Dark Photon and Dark Matter: theoretical motivations

Maxim Pospelov Perimeter Institute, Waterloo/University of Victoria, Victoria Lepton-photon meeting, 2015

1 Outline of the talk

1. Introduction. Portals to light new physics. 2. Model of dark photon and “millicharged” particles. 3. Connections to anomalies: Particle physics: g-2, proton charge radius, new anomalies at the LHC ? Astro: 511 keV, Pamela/ Fermi/AMS-2 positron rise, “too-big-to-fail”. 3. Detecting light dark matter in the beam dump experiments and neutrino experiments. 4. Conclusions

2 Big Questions in Physics

“Missing mass” – what is it? New particle, new force, …? Both? How to find out? (History lesson: first “dark matter” problem occurred at the nuclear level, and eventually new particles, neutrons, were identified as a source of a “hidden mass” – and of course immediately with the new force of nature, the strong interaction force.)

Intensity and Energy Frontiers

Log αX Energy Frontier -1 SM corner αSM -2 α X = G m2 Fermi unknown X forces Log mX 100 GeV Intensity Frontier

!X !X !X V(r) = exp(!r / "X ) = exp(!rmX ) ""#Amplitude $ 2 2 r r q + mX

Exploring this plot in the downward direction requires large intensities. It also requires a framework of how to describe “progress”4 Neutral “portals” to the SM Let us classify possible connections between Dark sector and SM H+H (λ S2 + A S) Higgs-singlet scalar interactions (scalar portal)

Bµν Vµν “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 ……….

5 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 effects of new physics encoded in higher-dimensional n operators with Wilson coefficients given by C/(ΛNP) , where C is dimensionless, n 1, and ΛNP ≥ is an energy scale. Many extensions of the Standard Model predict that ΛNP 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 ΛNP 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 ΛNP > 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 effective 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)/ΛUV with ΛUV 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/ΛUV.There of Dirac 7]. Their reach in energy scale, through loop-induced are also a variety of different 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- However,would there typically are models be veryof DM weakly where coupled NP lives to thecompletely SM, thus in the ations from SM predictions unambiguously be identified escaping direct detection. The most prominent model in with short-distance NP at the electroweak (EW) scaleIR, and no new scales are necessary. 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 physics attention (or. 6 question we will address in this paper. 1.1 Kinetic mixing 1.1 Kinetic mixing

ConsiderConsider a QED-like a QED-like theory theory with with one one (or (or several) several) extra extra vector vector particle(s), particle(s), coupled coupled to the to the electromagneticelectromagnetic current. current. A mass A mass term, term, or or in in general general a a mass mass matrix matrix for for the the vector vector states, states, is is protectedprotected against against additive additive renormalization renormalization due due to to the the conservation conservation of of the the electromagnetic electromagnetic 2 2 current.current. If the If mass the mass matrix matrix for for such such vector vector states states has a a zero zero determinant, determinant, det( det(MV )=0,thenMV )=0,then the theorythe theory contains contains one one massless massless vector, vector, to to be be identified identified with with a a photon, photon, and and several several massive massive vectorvector states. states. This is thee model of ‘paraphotons’, introduced by Okun in early 1980s [6], that can be This is the model of ‘paraphotons’, introduced by Okun in early 1980s [6], that can be reformulated in equivalent language using the kinetic mixing portal. Following Holdom [7], reformulated in equivalent language using the kinetic mixing portal. Following Holdom [7], one writes a QED-like“Simplified theory withγ twomodel”U(1) groups, for supplemented dark sector by the cross term in the one writeskinetic a Lagrangian, QED-like theory and a mass with term two forU(1) one groups, of the vector supplemented fields. by the cross term in the kinetic Lagrangian, and a mass term for(Okun one￿ ’, ofHoldom the, vector…) fields. ￿ 1 2 2 = ψ,A + χ,A FµνF ￿ + m (A￿ ) . (1.1) γ ￿ µν A￿ µ L L ￿ L −￿2 21 2 2 = + F F ￿ + m (A￿ ) . (1.1) ψ,A χ,A￿ µν µν A￿ µ ψ,A and χ,A are theL standardL QED-typeL − 2 Lagrangians,2 L L χ￿ 1 ψ,A and χ,A￿ are the standard QED-type2 ¯ Lagrangians, L L ψ,A = Fµν + ψ[γµ(i∂µ eAµ) mψ]ψ Figure 1: The interaction throughL the exchange−4 by a mixed−γ A− propagator between the 1 2 ￿ = 1 F 2+ ψ¯[γ (i∂ eA− ) m ]ψ SM particles and particles χ chargedψ,A= under(F ￿ µ new)ν +¯χU[(1)γ µ(￿i∂group.µ g￿A￿ In)µ them limit]χψ, of mA 0the(1.2) LLχ,A￿ −−4 4 µν µ µ −− µ −− χ ￿ → apparent electromagentioc charge of χ1 is e￿. e 2 with Fµν and Fµ￿ ν standing= for(F the￿ ) fields+¯χ[γ strength(i∂ tensors.g￿A￿ ) Statesm ]χ, ψ represent the QED (1.2) Lχ,A￿ −4 µν µ µ − µ − χ electron fields, and states χ are similar particles,A charged– photon, under A’ ”dark”– “darkU photon”,(1)￿. In the limit In the simplest example, aγ new fermionic field charged under both U(1)’s will gener- with Fof ￿ and0, theF ￿ twostanding sectors become for the completely fields strength decoupled. tensors. In eq. States (1.1), theψ massrepresent term for theA￿ QED µν µν ￿ ψ - an electron, χ - a DM state,2 ate an additional→ contribution to the mixing angle that scales as ∆￿ g￿e/(12π ) electronexplicitly fields, breaks and states the secondγ χ areU(1), similar but is particles, protected charged from additive under renormalization, ”dark” U(1)￿ and. In hence the limit 2 2 ￿ g’ – a “dark” chargeEM ∼ × log(ΛisUV technically/M ) . In principle, natural. Using the two the sectors equations can of be motion, ”several∂ F loop= removed”,eJ , the so interaction that one term of ￿ 0, the two sectors become completely decoupled.µ Inµν eq. (1.1),ν the mass term for A￿ can→ entertaincan be rewritten aχ wide rangeas of mixing angles. explicitly breaks the second U(1), but￿ is protected from additiveEM renormalization, and hence Figure 1: The interaction through the exchange by a mixed γ A￿ propagator between the F−µνFµ￿ ν = Aµ￿ (e￿)Jµ , EM (1.3) SM particles and particles§ “Effective”χ charged under newchargeU(1)￿ group. of the In the “dark limit of msector”0the particle χ is Q = e × ε 2.is If technically both groups natural. are unbroken, Usingm the equations− 20, then ofχ represent motion,A￿× ∂ theF ”millicharged= eJ , the particles” interaction term V → µ µν ν apparentshowing electromagentioc that charge the of newχ is e vector￿. particle→ couples2 to the2 electromagnetic current with strength, canwith be electric rewritten charge(if as momentumqχ = e￿.For scalemV =0,atq > mV q). Atvector boson, plasma frequency, interacting and all processes with with the emission SM via or aborption the electromagnetic of dark current, conserves instructive features.2 chapterphotons assume decouple as￿ mV [8].1. In contrast, one does not have to assume a smallness of g￿ coupling, all discrete symmetries∼￿ (parity, flavour, CP etc). Also, importaintly, A￿ does not couple whichdirectly4. New can vector to be neutrinos.boson, comparable interacting As with a the toconsequence, SM the via the gauge electromagnetic the couplings interaction current, of conserves the strength SM, g due￿ togSM the. exchange of all discrete1. symmetries The mixing (parity, parameter flavour, CP etc).￿ Also,is dimensionless, importaintly, A￿ does and not couple therefore can∼ retain information about 2 2 2 A￿ candirectly be to taken neutrinos. to As be a consequence, stronger the than interaction that strength of weak due to the interactions, exchange of (e￿) /m ;(e￿g￿)/m the loops of charged particles at some2 2 heavy scale2 M withoutA power-like￿ decoupling.A￿ AthoughA￿ can be taken the to be model stronger than of that this of weak type interactions, is exceedingly (e￿) /mA ;(e￿g￿) simple,/mA one can already learn a￿ number of G . This property proves very useful in constructing￿ the￿ ￿ light dark matter models with instructiveF GF . This property features. proves very useful in constructing the light dark matter models with thethe use use of of vector vector portal. portal. 2 1.Although The this mixing model was parameter known to theorists￿ andis well-studied dimensionless, over the years and (e.g. Refs. therefore can retain information about Although[9,10]), a revival this of interest model to models was based known on kinetically-mixed to theoristsA￿ occurred and in well-studied last 10 years, over the years (e.g. Refs. as a responsethe to loops various astrophysical of charged anomalies, particles that this model at some allows to heavy explain in termsscale M without power-like decoupling. [9,10]),of weakly-interacting a revival of interest dark matter. to Subsequent models searches based of the on dark kinetically-mixed photon triggered new A￿ occurred in last 10 years, analyses of the past or existing experiments [11–20], and generated new dedicated experi- as a responsements in different to various stages of implementation astrophysical [21–24]. anomalies, In this chapter, we that are going this to model show allows to explain in terms of weakly-interacting dark matter. Subsequent searches2 of the dark photon triggered new analyses of the past or existing experiments3 [11–20], and generated new dedicated experi- ments in different stages of implementation [21–24]. In this chapter, we are going to show

3 Dark photon (Holdom 1986; earlier paper by Okun’)

This Lagrangian describes an extra U(1)’ group (dark force, hidden photon, secluded gauge boson, shadow boson etc, also known as U-boson, V-boson, A-prime, gamma-prime etc), attached to the SM via a vector portal (kinetic mixing). Mixing angle κ (also known as ε, η) controls the coupling to the SM. New gauge bosons can be light if the mixing angle is small. In this talk κ = ε Low-energy content: Additional massive photon-like vector V, and possibly a new light Higgs h’, both with small couplings.

