text: and

text: an-

text: tideuteron

text: searches.

text: In

text: the

text: former,

text: only

text: the

text: experiment

text: could

text: be

text: able

text: to

text: probe

text: the

text: vicinity

text: of

text: the

text: resonance,

text: a

text: region

text: excluded

text: by

text: all

text: the

text: above

text: discussed

text: channels.

text: The

text: antideuterons

text: on

text: the

text: other

text: hand

text: constitute

text: also

text: a

text: quite

text: promising

text: channel

text: for

text: the

text: low

text: mass

text: region,

text: however

text: masses

text: below

text: around

text: GeV

text: GeV)

text: are

text: already

text: ruled

text: out

text: (constrained)

text: by

text: antiprotons,

text: dSphs

text: and

text: leptons.

text: Moreover,

text: this

text: channel

text: has

text: very

text: large

text: uncertainties

text: related

text: to

text: both

text: propagation

text: and

text: antideuterons’

text: production.

text: More

text: promising

text: prospects,

text: can

text: be

text: expected

text: in

text: the

text: high

text: latitude

text: γ-rays,

text: where

text: the

text: yr

text: Fermi

text: data

text: will

text: have

text: the

text: potential

text: to

text: probe

text: the

text: entire

text: (cosmologically

text: relevant)

text: Wino

text: mass

text: range

text: discussed,

text: if

text: the

text: extragalactic

text: DM

text: substructures

text: are

text: included

text: (see

text: Finally

text: the

text: CMB

text: limits

text: from

text: Planck

text: are

text: expected

text: to

text: be

text: a

text: factor

text: tighter

text: than

text: the

text: current

text: ones

text: after

text: the

text: polarization

text: data

text: are

text: released.


text: UpperlimitsontheWinomodel,if itaccountsforthewholeDM CMB Γ(cid:45)line Γ dSph Γ HL Γ LL e(cid:43) p 500 1000 1500 2000 2500 3000 (cid:64) (cid:68) m GeV Χ Figure 16. Combination of the 95% CL upper limits for the Wino DM mass. The black vertical line shows the position of the peak of the resonance. For a given channel diﬀerent shaded regions correspond to limits derived using diﬀerent assumptions. For antiprotons (p¯) this is related to the diﬀusion zone thickness, leptons (e+) the local DM density and energy density in the ISRF and magnetic ﬁeld, low latitude γ-rays (γ LL) the radiation ﬁeld in the inner galaxy and interstellar gas, high latitude γ-rays (γ HL) the extragalactic DM substructures, for dwarf spheroidal galaxies (γ dSph) the J-factor and foreground emission, for γ-line the DM ◦ proﬁle in the inner 1 and in the case of the CMB constraints diﬀerent combinations of data sets. See text and sections corresponding to its given channel for details. UpperlimitsontheWinomodel,varyingitscontributiontowholeDM (cid:37) ... (cid:37) (cid:37) CMB 10 90100 Γ(cid:45)line Γ dSph Γ HL Γ LL e(cid:43) p 500 1000 1500 2000 2500 3000 (cid:64) (cid:68) m GeV Χ Figure 17. Combination of the most stringent 95% CL upper limits for the Wino DM mass, relaxing the condition of the Wino accounting for the whole dark matter. The shaded regions correspond to reducing the Wino contribution from 100% (lighter regions) to 10% (darker regions) in steps of 10%. Speciﬁcally for the case of dwarf spheroidal limits, we use those derived by Ursa Minor which we derive ourselves (see section and following [105]) rather than those from a joint likelihood analysis as those from [103] which can exclude an (cid:39) additional 100 GeV in mass on each side of the maximum excluded mass range. The black vertical line shows the position of the peak of the resonance. – 31 – ##LTFigure## ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: UpperlimitsontheWinomodel,if

text: itaccountsforthewholeDM

text: CMB

text: Γ

text: dSph

text: Γ

text: HL

text: Γ

text: LL

text: p

text: m

text: GeV

text: Χ

text: Figure

text: Combination

text: of

text: the

text: CL

text: upper

text: limits

text: for

text: the

text: Wino

text: DM

text: mass.

