Simplified TeV leptophilic dark matter in light of DAMPE data

Journal of High Energy Physics, Feb 2018

Abstract Using a simplified framework, we attempt to explain the recent DAMPE cosmic e+ + e− flux excess by leptophilic Dirac fermion dark matter (LDM). The scalar (Φ0) and vector (Φ1) mediator fields connecting LDM and Standard Model particles are discussed. We find that the couplings P ⊗ S, P ⊗ P , V ⊗ A and V ⊗ V can produce the right bump in e+ + e− flux for a DM mass around 1.5 TeV with a natural thermal annihilation cross-section < σv >∼ 3×10−26cm3/s today. Among them, V ⊗V coupling is tightly constrained by PandaX-II data (although LDM-nucleus scattering appears at one-loop level) and the surviving samples appear in the resonant region, \( {m_{\varPhi}}_{{}_1}\simeq 2{m}_{\chi } \). We also study the related collider signatures, such as dilepton production pp → Φ1 → ℓ+ℓ−, and muon g − 2 anomaly. Finally, we present a possible U(1) X realization for such leptophilic dark matter.

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Simplified TeV leptophilic dark matter in light of DAMPE data

HJE Simpli ed TeV leptophilic dark matter in light of DAMPE data Guang Hua Duan 1 2 4 6 7 8 9 10 Lei Feng 1 2 3 4 9 10 Fei Wang 1 2 4 5 9 10 Lei Wu 1 2 4 8 9 10 Jin Min Yang 0 1 2 4 6 7 9 10 Rui Zhengg 1 2 4 9 10 0 Department of Physics, Tohoku University 1 Beijing 100049 , China 2 Chinese Academy of Sciences 3 Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory 4 Nanjing , Jiangsu 210023 , China 5 School of Physics, Zhengzhou University 6 CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics 7 School of Physical Sciences, University of Chinese Academy of Sciences 8 Department of Physics and Institute of Theoretical Physics, Nanjing Normal University 9 Davis , CA 95616 , U.S.A 10 Zhengzhou 450000 , P. R. China Using a simpli ed framework, we attempt to explain the recent DAMPE cosmic ux excess by leptophilic Dirac fermion dark matter (LDM). The scalar ( 0) and vector ( 1) mediator elds connecting LDM and Standard Model particles are discussed. We nd that the couplings P P , V A and V V can produce the right bump in e+ + e section < v > ux for a DM mass around 1.5 TeV with a natural thermal annihilation cross3 10 26cm3=s today. Among them, V V coupling is tightly constrained by PandaX-II data (although LDM-nucleus scattering appears at one-loop level) and the surviving samples appear in the resonant region, m 1 ' 2m . We also study the related collider signatures, such as dilepton production pp ! 1 ! `+` , and muon g 2 anomaly. Finally, we present a possible U(1)X realization for such leptophilic dark matter. 1 Introduction 2 3 4 5 1:4 TeV was reported in DAMPE data, which implies the existence of a nearby monoenergetic electron sources because of the cooling process of high energy cosmic-ray electrons [4, 5]. No associated excess in the anti-proton ux has been observed. Both astrophysical sources (e.g., pulsars) and DM interpretations are discussed in ref. [4]. It is found that DM should annihilate to e or fe ; ; g with 1:1:1 and the mass of DM particle is about 1.5 TeV if the nearby DM sub-halo located at 0:1 0:3 kpc away from the solar system [4]. Several leptophilic DM model have been proposed to explain this excess [6, 7]. In this work, we attempt to explain this tentative cosmic-ray eletron+positron excess by using a simpli ed framework, in which the DM sector has no direct couplings to quarks, only couples with leptons mediated by a scalar or vector eld. Such a leptophilic DM can satisfy the measured relic density at tree level and may accommodate the null results from direct detections by inducing interactions between dark matter and quarks at the loop level. Many studies have been devoted into the idea that DM does not interact with quarks at { 1 { avor blind [8, 8{39], while a few other studies assume gauged avor interactions [33, 40{ 48]. The leptophilic DM framework allows for a more general analysis of interactions that involve only DM and leptons at the tree level. It permits di erent coupling strengths between lepton avors, o -diagonal avor couplings, and lepton- avor violation.1 The structure of this paper is organized as follows. In section 2, we introduce the e ective lagrangian for leptophilic DM and loop induced LDM-hadron interactions. In section 3, we present our numerical results for the DAMPE excess and discuss the related collider signatures. In section 4, we give a possible realization of leptophilic DM in U(1) extensions. Finally, we draw our conclusions in section 5. 