8

“Non-decoupling” of secluded U(1) Theoretical expectations for masses and mixing

Suppose that the SM particles are not charged under new US(1), and communicate with it only via extremely heavy particles of mass scale Λ (however heavy!, e.g. 100000 TeV) charged under the SM UY(1) and US(1) (B. Holdom, 1986) Λ Diagram U Y (1 ) U V (1 ) does not decouple! Y S A mixing term is induced, κ F µνF µν, With κ having only the log dependence on mass scale Λ 1/2 -1 -3 κ ~ (αα’) (3π) log(ΛUV/Λ) ~ 10

MV ~ e’κ MEW (MZ or TeV) ~ MeV – GeV This is very “realistic” in terms of experimental sensitivity range of parameters.

9 Variations of vector portal: gauged B - L, Lµ - Lτ ,.. symmetries • Anomaly-free, can be UV complete.

• A non-zero kinetic mixing will be developed out of RG evolution • Neutrinos get extra interaction – already constrained!

• Lµ - Lτ is the least constrained possibility because neither electrons nor nucleons have extra interactions with neutrinos. In recent years there has been some increase of experimental activity searching for light particles in MeV-GeV range because of the following speculative motivations. 1. Light New Physics helps to solve some particle physics anomalies (muon g-2,…). 2. It helps to tie some astrophysical anomalies (511 keV excess from the

bulge, positron excess above 10 GeV etc) with models of dark matter10 without large fine tuning. Some specific motivations for new states/ new forces below GeV

1. A 1.5 decade old discrepancy of the muon g-2. 2. Discrepancy of the muonic hydrogen Lamb shift. 3. Theoretical motivation to look for an extra U(1) gauge group. 4. Recent intriguing results in astrophysics. 511 keV line, PAMELA positron rise. 5. Too-big-to-fail etc problems of CDM 6. Other motivations.

11 g-2 of muon

More than 3 sigma discrepancy for most of the analyses. Possibly a sign of new physics, but some complicated strong interaction dynamics could still be at play. Supersymmetric models with large-ish tanβ; light-ish sleptons, and right sign of µ parameter can account for the discrepancy. Sub-GeV scale vectors/scalars can also be at play. 12

MoreResults discrepancies on muonic discovered hydrogen using muons !

F =1 F =2 ν(2S1/2 → 2P3/2 ) =49881.88(76)GHz R. Pohl et al.,Nature466,213(2010) 49881.35(64) GHz preliminary

F =0 F =1 ν(2S1/2 → 2P3/2 ) =54611.16(1.04)GHzpreliminary

Proton charge radius: rp = 0.84089 (26)exp (29)th = 0.84089 (39) fm (prel.)

µp theory: A. Antogini et al., arXiv :1208.2637 (atom-ph)

µp 2012 CODATA 2010 Mainz 2010 µp 2010 H spectr. dispersion e-p scatt.

0.8 0.82 0.84 0.86 0.88 0.9 proton rms charge radius rp (fm) If newRandolf physics Pohl is responsible for that, it cannotECT* Trento, be 28.10.2012 weak scale, only very light, as rp.p 15will13 4 require ~ 10 GF effects… May be some “relative” of dark photon? κ-mV parameter space If g-2 discrepancy taken seriously, a new vector force can account for deficit. (Krasnikov, Gninenko; Fayet; Pospelov)

E.g. mixing of order few 0.001 and mass mV ~ mµ

2 ε MP, 2008

γ￿ ￿￿

α / e eff γ α

This axis is also called called is also axis This or Figure 2: One-loop correction to the muon magnetic moment due to dark photon exchange diagram.

3.1 A possibility of extra U(1)s in top-down physics, and natural range for masses and mixing angles

3.2 Putative solution to the muon g 2 discrepancy − Since 2008 a lot more of parameter space gotThe persistent constrained discrepancy of the measured muon g 2andthestandardmodel(SM) prediction at the level of 3σ [44] has generated a lot of experimental− and theoretical activity in search of a possible explanation.∼ The intense scrutiny14 of the SM contributions to the 9 g 2hasnotproducedanyobviouscandidateforanextracontribution∆ae +3 10− that− would cover a theoretical shortfall and match the observed value. Among∼ the× new physics explanations for this discrepancy are weak scale solutions [45], as well as possible new contributions from light and very weakly coupled new particles (see, e.g., [13,46,47]). With the LHC continuously squeezing the available parameter space for the weak-scale g 2- relevant new physics, solutions with light particles appear as an attractive opportunity.− It is easy to see that light vector particles coupled to muons via vector portal provide an upward correction to the g 2. In most models the new vector particle does not have an axial-vector coupling to charged− leptons, and the simple one loop diagram, Fig. 2 gives a positive correction to the magnetic anomaly

2 1 2 2 2 α g 2m z(1 z) α g 1forml mV , V ￿ l ￿ ￿ al = dz 2 2− 2 = 2π e × 0 ml (1 z) + mV z 2π e ×  2m2/(3m2 )form m . ￿ ￿ ￿ − ￿ ￿  l V l ￿ V (3.1) In this expression, g￿/e is the strength of Vµ coupling to the muon vector current in units of electric charge. For the kinetically-mixed dark photon A￿, g￿/e = ￿. For the choice of 3 ￿ few 10− at mV mµ, the new contribution is capable to bring theory and experiment in∼ agreement.× Since 2008,∼ a lot of experimental and theoretical work has been done that scrutinized this possibility. The following picture has emerged:

8 Search for dark photons, Snowmass study, 2013

A' ￿ Standard Model A' ￿ Standard Model ￿2 10￿2 10 aΜ, 5 Σ WASA KLOE ￿3 aΜ, 5 Σ“bumpsWASA KLOE in mll” 10 E774 favored BaBar aΜ,￿2 Σ APEX MAMI Test Runs ae E141 favored 10￿4 aΜ,￿2 Σ MAMI Orsay ￿ 10￿3 BaBar E774 APEX MAMI ￿5 U70 Test Runs 10 ae ￿ ￿6 CHARM DarkLight MESA 10 APEX Ε Ε ￿ ￿ VEPP￿3 7 4 E141 10 E137 10 LSND ￿8 10 Orsay HPS 10￿9 ￿5 SN ￿10 10 10 U70 ￿11 10 ￿3 ￿2 ￿1 10￿3 10￿2 10￿1 1 10 10 10 1 mA' GeV mA' GeV

-3 FIG.Dark 6. photon Parameter models space with for dark mass photons under (A￿) 1 with GeV mass, andmA ￿mixing> 1 MeV angles (see Fig. ~ 10 7 for ￿ ￿ ￿ ￿ mrepresentA￿ < 1 MeV). a “window Shown are existingof opportunity” 90% confidence for level the limits high-intensity from the SLAC experiments, and Fermilab 2 beamnot dumpleast experiments because of E137, the E141, tantalizing and E774 [116–119]positive the ~ electron (α/π)ε and correction muon anomalous to the mag- 15 neticmuon moment g - a2µ. [120–122], KLOE [123] (see also [124]), WASA-at-COSY [125], the test run results reported by APEX [126] and MAMI [127], an estimate using a BaBar result [116, 128, 129], and a constraint from supernova cooling [116, 130, 131]. In the green band, the A￿ can explain the ob- served discrepancy between the calculated and measured muon anomalous magnetic moment [120] at 90% confidence level. On the right, we show in more detail the parameter space for larger values of ￿. This parameter space can be probed by several proposed experiments, including APEX [132], HPS [133], DarkLight [134], VEPP-3 [135, 136], MAMI, and MESA [137]. Existing and future + e e− colliders such as BABAR, BELLE, KLOE, SuperB, BELLE-2, and KLOE-2 can also probe large parts of the parameter space for ￿ > 10 4 10 3; their reach is not explicitly shown. − − − string theory constructions can generate much smaller ￿. While there is no clear minimum 12 3 for ￿, values in the 10− 10− range have been predicted in the literature [140–143]. − A dark sector consisting of particles that do not couple to any of the known forces and containing an A￿ is commonplace in many new physics scenarios. Such hidden sectors can have a rich structure, consisting of, for example, fermions and many other gauge bosons.