text: The

text: black

text: vertical

text: line

text: shows

text: the

text: position

text: of

text: the

text: peak

text: of

text: the

text: resonance.

text: For

text: a

text: given

text: channel

text: diﬀerent

text: shaded

text: regions

text: correspond

text: to

text: limits

text: derived

text: using

text: diﬀerent

text: assumptions.

text: For

text: antiprotons

text: (p¯)

text: this

text: is

text: related

text: to

text: the

text: diﬀusion

text: zone

text: thickness,

text: leptons

text: (e+)

text: the

text: local

text: DM

text: density

text: and

text: energy

text: density

text: in

text: the

text: ISRF

text: and

text: magnetic

text: ﬁeld,

text: low

text: latitude

text: γ-rays

text: (γ

text: LL)

text: the

text: radiation

text: ﬁeld

text: in

text: the

text: inner

text: galaxy

text: and

text: interstellar

text: gas,

text: high

text: latitude

text: γ-rays

text: (γ

text: HL)

text: the

text: extragalactic

text: DM

text: substructures,

text: for

text: dwarf

text: spheroidal

text: galaxies

text: (γ

text: dSph)

text: the

text: J-factor

text: and

text: foreground

text: emission,

text: for

text: γ-line

text: the

text: DM

text: proﬁle

text: in

text: the

text: inner

text: and

text: in

text: the

text: case

text: of

text: the

text: CMB

text: constraints

text: diﬀerent

text: combinations

text: of

text: data

text: sets.

text: See

text: text

text: and

text: sections

text: corresponding

text: to

text: its

text: given

text: channel

text: for

text: details.

text: CMB

text: Γ

text: dSph

text: Γ

text: HL

text: Γ

text: LL

text: p

text: m

text: GeV

text: Χ

text: Figure

text: Combination

text: of

text: the

text: most

text: stringent

text: CL

text: upper

text: limits

text: for

text: the

text: Wino

text: DM

text: mass,

text: relaxing

text: the

text: condition

text: of

text: the

text: Wino

text: accounting

text: for

text: the

text: whole

text: dark

text: matter.

text: The

text: shaded

text: regions

text: correspond

text: to

text: reducing

text: the

text: Wino

text: contribution

text: from

text: (lighter

text: regions)

text: to

text: (darker

text: regions)

text: in

text: steps

text: of

text: Speciﬁcally

text: for

text: the

text: case

text: of

text: dwarf

text: spheroidal

text: limits,

text: we

text: use

text: those

text: derived

text: by

text: Ursa

text: Minor

text: which

text: we

text: derive

text: ourselves

text: (see

text: section

text: and

text: following

text: rather

text: than

text: those

text: from

text: a

text: joint

text: likelihood

text: analysis

text: as

text: those

text: from

text: which

text: can

text: exclude

text: an

text: additional

text: GeV

text: in

text: mass

text: on

text: each

text: side

text: of

text: the

text: maximum

text: excluded

text: mass

text: range.

text: The

text: black

text: vertical

text: line

text: shows

text: the

text: position

text: of

text: the

text: peak

text: of

text: the

text: resonance.

