Higgs Portal Dark Matter for GeV Gamma-ray Excess · 2015. 10. 29. · for GeV Gamma-ray Excess....

Yong Tang(KIAS) Higgs Portal DM for Gamma-ray Excess TeVPA2015

TANG, Yong() Korea Institute for Advanced Study

TeVPA Workshop 2015, Kashiwa !

P.Ko,W-I.Park,YT, 1404.5257(JCAP) P. Ko,YT, 1407.5492(JCAP)&1504.03908

Higgs Portal Dark Matter !for GeV Gamma-ray Excess


Outline

• Introduction Galactic Center GeV Gamma-ray Excess !

• Higgs Portal DM models • Summary


Fermi GeV γ-ray ExcessGoodenough & Hooper 2009

Hooper & Goodenough 2011

Hooper & Linden 2011

Boyarsky+ 2011

Abazajian & Kaplinghat 2012

Gordon & Macias 2013

Macias & Gordon 2014

Abazajian+ 2014

Daylan+2014

Weniger+2014 (CCW)

…..

THE GAMMA-RAY SKY Fermi-LAT, 4 years, energies > 1 GeV

The Gamma-Ray Sky

Astrophysics or Dark Matter?


4

The Fermi GeV excess

Goodenough & Hooper 2009



Boyarsky+ 2011




Abazajian+ 2014

Daylan+2014

Hooper & Slatyer 2013

Huang+ 2013

Zhou+ 2014

Daylan+ 2014

At the Galactic center (roughly 7deg x 7deg)

In the inner Galaxy (roughly |b|>1 deg to tens of deg)

[Daylan+ 2014]

[Hooper & Slatyer 2013] 4

The Fermi GeV excess

Goodenough & Hooper 2009



Boyarsky+ 2011




Abazajian+ 2014

Daylan+2014

Hooper & Slatyer 2013

Huang+ 2013

Zhou+ 2014

Daylan+ 2014

At the Galactic center (roughly 7deg x 7deg)

In the inner Galaxy (roughly |b|>1 deg to tens of deg)

[Daylan+ 2014]

[Hooper & Slatyer 2013]

The Characterization of the Gamma-Ray Signal from the Central Milky Way:

A Compelling Case for Annihilating Dark Matter

Tansu Daylan,1 Douglas P. Finkbeiner,1, 2 Dan Hooper,3, 4 Tim Linden,5

Stephen K. N. Portillo,2 Nicholas L. Rodd,6 and Tracy R. Slatyer6, 7

1Department of Physics, Harvard University, Cambridge, MA2Harvard-Smithsonian Center for Astrophysics, Cambridge, MA

3Fermi National Accelerator Laboratory, Theoretical Astrophysics Group, Batavia, IL4University of Chicago, Department of Astronomy and Astrophysics, Chicago, IL

5University of Chicago, Kavli Institute for Cosmological Physics, Chicago, IL6Center for Theoretical Physics, Massachusetts Institute of Technology, Boston, MA

7School of Natural Sciences, Institute for Advanced Study, Princeton, NJ

Past studies have identified a spatially extended excess of 1-3 GeV gamma rays from the regionsurrounding the Galactic Center, consistent with the emission expected from annihilating dark mat-ter. We revisit and scrutinize this signal with the intention of further constraining its characteristicsand origin. By applying cuts to the Fermi event parameter CTBCORE, we suppress the tails ofthe point spread function and generate high resolution gamma-ray maps, enabling us to more easilyseparate the various gamma-ray components. Within these maps, we find the GeV excess to berobust and highly statistically significant, with a spectrum, angular distribution, and overall nor-malization that is in good agreement with that predicted by simple annihilating dark matter models.For example, the signal is very well fit by a 31-40 GeV dark matter particle annihilating to bb withan annihilation cross section of v = (1.4 2.0) 1026 cm3/s (normalized to a local dark matterdensity of 0.3 GeV/cm3). Furthermore, we confirm that the angular distribution of the excess isapproximately spherically symmetric and centered around the dynamical center of the Milky Way(within 0.05 of Sgr A), showing no sign of elongation along or perpendicular to the GalacticPlane. The signal is observed to extend to at least ' 10 from the Galactic Center, disfavoring thepossibility that this emission originates from millisecond pulsars.

PACS numbers: 95.85.Pw, 98.70.Rz, 95.35.+d; FERMILAB-PUB-14-032-A, MIT-CTP 4533

I. INTRODUCTION

Weakly interacting massive particles (WIMPs) are aleading class of candidates for the dark matter of our uni-verse. If the dark matter consists of such particles, thentheir annihilations are predicted to produce potentiallyobservable fluxes of energetic particles, including gammarays, cosmic rays, and neutrinos. Of particular interestare gamma rays from the region of the Galactic Centerwhich, due to its proximity and high dark matter density,is expected to be the brightest source of dark matter an-nihilation products on the sky, hundreds of times brighterthan the most promising dwarf spheroidal galaxies.

Over the past few years, several groups analyzing datafrom the Fermi Gamma-Ray Space Telescope have re-ported the detection of a gamma-ray signal from the in-ner few degrees around the Galactic Center (correspond-ing to a region several hundred parsecs in radius), with aspectrum and angular distribution compatible with thatanticipated from annihilating dark matter particles [1–7].More recently, this signal was shown to also be presentthroughout the larger Inner Galaxy region, extendingkiloparsecs from the center of the Milky Way [8, 9]. Whilethe spectrum and morphology of the Galactic Center andInner Galaxy signals have been shown to be compatiblewith that predicted from the annihilations of an approx-imately 30-40 GeV WIMP annihilating to quarks (or a7-10 GeV WIMP annihilating significantly to tau lep-

tons), other explanations have also been proposed. Inparticular, it has been argued that if our galaxy’s centralstellar cluster contains several thousand unresolved mil-lisecond pulsars, they might be able to account for theemission observed from the Galactic Center [2, 4–7, 10].The realization that this signal extends well beyond theboundaries of the central stellar cluster [8, 9] disfavorssuch interpretations, however. In particular, pulsar pop-ulation models capable of producing the observed emis-sion from the Inner Galaxy invariably predict that Fermi

should have resolved a much greater number of such ob-jects. Accounting for this constraint, Ref. [11] concludedthat no more than 5-10% of the anomalous gamma-ray emission from the Inner Galaxy can originate frompulsars. Furthermore, while it has been suggested thatthe Galactic Center signal might result from cosmic-rayinteractions with gas [2, 4–6], the analyses of Refs. [12]and [13] find that measured distributions of gas providea poor fit to the morphology of the observed signal. Italso appears implausible that such processes could ac-count for the more spatially extended emission observedfrom throughout the Inner Galaxy.

In this study, we revisit the anomalous gamma-rayemission from the Galactic Center and the Inner Galaxyregions and scrutinize the Fermi data in an e↵ort to con-strain and characterize this signal more definitively, withthe ultimate goal being to confidently determine its ori-gin. One way in which we expand upon previous work

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We show the differential intensity at a reference energy of2 GeV. At this energy the putative excess emission is—compared to other foregrounds/backgrounds—strongest, sothe uncertainties due to foreground/background subtractionsystematics are expected to be the smallest.The intensities were derived by a careful rescaling of

results in the literature that fully takes into account theassumed excess profiles. In most works, intensities arequoted as averaged over a given region of interest (ROI).Instead of showing these averaged values, which depend onthe details of the adopted ROI, we use the excess profiles tocalculate the differential intensity at a fixed angular dis-tance from the GC. These excess profiles usually follow thepredictions similar to those of a DM annihilation profilefrom a generalized Navarro-Frenk-White (NFW) densitydistribution, which is given by

ρðrÞ ¼ ρsr3s

rγðrþ rsÞ3−γ: ð1Þ

Here, rs denotes the scale radius, γ the slope of the innerpart of the profile, and ρs the scale density. As referencevalues we will—if not stated otherwise—adopt rs ¼20 kpc and γ ¼ 1.26, and ρs is fixed by the requirementthat the local DM density at r⊙ ¼ 8.5 kpc is ρ⊙ ¼0.4 GeVcm−3 [95,96].We note that the intensities that we quote from Ref. [26]

refer already to a bb spectrum and take into account

correlated foreground systematics as discussed below.In Ref. [26] a broken power law was found to give a fitas good as the DM bb spectrum. Assuming a broken powerlaw, the intensities in Fig. 1 would be somewhat larger.We find that all previous and current results (with the

exception of Ref. [7], which we do not show in Fig. 1)agree within a factor of about 2 with a signal morphologythat is compatible with a contracted NFW profile with slopeγ ¼ 1.26, as it was noted previously [15,26]. As mentionedin our Introduction, the indications for a higher-latitude tailof the GeV excess profile is a rather nontrivial test for theDM interpretation and provides a serious benchmark forany astrophysical explanation of the excess emission.However, we have to caution that most of the previousanalyses make use of the same model for Galactic diffuseemission (P6V11). An agreement between the variousresults is hence not too surprising. Instead in the workof Ref. [26], the π0, bremsstrahlung and ICS emissionmaps, where calculated as independent components, withtheir exact morphologies and spectra as predicted from awide variety of foreground/background models. As it wasshown in Ref. [26], the exact assumptions on the CRpropagation and the Galactic properties along the line ofsight can impact both the spectrum and the morphology(which also vary with energy) of the individual gamma-rayemission maps. To probe the associated uncertainties onthose diffuse emissions, the authors of Ref. [26] builtdifferent models allowing for extreme assumptions on the