2 Simpli ed leptophilic dark matter The main goal of our study is a model independent analysis of leptophilic Dirac fermion DM ( ) for the DAMPE excess. We parameterize the relevant DM-lepton interactions as L 3 i + i` ``; where i is a mediator eld with i = 0; 1 corresponding to spin-0 and spin-1 boson respectively. We assume that i only couples with leptons e; ; in our calculations. Then, the ;` are scalar (S), pseudo-scalar (P), vector (V) and axial-vector (A) scalar-type: vector-type: = gS + igP 5 ; = g V + g A 5 ; ` = g`S + ig`P 5 ; ` = g `V + g`A 5 ; and g` are the coupling strengthes of the mediator to DM and SM leptons, χ Φ (2.1) (2.2) (2.3) Lorentz structures of interactions given by where g respectively. ! ``; { 2 { In our framework, the dominant LDM annihilation channels are with the corresponding Feynman diagrams in gure 1. For a pair of LDM, the CP value of the system is given by ( 1)S+1. Due to the CP and total angular momentum conservation, 1For a review of avored dark matter, see ref. [49] and the references therein. S S P P V V A A χ N ` S P S P V A V A v( ! ``) ( N ! p-wave p-wave s-wave s-wave s-wave s-wave p-wave p-wave 2 em | e2mv2 | 1 | v 2 | the quantum states of j i are 3P and 1S for the scalar and pseudoscalar mediators, while the corresponding states for vector and axial-vector mediators are 3S and 1P , respectively. Then, one can estimate the dominant contributions of LDM annihilation cross section, as shown in table 1. It should be noted that the coupling A A can produce the s-wave contribution, however, which is highly suppressed by mass ratio m`2=m2 . Since the LDM only interacts with leptons, it can produce the signal by scattering with electron of atom at tree level or with nucleus at loop level in DM direct detection experiments, as shown in gure 2. The velocity of DM particles near the Earth is of the same order as the orbital velocity of the Sun, v 0:001c. So the recoil momenta is of order a few MeV, which is much smaller than our mediator mass. Then, we can integrate out heavy mediator elds and obtain the e ective operators: Le = 1 2 ( ) (` ``) ; where = m =pg g` is the cut-o scale for the e ective eld theory description. With this setup, one can calculate DM-electron scattering cross section at tree level: e0 = e1 = me2g2 g2 ( ` m4 0 me2g2 g2 ` m4 1 (gSgeS)2 + (gSgeP )2 + (gP geS)2 me2 m2 v 2 2 (gV geV )2 + 3(gAgeA)2 + (gV geA)2 + 3(gAgeV )2 v + (gP geP )2 me2 v4 ; ) 3 2 2 m2 : (2.4) (2.5) (2.6) { 3 { We can nd that DM-electron scattering cross sections for S P , P S and P are suppressed by both small mass ratio me=m and low velocity v 10 3, while for V A and A V couplings the cross sections are only suppressed by velocity. All of them are below the current sensitivity of DM-electron scattering experiments. The loop induced DM-nucleus scattering cross sections for spin-1/0 mediator at oneloop/two-loop level in leading log approximation [50] are given by: N0 = N1 = 2 where mN and Z are the nucleus's mass and charge respectively, and reduced mass of DM-nucleus system. The above two-loop result of operator product expansion in heavy lepton approximation. We set the renormalization scale = m and both nuclear form factors F (q) for 1 and F~(q) for 0 to unity for simplicity. According to eq. (2.7) and (2.8), we present the scattering cross section suppression by small parameters for loop induced DM-nucleon scattering for eight Lorentz structures in table. 1. It can be seen that the DM-nucleus scattering cross sections for P S and V couplings are suppressed by v2, as comparison with S S and V V couplings. N = m +mN m mN is the N1 is obtained by using Numerical results and discussions According to the analysis of ref. [4], the excess of e+ +e ux in DAMPE can be interpreted by a DM particle with the mass about 1.5 TeV if the nearby DM sub-halo locates at 0:1 0:3 kpc away form the solar system. We t the AMS-02 and DAMPE data assuming the DM annihilate into leptons with the branching ratio e : : = 1 : 1 : 1. Such a condition can evade the constraints from CMB and the di use gamma rays from dwarf spheroidal galaxies (dSphs) [4]. In the tting, we used numerical codes are GALPROP [51] and DRAGON [52] to calculate the propagation of CR electrons/positrons in the galaxy. We use the analytical solution presented in ref. [53] to calculate the propagation of nearby CR electrons. In the rst step, we use the LikeDM package [54] to calculate the likelihood (or 2) and t the AMS-02 and DAMPE data with power-lower background and extra astronomy contribution (see [ 55 ] for more details). Then we add the