text: ##LTFigure##

text: ##LTFigure##

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text: dNf (cid:90) (cid:16) (cid:17) (cid:16) (cid:17) tot (M, x) = δ D (x) dx fγ γ + (cid:90) 1 dz S Dtree(z) + D(cid:16)loop+rp((cid:17)z) dNWDS→f zM, x W W W dx z x 1 dND→S x + dz S D (z) Z f zM, . Z Z dx z x In this way we include properly annihilations to gauge bosons with the radiative corrections. However, PYTHIA also does not include electroweak splitting of gauge bosons into fermions (it includes only the decay). We incorporate them by adding all the additional splitting functions, taken from [27], computed at the leading double log level. The complete Sommerfeld corrected D(z) functions, separated with respect to the perturbation theory order, are then:(cid:0) (cid:1) (cid:16) (cid:17) | | → | | −→ ∗ → − σ D(4)(x) = s 2σ00 WW + s± 2σ+ WW + 2Re s s±σmix WW δ(1 x) (A.7) SE W 0 tree tree 0 tree | | → | | −→ ∗ → − σ D(6)(x) = s 2σ00 WW + s± 2σ+ WW + 2Re s s±σmix WW δ(1 x) (A.8) SE W 0 loop loop 0 loop | | dNW | | − dNW ∗ dNW + s 2σ00 WWZ + s± 2σ+ WWZ + 2Re s s±σmix WWZ 0 WWZ dx WWZ dx 0 WWZ dx | | dNW | | − dNW ∗ dNW + s 2σ00 WWγ + s± 2σ+ WWγ + 2Re s s±σmix WWγ 0 WWγ dx WWγ dx 0 WWγ dx (cid:16) (cid:17) | | −→ −→ − σ D(4)(x) = s± 2 2σ+ γγ + σ+ Zγ δ(1 x) (A.9) SE γ tree tree | | (cid:16) dNγ | | (cid:17) − dNγ (cid:16) ∗ dNγ (cid:17) σ D(6)(x) = s 2σ00 WWγ + s± 2σ+ WWγ + 2Re s s±σmix WWγ (A.10) SE γ 0 WWγ dx WWγ dx 0 WWγ dx | | −→ −→ − ∗ → → − + s± 2 2σ+ γγ + σ+ Zγ δ(1 x) + 2Re s s± 2σmix γγ + σmix Zγ δ(1 x) loop loop 0 loop loop and analogously for D . Note the multiplicity factor of 2 in front of the terms with production Z of two identical gauge bosons. In the same way as before, the ﬁnal spectra we obtain then from: dNf (cid:90) (cid:16) (cid:17) (cid:16) (cid:17) SE (M, x) = δ D(4)(x) + δ D(6)(x) dx fγ γ fγ γ + (cid:90) 1 dz S (cid:16) D(4)(z) + D(6)(z)(cid:17) dNWDS→f(cid:16) zM, x(cid:17) W W W dx z x 1 dND→S x + dz S D(4)(z) + D(6)(z) Z f zM, . Z Z Z dx z x References [1] G. Hinshaw et al. (WMAP), Astrophys.J.Suppl. 208, 19 (2013), 1212.5226. [2] P. Ade et al. (Planck Collaboration) (2013), 1303.5076. – 33 – ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: dNf

label: equation

text: tot

text: (M,

text: x)

text: δ

text: D

text: (x)

text: dx

text: fγ

text: γ

text: dz

text: S

text: Dtree(z)

text: dNWDS→f

text: zM,

text: x

text: W

text: W

text: W

text: dx

text: z

text: x

text: dND→S

text: x

text: dz

text: S

text: D

text: (z)

text: Z

text: f

text: zM,

text: Z

text: Z

text: dx

text: z

text: x

text: In

text: this

text: way

text: we

text: include

text: properly

text: annihilations

text: to

text: gauge

text: bosons

text: with

text: the

text: radiative

text: corrections.

text: However,

text: PYTHIA

text: also

text: does

text: not

text: include

text: electroweak

text: splitting

text: of

text: gauge

text: bosons

text: into

text: fermions

text: (it

text: includes

text: only

text: the

text: decay).

text: We

text: incorporate

text: them

text: by

text: adding

text: all

text: the

text: additional

text: splitting

text: functions,

text: taken

text: from

text: computed

text: at

text: the

text: leading

text: double

text: log

text: level.