FIG. 1 (color online). Intensity of the Fermi GeVexcess at 2 GeVas function of Galactic latitude (see text for details), compared withthe expectations for a contracted NFW profile (dotted line). Error bars refer to statistical %1σ uncertainties, except for Refs. [13,14] forwhich we take into account the quoted systematics coming from different astrophysical models. The result from Ref. [26] for the higher-latitude tail and the preliminary results by the Fermi-LAT team [17] on the Galactic center include an estimate of the impact offoreground systematics. In these cases, the adopted ROIs are shown as bands (for Ref. [26], overlapping regions correspond to the northand south parts of the sky). Gray areas indicate the intensity level of the Fermi bubbles, extrapolated from jbj > 10°, and the regionwhere HI and H2 gas emission from the inner Galaxy becomes important.

DARK MATTER INTERPRETATIONS OF THE FERMI GEV … PHYSICAL REVIEW D 91, 063003 (2015)

063003-3

A tale of tails: Dark matter interpretations of the Fermi GeV excess in lightof background model systematics

Francesca Calore,1,* Ilias Cholis,2,† Christopher McCabe,1,‡ and Christoph Weniger1,§1GRAPPA, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands

2Center for Particle Astrophysics, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA(Received 24 November 2014; published 10 March 2015)

Several groups have identified an extended excess of gamma rays over the modeled foreground andbackground emissions towards the Galactic center (GC) based on observations with the Fermi Large AreaTelescope. This excess emission is compatible in morphology and spectrum with a telltale sign from darkmatter (DM) annihilation. Here, we present a critical reassessment of DM interpretations of the GC signalin light of the foreground and background uncertainties that some of us recently outlaid in Calore et al.(2014). We find that a much larger number of DM models fits the gamma-ray data than previously noted.In particular: (1) In the case of DM annihilation into bb, we find that even large DM masses up tomχ ≃ 74 GeV are allowed at p-value > 0.05. (2) Surprisingly, annihilation into nonrelativistic hh gives agood fit to the data. (3) The inverse Compton emission from μþμ− with mχ ∼ 60–70 GeV can also accountfor the excess at higher latitudes, jbj > 2°, both in its spectrum and morphology. We also present novelconstraints on a large number of mixed annihilation channels, including cascade annihilation involvinghidden sector mediators. Finally, we show that the current limits from dwarf spheroidal observations are notin tension with a DM interpretation when uncertainties on the DM halo profile are accounted for.

DOI: 10.1103/PhysRevD.91.063003 PACS numbers: 95.30.Cq, 95.35.+d

I. INTRODUCTION

Shedding light onto the origin of Dark Matter (DM) isone of the biggest challenges of current particle physics andcosmology. The most appealing particle DM candidates arethe so-called weakly interacting massive particles (WIMPs)[1–3]. Among the different indirect messengers, gammarays play a dominant role and they have often been definedas the golden channel for DM indirect detection (seeRef. [4] for an extensive review). The main challenge isto disentangle putative DM signals from the large astro-physical foregrounds and backgrounds that are generallyexpected to dominate the measured fluxes. The bestexample of a challenging target is the Galactic center(GC), where on the one hand the DM signal is expected tobe brighter than anywhere else on the sky [5,6], but—givenour poor knowledge of the conditions in the inner Galaxy—the astrophysical foreground and background (either fromGalactic point sources or from diffuse emissions) is subjectto very large uncertainties.In this respect, it is not surprising for unmodeled gamma-

ray contributions to be found towards the inner part of theGalaxy, above or below the expected standard astrophysicalemission. Indeed, an extended excess in gamma rays at theGC was reported by different independent groups [7–16],using data from the Fermi Large Area Telescope (LAT),

and dubbed “Fermi GeV excess” as it appears to peak atenergies around 1–3 GeV. Intriguingly, the excess emissionshows spectral and morphological properties consistentwith signals expected from DM particles annihilating inthe halo of the Milky Way. Recently, the existence of aGeV excess emission towards the GC above the modeledastrophysical foreground/background was also confirmedby the Fermi-LAT Collaboration [17]. This revitalizes theimportance of understanding the origin of this excess.Given that the Galactic diffuse emission is maximal

along the Galactic disk and that a DM signal is expected tobe approximately spherical, the preferable region to searchfor a DM annihilation signal in Fermi-LAT data is actuallya region that, depending on the DM profile, extendsbetween a few degrees and a few tens of degrees awayfrom the GC, above and below the disk [18–23]. Indeed,different groups [15,24,25] extracted an excess with spec-tral properties similar to the GeVexcess at the GC from thegamma-ray data at higher Galactic latitudes, up to aboutjbj ∼ 20°. The extension to higher latitudes is a critical testthat the DM interpretation had to pass, and apparently haspassed.However, when talking about excesses, a rather central

question is An excess above what? The excess emission isdefined above the astrophysical foregrounds and back-grounds, i.e. the Galactic diffuse emission, point sourcesand extended sources, modeled in the data analysis. Mostprevious studies of the Fermi GeV excess are based on asmall number of fixed models for the Galactic diffuseemission. These models were built for the sole purpose ofpoint source analyses and hence introduce uncontrollable

*[email protected]†[email protected]‡[email protected]§[email protected]

PHYSICAL REVIEW D 91, 063003 (2015)

1550-7998=2015=91(6)=063003(18) 063003-1 © 2015 American Physical Society


Background Uncertainties

25

Theoretical vs. empirical model systematics

Empirical model uncertainties (yellow) and theoretical model uncertainties (blue lines) are significantly larger than the statistical error over the entire energy range.

Have to take into account systematics to get meaningful results in spectral fits.

Calore, Cholis&Weniger (CCW), 1409.0042


Evidence for DM• Rotation Curves of Galaxies • Gravitational Lensing • Large Scale Structure • CMB anisotropies • ……These evidences all come from gravitational interaction CDM: velocity is negligible for structure formation, a popular candidate, WIMP, M ~ O(GeV) -- O(TeV), hviann 3 1026cm3/s


DM-Induced Gamma Rays

DM-INDUCED GAMMA RAYS

JCAP07(2008)013

The Signal The gamma-ray signal from annihilating dark matter is described by:

1) Distinctive “bump-like” spectrum

Figure 6. The gamma ray spectrum per WIMP annihilation for a 100 GeV (left) and 500GeV (right) WIMP. Each curve denotes a different choice of the dominant annihilationmode: bb (solid cyan), ZZ (magenta dot-dashed), W+W− (blue dashed), τ+τ− (blacksolid), e+e− (green dotted) and µ+µ− (red dashed).

quarks, leptons, Higgs bosons or gauge bosons, dark matter particles canproduce gamma rays directly, leading to monoenergetic spectral signatures.If a gamma ray line could be identified, it would constitute a “smokinggun” for dark matter annihilations. By definition, however, WIMPs do notannihilate through tree level processes to final states containing photons(if they did, they would be EMIMPs rather than WIMPs). On the otherhand, they may be able to produce final states such as γγ, γZ or γh throughloop diagrams. Neutralinos, for example, can annihilate directly to γγ [57]or γZ [58] through a variety of charged loops. These final states lead togamma ray lines with energies of Eγ = mdm and Eγ = mdm(1−m2

Z/4m2dm),

respectively. Such photons are produced in only a very small fraction ofneutralino annihilations, however. The largest neutralino annihilation crosssections to γγ and γZ are about 10−28 cm3/s, and even smaller values aremore typical [59].

The Galactic Center has long been considered to be one of the mostpromising regions of the sky in which to search for gamma rays from darkmatter annihilations [59, 60]. The prospects for this depend, however, ona number of factors including the nature of the WIMP, the distribution ofdark matter in the region around the Galactic Center, and our ability tounderstand the astrophysical backgrounds present.