contribution of local DM halos directly as the local CR source only contributes the region around 1:5 TeV. The is 1 108m with a distance 0.1 kpc away from the solar system. tting result is shown in gure 3, in which the mass of DM particles is assumed as 1.5 TeV with the annihilation cross section h vi ' 3 10 26cm3s 1 and the mass of nearby subhalo In order to satisfy DM annihilation cross section, h vi ' 3 10 26cm3s 1, required by DAMPE data, we focus on P S, P P , V A and V V couplings which can produce s-wave contributions in our following study. In the following calculations, we assume a universal coupling of the mediator and three generation leptons, g` = ge = { 4 { , DAMPE HJEP02(18)7 mediators can induce the process e+e ! `+` , they are strongly constrained by LEP measurements of four-lepton contact interactions [58] and di-lepton resonance searches in e+e ! `+` of the coupling and mass of mediators 0;1 at 90% C.L., [59]. According the analysis in ref. [60], one can derive the following bounds g`V =m 1 < g`A=m 1 < gS;P =m 0 < ` (2:0 6:9 (2:4 6:9 (2:7 7:3 10 4GeV 1 ; 10 4 GeV 1 10 4GeV 1 ; 10 4 GeV 1 10 4GeV 1 ; 10 4 GeV 1 mZ0 > 200 GeV mZ0 > 200 GeV mZ0 > 200 GeV ; 100 GeV < mZ0 < 200 GeV ; 100 GeV < mZ0 < 200 GeV ; 100 GeV < mZ0 < 200 GeV (3.1) (3.2) (3.3) In gure 4 we project the samples satisfying the requirements of DM relic density within 2 range of Planck observed value, LEP bound and the DAMPE excess on the plane of g versus m for di erent values of g`. All samples are required to produce averaged annihilation cross-section h vi today within (2 mass of DM is close to m =2, DM annihilation cross section will be enhanced by resonance e ect. In order to satisfy the DM relic density requirement, the couplings gV and g`V have to become small, which will suppress the DM-nucleus scattering cross section so that the PandaX-II bound can be evaded [61]. For P S coupling, the DM-nucleus scattering cross section is highly reduced due to two-loop suppression, while for P P and V A couplings, 4) 10 26cm3=s. When the { 5 { P χ V χ g ℓV = g ℓV = g ℓV = g ℓV = m Φ 0 m Φ 1 ⊗ ⊗ g ℓS = g ℓS = g ℓS = g ℓS = g ℓA = g ℓA = g ℓA = g ℓA = g ℓS = g ℓS = g ℓS = g ℓS = m Φ 0 m Φ 1 today within (2 is also shown [61]. observed value, LEP bound and the DAMPE excess, projected on the plane of g versus m for g` = 0:05; 02; 0:5; 0:8. All samples are required to produce averaged annihilation cross-section h vi 4) 10 26cm3=s. The 90% C.L. exclusion limits from the current PandaX-II data the DM has no interactions with nucleus. The surviving samples for V V coupling are largely excluded by the PandaX-II limits of DM-nucleus scattering. There are also limits from other direct detection experiments such as XENON1T [62] and LUX [63]. However, their current bounds are weaker than that of PandaX-II. It should be mentioned that the vector mediator 1 can be produced at the LHC because of the loop-induced coupling between the mediator and light quarks, as shown in gure 5. The cross section in the narrow width limit is given by [64] pp!l+l = BR 1!l+l 3s X Cqq(m2 1 =s) gV 2 q + gqA2 ; q Cqq(m2 1 =s) for the quark q reads where BR 1!l+l is the branching ratio of the decay 1 ! l+l . The parton luminosity Cqq(y) = Z 1 y dx fq(x) fq(y=x) + fq(y=x) fq(x) ; x { 6 { ⊗ ⊗ (3.4) (3.5) ¯ q ℓ γ, Z Φ 1 ℓ − ℓ + 2.1 2.5 3.0 3.6 muon a . with fq;q(x) being the quark and antiquark parton distribution function (PDF). We use MRST [65] to calculate the PDFs. The loop-induced couplings to quarks g qV and gA q are evaluated with package runDM [66]. The renormalization scale of the PDF and the couplings to quarks is set at m 1 DM relic density, the DAMPE e+ + e . We choose some benchmark points that satisfy the ux excess and the PandaX limits and calculate the corresponding cross section of the dilepton process pp ! 1 ! `+` at the 13 TeV LHC, as given in table 2. We note that they are much lower than the current LHC-13 TeV sensitivity [67]. We also evaluate the associated production processes pp ! `+` 0;1 and nd they are negligibly small. In table 3, we give the corrections to the muon g 2 that arise from our leptophilic interactions [68]. It can be seen that the couplings V V and P S can produce a positive correction, which, however, is less than the value required by explaining the deviation of the muon g 2 from its experimental measurement. 