text: The

text: complete

text: Sommerfeld

text: corrected

text: D(z)

text: functions,

text: separated

text: with

text: respect

text: to

text: the

text: perturbation

text: theory

text: order,

text: are

text: σ

text: s

text: WW

text: s±

text: WW

text: s

text: s±σmix

text: WW

text: x)

text: SE

text: W

text: tree

text: tree

text: tree

text: σ

text: s

text: WW

text: s±

text: WW

text: s

text: s±σmix

text: WW

text: x)

text: SE

text: W

text: loop

text: loop

text: loop

text: dNW

text: dNW

text: dNW

text: s

text: WWZ

text: s±

text: WWZ

text: s

text: s±σmix

text: WWZ

text: WWZ

text: dx

text: WWZ

text: dx

text: WWZ

text: dx

text: dNW

text: dNW

text: dNW

text: s

text: WWγ

text: s±

text: WWγ

text: s

text: s±σmix

text: WWγ

text: WWγ

text: dx

text: WWγ

text: dx

text: WWγ

text: dx

text: σ

text: s±

text: γγ

text: σ+

text: Zγ

text: x)

text: SE

text: γ

text: tree

text: tree

text: dNγ

text: dNγ

text: dNγ

text: σ

text: s

text: WWγ

text: s±

text: WWγ

text: s

text: s±σmix

text: WWγ

text: SE

text: γ

text: WWγ

text: dx

text: WWγ

text: dx

text: WWγ

text: dx

text: s±

text: γγ

text: σ+

text: Zγ

text: x)

text: s

text: s±

text: γγ

text: σmix

text: Zγ

text: x)

text: loop

text: loop

text: loop

text: loop

text: and

text: analogously

text: for

text: D

text: Note

text: the

text: multiplicity

text: factor

text: of

text: in

text: front

text: of

text: the

text: terms

text: with

text: production

text: Z

text: of

text: two

text: identical

text: gauge

text: bosons.

text: In

text: the

text: same

text: way

text: as

text: before,

text: the

text: ﬁnal

text: spectra

text: we

text: obtain

text: then

text: from:

text: dNf

text: SE

text: (M,

text: x)

text: δ

text: δ

text: dx

text: fγ

text: γ

text: fγ

text: γ

text: dz

text: S

text: zM,

text: W

text: W

text: W

text: dx

text: z

text: x

text: dND→S

text: x

text: dz

text: S

text: Z

text: f

text: zM,

text: Z

text: Z

text: Z

text: dx

text: z

text: x

text: References

text: G.

text: Hinshaw

text: et

text: al.

text: (WMAP),

text: Astrophys.J.Suppl.

text: P.

text: Ade

text: et

text: al.

text: (Planck

text: Collaboration)

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text: 18 O. SAN, A. E. STAPLES, AND T. ILIESCU (a) N = 2 (b) N = 5 Figure 11. Time series of total enstrophy for the box ﬁlters. The second criterion is the correlation coeﬃcient between the DNS and the LES data. For any two ﬁelds f and g, which in our case will be velocity or vortic- ity components, the standard correlation coeﬃcient [51] is given by the following formula: (cid:104) (cid:105) − (cid:104) (cid:105)(cid:104) (cid:105) fg f g (46) C(f, g) = (cid:104) (cid:105) − (cid:104) (cid:105) (cid:104) (cid:105) − (cid:104) (cid:105) [( f2 f 2)( g2 g 2)]1/2 (cid:82) where the angle brackets denote the volume averages over the entire domain (cid:104) (cid:105) (e.g., f = fdV/V , where dV = dxdydz). The third criterion is the L2-norms of the ﬂow variables. The reference solution for computing the L2 norms is the DNS, which is obtained at a resolution of 2563, while all other LES computations are performed on a coarser resolution of 643. The same coarse resolution results without the AD procedure are also included for comparison purposes. The fourth criterion is the third-order structure function, which is deﬁned as (cid:104) (cid:105) (cid:104)| − | (cid:105) (47) δu(r)3 = u(x + r) u(x) 3 | | with r = r being the spatial separation. Note that, since the turbulence is assumed isotropic, the velocity increment depends only on the modulus of the vector r. According to the Kolmogorov theory of turbulence [28, 16], the nth-order (cid:104) (cid:105) ∼ (cid:28) (cid:28) structure function scales as δu(r)n rn/3 in the inertial range (η r L). In this section, we numerically investigate the AD-LES model in conjunction with the three box ﬁlters discussed in Section : the TP (25), the SF (26), and the 7PF (28). The resulting LES models are denoted as AD-TF, AD-SF, and AD-7PF, respectively. Fig. 11 presents the time series of the integrated enstrophy Q(t) deﬁned in (45) for the AD-TF, AD-SF and AD-7PF with N = 2 and N = 5. Results for the DNS and No-AD are also included for comparison purposes. For N = 2, the AD-7PF ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTLine##

text: O.

