Connecting multi-lepton anomalies at the LHC and in Astrophysics and the prospects of MeerKAT/SKA
Geoff Beck, Mukesh Kumar, Elias Malwa, Bruce Mellado, Ralekete Temo
CConnecting multi-lepton anomalies at the LHC and in Astrophysics and the prospectsof MeerKAT/SKA
Geoff Beck ∗ and Ralekete Temo † School of Physics and Centre for Astrophysics, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa.
Mukesh Kumar, ‡ Elias Malwa, § and Bruce Mellado ¶ School of Physics and Institute for Collider Particle Physics,University of the Witwatersrand, Johannesburg, Wits 2050, South Africa.
Multi-lepton anomalies at the Large Hadron Collider are reasonably well described by a two Higgsdoublet model with an additional singlet scalar. Here, we demonstrate that using this model weare also able to describe the excesses in gamma-ray flux from the galactic centre and the cosmic-rayspectra from AMS-02. This is achieved through Dark Matter (DM) annihilation via the singletscalar. Of great interest is the flux of synchrotron emissions which results from annihilation of DMin Milky-Way satellites. We make predictions for MeerKAT observations of the nearby dwarf galaxyReticulum II and we demonstrate the power of this instrument as a new frontier in indirect darkmatter searches.
INTRODUCTION
The discovery of a Higgs boson ( h ) [1–4] at the LargeHadron Collider (LHC) by the ATLAS [5] and CMS [6]experiments has opened a new chapter in particle physics.Measurements provided so far indicate that the quantumnumbers of this boson are consistent with those predictedby the Standard Model (SM) [7, 8], and that the relativebranching ratios (BRs) to SM particles are similarly welldescribed. With this in mind, a window of opportunitynow opens for the search for new bosons.One of the implications of a two-Higgs doublet modelwith an additional singlet scalar S (2HDM+ S ), is theproduction of multiple-leptons through the decay chain H → Sh, SS [9], where H is the heavy CP-even scalarand h is considered as the SM Higgs boson with mass m h = 125 GeV. Excesses in multi-lepton final states werereported in Ref. [10]. In order to further explore resultswith more data and new final states, while avoiding bi-ases and look-else-where effects, the parameters of themodel were fixed in 2017 according to Refs. [9, 10]. Thisincludes setting the scalar masses as m H = 270 GeV, m S = 150 GeV, treating S as a SM Higgs-like scalar andassuming the dominance of the decays H → Sh, SS . Sta-tistically compelling excesses in opposite sign di-leptons,same-sign di-leptons, and three leptons, with and withoutthe presence of b -tagged hadronic jets were reported inRefs. [11–13]. The possible connection with the anoma-lous magnetic moment of the muon g − ∗ geoff[email protected] † ‡ [email protected] § [email protected] ¶ [email protected] energy density in the universe while DM makes up morethan 24% [15]. The evidence behind this massive andlargely non-interacting matter is still indirect and onlystems from DM gravitational interactions [16–19].In this study we aim to use astrophysics as an indirectprobe of the 2HDM+ S model motivated by LHC anoma-lies. This is done via a DM particle coupling to S as amediator to the SM, where the parameters of the collidermodel are fixed to describe the LHC data. We make par-ticular use of the observed positron excess by the AlphaMagnetic Spectrometer (AMS-02) [20] and the excess ingamma-ray fluxes from the galactic centre measured byFermi-LAT [21]. This is motivated by the fact that theLHC anomalies triggering the 2HDM+ S model are alsoleptonic in nature. We ensure that measured spectra ofthe AMS-02 anti-proton results [22] and other constraintsare not exceeded. These particular astrophysical datasets are of interest as they have been extensively studiedas potential signatures of DM [23–31]. This DM modelis then used to make predictions for radio observationswith the MeerKAT precursor to the Square KilometreArray (SKA). These emissions would result from syn-chrotron radiation from electrons and positrons producedin DM annihilations. As such, we compute the numberof e + and p − as a result of DM annihilations using themodel described here from the collider physics perspec-tive, and with the input from the astrophysics, we extendthis by ensuring consistency with astrophysical observa-tions. With a constrained DM model our predictions canthen be tested independently via observations with theMeerKAT telescope. In this regard, the complementaritybetween collider and astroparticle physics is investigatedin the considered model. MEERKAT
Indirect detection of DM was traditionally mainly doneusing gamma-ray experiments, such as the Fermi-LAT a r X i v : . [ a s t r o - ph . H E ] F e b [32], because this mode of detection has low attenuationin the interstellar medium and has high detection effi-ciency. Recently, the indirect hunt for DM in radio-bandhas become prominent. This emerges from the fact thatradio interferometers have an angular resolution tran-scending that of gamma-ray experiments.The SKA is an international science project designedfor studies in the field of radio astronomy. This tele-scope array provide around 50 times the sensitivity and10,000 times the survey speed of the best current tele-scopes [33]. These capabilities have already been exten-sively argued to provide a powerful tool for exploring theproperties of DM via indirect detection of annihilationor decay products [30, 31, 34]. At present the precur-sor array MeerKAT is currently being operated by theSouth African Radio Astronomy Observatory (SARAO)with 64 antennae elements. Each of the elements is a13.5 m diameter dish, configured to achieve high sensi-tivity and wide imaging of the sky [35]. With 20 hours oftime on target it is estimated that MeerKAT can achievea point-source sensitivity of 2 . µ Jy beam − at robustweighting 0. This results in an rms sensitivity of ∼ µ Jy when taking into account the synthesized beam sizeof ≈
11 arcseconds.The sensitivity of MeerKAT is therefore around a fac-tor of 2 better than ATCA [36] which has previouslybeen used for indirect DM searches in dwarf galaxies [37].This notable sensitivity advantage is a consequence ofthe instrument exceeding its original design specifications(see [38] and [33]), making it an unexpected new leader inradio-frequency DM searches. Additionally, MeerKAT isexpected to receive an upgrade of an additional 20 dishes,taking it to 84, with construction expected to be completein 2023 [39].
THE MODEL
Here, we succinctly describe the model used to describethe multi-lepton anomalies observed in the LHC data andwith which to interpret the above mentioned excesses inastrophysics. The formalism is comprised of a modelof fundamental interactions interfaced with a model ofcosmic-ray fluxes that emerge from DM annihilation.The potential for a two Higgs-doublet model with anadditional real singlet field Φ S (2HDM+ S ) is given as inRef. [9]: V (Φ , Φ , Φ S )= m | Φ | + m | Φ | − m (cid:16) Φ † Φ + h . c . (cid:17) + λ (cid:16) Φ † Φ (cid:17) + λ (cid:16) Φ † Φ (cid:17) + λ (cid:16) Φ † Φ (cid:17) (cid:16) Φ † Φ (cid:17) + λ (cid:16) Φ † Φ (cid:17) (cid:16) Φ † Φ (cid:17) + λ (cid:20)(cid:16) Φ † Φ (cid:17) + h . c . (cid:21) + 12 m S Φ S + λ S + λ (cid:16) Φ † Φ (cid:17) Φ S + λ (cid:16) Φ † Φ (cid:17) Φ S . (1) The fields Φ , Φ in the potential are the SU (2) L Higgsdoublets. The first three lines in Eq. 1 are the contri-butions of the real 2HDM potential. The terms of thelast line are contributions of the singlet field Φ S . To pre-vent the tree-level flavour changing neutral currents weconsider a Z symmetry which can be softly broken bythe term m (cid:54) = 0. After the minimisation of the po-tential and electro-weak symmetry breaking, the scalarsector is populated with three CP even scalars h, H and S , one CP odd scalar A and charged scalar H ± . Formore details of this model and associated interactions’Lagrangians and parameter space we refer to Refs. [9, 40].Further, we consider interactions of S with three typesof DM candidates χ r , χ d and χ v with spins 0, 1/2 and 1,respectively: L int = 12 M χ r g Sχ r χ r χ r S + ¯ χ d ( g Sχ d + ig Pχ d γ ) χ d S + g Sχ v χ µv χ vµ S, (2)where g χ i and M χ i are the coupling strengths of DMswith the singlet real scalar S and masses of DM, respec-tively. Having these interactions in mind, we considerDM annihilation through S following 2 → → D ( E ) ∇ d n e + d E + ∂∂E [ b ( E ) d n e + d E ] + Q e + ( E, (cid:126)x ) = 0 , (3)where D is the diffusion function, b is the energy-lossfunction, Q e + is the source function for positrons, and d n e + d E = d n e + d E ( E, (cid:126)x ) is the equilibrium number densityper unit energy of positrons. The source function forpositrons Q e + is then given by: Q e + = 12 (cid:18) ρ (cid:12) M χ (cid:19) (cid:104) σV (cid:105) d n e + ,i d E , (4)where d n e + ,i d E is the injected number density of positronsper unit energy, ρ (cid:12) is the DM density in the solar neigh-bourhood, and (cid:104) σV (cid:105) is the velocity averaged annihilationcross-section for DM particles.The function D ( E ) depends upon assumptions aboutthe Milky-Way diffusion environment [42] and we exploreall three value sets MIN,MED, and MAX presented in[41]. The solution d n e + d E can then be leveraged to obtainthe flux at given position via:dΦ e + d E = c (cid:104) σV (cid:105) πb ( E ) (cid:18) ρ (cid:12) M χ (cid:19) × (cid:90) M χ E dE s d n e + ,i d E s I (cid:12) ( E, E s ) , (5)where E s is the energy of injected positrons, and I (cid:12) ( E, E s ) is a Green’s function solving Eq. (3) at thelocation of Earth, this being given by Ref. [41]. Simi-larly, the anti-proton flux can be determined, accordingto [41], as being given by:dΦ ¯ p d K = v ¯ p π (cid:104) σV (cid:105) (cid:18) ρ (cid:12) M χ (cid:19) R ( K ) (cid:104) σV (cid:105) d n ¯ p,i d K , (6)where K is anti-proton kinetic energy, v ¯ p is the anti-proton speed, R ( K ) are the propagation functions from[41], and d n ¯ p,i d K is the injected anti-proton spectrum.Primary photon fluxes within radius r of a halo centre,at frequency ν are found via: S γ ( ν, r ) = (cid:90) r d r (cid:48) Q γ ( ν, r (cid:48) )4 π ( d L + ( r (cid:48) ) ) , (7)where Q γ is the photon source function of similar formto Eq. (4), and where d L is the luminosity distance tothe halo centre.Secondary photon fluxes (from electrons produced byDM annihilation) are found using the equations: j i ( ν, r ) = (cid:90) M χ dE d n e ± d E ( E, r ) P i ( ν, E, r ) , (8)where d n e ± d E is the sum of the electron and positron dis-tributions within the source region and P i is the poweremitted at frequency ν through mechanism i by an elec-tron with energy E , at position r . The flux producedwithin a radius r is then found via: S i ( ν, r ) = (cid:90) r d r (cid:48) j i ( ν, r (cid:48) )4 π ( d L + ( r (cid:48) ) ) . (9)For synchrotron emission we then have [43, 44]: P synch ( ν, E, r ) = (cid:90) π dθ sin θ π √ r e m e cν g × F synch (cid:16) κ sin θ (cid:17) , (10)where ν g is the non-relativistic gyro-frequency, r e is theelectron radius, m e is the electron mass, and θ is theangle between the magnetic field and electron trajectory.The value of κ is found via: κ = 2 ν ν g γ (cid:20) (cid:16) γν p ν (cid:17) (cid:21) , (11)with γ = Em e c . Finally, F synch ( x ) (cid:39) . x e − x (cid:0)
648 + x (cid:1) . (12)The power produced by the inverse-Compton scatter-ing (ICS) at a photon of frequency ν from an electronwith energy E is given by [43, 44]: P IC ( ν, E ) = cE γ ( z ) (cid:90) d(cid:15) n ( (cid:15) ) σ ( E, (cid:15), E γ ) , (13) where (cid:15) is the energy of the seed photons distributedaccording to n ( (cid:15) ) (this will taken to be that of the CMB),and σ ( E, (cid:15), E γ ) = 3 σ T (cid:15)γ G ( q, Γ e ) , (14)with σ T being the Thompson cross-section and G ( q, Γ e ) = 2 q ln q +(1+2 q )(1 − q )+ (Γ e q ) (1 − q )2(1 + Γ e q ) , (15)with q = E γ Γ e ( γm e c + E γ ) , Γ e = 4 (cid:15)γm e c , (16)where m e is the electron mass.Finally, the power from bremsstrahlung at photon en-ergy E γ from an electron at energy E is given by [43, 44]: P B ( E γ , E, r ) = cE γ (cid:88) j n j ( r ) σ B ( E γ , E ) , (17)where n j is the distribution of target nuclei of species j and the cross-section is given by: σ B ( E γ , E )= 3 ασ T πE γ (cid:34)(cid:32) (cid:18) − E γ E (cid:19) (cid:33) φ − (cid:18) − E γ E (cid:19) φ (cid:35) , (18)with φ and φ being energy dependent factors deter-mined by the species j (see Ref. [43, 44]). METHODOLOGY
We use a Monte Carlo (MC) generator to simulate theproduction of particles as a result of the annihilation ofDM through S according to the model described in Sec-tion . We make use of MG5 @MC [45] as our primary tool togenerate events of the 2 → → Pythia 8 [46] withthe purpose of hadronizing partons. The resulting de-cays are stored as
HepMC format for further processing.We varied the DM mass between 200 to 1000 GeV forthe 2 → → M χ and (cid:104) σV (cid:105) ) using -5 -4 -3 -2 -1
200 400 600 800 1000 d N / d E ( G e V - ) e + energy (GeV)
75 GeV200 GeV400 GeV600 GeV800 GeV1000 GeV -5 -4 -3 -2 -1
100 200 300 400 500 600 d N / d E ( G e V - ) p - energy (GeV)
75 GeV200 GeV400 GeV600 GeV800 GeV1000 GeV
FIG. 1. Differential yields of positions and anti-protons thefor the 2 → cosmic-ray and gamma-ray data. After this step we makepredictions for MeerKAT observations based upon theconstrained DM parameter space. The predicted spectrafor cosmic-ray fluxes at Earth are compared to data fromAMS-02 [20, 22]. In the case of the anti-protons we usethe background model found in [47], while for positronswe use a nearby pulsar model for the high-energy back-ground [48]. When we model gamma-ray fluxes from thegalactic centre we use data from [21], making use of theexcess spectrum for a 10 ◦ region of interest around thegalactic centre. In all cases our Milky-Way halo modelsfollow those presented in [41].We note that both AMS-02 anomalies have been widelystudied, either as constraints on DM models or as poten-tial signatures thereof [23–29]. The anti-proton case hasbeen argued to be highly significant and most in agree-ment with the annihilation via b -quarks of a 40 −
70 GeVWIMP with some potential for heavier masses [23]. How-ever, an accounting for possibility of correlated errors [47]reveals no preference for a DM contribution from WIMPSbetween 10 and 1000 GeV in mass. It is also difficult to reconcile such models with existing radio data [30]. In thecase of positrons there is a stark unexplained excess ofpositrons at around a few hundred GeV that can poten-tially be described in terms of DM models and has greatpotential to be used as a probe of DM physics even withastrophysical backgrounds [49]. Additionally, we notethat the significance of the widely studied Fermi-LATgalactic centre gamma-ray excess is highly uncertain dueto systematics [21].
RESULTS
In Fig. 2 we display the best-fit parameter spacefor 2 → S model that describes LHC and astro-physics data are notexcluded by direct DM searches. In particular, for aType-II 2HDM+ S limits become weak when the ratio ofthe vacuum expectation values of the complex doublets,tan β < (cid:104) σV (cid:105) = 2 . × − cm s − and include uncertaintieson the J-factor and magnetic field of the dwarf galaxy.We make use of a cored density profile following argu-ments from [53, 54]. This being an Einasto profile [55](which can be cored for certain parameter choices), given FIG. 2. The parameter space fitting the 2 → σ confidence interval. The region between the thermal relic linesrepresents the uncertainties in local DM density and galactichalo profile. This plot assumes the MED diffusion scenarioand an Einasto profile for the Milky-Way halo from [41]. by: ρ e ( r ) = ρ s exp (cid:20) − α (cid:18)(cid:20) rr s (cid:21) α − (cid:19)(cid:21) , (19)where we follow [37] in having α = 0 . r s = 0 . ρ s = 7 × M (cid:12) kpc − .We then follow [37] in using the profiles for gas densityand magnetic field strength: n e ( r ) = n exp (cid:18) − rr d (cid:19) , (20)and B ( r ) = B exp (cid:18) − rr d (cid:19) . (21)We take r d to be given by the stellar-half-light radiuswith a value of 35 pc [56, 57] and we assume B ≈ µ G, n ≈ − cm − .Results are displayed for 75 and 200 GeV mass modelsfor the 2 → µ G, and the J-factor of Reticulum II.Figure 3 shows that Reticulum II with the Einasto pro-file produces radio fluxes close to the detectable level, butthe gamma-ray region of the spectrum is not stronglyimpacted by Fermi-LAT limits. For the 2 σ confidenceinterval the relic cross-section can be excluded for themass below 75 GeV, and the upper edge of the 200 GeVmass uncertainty region can be explored. A 5 σ confi-dence level detection is almost possible at lower end of themass range. What is very notable is that the MeerKAT ν (MHz)10 − − − − − − − ν S ( ν )( e r g c m − s − ) M χ = 75 GeVM χ = 200 GeVSKA 100 hrs 5 σ Fermi-LATMeerKAT 100 hrs 2 σ MeerKAT 100 hrs 5 σ ν (MHz)10 − − − − − − − ν S ( ν )( e r g c m − s − ) M χ = 200 GeVM χ = 400 GeVSKA 100 hrs 5 σ Fermi-LATMeerKAT 100 hrs 2 σ MeerKAT 100 hrs 5 σ FIG. 3. Multi-frequency spectrum prediction for Reticulum IIwith the Einasto profile. The shaded regions encompass thecross-section uncertainties from Figs. 2 as well as those fromthe J-factor of the halo. The Fermi-LAT limits are drawnfrom [52]. Top: 2 → → sensitivity estimates have highly competitive constrain-ing power when compared to the Fermi-LAT data. The2 → →
2. Notably, the gamma-ray limits from Fermi-LAT are substantially less effective in probing the 2 → → → σ confidence interval within 100 hours ofobserving time.Above it was stated that a 20 hour observation achievesan rms sensitivity of 66 µ Jy, not achieving the levels re-quired for detection in Fig. 3. For any detection prospectsaround the relic cross-section at least 200 hours of ob-servation time would be necessary. Notably this when B = 1 µ G and m χ = 75 GeV. It must be mentionedthat larger masses would require substantially more ob-serving time with MeerKAT. Despite this, the two-foldsensitivity advantage over previous observations of Retic-ulum II suggest that even 20 hours on target would yieldcutting edge model-independent constraints on channelslike b quarks. For the 2HDM+ S model, when B = 1 µ G, 20 hours would translate to a 95% confidence inter-val limit of (cid:104) σV (cid:105) (cid:46) . × − cm s − with the Einastohalo and M χ = 75 GeV. The limit for 200 GeV WIMPsis around an order of magnitude larger.The fact that detection would require at least 300hours of MeerKAT observation time suggests that thisis improbable when B = 1 µ G. However, an increasein sensitivity to 0 . µ Jy beam − at 20 hours would dropthe required time to at least 7 hours. Thus, obtainingsub-micro-Jansky sensitivities starts to bring about thepractical possibility of detection. This, however, wouldrequire the full SKA [33]. It should noted that sufficientsensitivity for 2 σ exclusion of 2HDM+ S model at therelic level, with the lowest studied DM mass, can be ob-tained with at least 30 hours on MeerKAT or 2 hours onthe sub-micro-Jansky case. The time required to probea 200 GeV WIMP is a hundred times longer than the75 GeV case. This is largely due to MeerKAT’s limitedfrequency coverage, which will be ameliorated in the fullSKA. One caveat of these sensitivity estimates is thatthey are strictly applicable to point sources and a nearbydwarf galaxy like Reticulum II is likely to be extendedon the order of arcminutes. CONCLUSIONS
In this letter we use a 2HDM+ S model that is moti-vated by multi-lepton anomalies at the LHC to describethe excesses in gamma-ray flux from the galactic cen-tre and the cosmic-ray spectra from AMS-02. This isachieved through DM annihilation via the singlet scalarinto particles of the SM. The parameters of the model arefixed to the LHC data, except for the mass of the DM andthe size of the coupling to the mediator S . The mass ofthe DM is scanned, where the coupling of the DM to themediator S is varied, and various diffusion scenarios areconsidered. A satisfactory description of the gamma-rayflux from the galactic centre and the cosmic-ray spectrafrom AMS-02 is obtained with the MED diffusion sce-nario. The best description of the excesses is obtainedfor DM masses below 200 GeV. Although complete over-lap between all the best-fit regions is not achieved, it is notable that there are unresolved systematics in much ofthe data. Nonetheless, it is still remarkable that suchclose agreement can be obtained for a model whose par-ticle physics is set by LHC anomalies.Predictions of the synchrotron spectrum are made withthe model in order to assess the detection sensitivity ofMeerKAT. For the 2 σ confidence interval the relic cross-section can be excluded for the mass below 75 GeV, andthe upper edge of the 200 GeV mass uncertainty regioncan be explored. A 5 σ confidence level detection is al-most possible at lower end of the mass range. It is worthhighlighting that the MeerKAT sensitivity estimates havehighly competitive constraining power, even somewhatexceeding that of Fermi-LAT data. In addition to this,the full SKA will likely be capable of achieving a 5 σ probeof the thermal relic cross-section for 2HDM+ S models,with WIMP masses below a few hundred GeV, with lessthan 100 hours of integration time. However, at presentMeerKAT will be the frontier in radio instruments forDM searches, especially since it has begun observing callsalready and will be upgraded in the near future with 30%more dishes.The results documented in this letter have implicationson searches for DM at the LHC. Being a SM singlet, S is predominantly produced via the decay of the heavyscalar. Through the decay H → SS the production ofDM from the decay of S can recoil against SM parti-cles that S can also decay into [9]. Of particular interestwould be the resonant search for S → ZZ, Zγ, γγ in asso-ciation with moderate missing transverse energy carriedby the DM.
ACKNOWLEDGMENTS
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