26

bb

ZZ

WW

ττ

##

Dan Hooper – Indirect Searches For Dark Matter

g=1.00

g=1.20

g=1.26

1 2 5 10 20 50

50100

5001000

50001¥ 104

qHdegreeLI

Particle Physics Spectral Information

Astrophysics DM distribution Spatial information

g=1.00

g=1.20

g=1.26

1 2 5 10 20 50

50100

5001000

50001¥ 104

qHdegreeL

I

FIG. 3: Dependence of I on the index and the angle . = 1 is for standard NFW densityprofile. The purpose of this plot is to show that there is a large uncertainty in dark matter density near the galaxy center.

constrained by DM direct searches, the invisible branching ratio of Higgs boson, and colliderbounds, discussion of which is beyond the scope of this paper.

The -ray flux from self-conjugate DM (semi-)annihilation is determined by particlephysics factors, hviann and dN/dE, and astrophysical factor, DM density profile :

d2

dEd=

1

8

hviannM2

DM

dN

dE

Z 1

0

dr2 (r0, ) . (3.1)

Here r0 =p

r2 + r2 2rr cos , where r is the distance to earth from the DM annihilationpoint, r ' 8.5kpc and is the observation angle between the line of sight and the center ofMilky Way, respectively. An extra factor 1/2 has to be included when X annihilates withits anti-particle X, which is relevant to the local Z3 scalar DM model.

We use the generalized NFW profile [60] for DM density, which is parametrized as

(r) = hrr

i 1 + r/rc1 + r/rc

3

, (3.2)

with rc ' 20kpc and ' 0.3GeV/cm3. Defining a dimensionless function I,

I Z 1

0

dr

r( (r0, ) /)

2 , (3.3)

we show how I depends on the power index in Fig. 3. Because of the large uncertainty of ,it is not so meaningful to quantify the exact value for hviann in Eq. (3.1), as long as it is at theorder of 1026cm3/s. We can roughly estimate hviann in our model by fixing index = 1.26.For self-conjugate DM annihilation, it was shown in [1] that hviann ' 1.7(1.1)1026cm3/s

6

prompt

d2

dE

d=

X

i

dN i

dE

hvii

8M2DM

Z

l.o.s

2 (r(r0, )) dr0


Channels

• heavy quark channel are favored, • Naturally higgs-like couplings?

13

FIG. 14: The quality of the fit (2, over 25-1 degrees-of-freedom) for various annihilating dark matter models to the spectrumof the anomalous gamma-ray emission from the Inner Galaxy (as shown in Fig. 5) as a function of mass, and marginalizedover the value of the annihilation cross section. In the left frame, we show results for dark matter particles which annihilateuniquely to bb, cc, ss, light quarks (uu and/or dd), or +. In the right frame, we consider models in which the dark matterannihilates to a combination of channels, with cross sections proportional to the square of the mass of the final state particles,the square of the charge of the final state particles, democratically to all kinematically accessible Standard Model fermions, or80% to + and 20% to bb. The best fits are found for dark matter particles with masses in the range of 20-40 GeV andwhich annihilate mostly to quarks.

FIG. 15: The range of the dark matter mass and annihilation cross section required to fit the gamma-ray spectrum observedfrom the Inner Galaxy, for a variety of annihilation channels or combination of channels (see Fig. 14). The observed gamma-rayspectrum is generally best fit by dark matter particles with a mass of 20-40 GeV and that annihilate to quarks with a crosssection of v (1 2) 1026 cm3/s.

VII. IMPLICATIONS FOR DARK MATTER

In this section, we use the results of the previous sec-tions to constrain the characteristics of the dark matterparticle species potentially responsible for the observedgamma-ray excess. We begin by fitting various dark mat-ter models to the spectrum of the gamma-ray excess asfound in our Inner Galaxy analysis (as shown in Fig. 5).In Fig. 14, we plot the quality of this fit (2) as a function

of the WIMP mass, for a number of dark matter annihila-tion channels (or combination of channels), marginalizedover the value of the annihilation cross section. Giventhat this fit is performed over 25-1 degrees-of-freedom,a goodness-of-fit with a p-value of 0.05 (95% CL) cor-responds to a 2 of approximately 36.8. We take anyvalue less than this to constitute a “good fit” to the InnerGalaxy spectrum. Excellent fits are found for dark mat-ter that annihilates to bottom, strange, or charm quarks

13

FIG. 14: The quality of the fit (2, over 25-1 degrees-of-freedom) for various annihilating dark matter models to the spectrumof the anomalous gamma-ray emission from the Inner Galaxy (as shown in Fig. 5) as a function of mass, and marginalizedover the value of the annihilation cross section. In the left frame, we show results for dark matter particles which annihilateuniquely to bb, cc, ss, light quarks (uu and/or dd), or +. In the right frame, we consider models in which the dark matterannihilates to a combination of channels, with cross sections proportional to the square of the mass of the final state particles,the square of the charge of the final state particles, democratically to all kinematically accessible Standard Model fermions, or80% to + and 20% to bb. The best fits are found for dark matter particles with masses in the range of 20-40 GeV andwhich annihilate mostly to quarks.

FIG. 15: The range of the dark matter mass and annihilation cross section required to fit the gamma-ray spectrum observedfrom the Inner Galaxy, for a variety of annihilation channels or combination of channels (see Fig. 14). The observed gamma-rayspectrum is generally best fit by dark matter particles with a mass of 20-40 GeV and that annihilate to quarks with a crosssection of v (1 2) 1026 cm3/s.

VII. IMPLICATIONS FOR DARK MATTER

In this section, we use the results of the previous sec-tions to constrain the characteristics of the dark matterparticle species potentially responsible for the observedgamma-ray excess. We begin by fitting various dark mat-ter models to the spectrum of the gamma-ray excess asfound in our Inner Galaxy analysis (as shown in Fig. 5).In Fig. 14, we plot the quality of this fit (2) as a function

of the WIMP mass, for a number of dark matter annihila-tion channels (or combination of channels), marginalizedover the value of the annihilation cross section. Giventhat this fit is performed over 25-1 degrees-of-freedom,a goodness-of-fit with a p-value of 0.05 (95% CL) cor-responds to a 2 of approximately 36.8. We take anyvalue less than this to constitute a “good fit” to the InnerGalaxy spectrum. Excellent fits are found for dark mat-ter that annihilates to bottom, strange, or charm quarks

Daylan+2014


Higgs Portal DMLS = 1

2m2

SS2 1

4SS

4 1

4hSSH

†HS2 ,

LV =1

2m2

V VµVµ+

1

4V (VµV

µ)2+1

4hV V H

†HVµVµ,

Lf = 1

2mf 1

4

hff

H†H.

10!2 10!1

10!2

10!1

Α

gX

10!2 10!1

10!2

10!1

Α

gX

Figure 1. A bound of ↵ and gX from collider experiments, LUX and projected XENON1T direct DMsearches [17] for mh = 125. Left: mV = 35GeV, m = 60GeV, and

= 0.1. Right: mV = 80GeV,m = 75GeV. Yellow region is excluded by collider constraint on BrnonSM

h . Solid and dashed redlines are upper-bound of DM-nucleon scattering cross section from LUX and XENON1T, respectively.

X

X

b

¯b

H1,2

Figure 2. Dominant s channel b+¯b production

Xµ

X

H2

H2

H1,2

Xµ H2

X H2

Xµ H2

X H2

Figure 3. Dominant s/t-channel production of H2

s that decay dominantly to b+¯b

achieved only around the resonance region. However in the resonance region the annihilationcross section varies a lot, as the Mandalstam s-variable varies from the value at freeze-out tothe value in a dark matter halo at present. Therefore, this process can not be used for theGeV scale -ray spectrum from the galactic center.

On the other hand, in the process of Fig. 3 for m mV . 80GeV, the thermally-

– 5 –

Xµ Xµ

H1/H2


Direct Detection Bounds

Highly constrained, GeV favored region excluded.3

DM

1

50

XENON100

−2

WMAP

10−3

λ hSS

Br = 10%inv

10

10

−1

XENON1T

XENONUP

Max

MinLattice

150100 200

M (GeV)

FIG. 1. Scalar Higgs-portal parameter space allowed by WMAP(between the solid red curves), XENON100 and BRinv = 10% formh=125 GeV. Shown also are the prospects for XENON upgrades.

the case of scalar DM with a mass of 5–10 GeV consid-ered, for instance, in Ref. [8]. On the other hand, heavierdark matter, particularly for MDM >∼ 80 GeV, is allowed

by both BRinv and XENON100. We note that almost theentire available parameter space will be probed by theXENON100 upgrade. The exception is a small resonantregion around 62 GeV, where the Higgs–DM coupling isextremely small.

In the case of vector Higgs-portal DM, the results areshown in Fig. 2 and are quite similar to the scalar case.WMAP requires the Higgs–DM coupling to be almosttwice as large as that in the scalar case. This is becauseonly opposite polarization states can annihilate throughthe Higgs channel, which reduces the annihilation crosssection by a factor of 3. The resulting direct detectionrates are therefore somewhat higher in the vector case.Note that for DM masses below mh/2, only very smallvalues λhV V <O(10−2) are allowed if BRinv<10%.

Similarly, the fermion Higgs-portal results are shownin Fig. 3. We find no parameter regions satisfying theconstraints, most notably the XENON100 bound, andthis scenario is thus ruled out for λhff/Λ >∼ 10−3.

This can also be seen from Fig. 4, which displays pre-dictions for the spin–independent DM–nucleon cross sec-tion σSI (based on the lattice fN) subject to the WMAPand BRinv < 10% bounds. The upper band correspondsto the fermion Higgs-portal DM and is excluded byXENON100. On the other hand, scalar and vector DMare both allowed for a wide range of masses. Apart froma very small region around 1

2mh, this parameter space

will be probed by XENON100–upgrade and XENON1T.The typical value for the scalar σSI is a few times 10−9

pb, whereas σSI for vectors is larger by a factor of 3 whichaccounts for the number of degrees of freedom.

WMAP Br = 10%

hVVλ

−310

−210

−110

XENON1T

XENONUP

Max

MinLattice

150100 200

M (GeV)DM

1

50

XENON100

inv

FIG. 2. Same as Fig. 1 for vector DM particles.

10−3

λ /Λhff

10−1

MinLattice

150100 200

M (GeV)DM

1

XENON100

WMAP

50

10

inv

−2

Br = 10%

FIG. 3. Same as in Fig.1 for fermion DM; λhff/Λ is in GeV−1.

DARK MATTER PRODUCTION AT COLLIDERS

The next issue to discuss is how to observe directly theHiggs-portal DM particles at high energy colliders. Thereare essentially two ways, depending on the Higgs versusDM particle masses. If the DM particles are light enoughfor the invisible Higgs decay to occur, MDM <∼

12mh, the

Higgs cross sections times the branching ratios for thevisible decays will be altered, providing indirect evidencefor the invisible decay channel. In the case of the LHC,a detailed analysis of this issue has been performed inRef. [7] for instance and we have little to add to it. Nev-ertheless, if the invisible Higgs branching ratio is smallerthan ≈ 10%, its observation would be extremely difficultin view of the large QCD uncertainties that affect theHiggs production cross sections, in particular in the mainproduction channel, the gluon fusion mechanism gg → h

3

DM

1

50

XENON100

−2

WMAP

10−3

λ hSS

Br = 10%inv

10

10

−1

XENON1T

XENONUP

Max

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M (GeV)










WMAP Br = 10%

hVVλ

−310

−210

−110

XENON1T

XENONUP

Max

MinLattice

150100 200

M (GeV)DM

1

50

XENON100

inv


10−3

λ /Λhff

10−1

MinLattice

150100 200

M (GeV)DM

1

XENON100

WMAP

50

10

inv

−2

Br = 10%




12mh, the


3

DM

1

50

XENON100

−2

WMAP

10−3

λ hSS

Br = 10%inv

10

10

−1

XENON1T

XENONUP

Max

MinLattice

150100 200

M (GeV)










WMAP Br = 10%

hVVλ

−310

−210

−110

XENON1T

XENONUP

Max

MinLattice

150100 200

M (GeV)DM

1

50

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inv


10−3

λ /Λhff

10−1

MinLattice

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M (GeV)DM

1

XENON100

WMAP

50

10

inv

−2

Br = 10%




12mh, the


Djouadi et al 2011


Vector DM• U(1) dark gauge symmetry, !

!

!

• dark Higgs field !

• symmetry breaking

L = 1

4XµX

µ + (Dµ)†(Dµ)

† v2

2

2

H

H†H v2H

2

† v2

2

H

H†H v2H

2

2

+ LSM.

Dµ = (@µ + igXQXµ),

(x) =1p2(v + '(x)) ,

U(1)XP.Ko, W-I.Park, YT,1404.5257(JCAP)


Particle spectrum• Massive gauge boson X is the Dark Matter • Mixed two scalars !

!

• mixing angle

h'

=

c↵ s↵s↵ c↵

H1

H2

O

H1

H2

M

2Hv2H HvHvHvHv 2v2

=

M2

H1c2↵ +M2

H2s2↵

M2

H2M2

H1

s↵c↵

M2H2

M2H1

s↵c↵ M2

H1s2↵ +M2

H2c2↵

.

tan 2↵ =

2M12

M22 M11, or sin 2↵ =

2HvHvM2

H2M2

H1

.

s↵(c↵) sin↵(cos↵)


Direct Detection

Xµ Xµ

H1/H210!2 10!1

10!2

10!1

Α

gX

10!2 10!1

10!2

10!1

Α

gX




X

X

b

¯b

H1,2


Xµ

X

H2

H2

H1,2

Xµ H2

X H2

Xµ H2

X H2





– 5 –

with

h = HvHc3↵ + 2 (3H H) vHc↵s2

↵ 2 [3 (

H) vS ] c2

↵s↵ Hv

s3↵

HvHc3↵ 's↵c4↵

m2

h m2

v(3.7)

In the second line of the above equation, we assumed the first term dominates over the othersin the small mixing limit.

Using Eqs. (3.2) and (3.3), we can constrain the allowed ranges of gX and ↵ as shownin the white region of the left-panel of Fig. 1. Note that in the figure the mixing angle isconstrained to be ↵ . 7 10

2 for m = 60GeV. The the upper-bound of ↵ is lowered downfor a lighter m.

3.2 Direct detection

For 30GeV . mV . 80GeV, LUX experiment for direct detection of WIMP imposes a strongupper bound on the spin-independent (SI) dark matter-proton scattering cross section [17]as:

SI

p . (7 9) 10

46

cm

2 (3.8)

The SI-elastic scattering cross section for VDM to scatter off a proton target is given by

SI

p =

4µ2

V

gXs↵c↵mp

2vH

2

1

m2

H1

1

m2

H2

!2

f2

p ,

' 2.2 10

45

cm

2

gXs↵c↵10

2

2

75GeV

mH2

4

1 m2

H2

m2

H1

!2

(3.9)

where µV = mV mp/(mV + mp) and fp = 0.326 [23] was used. Note that m mh resultsin some amount of cancellation between contributions of and h to SI

p . As the result, theLUX bound can be satisfied rather easily for gXs↵c↵ . 10

2.

3.3 Dark matter relic density

The observed GeV scale -ray spectrum can be explained if DM annihilates mainly into bbwith a velocity-averaged annihilation cross section close to the canonical value of thermal relicdark matter. This implies that 30 . mV . 40GeV in s-channel annihilation (Fig. 2). It is alsopossible to produce b+¯b with the nearly same energy from the decay of highly non-relativistic which is produced from the annihilation of DM having mass of 60GeV . mV . 80GeV

(Fig. 3). The shapes of spectra in two cases are almost the same as long as MH1 is close toMV , see Fig. 4.

In the process of Fig. 2, the thermally-averaged annihilation cross section of VDM isgiven by

hvrel

if ¯f =

X

f

(gXs↵c↵)2

3m2

X

X

i

1

sm2

i + imii

2mf

vH

2

1 4m2

f

s

!3/2

(3.10)

where mf is the mass of a SM fermion f . Note that Eq. (3.10) is suppressed by a factor s2↵m2

f .Hence a large enough annihilation cross section for the right amount of relic density can be

– 4 –

10!2 10!1

10!2

10!1

Α

g X

10!2 10!1

10!2

10!1

Α

g X




X

X

b

¯b

H1,2


Xµ

X

H2

H2

H1,2

Xµ H2

X H2

Xµ H2

X H2





– 5 –

mX = 80GeV,mH2 = 75GeV


Annihilation

• These are the dominant annihilating processes, • The on-shell final particles decay into standard

model fermions, • mostly bb for dark Higgs with mass <130 GeV

X

X

X

X

X

X

X

X

H2

H2

H2

H2

H2

H2

H2

H2

H2

FIG. 4: Main feynman diagrams for annihilation XX ! H2

H2

, with vertex functions, gXXH2 /MX and gXXH2H2 / M2

X/v2

. The last one can be neglected due to the smallness of

.

XX ! H2

H2

. Then the quantity v relevant to thermal relic density is calculated as

v =1

3 3 2

1

2MX

ps

Z |M|2(4)2

|p1

|psd

' g4X144M2

X

"3 8

M2

H2 4M2

X

M2

H2 2M2

X

+16

M4

H2 4M2

H2M2

X + 6M4

X

M2

H2 2M2

X

2

#, (3.1)

where 1

332

accounts for the averaging over polarizations for initial states and identicalfactor for final states, s ' 4M2

X at decoupling time, and

|M|2 = g4X

"12 32

M2

H2 4M2

X

M2

H2 2M2

X

+64

M4

H2 4M2

H2M2

X + 6M4

X

M2

H2 2M2

X

2

#.