text: SAN,

text: A.

text: E.

text: STAPLES,

text: AND

text: T.

text: ILIESCU

text: (a)

text: N

text: (b)

text: N

text: Figure

text: Time

text: series

text: of

text: total

text: enstrophy

text: for

text: the

text: box

text: ﬁlters.

text: The

text: second

text: criterion

text: is

text: the

text: correlation

text: coeﬃcient

text: between

text: the

text: DNS

text: and

text: the

text: LES

text: data.

text: For

text: any

text: two

text: ﬁelds

text: f

text: and

text: g,

text: which

text: in

text: our

text: case

text: will

text: be

text: velocity

text: or

text: vortic-

text: ity

text: components,

text: the

text: standard

text: correlation

text: coeﬃcient

text: is

text: given

text: by

text: the

text: following

text: formula:

text: fg

text: f

text: g

text: C(f,

text: g)

text: f

text: g

text: where

text: the

text: angle

text: brackets

text: denote

text: the

text: volume

text: averages

text: over

text: the

text: entire

text: domain

text: (e.g.,

text: f

text: fdV/V

text: where

text: dV

text: dxdydz).

text: The

text: third

text: criterion

text: is

text: the

text: of

text: the

text: ﬂow

text: variables.

text: The

text: reference

text: solution

text: for

text: computing

text: the

text: norms

text: is

text: the

text: DNS,

text: which

text: is

text: obtained

text: at

text: a

text: resolution

text: of

text: while

text: all

text: other

text: LES

text: computations

text: are

text: performed

text: on

text: a

text: coarser

text: resolution

text: of

text: The

text: same

text: coarse

text: resolution

text: results

text: without

text: the

text: AD

text: procedure

text: are

text: also

text: included

text: for

text: comparison

text: purposes.

text: The

text: fourth

text: criterion

text: is

text: the

text: third-order

text: structure

text: function,

text: which

text: is

text: deﬁned

text: as

text: u(x

text: r)

text: u(x)

text: with

text: r

text: r

text: being

text: the

text: spatial

text: separation.

text: Note

text: that,

text: since

text: the

text: turbulence

text: is

text: assumed

text: isotropic,

text: the

text: velocity

text: increment

text: depends

text: only

text: on

text: the

text: modulus

text: of

text: the

text: vector

text: r.

text: According

text: to

text: the

text: Kolmogorov

text: theory

text: of

text: turbulence

text: the

text: nth-order

text: structure

text: function

text: scales

text: as

text: δu(r)n

text: in

text: the

text: inertial

text: range

text: (η

text: r

text: L).

text: In

text: this

text: section,

text: we

text: numerically

text: investigate

text: the

text: AD-LES

text: model

text: in

text: conjunction

text: with

text: the

text: three

text: box

text: ﬁlters

text: discussed

text: in

text: Section

text: the

text: TP

text: the

text: SF

text: and

text: the

text: The

text: resulting

text: LES

text: models

text: are

text: denoted

text: as

text: AD-TF,

text: AD-SF,

text: and

text: respectively.

text: Fig.

text: presents

text: the

text: time

text: series

text: of

text: the

text: integrated

text: enstrophy

text: Q(t)

text: deﬁned

text: in

text: for

text: the

text: AD-TF,

text: AD-SF

text: and

text: with

text: N

text: and

text: N

text: Results

text: for

text: the

text: DNS

text: and

text: No-AD

text: are

text: also

text: included

text: for

text: comparison

text: purposes.

text: For

text: N

text: the

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTLine##