Light dark matter
Maxim Pospelov Perimeter Institute, Waterloo/University of Victoria, Victoria CERN-Korea Theory Institute, 2016
1 Light dark matter
§ What does ”light DM” mean ? Gravity does not care whether these are 10-30, 1 or 1030 kg objects as long as they have same velocity distribution.
§ What does ”light DM” mean ? Gravity does not care whether these are 10-30, 1 or 1030 kg objects as long as they have same velocity distribution. § Working definition: light dark matter is some form of particle dark matter with mass lighter than the range where most search efforts and $ are currently being spent.
3 Big Questions in Physics
“Missing mass” – what is it? New particle, new force, …? Both? How to find out? Challenges ?? Too many options for DM. In “direct detection” or collider experiments there is an extrapolations from ~ kpc scale (~ 1021 cm) down to 102 cm scale. Outline of the talk
1. Introduction. Types of dark matter. Weakly interacting massive particles (WIMPs). 2. Light dark matter and light mediators. Examples of models that pass current experimental constraints. 3. Searches at short baseline neutrino experiments and missing energy searches. Searches of mediators. 4. Ways to improve sensitivity: SHiP, electron beam experiments, underground experiments. 5. Direct detection of light dark matter using the electron recoil – bridge to detecting super-weakly interacting DM. 6. Conclusions.
5 DM classification
At some early cosmological epoch of hot Universe, with temperature T >> DM mass, the abundance of these particles relative to a species of SM (e.g. photons) was
Normal: Sizable interaction rates ensure thermal equilibrium, NDM/Ng =1. Stability of particles on the scale tUniverse is required. Freeze-out calculation gives the required annihilation cross section for DM --> SM of order ~ 1 pbn, which points towards weak scale. These are WIMPs. Asymmetric DM is also in this category.
Very small: Very tiny interaction rates (e.g. 10-10 couplings from WIMPs). Never in thermal equilibrium. Populated by thermal leakage of SM fields with sub-Hubble rate (freeze-in) or by decays of parent WIMPs. [Gravitinos, sterile neutrinos, and other “feeble” creatures – call them superweakly interacting MPs]
Huge: Almost non-interacting light, m< eV, particles with huge occupation numbers 10 of lowest momentum states, e.g. NDM/Ng ~10 . “Super-cool DM”. Must be bosonic. Axions, or other very light scalar fields – call them super-cold DM. Weakly interacting massive particles In case of electrons and positrons (when the particle asymmetry = 0), the -17 end point is ne/ngamma ~ 10 . It is easy to see that this is a 2 2 consequence of a large annihilation cross section (~ a /me ). We need a particle “X” with smaller annihilation cross section, X + X à SM states.
Honest solution of Boltzmann equation gives a remarkably simple
result. WX = WDM, observed if the annihilation rate is
10-36 cm2 = a2/L2 à L = 140 GeV. L ~ weak scale (!) First
implementations by (Lee, Weinberg; Dolgov, Zeldovich,….) 7 WIMP paradigm, some highlights
DM-SM mediators nucleus nucleus - DM states SM states Cosmological (also galactic) annihilation WIMP scattering Collider WIMP pair-production
1. What is inside this green box? I.e. what forces mediate WIMP-SM interaction? 2. Do sizable annihilation cross section always imply sizable scattering rate and collider DM production? (What is the mass range?) Examples of DM-SM mediation DM particles themselves + may be extra extra be may + themselves DM particles Very economical extensions of the SM. of the extensions economical Very predictive. very be Can force. mediator
9 Theoretical predictions for sDM-N • Unlike annihilation of WIMP DM (whose inferred cross section is
quite model independent), the scattering cross section sDM-N does depend on the model.
• Take an “original” WIMP model with a ~ 10 GeV Dirac fermion annihilating into SM particles via an intermediate Z-boson.
2 2 -39 -38 2 sDM-Nucleon (Z-mediated) ~ (1/8p) mp (GF) ~ (10 -10 ) cm range. -4 -5 sDM-Nucleon (Higgs-mediated) ~ (10 -10 ) × sDM-Nucleon (Z-mediated) -9 sDM-Nucleon (EW loop) ~ 10 × sDM-Nucleon (Z-mediated)
Looks tiny, but how does it compare with the today’s limits? Progress in direct detection of WIMPs (latest 2016 LUX and CRESST results) 7
A Due to the anticipated A2-dependence of the cross sec- tion, dark matter particles are supposed to dominantly scat- ter off the heavy tungsten. The energy transferred in the scat- tering process is a function of the reduced mass of target nucleus and dark matter particle. Thus, for a given mass of the dark matter particle the fraction of the expected energy spectrum above threshold depends on the mass of the target nucleus. As a result, for dark matter particles with masses above 5 GeV/c2 recoils off tungsten are expected to be far more nu- merous compared to oxygen and calcium. For lighter masses a substantial part of the tungsten recoils have energies be- low threshold leading to a strong decrease of the number of counts. This results in a mass range completely dominated by scatterings off oxygen, because the drop for oxygen and Fig. 8 Parameter space for elastic spin-independent dark matter- calcium is shifted towards lower masses (see figure 7). nucleon scattering. The result from this blind analysis is drawn in solid In the limit of very low masses, the reduced mass con- red together with the expected sensitivity (1 confidence level (C.L.)) Spin-independent Z-boson mediated scatteringfrom the data-driven of background-only a Dirac modelWIMP (light red is band). The re- verges to the mass of the dark matter particles, causing less maining red lines correspond to previous CRESST-II limits [6,18]. The excludedpronounced differencesfrom ~ in 1 the GeV shape ofto the recoil100 spectra TeV on– i.e.favored over parameter the space entire reported by CRESST-IIWIMP phase mass 1 [8], CDMS- the different target nuclei. This effect is further augmented Si [19] and CoGeNT [20] are drawn as shaded regions. For com- range.by the influenceEW scale of the baseline Higgs noise. mediated Since the A2-scaling modelsparison, are exclusion heavily limits (90 constrained % C.L.) of the liquid noble (but gas experi- ments [21–23] are depicted in blue, from germanium and silicon based of the cross sections still persists, scatterings off tungsten there are exceptions). Next generation nobleexperiments- inliquid green and- blackbased [24–28]. experiments In the gray area coherent neu- account for a slightly larger proportion of the total expected trino nucleus scattering, dominantly from solar neutrinos, will be an willsignal begin again. probing EW loop level crossirreducible sections. background for a CaWO4-based dark matter search experi- ment [29]. 11
9 Result, Discussion and Outlook curve. Due to the lower threshold Lise starts to be domi- nated by scatterings off tungsten already at 3 GeV/c2 (see For each dark matter particle mass we use the Yellin op- figure 7) compared to 4.5 GeV/c2 for the 2014 result [6]. timum interval method [16, 17] to calculate an upper limit Due to the rather large number of leakage events into the with 90 % confidence level on the elastic spin-independent acceptance region the result is already not limited by expo- interaction cross-section of dark matter particles with nucle- sure any more. Consequently, only small statistical fluctua- ons. While this one-dimensional method does not rely on tions are expected. This is confirmed by calculating limits any assumption on the background, it exploits differences for 10,000 Monte Carlo sets sampled from the data-driven between the measured (see figure 6) and the expected en- background model discussed in section 4. The resulting 1 ergy spectrum (see section 8). contour is shaded in light red in figure 8. The resulting exclusion limit of this blind analysis is In CRESST-III we will substantially size down the ab- drawn in solid red in figure 8. For higher masses this module sorber crystals in order to achieve lower energy thresholds. does not have a competitive sensitivity, due to the large num- Furthermore, we expect two beneficial effects on the light ber of background events. In particular, the leakage from the signals: Firstly more light reaches the light detector and sec- 55Fe-source (see figure 6) results in an almost flat limit for ondly the light detector can also be scaled down which leads masses of 5–30 GeV/c2. However, for dark matter particles to an enhanced energy resolution. Both improvements will lighter than 1.7 GeV/c2 we explore new regions of parameter increase the background discrimination power. All modules space. will feature an upgraded holding scheme and will mainly The improvement compared to the 2014 result [6] (red be equipped with absorber crystals produced in-house due dashed line) is a consequence of the almost constant back- to their significantly lower level of intrinsic radioactive con- ground level down to the threshold which was reduced from taminations. Combining these measures with the enhanced 603 eV to 307 eV. The lower the mass of the dark matter par- discrimination power, a drastically reduced background leak- ticle the more relevant these improvements become. With age is expected. this analysis we explore masses down to 0.5 GeV/c2, a nov- In this letter we prove that a low energy threshold is elty in the field of direct dark matter searches. the key requirement to achieve sensitivity to dark matter The transition point of the dominant scattering target nu- particles of O(1 GeV/c2) and below. We expect significant cleus manifests itself as kink in the corresponding exclusion progress exploring the low mass regime with the upcoming Light DMDirect – Detectiondifficult to detect via nuclear recoil
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! =? 10!46 <> 012'' Most money spent Cross !47 <=><< 10 > < . K 10!3 10!2 10!1 <> 1 <> <> <> !"#$%#&''%()*+,-./ 3 • Nuclear recoil too weak - vDM 10 ⇠ • There is •a large,Can we potentially find a relativistic interesting source of Darkpart Matter?of WIMP DM parameter space that escapes constraints from DM-nuclear scattering, but is 6 potentially within reach of other probes • Viable models imply the dark sector, or accompanying particles facilitating the DM à SM annihilation. Can create additional 12 signatures worth exploring. The minimal dark photon model, with no light particles charged under U(1)⇥ is excluded •The minimal dark photon model, with no light particles charged under U(1)⇥ is excluded • (or close to be excluded) by experiments. The most di⌅cult part of the parameter (orspace, close the to vicinity be excluded) of m 30 by MeV, experiments. has been finally The ruled most out di⌅ ascult a solution part of to the the parameter A ⇤ space,g 2puzzleonlyrecently[18,20]. the vicinity of mA 30 MeV, has been finally ruled out as a solution to the g 2puzzleonlyrecently[18,20].⇤ A slightly extended model of dark photon, can still o⇥er a solution to the g 2dis- • + crepancy. A⇥ ⇥⇥¯ decay, for example, can dilute ”visible” A⇥ e e modes. In any A slightly extended⌃ model of dark photon, can still o⇥⌃er a solution to the g 2dis- • case, it appears that mA < 200 MeV is required [48]. + crepancy. A⇥ ⇥⇥¯ decay, for example, can dilute ”visible” A⇥ e e modes. In any ⌃ ⌃ case,Finally, it theappears least constrained that mA model< 200 is MeV based is on required gauged Lµ [48].L⇥ vector portal [27,28,30], • and the vector mass below m 400 MeV can still be considered as a potential solution V ⇤ Finally,to the muon the leastg 2discrepancy[49,50]. constrained model is based on gauged Lµ L⇥ vector portal [27,28,30], • and the vector mass below m 400 MeV can still be considered as a potential solution V ⇤ Toto summarize, the muon theg light2discrepancy[49,50]. vector particle remains an attractive solution to the muon g 2 discrepancy, and more experimental work is required to exclude this possibility in as much amodel-independentwayaspossible. To summarize, the light vector particle remains an attractive solution to the muon g 2 discrepancy, and more experimental work is required to exclude this possibility in as much amodel-independentwayaspossible.3.3 Mediator of interaction with DM (both heavy and light)
Vector portals may have an interesting relation to dark matter. In the last few years, the 3.3direct Mediator searches for dark of interaction matter have intensified, with DM paralleled (both by heavy the broad and investation light) of the- oretical opprtunities for dark matter. Weakly interacting dark matter (WIMP) paradigm o⇥ers perhaps the largest number of opportunities for the experimental discovery of dark Vectormatter portals via its non-gravitational may have an interesting interaction. In relation the standard to dark WIMP matter. paradigm, In the known last from few years, the direct1970s searches [51,52], the for correct dark cosmological matter have abundance intensified, of dark paralleled matter is by achieved the broad via its investation self an- of the- oreticalnihilation opprtunities at high temperatures, for darkT matter.m , where Weaklym is interacting the WIMP mass. dark Simple matter calculations (WIMP) paradigm ⇤ ⇤ ⇤ o⇥showers perhaps thatLight the required the WIMPs largest WIMP number are abundance facilitated of opportunitiesis achieved ifby forlight the mediators experimental discovery of dark matter via its non-gravitational interaction. In the standard WIMP paradigm, known from annih(v/c) 1pbn= DM 0.25, (3.2) 1970s [51,52], the correct cosmological⇤ abundance of⌥ dark matter is achieved via its self an- where v/c is the approximate relative velocity at the time of annihilation. The nature of a nihilation(Boehm, at highFayet temperatures,; MP, Riz, VoloshinT m⇤…), where Lightm ⇤darkis the matter WIMP is not mass. ruled Simple out calculations forceif one responsible adds a for light the mediator. self-annihilation ⇤ of WIMPs to the SM states is important. It sets showthe size that of the the self-annihilationrequired WIMP cross abundance section, and is ultimately achieved ifthe abundance of WIMP dark matter.WIMP If theparadigm: interactions are mediated(v/c) by forces1pbn= that have the weak0. strength,25, and operate (3.2) with the exchange of the weakannih scale particles,⇤ then for smallDM and⌥ large masses one would whereexpectElectroweakv/c theis following the approximatemediators scaling with lead relativethe to WIMP the velocity so mass,-called at Lee the- timeWeinberg of annihilation. window, The nature of a force responsible for the2 self-annihilation2 of WIMPs to the SM states is important. It sets GF m⇤ for m⇤ mW , the size of the(v/c) self-annihilation cross⌅ section,= andfew ultimately GeV
two2 orders of magnitude. In addition, models where the final state annihilation products 4⌅ 2 2 ⇠m ⇧annih(v/c) D ⇤ v are heavy. SM particles (b,(3.4) t, W, Z, h)willnecessarilyproduceantiprotons,andtherefore ⌅ 3 (m2 4m2 )2 A are tightly constrained by np¯/(np + np¯). 2 Here D =(g ) /(4⌅), and m me is assumed. MP: I need to check the numerical coe cient. The extra factor of velocity⇤ square in this formulaIt was is indicative soon realized of the thatp-wave these problems can be rather e ciently circumvented if the annihilation, and is what ulmitately allows this modelheavy escaping WIMP strong darkconstraints matter on islight interacting with the SM via relatively light mediators [64,65], dark matter annihilation imposed by the accurate measurementsand the DMof CMBSM anisotropies. annihilation The occurs via an intermediate stage of light mediators, Fig. 4. least constrained region of the parameter space corresponds to very light! mediators, m < In particular, for the light vectorA mediator one finds that
100 MeV, and 2m 11 Neutral “portals” to the SM Let us classify possible connections between Dark sector and SM H+H (l S2 + A S) Higgs-singlet scalar interactions (scalar portal) Bµn Vµn “Kinetic mixing” with additional U(1)’ group i (becomes a specific example of Jµ Aµ extension) LH N neutrino Yukawa coupling, N – RH neutrino i Jµ Aµ requires gauge invariance and anomaly cancellation It is very likely that the observed neutrino masses indicate that Nature may have used the LHN portal… Dim>4 A Jµ ¶µ a /f axionic portal ………. 14 “Simplified models” for light DM some examples § Scalar dark matter talking to the SM via a dark photon 2GF (variants: Lmu-L tau etc= gauge bosons).nn L Withn 2mDM < mmediator. (47) p2 ⇥ ⇥ ⇥ 2 2 2 1 2 1 2 2 ✏ = Dµ m Vµ⌫ + mV Vµ Vµ⌫Fµ⌫ (48) L | | | 2|G F 4 2 2 = nn L n (47) p2 ⇥ ⇥ ⇥ § Fermionic dark 2matter2 talking2 1 to2 the SM1 2 via2 a “dark✏ scalar” = Dµ m Vµ⌫ + mV Vµ Vµ⌫Fµ⌫ (48) that mixesL | with| the Higgs.| | With4 mDM2> mmediator 2. 1 2 1 2 2 = (i@ m ) + S + (@ S) m S AS(H†H)(49) L µ µ 2 µ 2 S After EW symmetry breaking S mixes with physical h, and can be light and weakly coupled provided that coupling A is small. (recall G Krnjaic’s talk). Let’s call it dark Higgs (P Ko’s talk). 15 5 5 2GF = nn L n (47) p2 ⇥ ⇥ ⇥ 2GF = 1nn 1L n ✏ (47) = D 2 m2 p22 ⇥ V 2⇥+ m⇥2 V 2 V F (48) L | µ | | | 4 µ⌫ 2 V µ 2 µ⌫ µ⌫ 2 2 2 1 2 1 2 2 ✏ = Dµ m Vµ⌫ + mV Vµ Vµ⌫Fµ⌫ (48) L Two| different| | | types4 1 of2 2annihilation1 2 22 = (i@µ µ m ) + S + (@µS) mSS AS(H†H)(49) L § Model 1: one step process: 2 2 1 2 1 2 2 = (i@µ µ m ) + S + (@µS) m S AS(H†H)(49) S+ L ⇤ o↵ shell dark2 photon 2 e e (50) ! ! + § Model ⇤ 2: two-stepo↵ process:shell dark annihilation photon to mediatorse e with (50) subsequent! decay ! + + S + S ... (e e )+(e e )(51) ! ! ! In both cases, the annihilation proceed in p-wave, and is very suppressed at the recombination time à no CMB constraints. Thus, (few MeV – to – GeV) range is not excluded by cosmology. 16 5 5 Two types of WIMPs Un-secluded Secluded Ultimately discoverable Potentially well-hidden Size of mixing*coupling is set by Mixing angle can be annihilation. Cannot be too small. 10-10 or so. It is not fixed by DM annihilation You think gravitino DM is depressing, but so can be WIMPs 6 17 How to look for light WIMP DM ? 1. Detect missing energy associated with DM produced in collisions of ordinary particles 2. Produce light dark matter in a beam dump experiment, and detect its subsequent scattering in a large [neutrino] detector 3. Detect scattering of light ambient DM on electrons, and keep lowering the thresholds in energy deposition. All three strategies are being actively worked on, and pursued by several ongoing and planned experiments. Anomalies? A simple concept of dark matter + mediator allows [speculatively] connecting DM to some on-going puzzles 1. Unexpectedly strong and uniform 511 keV emission from galactic bulge could be fit by annihilation of a few MeV galactic WIMPs. 2. If DM is heavy and mediator is light, one can fit its annihilation to the famous positron-to-electron ratio rise (thanks to Sommerfeld enhancement at low velocity, bound states effects, as well as lepto- phylic composition of the final states) 3. Inner density profiles of galaxies can smoothed out by the self- scattering WIMPs with 10-24cm2/GeV. For EW scale WIMPs, light mediators can easily provide such cross section. (S Tulin’s talk). 4. …. These connections are all rather interesting but not necessarily compelling. We’d like a laboratory probe (Exclusion or confirmation). Missing energy/momentum searches NA64 has recent results (great sensitivity after 3×109 e on target). Plot from Banerjee et al, 1610.02988. Much more data expected5 in future the corresponding zero-energy thresholds. The shape of ਲ the energy distributions in these detectors from the leak of signal shower energy from the ECAL was simulated for di⇥erent A⇥ masses [54] and cross-checked with measure- E Ƕ mentsSearch at the e beam.of a Theprocess uncertainty in the V2 and ᅲ 1d3d- Ԑ " " ` 1N9N HCAL e⌅ciency for the signal events, dominated mostly ܽၜ 7 pQ`2/ by the pile-up e⇥ect from penetrating hadrons in the high Ԁ ܽ ᅲᅳӶ ᅲ e + Z à e +Z + Và e +Z + cc ᅪ Ԑ intensity PbSc run, was estimated to be 3%. The ਲ ⇧ trigger (SRD) e⌅ciency is measured in unbiased random samples of events that bypass the trigger (SRD) selec- Le9 tion andSignificant the uncertainty new is 2% (3%).constraints Other e⇥ects, on e.g. e loss due to conversion into e ⇥ pair in the upstream Ԕ dark mediator parameter Ԑ detector material were measured to be . 3% (2% uncer- tainty). Finally, the dominant source of systematic errors on the expectedspace. number Complements of signal events comes fromvisible the ਲ R Ry uncertainty in the estimate of the yield nA0 (⇤,mA0 , EA0 ) ਲ ਲ decay searches (19%). The overall signal e⌅ciency ⇤A0 varied from 0.69 Ӷங ± Ԝ ӼԔԋ 0.09 to 0.55 0.07 decreasing for the higher A⇥ masses. FIG. 3: The NA64 90 % C.L. exclusion region in the (mA0 , ⇥) ± plane. Constraints from the BaBar [48, 55], and E787+ E949 In accordance with the CLs method [57], for zero ob- experiments [47, 56], as well as muon µ favored area are also served events the 90% C.L. upper limit for the number g 2 90% µ of signal events is N (mA )=2.3. Taking this and shown. Here, µ = 2 . For more limits obtained from A0 0 indirect searches and planned measurements see e.g. Refs. Eq.(2) into account and using the relation NA0 (mA0 ) < [5]. N 90%(m ) results in the 90% C.L. exclusion area in the A0 A0 (m ; ⇤) plane shown in Fig. 3. The limits are determined A0 20 There is a parallel effort in the US, mostlycalled by theLDMX number of, accumulatedpossibly eot. at These SLAC results exclude the invisible A⇥ as an explanation of the gµ 2 tance loss due to pile-up ( 8% for BGO and 7% for muon anomaly for the masses m 100 MeV. Moreover, PbSc runs). The number⇧ of collected n =2⇧.75 109 A0 . eot · the results also allow to restrict other models with light was estimated based on the recorded number of refer- particles interacting with electron and decaying predom- ence events from the e-m e Z interactions in the target inantly to invisible modes. For instance for light scalar taking into account dead time. The acceptance of the particle s with the interaction Les = se¯(hs + hasi⇥5)e signal events was evaluated by taking all relevant mo- 2 2 2 hs+has mentum and angular distributions into account. The the bound on ⇤s (⇤s 4⇥ ) is approximately 1.5 times weaker than the one⌅ obtained on ⇤ for the model A⇥ yield calculated as described in Ref.[54] was cross- checked with calculations of Ref.[55]. The 10% dis- with light vector bosons [58]. Here hs and has are scalar crepancy between these two calculations was⇧ accounted and pseudoscalar Yukawa coupling constants of the light scalar field s with electron field e,respectively. for as systematic uncertainty in nA0 (⇤,mA0 , EA0 )dueto a possible di⇥erence in treatment of the e-m shower de- We gratefully acknowledge the support of the CERN velopment. To estimate additional uncertainty in the A⇥ management and sta⇥ and the technical sta⇥s of the par- yield prediction, the cross-check between a clean sample ticipating institutions for their vital contributions. This 3 + of 5 10 observed and MC predicted µ µ events with work was supported by the HISKP, University of Bonn E ⇧ · 60 GeV was made, resulting in 15% di⇥er- (Germany), JINR (Dubna), MON and RAS (Russia), ECAL . ⇧ ence in the dimuon yield. The number of A⇥ and dimuon SNF (Switzerland), and grants FONDECYT 1140471 events are both proportional to the square of the Pb nu- and 1150792, Ring ACT1406 and Basal FB0821 CON- clear form factor F (q2) and are sensitive to its shape. As ICYT (Chile). Part of the work on MC simulations was the mass (m m ) and q2 (q m2 /E m2 /E ) supported by the RSF grant 14-12-01430. We thank S. A0 µ A0 A0 µ µ ranges for both⇧ reactions are similar,⇧ the observed⇧ dif- Andreas and A. Ringwald for their contribution at the ference can be interpreted as due to the accuracy of the earlier stage of the project, and V.Yu. Karjavin, J. Novy, dimuon yield calculation for heavy nuclei and, thus can V.I. Savrin, and I.I. Tkachev for their help. We thank be conservatively accounted for as additional systematic COMPASS DAQ group and the Institute for Hadronic uncertainty in nA0 (⇤,mA0 , EA0 ). The V2 and HCAL Structure and Fundamental Symmetries of TU Munich signal e⌅ciency was defined as a fraction of events below for the technical support. [1] L. B. Okun, Sov. Phys. JETP 56 (1982) 502 [Zh. Eksp. (1984). Teor. Fiz. 83 (1982) 892]. [3] B. Holdom, Phys. Lett. B 166,196(1986). [2] P. Galison and A. Manohar, Phys. Lett. B 136,279 [4] J. Jaeckel and A. Ringwald, Ann. Rev. Nucl. Part. Sci. 6 −6 ) ×10 σ 3 3 Bayesian limit 2.5 2.5 Profile-likelihood limit 2 Significance ( 2 1.5 1.5 Upper Limit at 90% CL 2 1 ε 1 0.5 0.5 0 0 1 2 3 4 5 6 7 8 0 0 1 2 3 4 5 6 7 8 mA' (GeV) mA' (GeV) Most recent BaBar results 0 FIG. 2: Signal significance as a function of the mass mA0 . FIG. 4: Upper limits at 90% CL on A mixing strength S 2 squared " as a function of mA0 . Shown are the Bayesian BaBar collaborationlimit computed has published with a uniform new prior results for "2 > two0 (solid weeks red ago, 2 line) and the profile-likelihood+ - limit (blue dashed line). Pull 0 1702.03327. Search of e e à g + V à g + cc −2 25 30 35 40 45 50 55 60 10−2 χ2/df = 69.0/77 K→πνν ) 2 ε 10 (g-2) ± 5σ µ favored BABAR 2017 −3 1 10 Events / ( 0.5 GeV (g-2) NA64 e −1 10 25 30 35 40 45 50 55 60 2 2 MX (GeV ) 10−4 10−3 10−2 10−1 1 10 mA' (GeV) FIG. 3: Bottom: signal fit for mA0 =6.21 GeV to a com- bination of ⌥ (2S)and⌥ (3S) datasets, shown for illustration purposes. The signal peak (red) corresponds to the local sig- § Complementary to NA64 0 nificance =3.1(globalsignificanceof2.6 ). Blue solid FIG. 5: Regions of the A parameter space (" vs mA0 )ex- line showsS the full PDF, while the magenta dashed line cor- cluded by this work (green area) compared to the previous responds to the background contribution. Top:§ distributionCovers all constraintsof the dark [7, 18–20] photon as well parameter as the region space, preferred decaying by the invisibly, 21 of the normalized fit residuals (pulls). (g 2)µ anomaly [5]. consistent with alleviating the muon g-2 discrepancy the frequentist profile-likelihood limits [29]. Figure 5 for the substantial dedicated e↵ort from the comput- compares our results to other limits on " in channels ing organizations that support BABAR . The collaborat- where A0 is allowed to decay invisibly, as well as to the ing institutions wish to thank SLAC for its support and region of parameter space consistent with the (g 2) kind hospitality. This work is supported by DOE and µ anomaly [5]. At each value of mA0 we compute a limit NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 on " as a square root of the Bayesian limit on "2 from (France), BMBF and DFG (Germany), INFN (Italy), Fig. 4. Our data rules out the dark-photon coupling as FOM (The Netherlands), NFR (Norway), MES (Russia), the explanation for the (g 2) anomaly. Our limits place MINECO (Spain), STFC (United Kingdom), BSF (USA- µ stringent constraints on dark-sector models over a broad Israel). Individuals have received support from the Marie range of parameter space, and represent a significant im- Curie EIF (European Union) and the A. P. Sloan Foun- provement over previously available results. dation (USA). We are grateful for the excellent luminosity and ma- We wish to acknowledge Adrian Down, Zachary Jud- chine conditions provided by our PEP-II colleagues, and kins, and Jesse Reiss for initiating the study of the Running NA64 in the muon mode? In connection with g-2 of the muon discrepancy, and in order to diversify from dark photons, one could run the NA64 in muon New leptonic Z (or Z ) from gauged L -L " 13." mode with up to 107 muons/secondµ . S. Gninenkoμ τ idea/slide: • Class of U(1) models: in SM it s possible to gauge " one of Le-Lμ, Le-Lτ, Lμ-Lτ LN differences. No anomaly." ! • Extra (broken) U(1)´, new massive boson Z´ coupled ! predominantly to µ and ( through the L L current" (leptonic dark photon)" Altmannshofer et al.," • M Z´ could be in sub-GeV range ! arXiv:1406.2332" + - Z´! μ μ or Z´! ## if M Z´ < 2 mµ ! • Impact on: ν-physics, explanation of (g-2)μ " Strong motivation for a sensitive " search for Z´->νν, μ+μ- in a near " future experiment by using (unique)" high intensity muon beam at CERN. " Invisibly decaying Lµ-Lt gauge boson and darkFrom scalar J.Heeck PLB’16below" the d- 22 muonS.N. Gninenkothreshold – Search canfor dark be sector probed physics – PBC this kickoff way. workshop, CERN, Sept 6–7, 2016" Fixed target probes - Neutrino Beams Proposed in Batell, MP, Ritz, 2009. Strongest constraints on MeV DM + e e + (near) detector p + p(n) V ¯ proton 0 ⇥ ⇥ + N beam ⇤ , ⇥ V ⌅⌅ ¯ ⇥ ⇥ + N We can use the neutrino (near) detector as a dark matter detector, looking for recoil, but now from a relativistic beam. E.g. T2K MINOS MiniBooNE 30 GeV protons 120 GeV protons 8.9 GeV protons (! ~5x1021 POT) 1021 POT 1021 POT 280m to on- and off- 1km to (~27ton) 540m to (~650ton) axis detectors segmented detector mineral oil detector23 30 DM Production & Scattering absorber detector target 0 ⇥ V, V ⇤⇤⇤ p ! ! p 0 + X decay volume Light! DM - trying to see productionN + scattering dirt q ⇥0, V V ⇤ q¯ ⇤ In the detector: Elastic scattering Elastic scattering Deep inelastic on electrons on nucleons scattering V V V e e N N q q Same force that is responsible for depletion of χ to acceptable levels in the early Universe will be responsible for it production at the collision point and subsequent scattering in the detector. 4 Signal scales as (mixing angle) . 24 Constraints on dark matter particles produced in beam dump collisions Best constraints are provided by the LSND and E137 (electron beam dump) experiments. deNiverville et al., 1609.01770. 25 Dark Matter Search in a Proton Beam Dump with MiniBooNE A.A. Aguilar-Arevalo,1 M. Backfish,2 A. Bashyal,3 B. Batell,4 B.C. Brown,2 R. Carr,5 A. Chatterjee,3 R.L. Cooper,6, 7 P. deNiverville,8 R. Dharmapalan,9 Z. Djurcic,9 R. Ford,2 F.G. Garcia,2 G.T. Garvey,10 J. Grange,9, 11 J.A. Green,10 W. Huelsnitz,10 I.L. de Icaza Astiz,1 G. Karagiorgi,5 T. Katori,12 W. Ketchum,10 T. Kobilarcik,2 Q. Liu,10 W.C. Louis,10 W. Marsh,2 C.D. Moore,2 G.B. Mills,10 J. Mirabal,10 P. Nienaber,13 Z. Pavlovic,10 D. Perevalov,2 H. Ray,11 B.P. Roe,14 M.H. Shaevitz,5 S. Shahsavarani,3 I. Stancu,15 R. Tayloe,6 C. Taylor,10 R.T. Thornton,6 R. Van de Water,10 W. Wester,2 D.H. White,10 and J. Yu3 1Instituto de Ciencias Nucleares, Universidad Nacional Aut´onomade M´exico, Mexico City 04510, Mexico 2Fermi National Accelerator Laboratory, Batavia, IL 60510 3University of Texas (Arlington), Arlington, TX 76019 4University of Pittsburgh, Pittsburgh, PA 15260, USA 5Columbia University; New York, NY 10027 6Indiana University, Bloomington, IN 47405 7New Mexico State University, Las Cruces, NM 88003 8Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Daejeon, 34051, Korea 9Argonne National Laboratory, Argonne, IL 60439 10Los Alamos National Laboratory, Los Alamos, NM 87545 11University of Florida, Gainesville, FL 32611 12Queen Mary University of London, London, E1 4NS, UK 13Saint Mary’s University of Minnesota, Winona, MN 55987 14University of Michigan, Ann Arbor, MI 48111 15University of Alabama, Tuscaloosa, AL 35487 (Dated: February 10, 2017) The MiniBooNE-DM collaboration searched for vector-boson mediated production of dark matter using the Fermilab 8 GeV Booster proton beam in a dedicated run with 1.86 1020 protons delivered to a steel beam dump. The MiniBooNE detector, 490 m downstream, is sensitive⇥ to dark matter via elastic scattering with nucleons in the detector mineral oil. Analysis methods developed for previous MiniBooNE scattering results were employed, and several constraining data sets were simultaneously analyzed to minimize systematic errors from neutrino flux and interaction rates. No excess of events over background was observed, leading to an 90% confidence limit on the dark- 2 4 8 matter cross section parameter, Y = ✏ ↵0(m /mv) . 10 , for ↵0 =0.5 and for dark-matter masses of 0.01 PACS numbers: 95.35.+d,13.15.+g MiniBooNE search for light DM MiniBooNE sensitivity to vector portal DM Introduction — There is strong evidence for dark mat- Target Decay Pipe Beam Dump MiniBooNE Detector † ter (DM) from observations of gravitational phenomena V p N across a wide range of distance scales [1]. A substantial 0 Be ⇡ program of experiments has evolved over the last sev- Air Steel Earth eral decades to search for non-gravitational interactions arXiv:1702.02688v1 [hep-ex] 9 Feb 2017 50 m 4m 487 m of DM, with yet no undisputed evidence in this sector. Most of these experiments target DM with weak scale FIG. 1. SchematicMiniBooNE illustration of this DM search using the masses and are less sensitive to DM with masses below a MiniBoonethe Fermilabhas completed BNB90% in C.L. o↵ a-target long run mode in togetherthe beam with dump the mode, Mini- as few GeV. To complement these approaches, new search suggestedBooNE in detector.[arXiv:1211.2258] The proton beam is steered above the beryl- strategies sensitive to DM with smaller masses should be lium target in o↵-target mode lowering the neutrino flux. considered [2]. By-passing Be target is crucial for reducing the neutrino background Fixed-target experiments using beams of protons or(Richard van de Water et al. …) . Currently, suppression of n flux ~50. electrons can expand the sensitivity to sub-GeV DM that place limits on the parameters within this class of models. Timing is used (10 MeV dark matter propagates slower than neutrinos) couples to ordinary matter via a light mediator parti- In this Letter, we report on the first dedicated search of cle [3–18]. In these experiments, DM particles may beto furtherthis type reduce (proposed backgrounds. in [6]), First which results employs – 2016, 8 GeV 2017 protons produced in collisions with nuclei in the fixed target, of-Importantfrom contribution the Fermilab from Booster P deNiverville Neutrino, BeamB Batell (BNB),. re- 26 ten a beam dump, and may be identified through interac- configured to reduce neutrino-induced backgrounds, com- tions with nuclei in a downstream detector. Results from bined with the downstream MiniBooNE (MB) neutrino past beam dump experiments have been reanalyzed to detector (Fig. 1). 23 On-going and future projects Full NCEOff Distribution From the W & C talk by Thornton, and a new paper NCE Off Data (stat errors) 250 Total Bkg (sys errors) Beam unrel. bkg νdet #events uncertainty Events/(1e20 POT) 200 ν dirt BUB 697 150 det bkg 775 dirt bkg 107 100 Total Bkg 1579 14.3% (pred. sys.) Data 1465 2.6% (stat.) 50 0 0.2 0.4 0.6 0.8 1 1.2 Q2 (GeV2) QE The offI-targetNo nuisance run of parameters MiniBoone appliedis a yet success (despite the absence of DM signal!):I Data consistent with background only • NeutrinoI Systematics background dominated from the beam is brought down to be comparable from cosmics • Data are well describedR. T. by Thornton MC September 23, 2016 39 27 Comparing to other experiments χN→χN m = 3m α' = 0.5 New parts of the parameterV χ space get excluded 4 ε ) V /m −8 J/ψ→ invis. + + χ 10 K →π +invis. '(m α BaBar 2 µ g-2 favored ε Y = BaBar + + 10−9 K →π +invis. µ g-2 favored LSND 10−3 10−10 E137 Direct Det. E137 Relic Density Relic Density mχ = 10 MeV, α' = 0.1 LSND Preliminary PreliminaryMiniBooNE 90% CL mV = 3mχ, α' = 0.5 MiniBooNE 90% CL 10−11 MiniBooNE 90% Sensitivity MiniBooNE 90% Sensitivity 10−2 10−1 1 10−1 1 mχ (GeV) mV (GeV) Improves over LSND, SLAC experiments, and Kaon decays in the range I First dedicated proton beam-dump search for DM of the mediator mass from ~ 100 to few 100 MeV. Details can be found 28 in 1702.02688. I Exclude new parameter space1 1Amount of parameter space newly excluded depends on slice plotted R. T. Thornton September 23, 2016 47 Future directions To improve on sensitivity to light dark matter in beam dump/fixed target experiments: • SHiP • NA64 with more intensity (LDMX) • More experiments at short neutrino baseline program and DUNE near detector (C. Frugiuele and collaborators) • …. • Ultimate beam dump experiment looking for light DM in scattering = powerful accelerator next to large neutrino detectors deep underground for least background. 29 Future: SHiP project at CERN The SHiP experiment ( as implemented in Geant4 ) A proposal for a large experiment!"#$%&'()%*+,'&*#-,.%/)0%1-2+.%/345% at CERN SPS to look for8% all types of hidden particles: sterile neutrinos, axion-like particles, dark photons, 30 dark Higgses. Can also be used to study scattering signature of light DM SHiP sensitivity to vector and scalar portals § SHiP will collect 2 × 1020 protons of 400 GeV dumped on target § Sensitivity to dark vectors is via the unflavored meson decays, and through direct production, pp à… V à…… l+l- § Sensitivity to light scalar mixed with Higgs is via B-meson decays, b à s + Scalar à … µ+µ- Visibly Decaying A' 10 4 g⇥2 ⌅ ⇤ 5⇧ 10 6 g⇥2 ⌅ 2⇧ ⇥ g⇥2 e E774 BaBar, NA48 2, PHENIX 8 ⇥ 10 E141 ⇥ SHiP, ⇤ 10 10 Orsay, U70 bremsstrahlung ⇥2 SHiP, 10 12 QCD Charm, Nu⇥Cal 10 14 E137, LSND 10 16 SN SHiP, 10 18 mesons 10 20 1 10 102 103 mA' MeV 7 31 Figure 5: Summary ofDetails constraints can on the be dark found photon in model. the The white limits atpaper,⇥ 10 1505.01865,; mA > Alekhin et al. 200 MeV range come from old experiments, and can be⇥ improved with SHiP. The⇤ g 2region of interest is shown as a green band. The projected SHiP sensitivity contour is derived using three modes of production: mesons, bremsstrahlung, and QCD production. (B) V was derived in [33]. The full analysis of constraints on (B),mV plane has not been performed yet. { } Some cases of other exotic particles produced in association with V have been constrained in experiment. BaBar studies have placed limits on dark Higgsstrahlung [124], by exploiting A⇥h⇥ production with subsequent decays of h⇥ to 2A⇥ and eventually to pairs of charged SM 4 particles. The ensuing constraints are quite strong (reaching down to ⇥ few 10 at ), but applicable only to m > 2m region of parameter space.⇤ Another⇥ study D ⇤ h A at KLOE [125] have searched for missing energy signature from h⇥ decays outside of the 3 detector, and reached the constraints at the level of ⇥ few 10 . Constraints on the most ⇤ ⇥ motivated case, mh mA ,aremoredi⇥cult to obtain because they involve stable h⇥ on the scale of the detector.⇧ 5.2 Production and detection of light vector portal DM New constraints on vector portals occur when direct production of light dark matter states + ⇧ opens up. The missing energy constraints on dark photons derived from e e colliders + were analyzed in [50]. Invisible decays of A⇥ are usually harder to detect, except K + + + + ⌅ ⌅ A⇥ ⌅ +missing energy, where the competing SM process, K ⌅ ⇤⇤¯ is extremely suppressed⌅ [49]. Also, fixed targets experiments sensitive to the missing⌅ energy decays of vector states have been proposed recently [126, 127]. 20 SHiP has unique sensitivity to RH neutrinos § Production channel is through charm pp à c cbar à NR. (NR are often called Heavy Neutral Leptons, or HNL) § Detection is through their occasional decay via small mixing angle U, with charged states in the final state, e.g. p+µ-, p-µ+, etc. § DecaysSensitivity are slow, to so HNLs that the for sensitivity representative is proportional scenarios to (Mixing angle)(moving4. down to ultimate see-saw limit) 2 2 2 U2 : U2 : U2 ~1:16:3.8 2 2 2 U e: U µ: U #~52:1:1 e µ # U e: U µ: U #~0.061:1:4.3 Inverted hierarchy Normal hierarchy Normal hierarchy 2 2 2 2 2 2 32 HNL production can be enhancedU e: U µ :in U non#~48:1:1-minimal models,U e: UBatellµ: U #~1:11:11et al. Inverted hierarchy Normal hierarchy Scenarios for which baryogenesis was numerically proven !"#$%&'()%*+,'&*#-,.%/)0%1-2+.%/345% /5% SHiP sensitivity to light DM • Estimated in deNiverville et al. 33 A comment on SHiP Details of physics motivation can be found in the white paper, 1505.01865, Alekhin et al. SHiP is not just a proton beam dump, it is beam dump of “everything” • Protons produce enormous amount of EM decaying particles (pi0, eta), that all cascade to photons, and EM showers. It is an enormous electron and photon beam dump! • Muons are also copiously produced and go through the tens of meters of material before being diverted/slowed down. It is a muon beam dump as well. So far the sensitivity studies to NP were mostly limited to the primary productions inside the target, but there is a lot to explore with these secondary “beams”, and sensitivty to many exotic candidates will improve 34 More coverage of dark sector using underground accelerators and neutrino MeV-Scale Dark Matter Deepdetectors Underground Eder Izaguirre,1 Gordan Krnjaic,1 and Maxim Pospelov1, 2 1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada 2Department of Physicswith and Astronomy, Eder University Izaguirre of Victoria, Victoria,and BritishGordan Columbia, CanadaKrnjaic, 2014, 2015 We demonstrate that current and planned underground neutrino experiments could o er a pow- erful probe of few-MeV dark matter when combined with a nearby high-intensity low-to-medium energy electron accelerator. This experimental setup, an underground beam-dump experiment, is capable of decisively testing the thermal freeze-out mechanism for several natural dark matter sce- narios in this mass range. We present the sensitivity reach in terms of the mass-coupling parameter space of existing and planned detectors, such as Super-K, SNO+, and JUNO,+ in conjunction with a hypothetical 100 MeV energy accelerator. This setup can also greatly extend the sensitivity of direct searches for new light weakly-coupled force-carriers independently of their connection to dark matter. 5 I. INTRODUCTION The existence of Dark Matter (DM) is clear evidence ⌅ of physics beyond Standard Model (SM) and has inspired = Overburden a major experimental e ort to to uncover its particle na- few km ⇥ = ture. If DM achieves thermal equilibrium with the SM in ⌅ the early universe, its present-day abundance can arise from DM annihilation with characteristic cross section Borexino26 3 , Kamland, LUNA, DIANA,…, ⇥v 3 10 cm /s. Alternatively if its abundance ⇥ at late times is set by a primordial particle-antiparticle Detector asymmetry,SNO+, a thermal origin SuperK requires at least, as large of 1 e-linac for an annihilation rate to avoid cosmological overproduc- Displaced decay e+ tion. ForHyper either scenario,-K this (?) requirement … sets a pre- (visible) calibration dictive target of opportunity to search for many of the e e simplest light DM models. ⇤ ············ A Current and planned direct and indirect detection, Beam ··············· and collider experiments will cover a vast subset of DM DM Prompt decay DM masses motivated by the thermal origin paradigm. How- (invisible) ever, significant gaps remain in our current search strate- gies for low-mass DM. Indeed, the MeV-to-GeV DM mass e, p, N . . . 35 window remains an elusive blind spot in the current search e ort [1], despite the existence of viable mod- els [2–8] – including those invoked to explain the ex- cess 511 keV photon line from the galactic bulge [9] with MeV scale DM annihilation into electron-positron FIG. 1. Schematic diagram of the proposed setup: a high pairs [3, 4]. Recent progress in our understanding of intensity electron accelerator is placed in the vicinity of a the status of MeV-scale DM has come from a combi- large, underground neutrino detector. The electron beam im- pinges on a fixed-target or beam-dump to produce a dark arXiv:1507.02681v1 [hep-ph] 9 Jul 2015 nation of re-interpretation of surface-level proton-beam + neutrino experiments results [10–13], rare meson decays force-carrier A⇥,whichcandecayeithervisiblytoe e or to [14–18], electron beam dump experiments [19–22], B- DM particles. If the A⇥ decays visibly and is long lived, it can factories [19, 23], precision measurements [5, 19, 24], the enter the detector and directly deposit a large electromag- netic signal. If the A⇥ decays invisibly to DM, the daughter CMB [25–29], and DM-electron scattering in direct de- particles inherit forward-peaked kinematics and scatter in the tection experiments [30]. detector inducing observable target-particle recoils. In this paper we propose a powerful new setup depicted schematically in Fig. 1 — the combination of a large un- derground detector such as those housed in neutrino fa- other existing e orts in this mass range. This concept cilities and a low-energy (10-100 MeV) but high inten- complements the DAE ALUS light-DM proposal [31] in- sity electron-beam — which is capable of sharply testing volving an underground proton beam as well as other the thermal origin scenario below few 10s of MeV in underground accelerator concepts [32–34] with di erent DM mass. While our proposal requires⇥ a substantial in- physics goals. vestment in an accelerator and beam-dump deep under- For concreteness, we consider light DM that interacts ground, it can significantly surpass the sensitivity of all with the visible sector through a kinetically-mixed [35] Sensitivity to light DM 2 Pseudo Dirac Inelastic Thermal Relic DM Scalar Thermal Relic DM 5 LEP 5 LEP 10 ⌃ 10 ⌃ 10 6 ⇥ 10 6 BaBar E787 E949 7 7 BaBar 10 10 ⌃ ⌃ 4 4 8 ⌃ ⇥ ⇥ 8 ' ' 10 10 CMB XENON 10 A A 9 m m 9 ⇤ ⇤ 10 10 ⌃ ⌅ ⇧ 10 ⌃ m 10 m 10 ⌃ E137 10 Density D 11 D 10 11 Relic ⇤ ⇤ 10 2 LSND 2 ⇧ 12 ⌅ 10 12 LSND x SIDM 10 ⇥ LSND ⇥ SIDM 13 Density x y LSND 10 Relic y 10 13 14 10 SNO 14 10 15 SNO 10 SuperK 15 JUNO 10 SuperK 16 JUNO 10 16 2 10 2 1 10 10 1 10 10 m⌅ MeV m⇧ MeV FIG. 2. Sensitivity production for 1024 electrons with 100-MeV energies impinging on an aluminum target positioned 10 m Onenear the will SNO+, significantly JUNO, and SuperK detectorsadvance⇥ – since sensitivity the latter two have to comparablelight DM fiducial in volumes, the⇥ sub their- projections100 are presented as a common curve. We conservatively assume24 thresholds of ER > 10 MeV for which the backgrounds are negligible. MeVThe CMB mass and direct range. detection Assuming constraints assume 10⇤/⌅ constitutes100 MeV all of electrons the dark matter on and regionstarget above the relic curve correspond to parameter space for which each scenario can accommodate a subdominant fraction of the total DM (note that for subdominant DM, the CMB and direct detection bounds would also weaken). For the pseudo-Dirac scenario the relic Izaguirrecurve was computed, Krnjaic assuming, onlyMP a, small 1507.02681, mass-splitting (100 PRD keV < Kaon, mono-photon, and beam-dump constraints don’t scale as y, we conservatively adopt D =0.5andm /'/mA0 =3to One of the topics to be discussed at a pre-TAUP meeting at PI, Jul204 -22 not overstate these bounds; the plotted arrows show how the constraint moves when the product D(m /mA0 ) is reduced36 by a factor of ten. The dotted LSND SIDM curve denotes where the LSND bound shifts if D is chosen to satisfy the bound on 2 DM self interactions ⇥self /m < 0.1cm /ginsteadofthenominal D =0.5 which is conservative in other regions of parameter space. Note that for scalar inelastic⇥ DM, the key di⇥erence relative to the right panel is that the Xenon10 region disappears as the scattering can be turned o⇥. massive dark-photon A⇤ [36]. Since light DM requires be generalized to the “split” states of Majorana/pseudo- a comparably light mediator to avoid overclosure, this Dirac fermions or real scalars, in which case A⇤ can cou- starting point loses no essential generality and our re- ple o -diagonally (inelastically) to the di erent mass- sults are qualitatively similar for di erent mediators. The eigenstates and m⇤(⌅) should be understood as a ma- most general renormalizable Lagrangian for this dark sec- trix acting on the split states. Moreover, each variation tor contains above can be particle/antiparticle asymmetric, which al- m2 lows for weaker bounds from late-time annihilations into Y A0 µ D Fµ⇤ ⇥ Bµ⇥ + Aµ⇤ A⇤ + DM , (1) the CMB than the symmetric case [26]. L ⇤ 2 2 L One of the most important questions for such a model where A⇤ is the dark photon that mediates an abelian is the hierarchy of masses in .Ifm = Y E (L ⇥†)+h.c. (33) Lmass ⇥ R L (L⇥)=⇤ ⇧0 e ⇧+ (34) L L 1 = (L⇥)(L⇥)(35) Le M = Y N (L⇥)+ N NN +(h.c.)(36) Lmass ⇥ R 2 1 (Y )2 = (37) MN 0 Y ⇥ 2 = m1 (Y ⇥ ) /MN ; m2 MN at Y ⇥ MN (38) Y ⇥ MN ⌃ ⇧ ⇧ ⌅ ⇥ Y ⇥ m (observed) ⇥ ⇥ (39) ⇤ MN ⇤ ⇤ MN 2GF = nn L n 1 (47) p2 ⇥ ⇥ ⇥ ⌃F ⌅µ⇥⌃ (40) 2 µ⇥ 1 1 ✏ = D 2 m2 2 V 2 + m2 V 2 V F (48) L | µ | | | 4 µ⌫ 2 V µ 2 µ⌫ µ1⌫ ⌃F ⌅µ⇥i 5⌃ (41) 2 µ⇥ 1 2 1 2 2 = (i@µ µ m ) + S + 2G(@FµS) mSS AS(H†H)(49) L = 2 n n 2 L n (47) p2 ⇥ ⇥ ⇥ 1 µ⇥ ⌃F˜µ⇥⌅ ⌃ (42) + 2 Search⇤ o↵ shell for dark small photon1 mass1e e mediators ✏ (50) != D 2 m2 2 V 2 !+ m2 V 2 V F (48) L | µ | | | 4 µ⌫ 2 V µ 2 µ⌫ µ⌫ 1 2 1 2 2 + Higgs portal+ = ( µS) m S ASH†H (43) S + S ... (e e )+(e e )(51)S L1 2 1 2 2 2 = (!i@ m!) + ! S + (@ S) m S AS(H†H)(49) L µ µ 2 µ 2 S 1 2 1 2 2 Av .... (@µS) m S + S✓(yf ff + ...)(52)⇥ = (44) ! 2 2 S 2 mh • If mmediator < mDM the best strategy is to look for the mediator itself directly. • Dark photon portal search (and any conserved vector current portal) does not induce large FCNC • Other portals (axial vectors, dark Higgses and scalars in general, ALPs, baryonic vector) are severely constrained by flavor physics. 4 37 5 5 Scalar currents are very different from conserved vector currents Conserved vector currents are uniquely positioned to avoid very strong flavor constraints. 4 suppressed by the cuto↵ scale will give sub-leading contri- butions (in the UV theory, the masses of the UV fermions in triangles will be much larger than the external mo- menta of these triangles). If, in the Stuckelberg picture, 2 a a the X Goldstone has a coupling Cg gX ('/mX )W W˜ (taking into account the WZ terms and the SM fermion triangles) phrasing?,thenthecoe cient of the e↵ective vertex is 4 2 3g m↵ g = g C V V ⇤ f + ... (17) Xdidj 16⇡2 X ↵i ↵j m2 ↵ u,c,t ✓ W ◆ 2X where x(1 + x(log x 1)) f(x) = x + (x2 log x) (18) ⌘ (1 x)2 O FIG. 1. E↵ective bsX FCNC vertex for a baryon2 number 2 Due to the m2/m2 dependence for small quark mass, vector X, obtained by integrating out the W loop. First q W For a conserved vector current, GF q For scalar current, GF mt the sum over up-type quarks is dominated by the top term from coupling to quarks, second from XBB WZ term, quark, for both bsX and sdX vertices. third from triangle diagrams (we’ve ignored kinetic mixing There is extremelywith hypercharge, strong which willsensitivity give a XBB vertex to through new scalars, For FCNC decays through a vector coupling to a con- mixing with Z —seeSection??). Since the baryon num- served current (and so dominantlypseudoscalars into the transverse beraxial current is- conservedvectors at tree in level, rare the diagram K fromand cou- B decays. vector modes), angular momentum conservation sup- pling to quarks gives higher-dimensional operator, suppressed presses (pseudo)scalar (pseudo)scalar + vector de- by ((external momenta)2/m2 (details in text ...). However, ! W 38 cays, since these demand thatGeneralization the vector’s spin is per- ofanomalous this argument/constraints: terms break U(1)X , giving unsuppressed contri- R Lasenby et al (in prep) pendicular to its momentum. As an example, there are bution. In a UV completion where the XWW anomaly is no B+ K+ decays. However, by (Goldstone boson cancelled by extra fermions vectorial under the SM, the WZ equivalence),! FCNC decays via a light longitudinal X term is obtained from the mass-dependent piece of the trian- have the same rates as the corresponding ALP decays, gle diagrams involving the new fermions, as described in [?]. As discussed in the text, the X WW triangle amplitude does so decays such as B+ K+X are unsuppressed. L ! not depend on the external momenta, so for longitudinal X The experimental signatures and constraints from emission, the triangle diagrams can be evaluated by treating FCNC processes involving X emission depend on how them as an extra e↵ective WZ term. Point about momentum X decays. At small mX and gX ,theX decay length will scales, UV finiteness, etc? be longer than the scale of the experiment, so will give a missing energy signature (at the small gX we are inter- ested in, X will generally not interact strongly enough to be detected by its scattering). In Figures 2 and [? ], 5. Kinetic mixing with hypercharge we show the limits coming from K+ ⇡++invisiblede- cays. These are deived from the results! of K+ ⇡+⌫⌫¯ ! It is always possible to write down a kinetic mixing seraches, which have measured this branching ratio at between X and the hypercharge gauge boson B, (1) relative error [5, 6] (finding it to be consistent with theO SM prediction). The future NA62 experiment should 1 µ⌫ reduce this error to 10% [? ](check). Dimension- ✏B Xµ⌫ (19) ally, the flavour-changing⇠ operator associated to decay L 2 via ⌫⌫¯ is suppressed by G2 , while that for X decay is F At low energies, this gives rise to a small ✏(m /m )2 suppressed by ⇤, so (as shown in Figure ??) it is possible X Z coupling of the low-mass state to the neutral⇠ current, and to constrain ⇤ significantly above the EW scale. a kinetic mixing ✏ with the photon. Moreover, even if It is possible to use very displaced X decays, as we set ✏ = 0 at some⇠ scale, it will be generated by RG searched for in beam dump experiments, to probe even evolution at other scales. smaller couplings. Figure 3 displays the bounds coming from the CHARM proton beam dump experiment, where 2 1 Q1 1 X particles would be (dominantly) produced in decays of log gX e Qq (20) ···' 12⇡2 Q2 3 0 q kaons produced in the proton-target collisions, some of X which would then decay 200 m away, to be observed by the far detector. At higher⇠ masses ... discussion of (worth putting in?) For commonality with other litera- 2 hadronic decays etc. ture [7] etc, we’ll set ✏ = egx/(4⇡) for plots etc. 2GF = nn L n (47) ′ signal, and does not presuppose anyp22G hierarchyF⇥ ⇥ of gauge⇥ couplings as α can be taken = nn L n (47) of order α.Therefore,thismodelappearsthemostnaturalcandidatefp2 ⇥ ⇥ ⇥ or MeV-scale 2 2 2 1 2 1 2 2 ✏ secluded dark matter,= D havingµ them chance toV explain+ m theV 511 keVµVlinefromthegalactic⌫Fµ⌫ (48) L | | | | 4 1µ⌫ 2 1 V µ 2✏ center. = D 2 m2 2 V 2 + m2 V 2 V F (48) L | µ | | | 4 µ⌫ 2 V µ 2 µ⌫ µ⌫ 1 1 (c) φ-mediator, mX >mφ:Inthisscenario,itisadvantageoustohaveafermionic2 2 2 = (i@µ µ m ) + S + (@µS) mSS AS(H†H)(49) L 2 1 2 21 2 2 darkNotice matter that candidate there=Top (i@ is ψ- noWwith smallnessm loop) scalar + (ratherand ofS any+ ( thanlight particular@ S) pseudoscalar) mediatorsm type.S AS Compare couplings(H†H)(49) it to withφ.The µ µ 2 µ 2 S annihilationthe light scalarψψL →Sφφ, mixedproceeeds with in the the Higgsp-wave via and a can small always angle be✓ tuned, analyzed to the many required −6 + level with a typical choice ⇤ λψ ∼o↵10shell.Since darkm photonψ ∼ few MeV,e e this value of the Yukawa(50) times• inCalculations the past (e.g. of the [5]),! “Higgs penguin” are !especially+ neat: coupling is natural. The subsequent⇤ o↵ shell decay dark of φ photondue to mixinge e with the Higgs is highly(50) ! ! suppressed by the electron Yukawa coupling, SM 2 S 3 (y+ ) VtbV+⇤ S=+ Sm s¯ b... ✓(e te )+(e tse )(51)(30) !S b!L R ! + 2 + λ v2 2 M mSv+2S m ...⇥ 2 (e e16 )+(⇡ e e λ)(51)v2 2 1 ! e ! φ > ! −1 1 > −8 Γφ ∼ 2 × × ∼ sec =⇒ 2 ∼ 10 . (24) m 1vEW 18π m Now, let! meh introduce" ! in" addition2 2 the2 hard mass m!2, soh that" I can vary • Notice the absence.... (@ 1ofµS any) complicatedm1 SS + S✓( yfunctionf ff + ...0 )(52)of m /m . The ! ....2 (@ S) 2 2 m2 S2 + S✓(y ff + ...)(52)t W ThemX naturalnessandreasongD independently, requirementbeing is! that for2 the theµ effectφ-mass 2 isS wouldsimilar impose tof scale a significant anomaly: constraint here. If we consider the contribution from Higgs mixing in (17), λ1v/mh < mφ/v,thisclearly h 2 2 2 2 @ ∼ favors am longttt φ-lifetime1+ (h∼mt1sec)andasmallmixingparameter.Eventhen,onemusttt mXH=.pengm0.+ gD( v .p) @SelfEnergy(mt/mW )(53)(31) m!ttt 1+S mttt! H.peng+ .⇠ +( · p@) v SelfEnergy(mt/mW )(53) ensure that the✓! “missing◆S energy”! decay K →⇠π +·SMφ 2@isv within the allowed range. At ✓ ◆ gDa (yt ) VtbVts⇤ theNow quark the level, amplitude the amplitude has become for them processbs¯LbR is given2 by a, Hi andggs we penguin can literally (see, e.g. @ mX @ ⇥ 16⇡ [34]):use the dark scalarSelfEnergy(@ case withmt/mW )= @SelfEnergy(yt/gW )=0? (54) @v SelfEnergy(2mt/mW2 )=@v 2 SelfEnergy(∗ yt/gW )=0? (54) @v λ1v 3gW msm@tvVtdVts ¯ Leff = 2 g v g d17LsR MeVφ +(h.c.), (25) mD2 64π2m2D v • The result ✓ise↵ not= g0axial becauseh =017.14 of MeV the Wscale5 dependence,. (32) !3 mgaxial" 17⇥ MeV10 ⇥ m V6 < 0.1✓ 1(55)X ◆ leading to theSelf (non-SM)-Energy missing 10~ Log(⇥6 energyL m/v decay,X) < 0.1 1(55) 10 ⇥✓ UV mX ◆ The last normalization is quite suggestive.✓ ◆ 2 2 2 ∗ 2 3 λq1v 3mt VtdVts mK Now, usingΓ [5]K→ weπ+φ get−mediator the following≃ 2 answers for2 2 branching2 . ratios (in the39(26) mh 16π v 64πv small mX limit so that phase space! loss" and! the from" factors are neglected), Requiring that this width not exceed the observed missing energy decay branching +1.3 −10 2 + 2 ratio Br = 1.5−0.9 × 10 5 [35]✓ associatede↵ with the SM process5 K →✓e↵πνν¯,resultsin BrB KX =4 10 2 ; BrB K⇤X =5 10 2 . (33) the following! constraint⇥ on⇥φ −10h mixing:! ! ⇥ ⇥ 10 ! 2 2 λ1v −7 I’d like to have a closer look2 at the< 2 experimental× 10 . situation, but in any(27) 5 m case, even using O(10 )limits,weget! h " This cuts out a significant part2 of the parameter6 space, but together with (24) still ✓ < 10 g < 10 for M =17MeV−.7 −8 (34) leaves a relatively narrowe↵ interval! forD the mixing parameteX r, 10 − 10 ,wherethe model survives all constraints (although not without a modest amount of fine-tuning Axial vector coupling is 1 g , and therefore the result is two orders of mag- of the mediator mass) and thus2 D can be the dominant dark matter component while still accommodatingnitude below David’s the positron desired signal range. through a combination of annihilation and decay. The constraintsIt is possible remain that essentially for general the values same of for tan a pseudosca , mH andlar choises coupling of ofquφ,qtod the fermionthere canψ,iftheHiggssectorinSMisassumedtobeminimal,inwhichca be additional cancellations, and for some spots in the parameterse the mixingspace constant the constraintλ1 is CP-violating. disappears. I The am additional not sure Iprocesses: want to investigates-wave annihilation this ψψwhole→ e+ tuninge− through situation, a virtual andφ,andalso there is aψψ reasonable→ φφφ if question kinematically where allowed, we would are too like to stop. weak in comparison with the p-wave annihilation5 ψψ → φφ to affect the constraints discussed above. In principle, with an extended5 Higgs sector, φ could also mix in a 12 8 2GF = nn L n (47) p2 ⇥ ⇥ ⇥ 1 1 ✏ = D 2 m2 2 V 2 + m2 V 2 V F (48) L | µ | | | 4 µ⌫ 2 V µ 2 µ⌫ µ⌫ 1 2 1 2 2 = (i@ m ) + S + (@ S) m S AS(H†H)(49) L µ µ 2 µ 2 S + Constraints ⇤ o↵ shell darkfrom photon flavore edecay (50) ! ! • Best constraints come from the Kà p nn (low mass, Brookhaven + + S + S ... (e e )+(e e )(51) exp, to be superseded! by! NA62!), and from search of di-muons peaks in B à K µµ at the LHCb. 1 1 2 2 22 -7 • Currently (Higgs.... (mixing@µS) angle)mSS <+ 2S×✓10(yf fffrom+ ... Kaons)(52) and similarly ! 2 2 and even better from LHCb. h @ m tt 1+ H.peng. ( p) SelfEnergy(m /m )(53) t ! S ! ⇠ · @v t W ✓ ◆ • To be topical, constraints on the axial vector couplings of light @ vectors is very strongSelfEnergy( = longitudinalmt/mW mode)=0? does not decouple, and (54) you are looking at@v the emission of a Goldstone enhanced by 2 (mB/mX) . g 17 MeV axial < 0.1 1(55) 10 6 ⇥ m ✓ X ◆ Normalization on 17 MeV is purely coincidental SHiP can improve many of the scalar/axial/Alps etc portal sensitivities40 5 1 Repulsive force ⇤ ⇥10 1 Attractive force ⇤X ⇥10 X 4 4 10 10 dw dw dw dw dw dw 0.1 10 1 0.1 MW 10 1 0.1 MW 0.1 ⇥ ⇥ MW 1000 MW 1000 1 1 cl 0.1 cl 0.1 cl 1 cl 1 ⇥ 100 ⇥ 100 GeV GeV X X 10 10 m m 1 1 0.1 0.1 10 4 0.001 0.01 0.1 1 10 10 4 0.001 0.01 0.1 1 m⌅ GeV m⌅ GeV 2 2 Attractive force ⇤X ⇥10 Repulsive force ⇤X ⇥10 4 4 10 dw 10 dw dw 0.1 ⇥ dw 0.1 ⇥ dw 1 dw 1 10 ⇥ 10 ⇥ 1000 MW 1000 DM with a hint on self-interaction? 0.1 MW 0.1 MW MW 1 1 cl 0.1 cl 0.1 ⇥ 100 •⇥ 100Comparison of observations and simulations seem to point to problems cl 1 cl 1 GeV GeV X 10 X 10with dwarf galaxy substructures (also known as “too-big-to-fail” problem). m m • It may or may not be a real problem (it is an astrophycist-dependent 1 1 problem). 0.1 • 0.1Self-scattering due to a dark force, at 1 cm2/g level, seems to help, as it 10 4 0.001 0.01 0.1 1 10 4 0.001 0.01 0.1 1 m⌅ GeV flattens out mcentral⌅ GeV spikes of DM (which is a reported problem). 3 3 Attractive force ⇤X ⇥10 Repulsive force ⇤X ⇥10 104 104 dw dw dw 0.1 ⇥ 0.1 ⇥ 1 dw 1 dw 10 ⇥ dw ⇥ 1000 1000 10 Example of parameter space that creates a MW 0.1 MW 0.1 MW core and solves the problem (from Tulin, Yu, 1 MW 1 ⇥ 100 ⇥ 100 cl 0.1 cl 0.1 Zurek) for ad = 0.1 GeV GeV cl 1 cl 1 X 10 X 10 m m Some of the parameter space is within reach 1 1 of B-factories. 0.1 0.1 10 4 0.001 0.01 0.1 1 10 4 0.001 0.01 0.1 1 41 Mediator mass, GeV m⌅ GeV m⌅ GeV FIG. 6: Parameter space consistent with⇥ astrophysical bounds for attractive (left) and⇥ repulsive (right) poten- tials for different X . Blue regions show where DM self-scattering solves small scale structure anomalies, while red (green) show bounds on Milky Way (cluster) scales. Numerical values give ⇥ /m in cm2/g T ⇥ X on dwarf (“dw”), Milky Way (“MW”), and cluster (“cl”) scales. See text for details. 16 2 As discussed in the introduction, su⇡ciently strong SM particles via kinetic mixing. These decays are all dark interaction strength and light dark photon will re- prompt for the relevant region of parameter space. The sult in the formation of dark matter particles (↵↵¯). The above decay chain eventually results in the final states 1 PC + 3 two lowest (1S) bound states, S0 (J =0 )and S1 containing six charged tracks, which can be electrons, J PC =1 ⇧ ⇤ ( ), will beCALT-TH-2015-051 called D and D,respectively. muons or pions, depending on the dark photon mass. The condition for their existence has been determined nu- We turn to the calculation of ⇤D production via ini- Probing the Dark Sector with Dark Matter Bound2 States 2 merically [26] , 1.68mV < Dm⌃, with D = gD/(4 ). tial state radiation (Fig. 1). In the ⇤D rest frame, the Haipeng An,1 Bertrand Echenard,2 MaximTheir Pospelov, quantum3, 4 and Yue numbers Zhang1 suggest the following production non-relativistic expansion can be used, taking the dark 1 im t T Walter Burke Institute for Theoretical Physics, Californiamechanisms Institute of Technology, at colliders: Pasadena, CA 91125 matter field in the form: ↵ = e [ , ⌦ p/(2m⌃) ] + 2California Institute of Technology, Pasadena, California 91125 · 3 im t T Department of Physics and Astronomy, University of Victoria, Victoria, BC, V8P 1A1 Canada e [⌦ p/(2m⌃)⌅, ⌅] , where , ⌅ are the 2-spinor an- 4 + + Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada · e e ⇧D +V ; e e ⇤D +⇥; p+p ⇤D +X (2) nihilation (creation) operators for particle (antiparticle). AmodelofdarksectorwhereO(few GeV)Darkmass dark matter matter particles⌃ ⌃ are bound supplied by a lighter⌃ states at ⌃B-factories dark force mediator V , mV m ,ismotivatedbytherecentlydiscoveredmismatchbetween We use the relation between matrix element and wave simulated and observed shapes of galactic haloes. SuchThe models, last in general, process provide represents a challenge for the direct production of ⇤D direct detection e⇣orts and collider searches. We show that for a large range of coupling constants function [30], • If ad > 0.2,from the subqq¯ fusion.-5 GeV+ AllDark production matter can processes increase the are sensitivity mediated to by dark force and masses, the production and decay of the bound states of ⌃,suchas0 and 1 states, ⇤D + and D,isanimportantsearchchannel.Weshowthatvia productione e of ⇤“darkD⇥+ V Vor Upsilon” D + ⇥ production that decays producing multiple charged particles amixed⇥ propagator, as shown in Fig. 1. µ 1 µ at B-factories for D > 0.1 is su⌘ciently strong to result in multiple pairs of charged leptons and + + 0 ⌅†⌦ ⇤D = R D (0) , (5) pions via ⇤D 2V 2(l l ) and D 3V 3(l l )(l = e, µ, ⇧).Theabsenceofsuch D ⇥ ⇥ ⇥ ⇥ ⌦ | | ↵ 2 final states in the existing searches performed at BABAR and Belle sets new constraints on the ⌃ parameter space of the model. We also show that a search for multiple bremsstrahlung of dark force µ + mediators, e e ⌃⌃¯ + nV , resulting in missing energy and multiple leptons, will further improve where is the polarization vector of ⇤D and R D (0) ⇥ D the sensitivity to self-interacting dark matter. ⌥ R⇤D (0) is the radial wave function at origin. Taking into account the kinetic mixing between dark photon and the Introduction. Identifying dark matter is an open ques- interacting dark matter within the kinematic reach of ex- tion of central importance in particle physics and cos- isting colliders provides opportunities for the new search photon,4 we derive the e⇠ective kinetic mixing term be- mology. In recent years, the paradigm of weakly inter- channels. We outline such possibilities in the minimal tween ⇤D and the photon, acting dark matter supplied by a new force in the dark setup where the dark force carrier also mediates the in- sector came to prominence [1, 2], motivated by a vari- teractionFIG. between 1. Diagram dark matter for and theD and SM particles.D production A and decay at 1 µ⇧ D ety of unexplained astrophysical signatures. It was later lightB mediator-factories. gives an attractive force between ⇤ and ⇤¯ e⇥ = ⌥⌥DFµ⇧ ⇤D , ⌥D = 3 R D (0) . (6) shown [3, 4]thatthismodelprovidesthebestrealization particles, leading to the formation of bound states, which L 2 2m⌃ of self-interaction dark matter [5], and helps to alleviate can be produced on-shell at colliders 1. In addition, the ⌃ tensions between observed and simulated shapes of dark productionIn order of continuum to obtain⇤⇤¯ leads to the final rate state radiation for the first process in (2), In the limit mV Dm⌃,theterm⌥D reduces to ⌥D = matter haloes (see, e.g. [6]). (FSR) of light mediators. Both channels typically result+ ⇧ we calculate the amplitude of e e ↵↵¯V with ↵, ↵¯ 2 /2.Weobtainadi⇠erential cross section: It is of great phenomenological interests to check in a striking multi-lepton final state, that can be searched ⌃ 2 2 D B p p = m whether such a dark force could be probed in labora- for athaving-factories the and same fixed target four experiments. momentum It is well(with ⌃), and known that heavy flavor mesons and heavy quarkonia 2 2 2 2 tories. The simplest way for dark matter to interact + 4m apply the projection operator, d⌦e e D 2 ⌥ ⌥D ⌃ with the standard model (SM) sector is through a vector were instrumental for uncovering a wealth of information ⇥ 1 or scalar mediators coupled to the SM fields via the ki- about the SM. Similarly, should a dark force exist, the d cos ⌃ ⌥ s s ⇥ netic mixing or the Higgs portals. For dark3 matter pairs heav- ofFIG. charged 2. aforementionedLeft: Constraint particles on channels the darkappear photon may1 parameterallow“for forfree” space genuine fromonce teststhe BUpsilon_darkAB ofAR dark Higgsstrahlungis produced. searches, adapted This to the is production and decay of dark bound states ⇥D and D.ThesolidpurplecurvecorrespondstothecurrentBABAR limit for the the detailed⇥ content⇤ = of the dark sector.R⇤D (0)(p + m⌃)⇥5(p m⌃) , (3) 2 2 4 2 ier than 4-5 GeV, direct detection experiments provideparameters D =0.5, m =3.5 GeV. The dashed3 purple curve shows the future reach of B-factories. Right:Currentconstraints 8s (s + 16m )sin ⌃ limited by previous searches of32 “dark m⌃ Higgsstrahlung2 7 ” by BaBar and Belle. An, ⌃ on the mDark mV matterplane for bound the SIDM⌥ states scenario production. are shown with We⇤ =10 illustrate and di erent values of D.Thegreen(blue)regionis the strongest constraints on such models. High-energy 42 1 , (7) favored for SIDM solving the galactic small-scale structure problems [3] for D =0.3(0.5).Thecombinedconstraintsviathe 2 2 2 2 collider probes typically require more e ectiveEchenard produc-+ , MP,these Zhang ideas in, thePRL, well-studied 2016 example of the vector me- + ⇤ e e (⇥DV, D) 3V channels are shown in thick purple curves, and the constraints via the e e ⌅⌅¯ +3V channel ⇤(s 4m⌃) (s +4me (s 4me) cos 2⌃) ⌅ ⇥ ⇥ ⇥ tion channels [7–11]. For dark matter lighter thanare 4- showndiator into thin model. select blue curves. The the AllowedLagrangian⇧D regionsbound for are dark in state the matter arrow [28 direction. and]. dark We Assuming find no a SM leading-order background, the constraints via + 5GeV,thelimitsfromdirectdetectionexperimentsarisethe e e photon⌅⌅¯ +2 isV channel are shown in dot-dashed black curves for D =0.3, 0.4, 0.5 (bottom-up). The brown region is ⇥ excluded by CDMSlitedi⇠erential [37]andLUX[ cross38]. The section: region mV 30 MeV is ruled out by the XENON10 electron recoil analysis [39where] ⌃ is the the angle between ⇥ and the initial e in from electron recoil and are much weaker. In this mass µ for D =0.3. = SM +¯⇤i (⌃µ igDVµ)⇤ m⇤⇤⇤¯ arXiv:1510.05020v1 [hep-ph] 16 Oct 2015 range, strong CMB constraints on dark matter annihi- L L 2 2 2 2 the CM frame. In the denominator, the electron mass + 1 ⇥ 1 lation naturally point to particle-antiparticle asymmetry d⌦e e ⇤Dµ⇥V 4 µ ⇥ D⌥2 [Rµ⇤D (0)] (1 + cos ⌃) 3 V⇥µ⇥ V =Fµ⇥ V + mV VµV , (1) p , (4) must be retained in order to regularize the ⌃ integral, as in the dark sector. Constituents of such a dark sector,beams, the most importantd cos4 ⌃ production 2 channel is2 from3/2 current uncertainties2 2 in estimating2 the background, we the quark-anti-quark fusion, qq¯ D.Generalizingcal-m⌃s (srefrain4 fromm⌃ showing+ mV the) potential| reach| of proton ex- light dark matter and a light mediator, can be searched ⇥ ⇤ for me =0the cross section is divergent in the forward culationswhere of [42], theis productionthe kinetic cross mixing section between is given bythe photonperiments and in Fig. 2,notingthatinanycase,itwould for in meson decays [12], fixed target experiments [13], the vector field V . The dark matter particle ⇤ is a Dirac 2 2 2 1 not cover the most interesting region for SIDM, namelydirection [31]. mono-photon events at colliders [14], or via the produc- where4⌅ ⇥ ⇥D⌃ is2 thedx angle between ⇧D and the ini- fermion, neutral under the SM gauge group, butmV charged< 200 MeV. ⇧pp(n) D = Qq + + tion/scattering sequence in proton [15]andelectron[16] ⇥ s x under the darke U(1)q D interaction⌅ that has a newOutlook. vectorAmong the various probes of dark sectors sug- Compared to the e e ⇧DV process, the e e beam dump experiments, or perhaps via new galactic tial ⇤in the center-of-mass (CM) frame, and ⌃ ⌃ particle Vµ (sometimes⌃ called a "dark⌃ photon")gested as a force and conducted in recent years, only a few are fq/p(x)fq/p¯ (n) + fq/p¯ (x)fq/p(n) , (10) ⇥⇤D cross section is suppressed by a factor / D,al- substructures and minihalos [17]. Most of the existing carrier.p isx the spatialx momentumsensitive to both of the dark⇧D force, andp dark matter= at the ⇧ ⇥ ⇥⌃ searches of light particles [18]areinsensitivetodarkmat- | 2| 2 same time. We have2 pointed out that| | in case of relativelythough the latter contains a logarithmic enhancement where ⌃ = mV[/ss, fq/p(2(n) mand⌃ f+q/p¯ (mn) areV ) the][ relevants (2m⌃ mV ) ]/(2 s).We ter with m⇤ >mmediator,andthereforewouldnotbeable strong self-interaction, the presence of dark force greatly structure functions for this process, and Qq is the quark from the angular integral. Moreover, the cross-section to establish any candidate signal as coming specificallycharge in unitsneglect of e.Unlike theB-factories, binding only muonic energy de- forfacilitates⇧D,andset the discoverym of the⇤D entire2 sector,m⌃. as it leads from the dark force carrier. ⇧ 3V 3(µ+µ ) to the formation of dark bound states,⌥ and causes dark+ 2 cays of dark1 Weakly bound coupled states, suchdark as matterD bound states have , been studied in e e ⇧DV contains an additional m⌃/s factor, which An analytic⇤ form⇤ for R⇤DFSR(0) radiation,thewavefunctionat that decay into multiple charged parti- In this Letter,weshowthatthepresenceofself-constitutevarious a useful contexts signature, [19–25 as]. backgrounds in other ⌃ channels are likely to be too large. The multi-dark pho- cles of the SM. The existing searchesV at(rB)=ABAR and Bellebrings additional suppression of lighter dark matter. For origin, is obtained using thealready Hulthén limit this potential possibility, and further advance in sen- ton FSR channels can also⇥r be relevant for⇥r the proton 2 sitivity can be made by searching for the missing energy D 0.1 and m⌃ s,thetwoprocesseshavesimilar beam experiments. D⇤e /(1 e ) with ⇤ =( /6)mV , which is ⌅ Among the possible candidates of proton-on-target ex- plus pairs of charged particles. cross-sections, and we will combine them to set the limit periments, weknown focus our asdiscussion a good on SeaQuest approximation [43]and Acknowledgement. of theWe Yukawa would like to poten- thank Cli!ord Che- the planned SHiP [44]facilities.NotethatonlyafixedmV r ung, Ying Fan, Ming Liu, Mark Wise and Hai-bo Yuon this model. tial V (r)= De /r [29]. In that case, R⇤D (0) = target mode of operation, rather than3/2 a beam dump for useful discussions. H.A. is supported by the Wal- mode that would try2 to remove2 1/2 prompt muons, is suit- ter Burke Institute at Caltech and by DOE Grant de- The ⇤D particle will subsequently decay into three (4 ⇤ a0) a0 , where a0 =2/( Dm⌃). able for the search of D.Takingapointintheparam- sc0011632. B.E. is supported by the U.S. Department 2 7 dark photons. We calculate the di⇠erential decay rate eter space, m⇥ The=2GeV, scalar⇥ = 10 bound , mV = state 300 MeV,⇧D ofdominantly Energy (DoE) under decays grant DE-FG02-92ER40701 into two and D =0.5 and the energy of incoming proton beam DE-SC0011925. Y.Z. is supported by the Gordon andfollowing the approach in Ref. [28]bygeneralizingitto of 400 GeV,dark we estimate photons, a probability each of producing subsequently a Betty Moore decaying Foundation into through a pair Grant #776 of to the + D decaying to 3(µ µ ) for a 1 mm tungsten target, Caltech Moore Center for Theoretical Cosmology andthe massive dark photon case, 17 20 P = n⇧⇣ 2 10 .WithO(10 ) particles on tar- Physics, and by the DOE Grant DE-FG02-92ER40701, ⇥ get, one could potentially expect up to 2 103 six muon and also by a DOE Early Career Award under Grant No. 3 2 d (⇤D 3V ) 2 [R (0)] events. The large multiplicity of signal events gives some DE-SC0010255. H.A., M.P. and Y.Z. acknowledge the ⌃ = D D hope that this signal could be extracted from large num- hospitality from the Aspen Center for Physics and the 2 2 dx1dx2 3 m⌃ ber of muons producedIt is known per each that proton too spill. large Given↵ theD wouldsupport run from to NSF the Grant Landau #PHY-1066293. pole very 8 6 4 2 quickly at higher scale [27]. Hereafter, we focus on ↵D 0.5, 39x +4x F6 16x F4 + 32x F2 + 256F0 ,(8) and work with leading-order results in ↵D. ⇤(x2 2x )2(x2 2x )2(x2 + 2(x + x 2))2 1 2 1 2 Pushing down the sensitivity to energy deposition in direct detection • In the last few years there has been a push to extend the sensitivity of direct detection to very light dark matter, and go below the 1 keV energy deposition scale Ionization, Large direct detection Large neutrino E > few eV, th experiments experiments E >200 102/kg/day/keV th E >1keV counting keV counting rates at th -2 rates ~ 10-2/kg/day/keV ~ 10 /ton/day/MeV for E ~ few keV for E ~ few MeV Active field of exploration, starting from Essig, Mardon, Sorensen, Volansky … 43 3 that if mechanisms (a) and (b) are the only sources that equation of motion sets the time-component of V to zero, populate the DM, they are not going to be compatible V 0 = 0. The spatial components may still have an arbi- with cold dark matter when mV keV. trary value and direction, and in a Friedman-Robertson- For mechanism (a), naive dimensional analysis sug- Walker Universe with scale factor a(t), the equations for 2 2 gests a dark photon interaction rate int ⇥ ne/⌦s, V = V /a are equivalent to those of a massive scalar field, ⌅ i i where ne is the electron number density and ⌦s is the centre-of-mass energy. At temperatures T me,where ¨ ˙ 2 ⌥ ⌥ V i +3HV i + mV Vi = (interactions). (4) the number density of charge carriers is maximal, ne T 3, this production rate scales linearly with temperature,⌅ 2 For 3H ⌥mV , the⌥ evolution⌥ in (4) is overdamped and whereas the Hubble rate is a quadratic function of T .It ⌥ Vi is frozen at its initial value VI,i. In the simplest case, follows that for sub-MeV mass dark vectors, the ther- mV is a ‘hard’, T -independent St¨uckelberg mass for the mal production of V is maximized at T me. However, dark⌥ photon and interactions⌥ with the plasma can be simple parametric estimates of this kind⌅ may require re- neglected. If so, the field remains frozen until 3H(Tosc)= finement due to matter e⌅ects that alter the most naive mV when it starts to oscillate around the origin. The picture. At finite temperature T ,thein-mediume⌅ects energy density, can be cast into a modification of the mixing angle, “Very Dark Photon”1 ˙ 2 dark matter m4 ⌅ = V + m2 V 2 , (5) ⇥2 = ⇥2 V , (2) V 2 i V i T,L ⇤ m2 ⇥ 2 ⇤ ⌅ -13 | V T,L| • Very weakly coupled dark photons (e.g. e ~ 10 ) can be dark matter ⌥ ⌥1 2 2 in sub-takeseV regime the initial due to value misalignment⌅V (Tosc) mechanismmV VI,i and or conse- in the keV where ⇥T,L(⇧, ⇠q ,T) are the transverse (T) and longi- ⇧ 2 tudinal (L) polarization| | functions of the photon in theregimequently due to redshiftsmisalignment with the + thermal scaling law emission. for nonrelativistic If couplings are matter. The corresponding present-day energy density isotropic primordial plasma. They depend on photonsmall, en- it is not going to be re-thermalized. ⌥ ergy ⇧ and momentum ⇠q and their temperature depen- parameter is then readily found to be, | | 2 dence is exposed by noting that Re ⇥T,L ⇧P where 2 3/4 ⇧ is the plasma frequency; for the cases of interest 2 g (Tosc) mV VI,i P ⇤V h 0.4 11 . (6) Im ⇥T,L Re ⇥T,L. ⇧ g (T ) 1 keV 10 GeV S osc ⇧ ⌃ The consequences⌃ of these in-medium e⌅ects are two- ⌥ fold. First, at high temperatures, they suppress the Undoubtedly, interactions between dark photons and mixing angle since ⇧2 T 2 (in the relativistic limit), the plasma are present, and the evolution of the vector- P ⌅ thereby diminishing contributions to thermal production• If mV § Vectors are long-lived if mV < 2 me. V has to decay to 3 photon via the light-by-light loop diagram: The g-background constraints are weak. (No monochromatic lines) 45 Can be viable DM model: MP, Ritz, Voloshin; Redondo, Postma “Super-WIMP” DM absorption signal An, MP,Pradler, Ritz, PRD 2014, Bloch et al (Tian-Tian Yu) 2 10−12 10−13 κ sun HB −14 10 RG kinetic mixing 10−15 XENON10 XENON100 XMASS diffuse γ CMB 10−16 1 101 102 103 104 105 106 mV (eV) FIG. 1. Asummaryofconstraintsonthedarkphotonkineticmixingparameter κ as a function of vector mass mV (see Secs. 2 and 3 for the details). The thick lines exclude the region above fordarkphotonswithdarkmatterrelicdensity.Thesolid(dashed) line is from XENON10 (XENON100); the limitLarge from XMASS DM is taken experiments from [21]. The dash-dotted can lines showcompete our newly derived with constraints stellar on the constraints and have diffuse γ-ray flux from V → 3γ decays, assuming that decays contribute 100% (thick line) or10%(thinline)totheobservedflux.The-15 thick dotted line is the correspondingsensitivity constraint from CMB to e nergymixing injection. Shadedangles regions depictdown (previously to conside ~10ered) astrophysical. (unfortunately, e = 0 is constraints that are independent of the dark photon relic density. The limits from anomalous energy loss in the sun (sun),horizontal 46 branch stars (HB), and red giantalso stars (RG) ok) are labeled. The shaded region that is mostly inside the solar constraint is theXENON10 limit derived from the solar flux [27]. careful analysis of the ‘ionization-only’ signal available strengths Vµν and Fµν is the most relevant, to a variety of DM experiments. Many experiments have already reported relevant analyses [14–21]. 1 1 κ m2 = F 2 V 2 F V µν + V V V µ + eJ µ A , The rest of this work is organized as follows. In Sec. 2 L −4 µν − 4 µν − 2 µν 2 µ em µ we introduce the dark photon model in some more detail, (1) describe existing constraints, and reconsider indirect lim- µ its. In Sec. 3 we compile the relevant formulæ for direct where Jem is the electromagnetic current and mV is the detection, confront the model with existing direct detec- dark photon mass. This model has been under signif- tion results and derive constraints on the mixing angle icant scrutiny over the last few years, as the minimal κ. The results are summarized in Fig. 1, which shows realization of one the few UV-complete extensions of the the new direct detection limits in comparison to various SM (portals) that allows for the existence of light weakly astrophysical constraints. In Sec. 4, we provide a gen- coupled particles [23]. For simplicity, we will consider eral discussion of super-weakly coupled DM, and possi- the St¨uckelberg version of this vector portal, in which ble improvements in sensitivity to (sub-)keV-scale DM mV can be added by hand, rather than being induced particles. via the Higgs mechanism. 2.1. Cosmological abundance 2. DARK PHOTON DARK MATTER Light vector particles with mV < 2me have multi- It has been well-known since 1980s that the SM allows ple contributions to their cosmological abundance, such for a natural UV-complete extension by a new massive or as (a) production through scattering or annihilation, massless U(1)′ field, coupled to the SM hypercharge U(1) γe± Ve± and e+e− V γ, possibly with sub-Hubble via the kinetic mixing term [22]. Below the electroweak rates,→ (b) resonant photon-dark→ photon conversion, or scale, the effective kinetic mixing of strength κ between (c) production from an initial dark photon condensate, the dark photon (V )andphoton(A) with respective field as could be seeded by inflationary perturbations. Notice Sensitivity to light weakly-coupled new physics at the precision frontier Matthias Le Dall,1 Maxim Pospelov,1, 2 and Adam Ritz1 1Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 5C2, Canada 2Perimeter Institute for Theoretical Physics, Waterloo, ON N2J 2W9, Canada (Dated: May 2015) Precision measurements of rare particle physics phenomena (flavor oscillations and decays, electric dipole moments, etc.) are often sensitive to the e⇥ects of new physics encoded in higher-dimensional n operators with Wilson coe⇧cients given by C/( NP) , where C is dimensionless, n 1, and NP ⇥ is an energy scale. Many extensions of the Standard Model predict that NP should be at the electroweak scale or above, and the search for new short-distance physics is often stated as the primary goal of experiments at the precision frontier. In rather general terms, we investigate the alternative possibility: C 1, and NP mW , to identify classes of precision measurements sensitive to light new physics⌅ (hidden sectors)⌅ that do not require an ultraviolet completion with additional states at or above the electroweak scale. We find that hadronic electric dipole moments, lepton number and flavor violation, non-universality, as well as lepton g 2canbeinducedat interesting levels by hidden sectors with light degrees of freedom. In contrast, many hadronic flavor- and baryon number-violating observables, and precision probes of charged currents, typically require new physics with NP > mW . Among the leptonic observables, we find that a non-zero electron electric dipole moment⇤ near the current level of sensitivity would point to the existence of new physics at or above the electroweak scale. 1. INTRODUCTION The sensitivity of any constraint on new physics is de- termined on one hand by the precision of the measure- Accelerator-based particle physics has the goal of prob- ment in question, and on the other by the accuracy and ing the shortest distance scales directly, by colliding par- precision of any SM calculations required to disentangle ticles and their constituents at high energies. Thus far, background contributions. If the e⇥ective Lagrangian is schematically written in the form = + , all high energy data is well described by the Standard L LSM LNP Model (SM) of particles and fields, with the last missing the possibility of discovery relies on being able to reli- element, the Higgs boson, identified recently [1, 2]. Con- ably bound the NP contribution to the observable away siderable attention is therefore focussed on the search from zero. The natural tendency to interpret results in for ‘new physics’ (NP) that may complement the SM terms of operators in NP induced by ultraviolet NP can be problematic, asL can in general also receive by addressing some of its shortcomings. However, the LNP most prominent empirical evidence for new physics, asso- contributions from light weakly-coupled degrees of free- ciated for example with neutrino mass and dark matter, dom. This dilemma is nicely illustrated by the theoret- does not necessarily point to an origin at shorter distance ical interpretation of a NP discovery that has already scales. occurred, namely the observation of neutrino flavor os- New physics:cillations. The UV experimental or IR? results(let’s say are IR/UV most boundary straightfor- ~ EW scale) Fortunately, experiments at the energy frontier are wardly interpreted in terms of the masses and mixing of not the only tools available to probe NP; they are sup- the light active neutrino species [8, 9]. However, as is plemented by searches at the precision (and intensity)Neutrino oscillations: We know that new phenomenon exists, and if interpretedwell known, as neutrino there aremasses a number and mixing, of possible is it explanations coming from deep frontier (see e.g. [3]). Precision observables, particularly for their origin. These include a short-distance expla- those that probe violations of exact or approximate sym-UV, vianation e. .g in Weinberg’s terms of the operator dimension-five Weinberg operator metries of the Standard Model such as CP and flavor, [10], NP (HL)(HL)/ UV with UV H ,which play an important role in the search for new physics [4– L ⇤ ⇥⇧2 ⌃ or it is generatedgenerates by neutrino new IR massesfield, such scaling as RH as Hcomponent/ UV.There of Dirac 7]. Their reach in energy scale, through loop-induced are also a variety of di⇥erent UV completions⇧ ⌃ for this corrections from new UV physics, can often extend wellneutrinos?operator, with and without heavy right-handed neutrino beyond the direct reach of high energy colliders. How- states, present throughout the theory literature. While ever, measurements at low energies may be sensitive not Dark matterthis interpretation: 25% of Universe’s is certainly energy valid, balance there is is also in dark the pos- matter: only to NP corrections coming from the short distances, sibility of interpreting neutrino mass as a consequence of but also to NP at longer distances (lower mass) with ex-we can set constraints on both. If it is embedded in particle very light states N,withmN mW and the quantum tremely weak coupling to the SM. It is therefore prudentphysics,numbers then e.g. of right-handed neutralinos or neutrinos axions [11–16].imply new Such UV states scales. to ask for which precision observables can measured devi- would typically be very weakly coupled to the SM, thus ations from SM predictions unambiguously be identifiedHowever, there are models of DM where NP lives completely in the IR, andescaping no new direct scales detection. are necessary The most. prominent model in with short-distance NP at the electroweak (EW) scale this class is the simple three-generation extension of the or above? Alternatively, one can ask when such devia- SM with N states that allow Dirac masses for the active tions might also admit an interpretation in terms ofBoth new optionsneutrinos. deserve Thus a close we see look. that In neutrino particular, oscillations light and can very be weakly low-scale hidden sector degrees of freedom. This is thecoupledinterpreted states are as often the result overlooked, of UV but or IRdeserve new physicsattention (or. 47 question we will address in this paper. Conclusions 1. Light New Physics (not-so-large masses, tiny couplings) is a generic possibility. Some models (e.g. dark photon or dark Higgs- mediated models) are quite minimal yet UV complete, and have diverse DM phenomenology. 2. Sub-GeV WIMP dark matter can be searched for via production & scattering or missing energy. New results from NA64, BaBar, MiniBoone are all less than few months/weeks old. No signal, improved constraints. SHiP will improve on that. 3. Search for mediators (diversifying away from dark photon) benefit significantly from flavor searches. In some cases, bound states of DM enhance sensitivity reach to mediators. CERN plays important role in these searches! 4. Taking direct detection below keV energy thresholds seriously allows probing sub-GeV masses of WIMPs and break into the super-weakly interacting DM territory probing freeze-in dark matter, absorption of DM particles etc. 48 On-going and future projects Fixed Target/beam dump experiments sensitive to § Dark Photons: HPS, DarkLight, APEX, Mainz, SHiP… § Light dark matter production + scattering: MiniBoNE, BDX, SHiP… § Right-handed neutrinos: SHiP § Missing energy via DM production: NA62 (Kàpnn mode), positron beam dumps… § Extra Z’ in neutrino scattering: DUNE near detector (?) 49 SHiP sensitivity to vector and scalar portals § SHiP will collect 2 × 1020 protons of 400 GeV dumped on target § Sensitivity to dark vectors is via the unflavored meson decays, and through direct production, pp à… V à…… l+l- § Sensitivity to light scalar mixed with Higgs is via B-meson decays, b à s + Scalar à … µ+µ- Visibly Decaying A' 10 4 g⇥2 ⌅ ⇤ 5⇧ 10 6 g⇥2 ⌅ 2⇧ ⇥ g⇥2 e E774 BaBar, NA48 2, PHENIX 8 ⇥ 10 E141 ⇥ SHiP, ⇤ 10 10 Orsay, U70 bremsstrahlung ⇥2 SHiP, 10 12 QCD Charm, Nu⇥Cal 10 14 E137, LSND 10 16 SN SHiP, 10 18 mesons 10 20 1 10 102 103 mA' MeV 7 50 Figure 5: Summary ofDetails constraints can on the be dark found photon in model. the The white limits atpaper,⇥ 10 1505.01865,; mA > Alekhin et al. 200 MeV range come from old experiments, and can be⇥ improved with SHiP. The⇤ g 2region of interest is shown as a green band. The projected SHiP sensitivity contour is derived using three modes of production: mesons, bremsstrahlung, and QCD production. (B) V was derived in [33]. The full analysis of constraints on (B),mV plane has not been performed yet. { } Some cases of other exotic particles produced in association with V have been constrained in experiment. BaBar studies have placed limits on dark Higgsstrahlung [124], by exploiting A⇥h⇥ production with subsequent decays of h⇥ to 2A⇥ and eventually to pairs of charged SM 4 particles. The ensuing constraints are quite strong (reaching down to ⇥ few 10 at ), but applicable only to m > 2m region of parameter space.⇤ Another⇥ study D ⇤ h A at KLOE [125] have searched for missing energy signature from h⇥ decays outside of the 3 detector, and reached the constraints at the level of ⇥ few 10 . Constraints on the most ⇤ ⇥ motivated case, mh mA ,aremoredi⇥cult to obtain because they involve stable h⇥ on the scale of the detector.⇧ 5.2 Production and detection of light vector portal DM New constraints on vector portals occur when direct production of light dark matter states + ⇧ opens up. The missing energy constraints on dark photons derived from e e colliders + were analyzed in [50]. Invisible decays of A⇥ are usually harder to detect, except K + + + + ⌅ ⌅ A⇥ ⌅ +missing energy, where the competing SM process, K ⌅ ⇤⇤¯ is extremely suppressed⌅ [49]. Also, fixed targets experiments sensitive to the missing⌅ energy decays of vector states have been proposed recently [126, 127]. 20