Since v is independent of v at the leading order in v, we can replace the thermal averagedhvi with Eq. (3.1) in the calculation of relic density. For hvi 31026cm3s1,MX TeVand MH2 MX , we have

gX 0.57

MX

1TeV

12

. (3.2)

As shown in Fig. 2, the red and blue vertical bands display the correct relic density(h2 = 0.1199 ± 0.0027 [1]) of DM for MX = 2 TeV and MX = 3 TeV, respectively.The precise relation between gX and MX is shown in the right panel of Fig. 2, where weused micrOMEGAs3.1 [64] for the numerical calculation.

8


Gamma-Ray spectrum

-1e-06

0

1e-06

2e-06

3e-06

4e-06

1 10 100

E2 d\

/dE

d1 (G

eV/c

m2 /s

/sr)

Ea(GeV)

a-ray spectra at e=5°

Hooper mX=72, mH2

=71mX=60, mH2

=59

P.Ko, W-I.Park, YT,1404.5257(JCAP)


Extensions: Hidden sector DM• hidden sector for DM with gauge symmetry • residual symmetry, dark Higgs, new gauge

boson(s), and they decay into SM fermions through Higgs portal and kinetic mixing,

• Example:

mixing operator only, and consider various constraints from direct/indirect detections andthermal relic density altogether. However, couplings between DM and dark photon criticallydepend on the charge assignments to DM and dark Higgs fields (for example, compare thelocal Z3 model [39] and the local Z2 model [59]), which is often overlooked in many works.Within local dark gauge theories, it is inconsistent to give mass to the dark gauge bosonby hand, since it breaks local dark gauge symmetry explicitly. It is important to introduceeither dark Higgs field or some nonperturbative dynamical symmetry breaking mechanismto generate the dark gauge boson mass, while respecting local dark gauge symmetry andkeeping all the allowed (renormalizable) operators. Otherwise, the resulting phenomenologycould be misleading and sometimes even wrong, as shown in Ref. [69].

We note that DM models are also constrained by indirect searches. Stringent limitscome from anti-proton and positron fluxes and radio signals [30, 33, 34]. However, suchconstraints vary for di↵erent DM annihilation channels and also depend sensitively on variousastrophysical factors as well: for example, the propagation parameters for the anti-protonflux, the local DM density for the positron flux, and the DM density-profile at small radiir < 5pc for radio signals [33], respectively. Currently, conservative limits still allow viablespace for DM explanation of -ray excess. Due to the large astrophysical uncertainties, weshall not impose such constraints in our discussion, but will show how the anti-proton fluxdepends on the propagation parameters as an example.

This paper is organized as follows. In Section. II, we first introduce the scalar DM modelwith local Z3 symmetry briefly, establishing the notations for later discussion. Then, inSection. III, we focus on the -ray spectrum from Z3 scalar DM (semi-)annihilation fromthe GC and compare with the data. In Sec. IV, we generalize our finding to the generalhidden sector DM models with dark gauge symmetries. Finally, we summarize the resultsin Sec. V.

II. SCALAR DM MODEL WITH LOCAL Z3 SYMMETRY

In this section, we give a brief introduction of scalar DM model with local Z3 symme-try [39]. The dark sector has a local U(1)X gauge symmetry that is spontaneously brokeninto Z3 by the nonzero vacuum expectation value (VEV) of dark Higgs X . This can berealized with two complex scalar fields,

X (R + iI) /p2, X (XR + iXI) /

p2,

with the U(1)X charges equal to 1 and 1/3, respectively. Then we can write down the mostgeneral renormalizable Lagrangian for the SM and dark sector fields, eXµ,X and X:

L = LSM 1

4XµX

µ 1

2sin XµB

µ +Dµ†XD

µX +DµX†DµX V,

V = µ2HH

†H + H

H†H

2 µ2

†XX +

†XX

2

+ µ2XX

†X + X

X†X

2

+ H†XXH

†H + XX†X†

XX + HXX†XH†H +

3X

3†X +H.c.

, (2.1)

where the covariant derivative associated with the U(1)X gauge field Xµ is defined as Dµ @µ igXQX

eXµ. The coupling 3 is chosen as real and positive, since one can always redefinethe field X and absorb the phase of 3.

3

Z3P. Ko, YT, 1407.5492(JCAP)


Annihilation Channels

• Standard

!

!

!• Semi-Annihilation

X

X

H2

H2

XX

X H1/H2

H2

H2

X

X

H2

H2

(a) (b) (c)

X

X

X

X H1/H2

X

X

Z 0

Z 0

Z 0

Z 0

Z 0

Z 0

(d) (e) (f)

FIG. 1: Feynman diagrams for XX annihilation into H2 and Z 0.

(a) (b)

X

X

X

H2 H2

X

X

X

(c)

H2

XX

X

(d)

H2

XX

X

(e) (f)

X

X

X

Z 0 Z 0

X

X

X

(g)

Z 0

XX

X

FIG. 2: Feynman diagrams for XX semi-annihilation into H2 and Z 0.

In the scalar DM models with global Z3 symmetry [40], light dark matter (mDM . 125GeV) is generally excluded by LUX direct search experiment except for the resonance regime.On the other hand, in the scalar DM models with local Z3 gauge symmetry, such light darkmatter is still allowed due to the newly open annihilation channels (see Ref. [39] for details).In this paper, we shall focus only on the indirect signatures in terms of -ray, anti-protonand positron fluxes within the local Z3 scalar DM model.

III. -RAY FROM DM (SEMI-)ANNIHILATION

In the section, we shall discuss the -ray spectrum from dark matter (semi-)annihilationin the scalar DM model with local Z3 symmetry. We shall focus on the channels shownin Figs. 1 and 2, where H2s and Z 0s in the final states decay into SM particles. DM pairannihilations directly into a pair of SM particles such as

XX ! (Z0 or H

02 ) ! ff,

are suppressed by the small mixing parameters, ↵ and . In the parameter regions we areinterested in, we can take ↵ and to be smaller than 104, which is definitely allowedby direct searches so far. For simplicity, we also assume vanishing H and HX . Non-vanishing H and HX would not change qualitatively our discussion. Both parameters are

5

X

X

H2

H2

XX

X H1/H2

H2

H2

X

X

H2

H2

(a) (b) (c)

X

X

X

X H1/H2

X

X

Z 0

Z 0

Z 0

Z 0

Z 0

Z 0

(d) (e) (f)

FIG. 1: Feynman diagrams for XX annihilation into H2 and Z 0.

(a) (b)

X

X

X

H2 H2

X

X

X

(c)

H2

XX

X

(d)

H2

XX

X

(e) (f)

X

X

X

Z 0 Z 0

X

X

X

(g)

Z 0

XX

X

FIG. 2: Feynman diagrams for XX semi-annihilation into H2 and Z 0.

In the scalar DM models with global Z3 symmetry [40], light dark matter (mDM . 125GeV) is generally excluded by LUX direct search experiment except for the resonance regime.On the other hand, in the scalar DM models with local Z3 gauge symmetry, such light darkmatter is still allowed due to the newly open annihilation channels (see Ref. [39] for details).In this paper, we shall focus only on the indirect signatures in terms of -ray, anti-protonand positron fluxes within the local Z3 scalar DM model.

III. -RAY FROM DM (SEMI-)ANNIHILATION

In the section, we shall discuss the -ray spectrum from dark matter (semi-)annihilationin the scalar DM model with local Z3 symmetry. We shall focus on the channels shownin Figs. 1 and 2, where H2s and Z 0s in the final states decay into SM particles. DM pairannihilations directly into a pair of SM particles such as

XX ! (Z0 or H

02 ) ! ff,

are suppressed by the small mixing parameters, ↵ and . In the parameter regions we areinterested in, we can take ↵ and to be smaller than 104, which is definitely allowedby direct searches so far. For simplicity, we also assume vanishing H and HX . Non-vanishing H and HX would not change qualitatively our discussion. Both parameters are

5

micrOMEGAs-3


-1e-06

0

1e-06

2e-06

3e-06

4e-06

1 10 100

E2d

Φ/d

Ed

Ω (

GeV

/cm

2/s

/sr)

Eγ(GeV)

γ-ray spectra at θ=5°

data mX=72, mH2

=71, mZ′=90mX=60, mH2

=59, mZ′=90

-1e-06

0

1e-06

2e-06

3e-06

4e-06

1 10 100

E2d

Φ/d

Ed

Ω (

GeV

/cm

2/s

/sr)

Eγ(GeV)

γ-ray spectra at θ=5°

data mX=35, mH2

=50, mZ′=34 mX=30, mH2

=50, mZ′=29

FIG. 4: -ray spectra from dark matter (semi-)annihilation with H2(left) and Z 0(right) as finalstates. In each case, mass of H2 or Z 0 is chosen to be close to mX to avoid large lorentz boost.Masses are in GeV unit. Data points at = 5 degree are extracted from [1].

1.0⋅10-4

1.0⋅10-3

1.0⋅10-2

1.0⋅10-1

0.1 1 10 100

Φ- p[(

GeV

m2 s

tr s

)-1]

E(GeV)

PAMELA mX=35, mH2

=50, mZ′=34mX=30, mH2

=50, mZ′=29mX=72, mH2

=71, mZ′=90mX=60, mH2

=59, mZ′=90

1.0⋅10-2

1.0⋅10-1

1.0⋅100

1.0⋅101

1.0⋅102

0.1 1 10 100

E3Φ

e+[G

eV

2m

-2s

-1sr-1

]

E(GeV)

PAMELA mX=35, mH2

=50, mZ′=34mX=30, mH2

=50, mZ′=29mX=72, mH2

=71, mZ′=90mX=60, mH2

=59, mZ′=90

FIG. 5: p and e+ spectra from dark matter (semi-)annihilation with H2(left) and Z 0(right) as finalstates. In each case, mass of H2 or Z 0 is chosen to be close to mX to avoid large lorentz boost.Masses are in GeV unit. hviann ' 6.8(4.4)1026cm3/s for H2(Z 0) final states are assumed. Datapoint are taken from [62] for anti-proton and [63] for positron fluxes, using the database [64].

PAMELA [62, 63]. The constraints from p and e+ can provide important and comple-mentary information for DM models explaining -ray excess. It should be pointed out thatpotentially stringent constraints from indirect detections of cosmic rays depend sensitivelyon astrophysical parameters involved in the calculations of cosmic ray production and prop-agation.

The propagation equation that describes the evolution of energy distribution for charged

8

-ray spectra


Model-Independent

• Assume dark matter annihilate into dark higgs

X

X

H2

H2

FIG. 1: Feynman diagram due to the e↵ective operator X2H22 (X5XH2

2 for fermionic X orXµX

µH22 for vector X). The actual annihilation process may occur through s or t channel, and

contact interaction. Details in the gray bubble depend on various ultraviolet completions. Theproduced H2s can have two-, three- or even four-body decay channels.

For DM density distribution, we use the following generalized NFW profile [88],

(r) =

hrr

i 1 + r/rc1 + r/rc

3

, (2.8)

with parameters rc ' 20kpc and ' 0.4GeV/cm3. We shall adopt the index = 1.26 ifnot stated otherwise.

III. NUMERICAL ANALYSIS

We first show three cases for the gamma-ray spectrum in Fig. 2. The vertical axis marksthe conventional

E2dN

dE E2

1

Z

d2

dEd, (3.1)

where indicates the region of interest. The 24 data points we used to compare with arefrom Ref. [10], denoted as CCW hereafter.

As we can see, di↵erent parameter sets can give di↵erent spectrum shape, especially inthe high energy regime. When the branching ratios of H2 ! , Z are increasing, we cansee the gamma lines more easily around E ' MH2/2. Since the annihilation cross section isat order of 1026cm3/s and the branching ratios of H2 ! , Z are around 0.2% at most,the considered parameters are still consistent with constraint from gamma-line searches.

We now use the 2 function and find its minimum to find out the best fit:

2 (MX ,MH2 , hvi) =X

i,j

(µi fi)1ij (µj fj) , (3.2)

where µi and fi are the predicted and measured fluxes in the i-th energy bin respectively, and is the 2424 covariance matrix. We take the numerical values for fi and from CCW [10].Minimizing the 2 against fi with respect to MX , MH2 and hvi gives the best-fit points,and then two-dimensional 1, 2 and 3 contours are defined at 2 2 2

min = 2.3,6.2 and 11.8, respectively.

Fig. 3 is our main result. In the left panel, MX , MH2 and hvi are freely varied, so thatthe total degree of freedom (d.o.f.) is 21. The red dot represents the best-fit point with

MX ' 95.0GeV, MH2 ' 86.7GeV, hvi ' 4.0 1026cm3/s, (3.3)

4

1.0⋅10-8

1.0⋅10-7

1.0⋅10-6

1 10 100 1000

E2d

N/d

E[G

eV

(cm

2 s

tr s

)-1]

E(GeV)

CCW<σv>=5.8×10-26,Mx=125,MH2=125<σv>=4.0×10-26,Mx=95, MH2=87.0<σv>=1.0×10-26,Mx=25, MH2=5.0

FIG. 2: Three illustrative cases for gamma-ray spectra in contrast with CCW data points [10]. Allmasses are in GeV unit and v with cm3/s. Line shape around E ' MH2/2 is due to decay modes,H2 ! , Z.

gives 2min ' 22.0, with the corresponding p-value equal to 0.40.

We also notice that there are two separate regimes, one in the low mass region and theother in high mass region. The higher mass region is basically aligned with MH2 ' MX sinceotherwise a highly-boosted H2 would give a harder gamma-ray spectrum. In this region,H2 mostly decays into bb. As one increases the mass of H2, H2 ! W±l, H2 ! Zl±l,H2 ! and H2 ! Z become more and more important, and all of them give hardergamma-ray spectra either due to the leptonic final states or the gamma lines. Eventually,2 increases significantly when MH2 150GeV.

In the low mass region, the contours are scattered but centered around MH2 ' 10GeVand such a light H2 most likely decays into bb, cc and +. Since cc and + would giveharder spectra than bb does, we would need a lower MX to fit the data, which is exactlywhat we see in Fig. 2 (dotted curve). Increasing the branching ratios of cc and + wouldrequire a even lower MX .

In the right panel, we show a special case in which MH2 ' MX , so that the produced H2sare non-relativistic. In such a case, the d.o.f. is now 22. The best-fit parameters are

MX ' MH2 ' 97.1GeV, hvi ' 4.2 1026cm3/s, (3.4)

which gives 2min ' 22.5 and the p-value equal to 0.43. An interesting thing is that MX '

MH2 ' 125GeV also give a good-fit. This point is equivalent to the channel that DM Xannihilates into SM Higgs, which has been already found in previous study [55, 61].

In the left panel of Fig. 4, we fix the mass of dark Higgs to the best-point value, MH2 =86.7, and vary MX and hvi. We show 1, 2 and 3 contours in terms of solid(black),

5

I. INTRODUCTION

Firm evidences for dark matter (DM) come exclusively from the gravitational inter-action at the moment. A popular scenario in particle physics models, DM as weakly-interacting massive particles (WIMP), generally predicts that DM should have a mass be-tweenO(GeV)O(TeV), with a weak-scale annihilation cross section around 31026cm3/s.If those annihilation final states go to standard model particles eventually, there might benotable excesses in cosmic rays and gamma ray searches.

By analyzing Fermi-LAT ’s public data, several groups [1–10] have been claiming thatthere might be some excess in the gamma-ray signals from Galactic center, inner Galaxyand even some Dwarf Galaxy [11]. The excess is at E O(GeV) energy scale and itsmorphology against the distance to galaxy center is consistent with signals from WIMPDM annihilation, which has motivated intense discussions about DM model-constructionsand constraints [12–77]. Besides DM interpretation, astrophysical origins of the excess havealso been actively investigated [78–88]. For instance, Refs. [78, 86–88] showed that gamma-ray emission from unresolved millisecond pulsars is compatible with the excess and mightaccount for, at least partial of if not all of, the excess.

In this paper, we shall exclusively consider DM interpretations. As a first step, it isnatural to investigate the GeV excess through annihilation channels that a pair of DM goes totwo SM particles directly, such as qq, cc, bb, tt, ll±, gg, hh,WW,ZZ and also their di↵erentcombinations with some branching fractions. After all, no new particle has been found yetat the LHC, except the Higgs boson. This method has provided valuable information for thefavored DM mass and annihilation cross section ranges. Discussions has been extended tocascade two-body decay through new mediators, such as Z 0 and dark Higgs H2, which areubiquitous in new physics beyond SM. In particular, light mediator (MZ0,H2 < 1GeV) [54]and heavy Z

0[26] cases have been investigated thoroughly.

This work is intended to investigate GeV scale gamma-ray excess in models where DMannihilates into a pair of heavy dark Higgs (> 1GeV) which subsequently could decay intomulti-body final states such as WW or W W , where W is a virtual W boson. The aimis to provide the ranges of the favored dark Higgs mass, DM mass and the annihilationcross section, which might be useful for particle physics model building, such as hiddensector DM models with local dark gauge symmetries. This work di↵ers from many previousinvestigation in one essential aspect: we take into account consistently all possible decaymodes for heavy dark Higgs, not restricted to its two-body decays.

This paper is organized as follows. In Sec. II, we discuss the theoretical motivation andestablish our formalism and notations. In Sec. III, we present our numerical results on thebest-fit parameters. Then in Sec. IV, we briefly discuss the implications for DM relic densityand constraints from our results. Finally, we give a summary.