The photon coupling to the A￿ could provide the only non-gravitational window into their existence. Hidden sectors are generic, for example, in string theory constructions [144–147]. and recent studies have drawn a very clear picture of the different possibilities obtainable in type-II compactifications (see dotted contours in Fig. 7). Several portals beyond the kinetic

21 Latest results: A1, Babar, NA48 + - Signature: “bump” at invariant mass of e e pairs = mA’Dark Matter, Hadron Physics and Fusion Physics

2 6 2 2 ε < 10− for 12 MeV/c < mA! < 55 MeV/c ,andthe '2 ε2 = 7 / 2 KLOE ee &$ ee WASA KLOE #$% ee strongest limits reach 6 10− at mA! 20 MeV c . + - + - × ≈ preliminary ) Combined with the other available data, this result rules Babar: e e à γ V à γ l l ! (3 out the DP as an explanation for the muon (g 2) anomaly, 2) e − " assuming DP couples to quarks and decays predominantly - - -5 (g A1(+ APEX): Z e à Z e V 10 into SM fermions. The performed search for the prompt A e+e de- - + - HADES ! − à Z 0 → e e e cay is limited by the irreducible πD background: the ob- (g"2) APEX µ A1 tained upper limits on ε2 in the mass range 10–60 MeV/c2 0 + - are about three orders of magnitude higher than the sin- NA48: π à γ V à γ e e -6 10 gle event sensitivity. The sensitivity to ε2 achievable with BaBar the employed method scales as the inverse square root of NA48/2 preliminary the integrated beam flux, and therefore this technique is 2 7 unlikely to advance much below ε = 10− in the near E774 future, either by improving on the NA48/2analysisorby 10-7 E141 exploiting larger future π0 samples (e.g. the one expected to be collected by the NA62 experiment at CERN [16]). -2 -1 10 10 2 On the other hand, a search for a long-lived (i.e. low m mA’, GeV/c A! and low ε2)DPproducedintheπ0 decay from high mo- Latest results by NA48 excludeFigure the 6.remainderThe NA48/2preliminaryupperlimitsat90%CLon of parameter space mentum kaon decay in flight using the displaced vertex the mixing parameter ε2 versus the DP mass m ,comparedtothe 0 A! method would be limited by the π background to a lesser relevant for g-2 discrepancy. other published exclusion limits from meson decay, beam dump D + extent, and its sensitivity is worth investigating. and e e− collider experiments [14]. Also shown are the band where the consistency of theoretical and experimental values of Only more contrived options formuon muong 2improvesto g-2 explanation2σ or less, and the region remain, excluded by − ± References the electron g 2measurement[3,15]. − 16 e.g. Lµ – Lτ , or dark photons decaying to light dark matter. [1] J.R. Batley et al.,Eur.Phys.J.C52,875(2007). [2] B. Holdom, Phys. Lett. B166,196(1986). 0 [3] M. Pospelov, Phys. Rev. D80,095002(2009). both the kinematic suppression of the π γA! decay and the decreasing acceptance. → [4] B. Batell, M. Pospelov and A. Ritz, Phys. Rev. D80, The assumption of prompt DP decay that is funda- 095024 (2009). mental to this analysis is justified a posteriori by the ob- [5] B. Batell, M. Pospelov and A. Ritz, Phys. Rev. D79, 2 2 115019 (2009). tained results: all upper limits on ε mA are above 6 5 2 2 ! × 10− (MeV/c ) ,correspondingtomaximumDPmean [6] V. Fanti et al.,Nucl.Instrum.MethodsA574,443 paths in the NA48/2referenceframebelow10cm(see (2007). Section 1). The corresponding loss of efficiency of the [7] K.O. Mikaelian and J. Smith, Phys. Rev. D5,1763 trigger and event selection (both relying on 3-track vertex (1972). reconstruction) is negligible, as the typical resolution on [8] T. Husek, K. Kampf and J. Novotn!,tobepublished. the vertex longitudinal coordinate in the forward NA48/2 [9] M. Hoferichter et al.,Eur.Phys.J.C74,3180(2014). geometry is 1m. ≈ [10] K.A. Olive et al. (Particle Data Group), Chin. Phys. C38,090001(2014). 6Summaryandoutlook [11] H.-J. Behrend et al.,Z.Phys.C49,401(1991). [12] K. Kampf, M. Knecht and J. Novotn!,Eur.Phys.J. The NA48/2experimentatCERNwasexposedtoabout C46,191(2006). 11 2 10 K± decays in flight in 2003–2004. The large in- [13] W.A. Rolke and A.M. López, Nucl. Instrum. Meth. × 0 tegrated kaon flux makes it a precision kaon by also π A458,745(2001). π0 physics facility, and the studies of the decay physics [14] J.P. Lees et al.,Phys.Rev.Lett.113,201801(2014) / with the NA48 2datahavestarted.Preliminaryresultson and references therein. dark photon search in π0 decays are reported: no signal is [15] H. Davoudiasl, H.-S. Lee and W.J. Marciano, Phys. observed, and the obtained upper limits on the mixing pa- Rev. D89,095006(2014). rameter ε2 improve over the world data in the mass range [16] G. Ruggiero, PoS(KAON13)032. 10–60 MeV/c2.Inparticular,thelimitsat90%CLare VOLUME 66, NUMBER 24 PHYSICAL REVIEW LETTERS 17 JUNE 1991

Neutrino Tridents and JY-Z Interference 9

S. R. Mishra, ' S. A. Rabinowitz, C. Arroyo, K. T. Bachmann, R. E. Blair, ' C. Foudas, B. J. King, W. C. Lefmann, W. C. Leung, E. Oltman, ' P. Z. Quintas, F. J. Sciulli, B. G. Seligman, and M. H. Shaevitz Columbia University, Ne~ York, Ne~ York 10027

dentF. S. Merritt, cross-sectionM. J. Oreglia, and B. A. Schumm to the SM prediction is given by V. OUTLOOK AND CONCLUSIONS University of Chicago, Chicago, Illinois 60637 R. H. Bernstein, F. Borcherding, H. E. Fisk, M. J. Lamm, W. Marsh, K. W. B. Merritt, H. Schellman, 2 and D. D. Yovanovitch 2 2 2 Fermilab, Batavia, Illinois 60510 1+ 1+4sW +2v /vφ A. Bodek, H. S. Budd, P. de Barbaro, andσW. K. Sakumoto This work was devoted to a comprehensive study of University of Rochester, Rochester, New York 14627 2 . (34) P. H. Sandier and W.σH. Smith ￿ ￿ 2 ￿ a model with a Z￿ vector-boson that couples to lep- University of WisconsinMad, ison, WisconsinSM 53706 1+(1+4s ) (Received 12 February 1991) W tons through the Lµ Lτ portal, and to quarks through We present a measurement of neutrino tridents, muon pairs induced by neutrino scattering in the Coulomb field of a target nucleus,Neutrinoin the Columbia-Chicago-Fermilab-Rochester tridentneutrino experiment productionat has been observed by − the Fermilab Tevatron. The observed number of tridents after geometric and kinematic corrections, general effective couplings. Our goal was to determine 37.0+ 12.4, supports the standard-model prediction of 45.3+ 2.3 events. This is the first demonstration of the 8 -Z destructive interference from neutrino tridents, and rules at the V — three experiments:out, 99% C.L., the2 predic- first positive results came from tion without the interference. whether such a model yields a plausible explanation for PACS numbers: 13.10.+q,the12.15.3i, 14. CHARM-II80.Er, 25.30.Pt collaboration [53]; the next measurement the recent discrepancy shown by the LHCb collabora- A neutrino trident is the scattering of a neutrino in the of this destructive interference in v tridents, Coulomb field of a target nucleus (N), Many theoretical papers discuss v-trident produc- + was by the CCFR' collaboration [54], further confirmed by v„(v„)+N~ v„(v„)+p+p +N. tion. As an almost purely leptonic process, its cross tion in angular distributions of the B K∗µ µ− de- section can be precisely calculated using the known elec- tromagnetic form factor of the iron nucleus. Most Momentum is balanced by the thecoherent exchange NuTeVof a8 collaboration— [55].early Combining the measured → virtual photon between one of the emergent muons and theoretical papers deal only with the V A theory (W cay products. We conclude that such an explanation is the nucleus. The signature is a dimuon event with zero exchange alone) ignoring the W-Z interference. Howev- visible hadron energy. In the standardcrossmodel this sectionsreac- er, in the standard withmodel thethe neutral-current correspondingchannel SM predictions we Signaturestion can proceed via two channels (Fig. 1): charged of(Z Z’mode) interferesofdestructively L with- theLcharged- (W) — viable, and it is such that future measurements in the where KF is a loop function that can be found e.g. in [43]. and neutral (Z) boson exchange. A measurement of this current channel (W ). Assumingµthe standard vectorτ process determines the interferencefindbetween 8' and Z and axial-vector couplings, the interference causes an ap- Out of the three SM neutrinos only the muon-neutrino q channels providingµ a crucial test of the gauge structure proximate 40% suppression of the trident production as high-energy and high-intensity frontiers may reveal fur- of the standard model. We report the first measurement compared to the prediction using 8'exchange only. ' and tau-neutrino are affected by Z￿ loops. Therefore, the Experimental results on “trident”µ In spite of the elegance of the theoretical prediction, Z the experimental study of v tridents has been difficult for ther deviations from the SM tied to the manifestations correction to the Z coupling to neutrinos is effectively two reasons:σ (a) the extremely small cross/section,σ about =1.58 0.57 , (35) Z￿ 2.3 && 10 CHARM(4.6 x 10 ) of the inclusiveII v„N(v„N)--SM given by charged-current process at (E,)−=160 GeV; and (b) the ± of this new vector-boson. Unlike models based on a Z￿ µ relatively low energy of the secondary muon associated 2 with the trident. TheseσCCFRdifficulties are/overcomeσSMin a =0.82 0.28 , (36) gV ν gAν 2 (g￿) high-statistics high-energy neutrino experiment. Early that couples with full strength to all leptons and quarks, = = 1+ K (m ) . (33) experimental investigations of v tridents (for a review, ± SM SM 2 F Z￿ see Ref. 10) failed to conclusively demonstrate their ex- g g 3 (4π) q µ ' ' ' ' V ν Aν istence. Moreσrecently,NuTeVthe CCFR/experimentσSM =0.67 0.27 . (37) ￿ ￿ and, notably, the CHARM II experiment' have report- the model we consider in this paper is well-hidden. In ￿ ￿ FIG. 1. Feynman diagram showing the neutrino trident pro- ed clear evidence for v tridents. Although these data are ± In order to obtain constraints￿ on the mass and￿ coupling duction in v„-8 scattering via the 8'and the Z channels. consistent with the standard-model prediction, there has ￿ ￿ contradistinction to most of the Z￿ proposals made in of the Z￿, we combine the experimental results from LEP A weighted1991 The American Physical averageSociety gives 3117 3 FIG.Hypothetical 5. The main NP Z’ contribution (any Z’ to thecoupledZ 4￿ process to L at ) contributesFull result constructively on M -to g’ cross parameter space and SLC [44] on the Z couplings to all leptons and neu- → µ Z’ connection with the LHCb discrepancy, which envision a trinos, taking into account the error correlations. We the LHC. 2 solidsection. angle Ω￿, ￿ solid 1 ± We note also that the constraint on the parameter spaceangle, then over t and ￿ (see also ref. [23]). Keepingwhich only leaves onlyCCFR little roomZ￿4 Μ for￿LH C positive NPMuon contribu- pair productionered inprocess this work can be very low, possibly well below the would be stronger, if we had a sizable kinetic mixing [45].leading order terms in the muon mass we find the follow-ν excludes solutionselectroweak to muon g-2 scale! While a variety of UV-completions are ing expression for the inclusive SM cross-section, tions. Combining Eq. (38) with (34) we find ν Z 4￿ searches at the LHC. Both ATLAS and 0.1 discrepancy via gaugedpossible muon for the coupling of Z￿ to quarks, we have chosen • → 1 2G2 α s s 19 CMS collaborations have reported the measurement of σ(SM) C2 + C2 F log . (9) vφ 750 GeV . (39) ￿ 2 V A 9π2 m2 − 6 µ− ￿ number in the wholeone range with vector-likeof quarks in the multi-TeV mass scale. the branching ratio of Z decaying into four charged lep- Z ￿ ￿ tons [46, 47]3. In particular, the ATLAS analysis [47] has ￿ ￿ ￿ ￿ ￿ While this model can hardly be imagined to be the fi- The destructive interference between the chargedThis and boundg ' completely excludes an explanationM > of400 the MeV been performed with the full 7+8 TeV LHC data set andneutral vector-boson contributions leads to a reduction 0.01 Z’ 6 µ+ nal word, it does offer a general and consistent frame- it gives BR(Z 4￿)=(4.2 0.4)10− , to be compared (g 2)µ anomaly for the mZ￿ ￿ 10 GeV region we con- → ± 6of about 40% of the SM cross-section compared to the to the SM prediction BR(Z 4￿)=(4.37 0.03)10− . − In the “contact” regimework within of which it is possible to discuss the different → ± pure V-A theory. Our results corrects a missing factorsider of in this paper. The constraint coming from Eq. (38) Our model gives a positive NP contribution to the pro-2 in the corresponding expression in ref. [16]. heavy Z’>5 GeV,low-energy the best constraints and structures likely to emerge in as well as￿3 the individual constraints from Eqs. (35) cess. The most important effect comes from the Feynman We can obtain a similarly concise expressionγ for the Z￿ 10 diagram shown in Fig. 5, with an intermediate on-shell 2Σ more refined constructions. contribution in the heavy mass limit, mZ √s [13], ￿2 Μ ￿ resolution to g-2 overpredicts ￿ ￿ and (36) are showng by the red lines in Fig. 3 in the mZ￿ Z￿ boson dominating the rate for mZ 20, 15, 8 GeV, and if the third lepton is an electron − Ina theW limit-boson of (Z-boson). light Z￿, mZ √s,wewrite Remarkably,of the neutrino a major trident cross-section. part of The the grey parameter region with space rel- lar, we find that the tentative explanation of the (g 2)µ it must have p > 10 GeV. Lepton identification efficien- ￿ *** This is the prime example of an old measurement “reprocessed” to T ￿ the dotted contour is excluded by+ measurements of the SM − cies have been taken from [51]. The invariant mass of the (SM+Z￿) (SM) (inter) (Z￿) evant forkill thea significantB K part∗µ ofµ −theanomaly, “dark force” and parameterall of thespace ***discrepancy in this model is fully ruled out by the latter σ = σ + σ + σ , (11) Z boson decay to→ four leptons at the LHC [24, 25]. The opposite sign same flavor (OSSF) lepton pair closest to Neutrino trident production. In theparameter last partpurple (dark-grey) space relevant region is favored for by the the discrepancy muon in theg 2 anomaly, process, at22 least for multi-GeV and heavier Z￿.While the Z mass should be m1 > 20 GeV. The second OSSFwhere the• second term stands for the interference be- muon g-2 and corresponds to an additional contribution of of this section, we present a powerful new constraintCan on it be improved9 in the future at LBNE− (O(50) events /yr ) ??? tween the SM and the Z contributions. In the leading ∆aµ =(2.9 1.8) 10− to the theoretical value [26]. in this work we have applied it to the Lµ Lτ portal, lepton invariant mass should be m2 > 5 GeV. Finally, the L L current￿ coming from measurementsis probed of neu- by the± observation× of neutrino trident produc- log approximation,µ τ this contribution is given by − the invariant mass of the four lepton system should be trino trident− production, i.e. the productiontion. of a muon The enormous potential of this process in providing it is absolutely clear that neutrino trident production is close to the Z mass: 80 GeV fermion operator is + and decouples2 as mZ− α. For light2 Z4￿, on the other hand, agreement with the SM predictions, of the four-fermion final state arising from the process e e− (g￿) (¯µγαµ)(¯νγ￿ PLν) /m , the ratio of theis well total tri- within the uncertainty of the SM prediction, for We would like to thank P. Langacker and A. Ritz + ¯ → Z￿ ￿ ￿−ff where ￿ is a charged or neutral lepton and f any chargedthe cross-section is only log sensitive to mZ￿ and the cen- fermion [48]. However, as also shown in [15], the constraints onter of mass energy of the event. generic valuesσ ofCHARM the YukawaII/σSM =1.58 couplings0.57 , one(15) should expect for useful discussions. We acknowledge the useful cor- + − ± the g￿ mZ parameter space coming from this measurement are To get the total ν N ν Nµ µ cross-section, the − ￿ µ µ − an effect of the sameσCCFR order/σSM =0 also.82 0 in.28 the. theoretically(16) clean slightly less stringent than the LHC constraints discussed in thereal-photon contribution→ can be easily integrated against ± respondence with K. Harigaya, T. Igari, M. M. Nojiri, following. 4 the Weizs¨acker-WilliamsWe estimate that the probability description of distribution the Z￿ contributionB func-s mixing by(Corresponding an phase, results which from NuTeV should can also be be detectable used al- with an M. Takeuchi and K. Tobe. WA and SG acknowledge the 2 2 2 tion, Eq. (2), in s /(4Eν )

D. Summary of observational constraints TABLE I Two model fits of the Galactic 511 keV emission (from Weidenspointner et al.,2008b):fluxes,photonemissiv- + The results of the analysis of Galactic γ-ray emissions ities and e annihilation rates (computed for a positronium in the MeV range can be summarized as follows: fraction of f =0.967, see Sec. II.B.4). Notice that ”thin” ps 1) Intensity: The total rate of positron annihilation and ”thick” disks have not the same meaning as in Sec. III. 43 −1 observed in γ-rays is at least Le+ =2 10 s , depending ˙ on the adopted source configuration. Most of it comes F511 L511 Ne+ −4 −2 −1 42 −1 42 −1 from the bulge (unless there is important emission from (10 cm s )(10 s )(10 s ) an extended, low surface brightness, disk). Bulge + thick disk 2) Morphology: The bulge/disk ratio of e+ annihilation +0.9 +0.8 +1.5 rates is B/D 1.4; however, substantially different ratios Narrow bulge 2.7−0.4 2.3−0.7 4.1−1.2 ∼ +0.7 +0.6 +1.0 cannot be excluded if there is important emission of low Broad bulge 4.8−0.4 4.1−0.4 7.4−0.8 +1.8 +0.8 +1.5 surface brightness (currently undetectable by SPI) either FIG. 4 511 keV line map derived from 5 years of INTE- Thick disk 9.4 26 4.5 8.1 FIG. 7 Map of Galactic−1.4 Al γ-ray emission−0.7 after− 9-year1.4 from the disk or the spheroid. About half of the disk GRAL/SPI data (from Weidenspointner et al.,2008a). Totalobservations with COMPTEL/CGRO 17.1 10.9 (from Pl¨uschke 19.6et al., Bulge/Disk 0.8 1.4 1.4 emission can be explained by the observed radioactivity 2001). of 26Al (provided its positrons annihilate in the disk). Halo + thin disk There are hints for an asymmetric disk emission with o o based on approximately one year of SPI data (Fig. 3). Halo 21.4+1.1 17.4+0.9 31.3+2.2 flux ratio F (l<0 )/F (l>0 ) 1.8, which has yet to be 26 −1.2 −1.1 −2.6 ∼ ThereThe is two a maps lot aremore compatible positrons with each othercoming (within fromto Galacticthe GalacticAl, as suggested+2.6 Center at a time+0 and. when6 thethe+1 mor-.1 confirmed. Disk26 7.3−1.9 2.9−0.6 5.2−1.1 their uncertainties), suggesting that the positronium Totalphology of Al emission 28.7 was unknown 20.3 (Prantzos, 36.5 1991 3) Spectroscopy: The ratio of the 511 keV line to the bulgefraction that does expected. not vary over the The sky. Theemission images illustrate seemsHalo/Diskand to Sec. be IV.A.2). diffuse. 2.9 It is consistent with 6 the (statistically 6 E<511 keV continuum suggests a positronium fraction the remarkable predominance of the spheroidal compo- significant) similarity to the Galactic free-free emission of 97 2 % and constrain the physical conditions in the map, which reflects electron radiation from HII regions annihilation± region. The observed continuum at MeV nent. In contrast to OSSE data, which suggested a rela- ∼ 1. Positronstively strong disk transported component, the Galactic into disk GC seemed by to B-fields?ionized from the same massive stars that eventually re- energies can be mostly explained with standard inverse tivelease (Weidenspointner26Al(Kn¨odlseder,et 1999). al., 2008b) involves a centrally be completely absent in the first year SPI images. Model Compton emission from cosmic ray electrons. A con- condensed but very26 extended halo and a thinner disk tribution from unresolved compact sources is possible, fitting indicated only a marginal signal from the Galac- The total flux of Al γ-rays depends slightly on the (projectedmeasuring vertical instrument. extent In terms of 4o), of with statistical a spheroid/disk precision, while a (small) contribution from high-energy (>MeV) 2. Positronstic disk, corresponding are created to a bulge-to-disk by episodic flux ratio > 1 violent events near central BH? ratiothe of SMM 6 (Table result I). of 4.0 0.4 10−4 ph cm−2s−1rad−1 has positrons annihilating in flight cannot be excluded. (Kn¨odlseder et al., 2005). This strong predominance of been considered the canonical± value. Imaging instru- These are the key observational constraints that should the Galactic bulge, unseen in any other wavelength, stim- With more SPI data, it was possible to proceed to 3. Positrons being produced by DM? Eithermorements, detailed however,annihilation constraints have consistently on the or morphology reporteddecay? lower of the flux18 disk be satisfied by the source(s) and annihilation site(s) of ulated ”unconventional” models involving dark matter values of 2.6 0.8 10−4 ph cm−2s−1rad−1 (COMPTEL) Galactic positrons. We shall reassess them in the light of emission. The flux in the disk component remains con- (Sec. IV.C). However, Prantzos (2006) pointed out that and 3.1 0.4± 10−4 ph cm−2s−1rad−1 (SPI), respectively. theoretical analysis in the end of Sec. IV and V. centrated± to longitudes l < 50◦; no significant 511 keV the data could not exclude the presence of disk emission The latest SPI value is| compatible| with the full range of a larger latitudinal extent (resulting from positrons lineof emission measured has values been by detected other instruments from beyond (within this statis- interval propagating far away from their sources), which could be sotical far. uncertainties),The accumulated and SPIwe adopt data ityield here. a flux The from detected nega- III. THE GALAXY 26 rather luminous and still undetectable by SPI, because tiveflux longitudes translates of into the a Galactic decay rate disk of thatAl which is twice depends as large 26 of its low surface brightness. asslightly the flux on from the adopted an equivalent 3D distribution region at of positiveAl in longi-the The expected spatial distribution and intensity of the tudes.Galaxy The (Diehl significanceet al., 2006). of this The asymmetry most recent is analysis still rather of positron annihilation emission obviously depends on the After accumulating 5 years of INTEGRAL/SPI data ˙ 42 −1 + low,SPI about data results4σ. in Indications a rate of N26 for= 4.3 such 10 ans asymmetryor 2.7 corresponding distribution of the potential e sources, as the 511 keV line emission all-sky image revealed also ∼ wereM" already/Myr (Wang noticedet al. in, 2009).the OSSE Assuming data (M. a steady Leising, state, pri- well as on the properties of the ISM in which positrons fainter emission extending along the Galactic plane vatei.e. communication). equality between production It should beand noted, decay rates, however, thisthat is first slow down and then annihilate. One may distin- (Fig. 4). With a much improved exposure with respect 26 + adialsofferent the present analysis production of the same rate of SPIAl data in the finds Galaxy; no evi- guish two types of e sources, depending on whether to the first year (in particular along the Galactic plane), recent models of massive star nucleosynthesis can read- dence for a disk asymmetry (Bouchet et al.,2008,2010), their lifetimes (τS ) are shorter or longer than the lifetime + 511 keV emission from the Galactic disk is now clearly ily explain such a production rate (Diehl et al.,2006and + although it cannot exclude it, either. Clearly, clarifying of positrons in the ISM (τe ). Calculation of the total e detected (Weidenspointner et al.,2008a).However,the Sec. IV.A.2). production rate requires in the former case (τS < τe+ )an the asymmetric or symmetric+ nature of the disk profile detailed quantitative characterization of components of Being predominantly a β -emitter (with a branching estimate of (i) the Galactic birthrate RS of the sources should be a major aim of the 511 keV26 studies in the years + 511 keV emission requires parameterizing these in the ratio of f + =82%, see Table VII) Al is itself a source and (ii) the individual e yields ne+ (i.e. the average to come4. e ,26 form of (necessarily idealized) spatial emission models of positrons. The corresponding Galactic e+ production amount of positrons released by each source). In the lat- ˙ ˙ 42 −1 fitted to the data. No unique description emerges at rate is Ne+,26= fe+,26N26 3.5 10 s . This consti- ter case (τS > τe+ ), the total number of such sources ∼ + tutes a significant contribution to the total Galactic e in the Galaxy NS is required, as well as the individual present, since both the spheroid and the disk may have + faint extensions contributing substantially to their total 4.production Spectroscopy rate with (Sec. INTEGRAL/SPI II.A.3 and Table I): 17% of the e production raten ˙ e+ of each source. In the former total e+ annihilation rate and almost half of the (thick) class belong supernovae or novae and the corresponding γ-ray emissivities. It turns out that the bulge emission ˙ disk in the double bulge+thick disk model, or 10% of positron production rate is Ne+ = RSne+ ; in the lat- is best described by combining a narrow and a broad theBefore total INTEGRAL, and 70% of the the thin spectral disk in shape the Halo+thin of the positron disk ter class belong e.g. low mass XRBs or millisecond pul- Gaussian, with widths (FWHM, projected onto the sky) annihilationmodel. We emissionshall see in was Sec. only IV that poorly positrons constrained from other by ob- sars, and the corresponding positron production rate is o o + ˙ of 3 and 11 , respectively. Another, more extended com- servations.β -decaying All nuclei high-resolution can readily explain observations the remaining suggested disk a Ne+ = NSn˙ e+ . ponent is needed to fit the data, a rather thick disk of modestemissivity, line broadening while the bulge of FWHM emissivity remains2 keV (Harris hard toet ex- al., The galactic distribution of any kind of stellar source of vertical extent 7o (FWHM projected on the sky). The 1998;plain. Leventhal et al.,1993;Mahoney∼ et al.,1994;positrons is somewhat related to the distribution of stars model implies a total e+ annihilation rate of 2 1043 e+ Smith et al., 1993). The excellent spectral resolution of s−1 and a spheroid/disk ratio of 1.4 (Table I). It should be noted, however, that alternative models, involving ex- tended components of low surface brightness (thus far undetected by SPI) are also possible. One such alterna- 4 INTEGRAL will continue operations until 2012, at least. PAMELA positron fraction

No surprises with antiprotons, but there is seemingly a need for a new source of positrons! This is a “boost” factor of 100-1000 “needed” for the WIMP interpretation of PAMELA signal. E.g. SUSY neutralinos would not work, because <σv > is too small. Enhancing it “by hand” does not work because WIMP abundance goes down. Dark forces allow bridging this gap due to the late time enhancement by Coulomb (Sommerfeld).19 Secluded WIMP idea – heavy WIMPs, light mediators

ψ – weak scale Dark Matter; V –mediator particle.

mmediator > mWIMP mmediator < mWIMP

Second regime of annihilation into on-shell mediators (called secluded) does not have any restrictions on the size of mixing angle κ.

It turns out mDM >> mmediator regime helps to tie PAMELA positron rise and WIMP idea together. (Also explains the lack of enhancement in 20 antiprotons, and photons) ￿1 Repulsive force Α ￿10￿1 Attractive force ΑX ￿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 mΦ GeV mΦ GeV ￿2 ￿2 Attractive force ΑX ￿10 Repulsive force ΑX ￿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 mΦ GeV flattens out mcentralΦ GeV spikes of DM (which is a reported problem). ￿3 ￿3 Attractive force ΑX ￿10 Repulsive force ΑX ￿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 αd = 0.1 GeV GeV ￿ cl 1 ￿ cl 1 X 10 X 10 m m 1 1 “Discoverable” mass range for the mediators.

0.1 0.1 10￿4 0.001 0.01 0.1 1 10￿4 0.001 0.01 0.1 1 21 Mediator mass, GeV mΦ GeV mΦ GeV

FIG. 6: Parameter space consistent￿ with￿ astrophysical bounds for attractive (left)￿ and￿ repulsive (right) poten- tials for different αX . 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 σ /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, sufficiently 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 (χχ¯). 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 η Υ ( −−), 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 ΥD production via ini- Probing the Dark Sector with Dark Matter Bound2 States 2 merically [26] , 1.68mV < αDmχ, with αD = gD/(4π). tial state radiation (Fig. 1). In the ΥD 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 imχt T Walter Burke Institute for Theoretical Physics, Californiamechanisms Institute of Technology, at colliders: Pasadena, CA 91125 matter field in the form: χ = e [ξ, σ p/(2mχ)ξ] + 2California Institute of Technology, Pasadena, California 91125 · 3 imχt T Department of Physics and Astronomy, University of Victoria, Victoria, BC, V8P 1A1 Canada e− [σ p/(2mχ)ζ, ζ] , where ξ, ζ are the 2-spinor an- 4 + + Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada · e e− ηD +V ; e e− ΥD +γ; p+p ΥD +X (2) nihilation (creation) operators for particle (antiparticle). AmodelofdarksectorwhereO(few GeV)Darkmass dark matter matter particles→ χ are bound supplied by a lighter→ states at →B-factories dark force mediator V , mV mχ,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 ΥD direct detection efforts and collider searches. We show that for a large range of coupling constants function [30], • If αd > 0.2,from the sub-5qq¯ fusion. 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 χ,suchas0− and 1−− states, ηD + and ΥD,isanimportantsearchchannel.Weshowthatvia productione e− of η“darkDγ+ V Vor Upsilon”ΥD + γ production that decays producing multiple charged particles amixed→ propagator, as shown in Fig. 1. µ 1 µ at B-factories for αD > 0.1 is sufficiently strong to result in multiple pairs− of charged leptons and + + 0 ζ†σ ξ ΥD = RΥD (0) ε , (5) pions via ηD 2V 2(l l−) and ΥD 3V 3(l l−)(l = e, µ, π).Theabsenceofsuch ΥD → → → → ￿ | | ￿ 2π 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− χχ¯ + nV , resulting in missing energy and multiple leptons, will further improve where εΥ is the polarization vector of ΥD and RΥD (0) → D the sensitivity to self-interacting dark matter. ￿ RηD (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 effective kinetic mixing term be- mology. In recent years, the paradigm of weakly inter- channels. We outline such possibilities in the minimal tween ΥD and the photon, acting dark matter supplied by a new force in the dark setup where the dark force carrierη also mediatesΥ 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 µν αD ety of unexplained astrophysical signatures. It was later lightB mediator-factories. gives an attractive force between χ and χ¯ eff = κκDFµν ΥD , κD = 3 RΥD (0) . (6) shown [3, 4]thatthismodelprovidesthebestrealization particles, leading to the formation of bound states, which L −2 2mχ 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 obtainχχ¯ leads to the final rate state radiation for the first process in (2), In the limit mV αDmχ,thetermκD reduces to κD = matter haloes (see, e.g. [6]). (FSR) of light mediators. Both channels typically result+ ￿ we calculate the amplitude of e e− χχ¯V with χ, χ¯ α2 /2.Weobtainadifferential 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 χ), 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, dσe e− γΥD 2πα κ κD χ 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 θ ￿ s ￿ − s ￿ netic mixing or the Higgs portals. For dark3 matter pairs heav- ofFIG. charged 2. aforementionedLeft: Constraint particles on channels the dark appear photon may1 parameterallow“for forfree” space genuine fromonce teststhe BUpsilon_darkAB ofAR dark Higgsstrahlung is produced. searches, adapted This to the is production and decay of dark bound states ηD and ΥD.ThesolidpurplecurvecorrespondstothecurrentBABAR limit for the the detailedΠ contentη = of the dark sector.RηD (0)(p + mχ)γ5(p mχ) , (3) 2 2 4 2 ier than 4-5 GeV, direct detection experiments provideparameters αD =0.5, mχ =3.5 GeV. The dashed3 purple curve shows the future reach of B-factories. Right:Currentconstraints 8s (s + 16m )sin θ limited by previous searches of32 “darkπmχ Higgsstrahlung2 ￿ 7 ” by BaBar￿ − and Belle. χ on the mDarkχ mV matterplane for bound the SIDM￿ states scenario production. are shown with Weκ =10 illustrate− and different values of αD.Thegreen(blue)regionis the strongest constraints on such models. High-energy − 22 1 , (7) favored for SIDM solving the galactic small-scale structure problems [3] for αD =0.3(0.5).Thecombinedconstraintsviathe 2 2 2 2 collider probes typically require more effectiveAn,Echenard produc-+ these, MP, ideas Zhang in the, well-studied PRL, to exampleappear of the vector me- + × − e e− (ηDV, ΥD) 3V channels are shown in thick purple curves, and the constraints via the e e− χχ¯ +3V channel ￿(s 4mχ) (s +4me (s 4me) cos 2θ) ￿ →diator model.→ The Lagrangian for dark matter and dark → tion channels [7–11]. For dark matter lighter thanare 4- shown into thin select blue curves. the AllowedηD regionsbound are in state the arrow [28 direction.]. We Assuming find no a SM leading-order background, the constraints via − − − + 5GeV,thelimitsfromdirectdetectionexperimentsarisethe e e−photonχχ¯ +2 isV channel are shown in dot-dashed black curves for αD =0.3, 0.4, 0.5 (bottom-up). The brown region is → excluded by CDMSlitedifferential [37]andLUX[ cross38]. The section: region mV ￿ 30 MeV is ruled out by the XENON10 electron recoil analysis [39where] θ is the the angle between γ and the initial e− in from electron recoil and are much weaker. In this mass µ for αD =0.3. = SM +¯χiγ (∂µ igDVµ)χ mχχχ¯ 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 κ 1 lation naturally point to particle-antiparticle asymmetry dσe e− ηDµνV 4πααµν Dκ2 [RµηD (0)] (1 + cos θ) 3 V→µν V =Fµν V + mV VµV , (1) p , (4) must be retained in order to regularize the θ integral, as in the dark sector. Constituents of such a dark sector,beams, the most importantd−cos4 θ production− 2 channel is2 from3/2 current uncertainties2 2 in estimating2 the background, we the quark-anti-quark fusion, qq¯ ΥD.Generalizingcal-mχs (srefrain4 frommχ showing+ mV the) potential| reach| of proton ex- light dark matter and a light mediator, can be searched κ → 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 χ 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- where4π ακ κDθ is2 thedx angle between ηD and the ini- fermion, neutral under the SM gauge group, butmV charged< 200 MeV. σpp(n) ΥD = Qq + + tion/scattering sequence in proton [15]andelectron[16] → s x under the darke U(1)q D interaction￿τ that has a newOutlook. vectorAmong the various probes of dark sectors sug- Compared to the e e− ηDV process, the e e− beam dump experiments, or perhaps via new galactic tial − ￿in the center-of-mass (CM) frame, and → → particle Vµ (sometimesτ called a "darkτ 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) γΥD cross section is suppressed by a factor α/αD,al- substructures and minihalos [17]. Most of the existing × carrier.p isx the spatialx momentumsensitive to both of the darkηD 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 τ = mV[/ss, fq/p(2(n) mandχ f+q/p¯ (mn) areV ) the][ relevants (2mχ mV ) ]/(2√s).We ter with mχ >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- forfacilitatesηD,andset the discoverym of theηD entire2 sector,mχ. as it leads from the dark force carrier. ￿ Υ 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− ηDV contains an additional mχ/s factor, which An analytic→ form→ for RηDFSR(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 alsoδr be relevant forδr the proton 2 sitivity can be made by searching for the missing energyαD ￿ 0.1 and mχ √s,thetwoprocesseshavesimilar beam experiments.αDδe− /(1 e− ) with δ =(π /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 Clifford Che- the planned SHiP [44]facilities.NotethatonlyafixedmV r ung, Ying Fan, Ming Liu, Mark Wise and Hai-bo Yuon this model. tial V (r)= αDe− /r [29]. In that case, RηD (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 ΥD particle will subsequently decay into three (4 δ a0) a0− , where a0 =2/(αDmχ). able for the search of ΥD.Takingapointintheparam- sc0011632. B.E. is supported by the U.S. Department − 2 7 dark photons. We calculate the differential decay rate eter space, mχ The=2GeV, scalarκ = 10 bound− , mV = state 300 MeV,ηD ofdominantly Energy (DoE) under decays grant DE-FG02-92ER40701 into two and αD =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 + ΥD 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 = nσ￿ 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 × dΓ(ΥD 3V ) 2α [RΥ (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 3πmχ ber of muons producedIt is known per each that proton too spill. large Givenα 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 αD 0.5, 39x +4x F6 16x F4 + 32x F2 + 256F0 ≤ − ,(8) and work with leading-order results in αD. ×(x2 2x )2(x2 2x )2(x2 + 2(x + x 2))2 − 1 − 2 1 2 − “Dark” di-photon resonance II. THEORETICAL MOTIVATION

DiphotonA. 750 GeVevents Scalar at the Resonance LHC are the events that pass the diphoton selection. It can be a pair of dark photons. So, dark photon 750 GeV In this sub-section, we consider a model of a heavy dark scalar (or pseudo-scalar) reso- resonance! g A￿ nance S produced via gluon fusion that decaysS to the pair of two metastable “dark photon” T ψ + particlesDark “simplified”A￿. Each A￿ givesmodel displaced decays to e e− pairs so that the whole chain can be represented as g A￿ FIG. 1: Representative Feynman diagrams for gg S +A￿A￿,where+ S is the 750 scalar resonance gg S A￿A￿ → (→e e−)(e e−). (1) and A￿ is the light on-shell dark→ photon→ that faking→ photons.

Here we explore a possibility that mS 750 GeV, but A￿ is light, mA < (few GeV). for the diphoton events, and successful reconstruction. It is the most complicated object.￿ It q¯ ￿ a O BecauseMarginalizing each dark over photon properties carries a significant of S, we fractionget preferred of energy region of the 750-GeVon ( , m scalar,) the depends on factors such as the detector geometry,Z￿ the detector acceptance, the reconstructionε A’

+ efficiency, as well as the decay length of A￿, and the mass of A￿ that affects the size and the + eplane,e− pair that from give the A’ decay decays of A￿ withinare extremely ~ meter collimated. scale that The may opening “fake” angle real of e e− pair + + shape of the shower in the EM calorimeter. We will abbreviate P (A￿A￿ (e e−)(e e−) γγ) photon conversion. q s → | is around 2mA /EA , where mA and EA are the mass and energy of A￿, respectively. For as P￿acc. The￿ existing excess￿ in the diphoton￿ channel found by ATLAS [91] is at the level of σ 5 10 fb, which corresponds to 16 to 32 events. sub-GeV A￿sthisangleislessthan0.01.ThereforeitisplausiblethateventsoriginatingSignal ￿ − ∼ from the decay of A￿ could pass the selection criteria for a real photon set by e.g. The 23 Production and decay of S in a U(1)D model ATLAS collaboration. Data suggest that the total width of S is around 5 45 GeV, and therefore the narrow Dark photon models have been studied extensively− in the literature since the 1980’s [88, width approximation for S suffices for our accuracy. The production cross section of S 89]. In recentthrough years, gluon the fusion attention is given by to dark photons have been spearheaded by their possible

2 1 2 connection to various particle physicsπ and astrophysicsdx “anomalies”2 mS/s 2 (see e.g. [34, 35, 61, 90]). σ(pp S)= Γ(S gg) fg(x, mS)fg ,mS , (7) → 8smS → m2 /s x x The minimal dark photon model consists of￿ aS new massive￿ vector￿ field that couples to the 2 where √s =13TeVisthecenterofmassenergyandfg(x, Q )isthegluonpartondistribu- SM U(1) viation the function so-called evaluated kinetic at Q2. mixing We assume operator, that the decay width of S gg entering in (7) is → mediated by the loop of heavy vector-like fermions T . The actual constraints on mT would 1 µν 1 µν ￿Y µν 1 2 µ criticallygauge depend= on T -fermionBµνB decay channels.F ￿ F ￿ To+ reduceF the￿ B number+ ofm parametersA￿ A￿ to be (2) L −4 − 4 µν 2 µν 2 A￿ µ scanned, we will adopt mT =1TeVthroughout,whichissaferelativetodirectsearches. Note that for such a massive particle in the loops, the form factor of the effective g g S where Fµ￿ ν = ∂[µAν￿ ] and Bµν = ∂[µBν] are field strengths of the U(1)D, U−(1)−Y gauge group vertex does not need to be taken into account. A very well known formula for the calculation respectively. The mass term breaks the U(1)D explicitly but does not ruin the renormal- of the width (e.g., see [92]) gives izability. ￿Y is the kinetic mixing parameter,2 3 which we will explicitly assume to be much αs mS 2 2 Γ(S gg)= 3 2 λT τT [1 + (1 τT )f(τT )] , (8) → 32π mT | − | smaller than one. It dictates the magnitude of the coupling of A￿ to the SM sector. Even if the boundary conditions in the deep UV are such6 that ￿Y (ΛUV )=0,thenon-zeromixingcan 1 be mediated by a loop process with heavy particles charged under both U(1) groups [88]. In such a scenario, the choice ￿ 1 is justified due to the expected loop suppression. After Y ￿ 3 electroweak symmetry breaking (EWSB), the SM gauge field Bµ,andWµ mix with the new gauge field Aµ￿ . The resulting mass eigenstate Z￿ couples to the SM electromagnetic and

4 Dark 750 GeV continued

Chen, Zhong, Lefebvre, MP, 1603.01256

-2 -2 4 Decay length scales as ~ ε mA’ . Due to large boosts (e.g. ~ 10 ) at the LHC, the preferred parameter space is in the allowed gap. Of course, decays of A’ can be differentiated from regular γ conversion – something better done by experimentalists. This is ROI of parameter24 space to be explored by experiments discussed here. 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 difficult part of the parameter (orspace, close the to vicinity be excluded) of m 30 by MeV, experiments. has been finally The ruled most out diffi 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 offer a solution to the g 2dis- • + − crepancy. A￿ χχ¯ decay, for example, can dilute ”visible” A￿ e−e modes. In any A slightly extended→ model of dark photon, can still off→er a solution to the g 2dis- • case, it appears that mA < 200 MeV is required [48]. + − crepancy. A￿ χχ¯ 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].Lτ 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 Lτ 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 offers 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 ∼ χ χ offshowers perhaps that the required theLight largest WIMP WIMPs number abundance ofdue opportunitiesis achieved to light if formediators the experimental discovery of dark matter via its non-gravitationaldirect production/detection interaction. In the standard WIMP paradigm, known from σannih(v/c) 1pbn= ΩDM 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 χ…), where Lightm χdarkis 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. If the interactions are mediated by forces that have the weak strength, and operate WIMP paradigm: σannih(v/c) 1pbn= ΩDM 0.25, (3.2) with the exchange of the weak scale particles,∼ then for⇒ small and￿ large masses one would whereexpectElectroweakv/c theis following the approximatemediators scaling with lead relativethe to WIMP the velocity so-called mass, at Lee-Weinberg the time of annihilation. window, The nature of a force responsible for the2 self-annihilation2 of WIMPs to the SM states is important. It sets GF mχ for mχ mW , the size ofσ the(v/c) self-annihilation cross￿ section,= andfew ultimately GeV

This famously determines the so-called ”Lee-Weinberg window”, or the mass range for the 25 DM in the assumption of weak-scaleχ∗ mediators. Accordinge− to this logic, MeV-GeV scale dark matter isFigure disfavored. 3: Light (m few MeV) scalar dark matter annihilating to electron-positron pairs χ ∼ due to mixed γ A￿ propagator. The annihilation occurs in the p-wave. − The crucial piece of assumption in the argument above9 is link between the weak scale and the mass of the mediator particles. As was argued in previous sections, some vector portal do allow interaction strengths much in excess of GF . This, in turn opens the door for the construction of rather natural models of light dark matter, which can be made as light as MeV [53]. It is important to realize that such WIMPs fall under the category of dark matter that is extremly difficult to discover via direct scattering of galactic DM particles on atoms [54], and therefore alternative ways of covering this mass range have to be provided. On the phenomenological side, the light dark matter can be behind an unexpectedly strong emission of 511 keV photons from the galactic bulge, as observed by the SPI/INTEGRAL [55]. It is presently unclear whether New Physics needs to be invoked for the explanation of such emission, and we refer readers to the on-going debate in the literature [56]. Nonetheless, the dark matter-related origin of 511 keV excess can be entertained, supplying the nonrela- tivistic or semi-relativistic positrons from the DM annihilation or decay [57]. For example, scalar dark matter charged under new U(1)￿ with masses in mχ few MeV range can pass all the existing constraints [53], and supply the requisit source for positrons.∼ Direct calculations in the model where mediation of the SM-DM interaction occurs due to the dark photon, Fig. 3, gives the annihilation cross-section in the form

4π m2 σ (v/c) α α￿2v2 χ . (3.4) annih ￿ 3 D (m2 4m2 )2 A￿ − χ 2 Here αD =(g￿) /(4π), and mχ me is assumed. MP: I need to check the numerical coefficient. The extra factor of velocity￿ square in this formula is indicative of the p-wave annihilation, and is what ulmitately allows this model escaping strong constraints on light dark matter annihilation imposed by the accurate measurements of CMB anisotropies. The

least constrained region of the parameter space corresponds to very light mediators, mA￿ <

100 MeV, and 2mχ

10 LightDirect DM Detection – direct production/detection

!39 $ 10 %%B33CD,,963228'EF12G5E*9:,% %%)&43'H*88I#&594-IJ484CC454 ï=> DAMA 10!40 <> CoGeNT 10!41

ï=. 10!42 <> CDMS-Si 511 keV !43 normalised to nucleon 10 what about here? /%75216&84'*9%32%5:-8*25; "# . 2 motivated !44 ï==

cm 10 <> ! XENON100XENON100 10!45 '*-3425%(-6 LUX LUX ï section

! ï=? 10!46 <> 012'' Cross !47 <=><< 10 > < . K 10!3 10!2 10!1 <> 1 <> <> <> !"#$%#&''%()*+,-./ [Holdom]3 • Nuclear recoil too weak - vDM 10− If WIMP dark matter is coupled to light∼ mediators,[Pospelov, Ritz, Voloshin], the WIMP mass 1. Vector portalCan we DM find (“dark a relativistic force”) source of Dark[Hooper, Matter? Zurek] • [Arkani-Hamed, Finkbeiner, Slatyer, Weiner] scale can be much lighter than nominal Lee-Weinberg... bound, 6 1 1 κ D χ 2 m2 χ 2 (V )2 ++ m2 (V )2 V F µν + ... L ⊃ | µ | − χ| | − 4 µν 2 V µ − 2 µν (see talk by D. Morrissey) Dµ = ∂µ igDVµ DM − mediation 26 • Dark photon mediates interaction between DM and SM

• 4 new parameters: mχ,mV , κ, α￿ (V = A￿, κ = ￿, α￿ = αD)

χ • Scalar DM annihilation is p-wave, CMB ok SM χ† V γ,Z [deNiverville, Pospelov, Ritz]

µ • Dark photon can address g-2 anomaly [Fayet, Pospelov] V

12 Fixed target probes - Neutrino Beams

Proposed in Batell, MP, Ritz, 2009. Strongest constraints on MeV DM χ + e e χ + → (near) detector p + p(n) V ∗ χχ¯ proton χ 0 −→ −→ + N beam π , η V γ χχγ¯ χ −→ −→ → + 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 detector27 30 Compilation of current constraints on dark Current constraints photons on vector decaying portal DM to light DM

!Χ ' "C! #$%: Ε D/$E$//$F +G #Μ: *@ Σ &"%&

!Χ " !" #$% &"%@

&"%= -.-./

%< !Χ " &" #$% &" 2&=8

% %!