4 An an example of realizations of LDM, we introduce a Dirac fermionic DM eld ( ) by imposing a Z2 symmetry, under which all SM matter particles are even while is odd. { 7 { U(1)X U(1)0 0 0 URa 0 0 DRa 0 0 QSX 0 0 Q0 T QFX Q0F 0 Q0 respectively. The Dirac fermion F that has charges of U(1), is introduced to generate kinetic mixing between the two U(1) gauge bosons. Besides, we add a new U(1)X gauge interactions for leptons only, with the corresponding possible way is to introduce new matter particles to cancel the anomaly. For example, we can add the fourth chiral-like family with non-trivial U(1)X quantum number, which satis es the anomaly cancelation condition X(3ni + mi) + 3k + l = 0; i with ni; mi; k; l being the U(1)X quantum numbers for quarks(ni), leptons(mi) of the rst three family and the fourth family quarks(k) and leptons (l), respectively, such as l = 3m with universal mi m for e; ; leptons and trivial quantum numbers for all quarks. The fourth family can be very heavy by mixing with heavy vector-like fermions and can be compatible with current collider constraints. Since the DM direct detection experiments will give stringent constraints, we require that the Dirac fermion DM will not carry U(1)X quantum number but will transform non-trivially under an additional U(1)0 gauge symmetry. Such U(1)0 gauge symmetry will be broken by additional complex scalar eld T . The couplings between DM and lepton pairs will be induced through kinetic mixing between U(1)X and U(1)0. Given the gauge interaction U(1)X is universal for all kinds of leptons, we can anticipate that the decay products will lead to equal nal states lepton species. This approach is similar to vectorportal DM scenario. Since the DM is vector-like, there will be no additional anomaly in the model. New scalar T or vector-like fermion F , which transform non-trivially under both U(1)X and U(1)0, will induce non-trivial mixing between the two new U(1) gauge symmetry through the following interactions, L jD Sj2 + jD T j2 3jSj2jT j2 + iF m2SjSj2 D F m2T jT j2 mF F F ; 1jSj4 2jT j4 with iQFX gX AX iQSX gX AX )S ; iQ0T g0A0 )T: iQ0F g0A0 )F ; { 8 { (4.1) (4.2) (4.3) As mentioned above, an odd Z2 parity is imposed for the Dirac fermion to act as a viable DM candidate. The masses of the scalar T are assumed to be heavier than the DM mass so that the DM will not annihilate into them. We should note that in the scalar potential, possible terms involving standard model Higgs elds H as (T yT )(HyH); (SyS)(HyH) etc could appear. Such terms could contribute to the DM direct detection at two loop level. The kinetic mixing between two gauge bosons can be parameterized as L 1 4 F F F 0 F 0 m12A A after integrating out heavy fermion loops, or after integrating out possible heavy scalar loops. The matrix to remove the mixing is given as 1 4 = 2 F 0 F gX g0 12 2 QFX Q0F log = 4g81g22 QF Q0F log 1 2 m2F 2 m2S 2 ; ; A ~ ! A~0 = with the Lagrangian involving the mass mixing L = 4 1 ~ F F ~ 4 Assuming identical masses for the scalars m21 = m22, we obtain ( ) L L =m22 : (4.4) (4.5) (4.6) (4.7) (4.8) (4.9) HJEP02(18)7 we can choose m2 ' 3 TeV and the mixing parameter obtained by requiring g1 = g2 0:3 with Q1 = Q2 = 1. 5 Conclusion To explain the DAMPE excess without con icting with direct detection experiments, 1:0 10 2. Such values can be In this work, we explained the recent DAMPE cosmic e++e excess in simpli ed leptophilic Dirac fermion dark matter (LDM) framework with a scalar ( 0) or vector ( 1) mediator. We found that the couplings P S, P P , V A and V V can t the DAMPE data under the constraints from gamma-rays and cosmic-rays. However, for the V V coupling, due to the stringent constraints from the PandaX-II data, the surviving samples only exist in the resonance region, m 1 ' 2m . But for other couplings, the direct detection bounds can easily be evaded. We also studied the possible collider signatures of LDM, such as the Drell-Yan process pp ! 1 ! `+` , and the muon g U(1) extension of the SM to realize our simpli ed LDM model. 2. In the end, we constructed an { 9 { Acknowledgments G. Duan was supported by a visitor program of Nanjing Normal University, during which this work was nished. This work was supported by the National Natural Science Foundation of China (NNSFC) under grant No. 11705093, 11675242 and 11773075, by the CAS Center for Excellence in Particle Physics (CCEPP), by the CAS Key Research Program of Frontier Sciences and by a Key R&D Program of Ministry of Science and Technology of China under number 2017YFA0402200-04. 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Guang Hua Duan, Lei Feng, Fei Wang, Lei Wu, Jin Min Yang, Rui Zheng. Simplified TeV leptophilic dark matter in light of DAMPE data, Journal of High Energy Physics, 2018, 107, DOI: 10.1007/JHEP02(2018)107