II. FORMALISM

We shall consider the following annihilation channel for self-conjugate DM X,

X + X ! H2 +H2, followed by

H2 ! SM + SM(+SM).

HereH2 denotes the dark Higgs, distinguishing it from the SM-like HiggsH1 withMH1 ' 125GeV. In Ref. [35], the present authors showed that dark Higgs is very generic in dark matter

2

X can be scalar, fermion and vector


Numeric Analysis

We now use the 2function and find its minimum to find out the best fit:

2(MX ,MH2 , hvi) =

X

i,j

(µi fi)1ij (µj fj) , (1)

where µi and fi are the predicted and measured fluxes in the i-th energy bin

respectively, and is the 24 24 covariance matrix. We take the numerical

values for fi and from CCW. Minimizing the 2against fi with respect to

MX , MH2 and hvi gives the best-fit points, and then two-dimensional 1, 2and 3 contours are defined at2 22

min = 2.3, 6.2 and 11.8, respectively.

E2 dN

dE E2

1

Z

d2

dEd,


0 50 100 150 2000

50

100

150

200 0 50 100 150 200

0

50

100

150

200

MX@GeVD

MH 2@GeV

DXXÆH2H2

0 50 100 150 200

2

4

6

8

10 0 50 100 150 200

2

4

6

8

10

MX@GeVD

<sv>@¥10

-26 cm

3 êsD

XXÆH2H2, MH2>MX

20 40 60 80 100 120 1400

2

4

6

8 20 40 60 80 100 120 140

0

2

4

6

8

MX@GeVD

<sv>@¥10

-26 cm

3 êsD

XXÆH2H2, MH2=86.7GeV

20 40 60 80 1000

1

2

3

4 20 40 60 80 100

0

1

2

3

4

MX@GeVD

<sv>@¥10

-26 cm

3 êsDXXÆbb

FIG. 5: Similar plots as Figs. 3 and 4, based on results from Ref. [9]. Regions inside solid(black),dashed(blue) and long-dashed(red) contours correspond to 1, 2 and 3, respectively. The reddots inside 1 contours are the best-fit points.

Universe. This can be easily achieved if we introduce the following interactions:

L = y1Y2X2 + y2MXY X2.

When y2 is small enough, say less than 1012, Y would decay into X pair after BBN epochor the freeze-out of X’s. Before its decay, Y ’s relic abundance was determined by y1 throughthe ecient annihilation process, Y + Y ! X +X.

For bb channel, the best-fit cross section, Eq. (3.5), is a little smaller than the canon-ical value. This is not a problem at this stage since the right panel of Fig. 4 shows thatcanonical value of thermal cross section is within 1-2 range. Even if it is a problem, we

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Favored Parameters

• Based on CCW

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FIG. 3: The regions inside solid(black), dashed(blue) and long-dashed(red) contours correspondto 1, 2 and 3, respectively. The red dots inside 1 contours are the best-fit points. In theleft panel, we vary freely MX , MH2 and hvi. While in the right panel, we fix the mass of H2,MH2 ' MX .

Channels Best-fit parameters 2min/d.o.f. p-value

XX ! H2H2 MX ' 95.0GeV,MH2 ' 86.7GeV 22.0/21 0.40

(with MH2 6= MX) hvi ' 4.0 1026cm3/s

XX ! H2H2 MX ' 97.1GeV 22.5/22 0.43

(with MH2 = MX) hvi ' 4.2 1026cm3/s

XX ! H1H1 MX ' 125GeV 24.8/22 0.30

(with MH1 = 125GeV) hvi ' 5.5 1026cm3/s

XX ! bb MX ' 49.4GeV 24.4/22 0.34

hvi ' 1.75 1026cm3/s

TABLE I: Summary table for the best fits with three di↵erent assumptions.

dashed(blue) and long-dashed(red) curves, respectively. To compare with bb channel, wealso present 3 region in the right panel of Fig. 4. The best-fit point is around

MX ' 49.4GeV, hvi ' 1.75 1026cm3/s, (3.5)

which gives 2min ' 24.4 and a p-value, 0.34.

IV. SUMMARY

In the letter, we have explored a possibility that the GeV scale -ray excess from thegalactic center is due to DM pair annihilation into a pair of dark Higgs, followed by the dark

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P.Ko, YT, 1504.03908


Contours do not fully consider uncertainties in the DM profile

A broader range of DM masses and annihilation channels

6

FIG. 1. Constraints on the DM annihilation cross section at 95% CL for the bb (left) and + (right) channels derived froma combined analysis of 15 dSphs. Bands for the expected sensitivity are calculated by repeating the same analysis on 300randomly selected sets of high-Galactic-latitude blank fields in the LAT data. The dashed line shows the median expectedsensitivity while the bands represent the 68% and 95% quantiles. For each set of random locations, nominal J-factors arerandomized in accord with their measurement uncertainties. The solid blue curve shows the limits derived from a previousanalysis of four years of Pass 7 Reprocessed data and the same sample of 15 dSphs [13]. The dashed gray curve in this andsubsequent figures corresponds to the thermal relic cross section from Steigman et al. [5].

101 102 103 104

DM Mass (GeV/c2)

1027

1026

1025

1024

1023

1022

hvi

(cm

3s

1)

bb

Pass 8 Combined dSphs

Fermi-LAT MW Halo

H.E.S.S. GC Halo

MAGIC Segue 1

Abazajian et al. 2014 (1)

Gordon & Macias 2013 (2)

Daylan et al. 2014 (2)

Calore et al. 2014 (2)

Thermal Relic Cross Section(Steigman et al. 2012)

FIG. 2. Comparison of constraints on the DM annihilation cross section for the bb (left) and + (right) channels from thiswork with previously published constraints from LAT analysis of the Milky Way halo (3 limit) [33], 112 hours of observationsof the Galactic Center with H.E.S.S. [34], and 157.9 hours of observations of Segue 1 with MAGIC [35]. Closed contours andthe marker with error bars show the best-fit cross section and mass from several interpretations of the Galactic center excess[16–19].

DM distribution can significantly enlarge the best-fit re-gions of hvi, channel, and mDM [36].

In conclusion, we present a combined analysis of 15Milky Way dSphs using a new and improved LAT dataset processed with the Pass 8 event-level analysis. We ex-clude the thermal relic annihilation cross section ( 2.21026 cm3 s1) for WIMPs with mDM

< 100 GeV annihi-lating through the quark and -lepton channels. Ourresults also constrain DM particles with mDM above100 GeV surpassing the best limits from Imaging Atmo-spheric Cherenkov Telescopes for masses up to 1 TeV.These constraints include the statistical uncertainty onthe DM content of the dSphs. The future sensitivity to

DM annihilation in dSphs will benefit from additionalLAT data taking and the discovery of new dSphs withupcoming optical surveys such as the Dark Energy Sur-vey [37] and the Large Synoptic Survey Telescope [38].

ACKNOWLEDGMENTS

The Fermi -LAT Collaboration acknowledges supportfor LAT development, operation and data analysisfrom NASA and DOE (United States), CEA/Irfu andIN2P3/CNRS (France), ASI and INFN (Italy), MEXT,KEK, and JAXA (Japan), and the K.A. Wallenberg

6

FIG. 1. Constraints on the DM annihilation cross section at 95% CL for the bb (left) and + (right) channels derived froma combined analysis of 15 dSphs. Bands for the expected sensitivity are calculated by repeating the same analysis on 300randomly selected sets of high-Galactic-latitude blank fields in the LAT data. The dashed line shows the median expectedsensitivity while the bands represent the 68% and 95% quantiles. For each set of random locations, nominal J-factors arerandomized in accord with their measurement uncertainties. The solid blue curve shows the limits derived from a previousanalysis of four years of Pass 7 Reprocessed data and the same sample of 15 dSphs [13]. The dashed gray curve in this andsubsequent figures corresponds to the thermal relic cross section from Steigman et al. [5].

101 102 103 104

DM Mass (GeV/c2)

1027

1026

1025

1024

1023

1022

hvi

(cm

3s

1)

+

Pass 8 Combined dSphs

Fermi-LAT MW Halo

MAGIC Segue 1

Abazajian et al. 2014 (1)

Daylan et al. 2014 (2)

Calore et al. 2014 (2)

Thermal Relic Cross Section(Steigman et al. 2012)

FIG. 2. Comparison of constraints on the DM annihilation cross section for the bb (left) and + (right) channels from thiswork with previously published constraints from LAT analysis of the Milky Way halo (3 limit) [33], 112 hours of observationsof the Galactic Center with H.E.S.S. [34], and 157.9 hours of observations of Segue 1 with MAGIC [35]. Closed contours andthe marker with error bars show the best-fit cross section and mass from several interpretations of the Galactic center excess[16–19].

DM distribution can significantly enlarge the best-fit re-gions of hvi, channel, and mDM [36].

In conclusion, we present a combined analysis of 15Milky Way dSphs using a new and improved LAT dataset processed with the Pass 8 event-level analysis. We ex-clude the thermal relic annihilation cross section ( 2.21026 cm3 s1) for WIMPs with mDM

< 100 GeV annihi-lating through the quark and -lepton channels. Ourresults also constrain DM particles with mDM above100 GeV surpassing the best limits from Imaging Atmo-spheric Cherenkov Telescopes for masses up to 1 TeV.These constraints include the statistical uncertainty onthe DM content of the dSphs. The future sensitivity to

DM annihilation in dSphs will benefit from additionalLAT data taking and the discovery of new dSphs withupcoming optical surveys such as the Dark Energy Sur-vey [37] and the Large Synoptic Survey Telescope [38].

ACKNOWLEDGMENTS

The Fermi -LAT Collaboration acknowledges supportfor LAT development, operation and data analysisfrom NASA and DOE (United States), CEA/Irfu andIN2P3/CNRS (France), ASI and INFN (Italy), MEXT,KEK, and JAXA (Japan), and the K.A. Wallenberg

Searching for Dark Matter Annihilation from Milky Way Dwarf Spheroidal Galaxies

with Six Years of Fermi-LAT Data

M. Ackermann,1 A. Albert,2 B. Anderson,3, W. B. Atwood,4 L. Baldini,5 G. Barbiellini,6, 7 D. Bastieri,8, 9

K. Bechtol,10 R. Bellazzini,11 E. Bissaldi,12 R. D. Blandford,2 E. D. Bloom,2 R. Bonino,13, 14 E. Bottacini,2

T. J. Brandt,15 J. Bregeon,16 P. Bruel,17 R. Buehler,1 G. A. Caliandro,2, 18 R. A. Cameron,2 R. Caputo,4

M. Caragiulo,12 P. A. Caraveo,19 C. Cecchi,20, 21 E. Charles,2 A. Chekhtman,22 J. Chiang,2 G. Chiaro,9

S. Ciprini,23, 20, 24 R. Claus,2 J. Cohen-Tanugi,16 J. Conrad,25, 26, 27 A. Cuoco,26, 13, 14 S. Cutini,23, 24, 20

F. D’Ammando,28, 29 A. de Angelis,30 F. de Palma,12, 31 R. Desiante,6, 32 S. W. Digel,2 L. Di Venere,33

P. S. Drell,2 A. Drlica-Wagner,34, † R. Essig,35 C. Favuzzi,33, 12 S. J. Fegan,17 E. C. Ferrara,15 W. B. Focke,2

A. Franckowiak,2 Y. Fukazawa,36 S. Funk,2 P. Fusco,33, 12 F. Gargano,12 D. Gasparrini,23, 24, 20 N. Giglietto,33, 12

F. Giordano,33, 12 M. Giroletti,28 T. Glanzman,2 G. Godfrey,2 G. A. Gomez-Vargas,37, 38 I. A. Grenier,39

S. Guiriec,15, 40 M. Gustafsson,41 E. Hays,15 J.W. Hewitt,42, 43 D. Horan,17 T. Jogler,2 G. Johannesson,44 M. Kuss,11

S. Larsson,25, 26, 45 L. Latronico,13 J. Li,46 L. Li,47, 26 M. Llena Garde,25, 26 F. Longo,6, 7 F. Loparco,33, 12

P. Lubrano,20, 21 D. Malyshev,2 M. Mayer,1 M. N. Mazziotta,12 J. E. McEnery,15, 48 P. F. Michelson,2 T. Mizuno,49

A. A. Moiseev,43, 48 M. E. Monzani,2 A. Morselli,37 S. Murgia,50 E. Nuss,16 T. Ohsugi,49 M. Orienti,28

E. Orlando,2 J. F. Ormes,51 D. Paneque,52, 2 J. S. Perkins,15 M. Pesce-Rollins,11 F. Piron,16 G. Pivato,11

T. A. Porter,2 S. Raino,33, 12 R. Rando,8, 9 M. Razzano,11, 53 A. Reimer,54, 2 O. Reimer,54, 2 S. Ritz,4

M. Sanchez-Conde,26, 25 A. Schulz,1 C. Sgro,11 E. J. Siskind,55 F. Spada,11 G. Spandre,11 P. Spinelli,33, 12

L. Strigari,56 H. Tajima,57, 2 H. Takahashi,36 J. B. Thayer,2 L. Tibaldo,2 D. F. Torres,46, 58 E. Troja,15, 48

G. Vianello,2 M. Werner,54 B. L. Winer,59 K. S. Wood,60 M. Wood,2, ‡ G. Zaharijas,61, 62 and S. Zimmer25, 26

(The Fermi-LAT Collaboration)1Deutsches Elektronen Synchrotron DESY, D-15738 Zeuthen, Germany

2W. W. Hansen Experimental Physics Laboratory,Kavli Institute for Particle Astrophysics and Cosmology,

Department of Physics and SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305, USA3Royal Swedish Academy of Sciences Research Fellow,

funded by a grant from the K. A. Wallenberg Foundation4Santa Cruz Institute for Particle Physics, Department of Physics and Department of Astronomy and Astrophysics,

University of California at Santa Cruz, Santa Cruz, CA 95064, USA5Universita di Pisa and Istituto Nazionale di Fisica Nucleare, Sezione di Pisa I-56127 Pisa, Italy

6Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34127 Trieste, Italy7Dipartimento di Fisica, Universita di Trieste, I-34127 Trieste, Italy

8Istituto Nazionale di Fisica Nucleare, Sezione di Padova, I-35131 Padova, Italy9Dipartimento di Fisica e Astronomia “G. Galilei”, Universita di Padova, I-35131 Padova, Italy

10Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA11Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, I-56127 Pisa, Italy12Istituto Nazionale di Fisica Nucleare, Sezione di Bari, 70126 Bari, Italy

13Istituto Nazionale di Fisica Nucleare, Sezione di Torino, I-10125 Torino, Italy14Dipartimento di Fisica Generale “Amadeo Avogadro” ,Universita degli Studi di Torino, I-10125 Torino, Italy

15NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA16Laboratoire Univers et Particules de Montpellier,

Universite Montpellier 2, CNRS/IN2P3, Montpellier, France17Laboratoire Leprince-Ringuet, Ecole polytechnique, CNRS/IN2P3, Palaiseau, France18Consorzio Interuniversitario per la Fisica Spaziale (CIFS), I-10133 Torino, Italy

19INAF-Istituto di Astrofisica Spaziale e Fisica Cosmica, I-20133 Milano, Italy20Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia, Italy21Dipartimento di Fisica, Universita degli Studi di Perugia, I-06123 Perugia, Italy

22College of Science, George Mason University, Fairfax, VA 22030,resident at Naval Research Laboratory, Washington, DC 20375, USA

23Agenzia Spaziale Italiana (ASI) Science Data Center, I-00133 Roma, Italy24INAF Osservatorio Astronomico di Roma, I-00040 Monte Porzio Catone (Roma), Italy25Department of Physics, Stockholm University, AlbaNova, SE-106 91 Stockholm, Sweden

26The Oskar Klein Centre for Cosmoparticle Physics, AlbaNova, SE-106 91 Stockholm, Sweden27Wallenberg Academy Fellow

28INAF Istituto di Radioastronomia, 40129 Bologna, Italy29Dipartimento di Astronomia, Universita di Bologna, I-40127 Bologna, Italy

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Fermi-LAT Collaboration, 1503.02641

bb tau tau


Summary

• We have briefly introduced the GeV gamma-ray excess from galactic center.

• Simple DM models with gauge symmetries are fully capable of providing the needed signal.

• We have specifically discussed a vector dark matter model, and a scalar dark matter with Z3 symmetry and conducted a model-independent analysis.


Thanks for your attention.


Backup


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FIG. 5: Similar plots as Figs. 3 and 4, based on results from Ref. [9]. Regions inside solid(black),dashed(blue) and long-dashed(red) contours correspond to 1, 2 and 3, respectively. The reddots inside 1 contours are the best-fit points.

Universe. This can be easily achieved if we introduce the following interactions:

L = y1Y2X2 + y2MXY X2.

When y2 is small enough, say less than 1012, Y would decay into X pair after BBN epochor the freeze-out of X’s. Before its decay, Y ’s relic abundance was determined by y1 throughthe ecient annihilation process, Y + Y ! X +X.

For bb channel, the best-fit cross section, Eq. (3.5), is a little smaller than the canon-ical value. This is not a problem at this stage since the right panel of Fig. 4 shows thatcanonical value of thermal cross section is within 1-2 range. Even if it is a problem, we

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Higgs Portal Dark Matter for GeV Gamma-ray Excess · 2015. 10. 29. · for GeV Gamma-ray Excess....

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