Α &"

#$ -75 %A &" 2898: 2;<; 5>7? %8 &" " " ! Χ "' #ΧΧ %9 0& $ 0123 $ &" 4562 $ -.-./ "' # ()*)+,$ 0& &"%; &"%= &"%@ &"%& & !"' B$% [BB, Essig, Surujon ’14] The sensitivity of electron beam dump experiments to! light" DM is 15 investigated in Izaguirre et al, 2013; Batell, Essig, Surujon, 2014. 28 MiniBooNE search for light DM MiniBooNE sensitivity to vector portal DM

MiniBooNE MiniBoone has completed90% C.L. a long run in the beam dump mode, as suggested in [arXiv:1211.2258] By-passing Be target is crucial for reducing the neutrino background (R. van de Water et al. …) . Currently, suppression of ν flux ~50. Timing is used (10 MeV dark matter propagates slower than neutrinos)

to further reduce backgrounds. First results – this year (2016) 29

23 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 (Kàπνν mode), positron beam dumps…

§ Extra Z’ in neutrino scattering: DUNE near detector (?)

30

Future: SHiP project at CERN

The SHiP experiment ( as implemented in Geant4 )

See e.g. A. Golutvin presentation,!"#$%&'()%*+,'&*#-,.%/)0%1-2+.%/345% CERN SHiP symposium,6% 2015

31 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 Μ ￿ 5Σ 10￿6 g￿2 Μ ￿ 2Σ ￿ ￿ g￿2 e E774 BaBar, NA48 2, PHENIX ￿8 ￿ ￿ 10 E141 ￿ ￿ SHiP, ￿ 10￿10 Orsay, U70 bremsstrahlung Ε2 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 32 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 α(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 α α), 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￿ ,aremoredifficult 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 + χ 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 + + + + → π A￿ π +missing energy, where the competing SM process, K π νν¯ 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. π+µ-, π-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 33 HNL production can be enhancedU e: U µ :in U non-minimal!~48:1:1 models,U e: UBatellµ: U !~1:11:11 et al. Inverted hierarchy Normal hierarchy

Scenarios for which baryogenesis was numerically proven

!"#$%&'()%*+,'&*#-,.%/)0%1-2+.%/345% /5% 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 Physics with and Astronomy, Eder University Izaguirre of Victoria, Victoria, and British Gordan Columbia, Canada Krnjaic, 2014, 2015 We demonstrate that current and planned underground neutrino experiments could offer 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 effort 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,…, σv 3 10− cm /s. Alternatively if its abundance ∼ × at late times is set by a primordial particle-antiparticle ν 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-K either scenario, 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 . . . 34 window remains an elusive blind spot in the current search effort [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 efforts in this mass range. This concept cilities and a low-energy (10-100 MeV) but high inten- complements the DAEδALUS 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 different 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 ￿ Χ ￿

￿10 ￿

m ￿ 10 m 10 ￿ ￿ E137 ￿ 10 Density D ￿11 D 10 ￿11 Relic Α Α 10 2 LSND 2 Ε ￿12 Ε 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 ￿ mΧ 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-100 their projections are presented as a common curve. We conservatively assume thresholds of ER > 10 MeV for which the backgrounds are negligible. The CMB and direct detection constraints assume χ24/ϕ constitutes all of the dark matter and regions above the relic curve MeVcorrespond mass to parameter range. space Assuming for which each scenario 10 can 100 accommodate MeV aelectrons subdominant fractionon target 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 curve was computed assuming only a small mass-splitting (100 keV < ∆

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 off-diagonally (inelastically) to the different mass- sults are qualitatively similar for different mediators. The eigenstates and mχ(ϕ) 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 A￿ µ D Fµ￿ ν Bµν + 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

mχ,A￿ are the appropriate dark sector masses. After elec- tion process that sets the relic density is t-channel (e.g. troweak symmetry breaking, diagonalizing the gauge bo- χχ¯ A￿A￿) and, thus, independent of the mediator’s → son mass matrices induces a kinetic mixing with the pho- coupling to the SM. However, if mA￿ >mχ(ϕ),thenthe + ton field strength ￿ ￿Y cos θW ,whereθW is the weak relic density is achieved through χχ¯ e e− annihila- ≡ → mixing angle. The DM Lagrangian contains a fermionic tion, which proceeds via a virtual s-channel A￿ exchange or bosonic MeV-scale DM particle charged under U(1)D, and depends on both DM and SM couplings to the medi- ator1. This latter scenario is predictive: since dark sec- χ¯(iD mχ)χ, fermionic DM, DM = ￿ 2− 2 (2) tor couplings are bounded by perturbativity, sufficient L Dµϕ m ϕ∗ϕ, bosonic DM, ￿ | | − ϕ where Dµ = ∂µ +ig￿Aµ￿ is the covariant derivative. These simplest realizations of assume a Dirac fermion or 1 In a certain region of parameter space, the m >m sce- D A￿ χ complex scalar DM states,L but the model can readily nario can still achieve the observed relic abundance through Sensitivity to scalar mediator § 16O de-excitation of 6.05 MeV as a source of scalars, 19F(p,α)16O

§ rp relevant region can be fully covered. 2

144 1.49 MeV energies from Nd∗ de-excitation. LSND 10￿7 The subsequent detection of a mono-energetic release in Rp favored ￿8 a Borexino-type detector with 6.05, 2.19, or 1.49 MeV 10 LUNA Borexino 400 keV can be free from substantial environmental backgrounds.

2 SOX 2.18 MeV

e ￿9 ￿ ￿

The strategy proposed in this Letter is capable of ad- p 10 SOX 1.48 MeV g e e m Cooling 2 vancing the sensitivity to such states by many orders of g ￿

￿ ￿10 10 Φ magnitude, completely covering the parameter space rel- 2 m Ε Stellar evant for the rp puzzle. Borexino Solar Scalar particles below 1 MeV. New particles in the MeV 10￿11 Borexino 3 MeV and sub-MeV mass range are motivated by the recent 7σ SuperK 3 MeV ￿12 discrepancy between the standard determinations of the 10 proton charge radius, rp based on e p interactions [2], 200 300 500 700 1000 − 36 and the recent, most precise determination of rp from mΦ keV the Lamb shift in muonic Hydrogen [3, 4]. One possible explanation for this anomaly is a new force between the FIG. 2: Sensitivity projections for￿ the￿ scenario in Eq. (3). electron(muon) and proton [5–7] mediated by a 100 fm The blue band shows the parameter space that resolves the ∼ range force (scalar- or vector-mediated) that shifts the rp puzzle. An important aspect of our proposal, as it relates binding energies of Hydrogenic systems and skews the to NP explanation of the rp anomaly, is the proportionality of the signal to the products of the couplings, ￿2e4 = g2g2. determination of rp. Motivated by this anomaly, we con- p e The “LUNA/Borexino” curve assumes a 400 keV proton beam sider a simple model with one light scalar φ that interacts 25 19 with 10 POT incident on a C3F8 target to induce p+ F with protons and leptons, 16 16 ( O∗ O+φ)+α reactions 100 m away from Borex- 1 1 ino.→ The→ Borexino 3 MeV and SuperK 3 MeV lines assume = (∂ φ)2 m2 φ2 +(g pp¯ + g ee¯ + g µµ¯ )φ , (3) Lφ 2 µ − 2 φ p e µ the same LUNA-type setup with a 3 MeV p-accelerator 10 m 2 2 away from each detector. The SOX lines assume a radioac- and define ￿ (gegp)/e . We assume mass-weighted tive 144Ce 144 Pr source 7.15 m away from Borexino. Shaded couplings to leptons,≡ g (m /m )g , and no couplings − e ∝ e µ µ in gray are constraints from a Borexino solar axion search to neutrons. UV completing such a theory is challenging, [8], LSND electron-neutrino scattering [9], and stellar cooling so we regard this as a purely phenomenological model. [10], for which we assume ge =(me/mp)gp. The apparent corrections to the charge radius of the pro- ton in regular and muonic hydrogen are [5–7] which determines the in-medium absorption probability 6￿2 6￿2(g /g ) ∆r2 = ; ∆r2 = µ e f(am ) (4) of φ. Absorption competes with the decay φ γγ,oc- p eH 2 p µH 2 φ → −mφ − mφ curring through loops of fermions f with the width given ￿ 1 ￿ by a standard formula, where￿a (α mµmp)− (m￿ µ + mp)istheµH Bohr radius ≡ 4 4 2 2 2 and f(x)=x (1 + x)− . Equating ∆rp ∆rp α2 m3 µH − eH φ gf 2 2 Γ(φ γγ)= N Q A (τ ) , (7) to the current discrepancy of 0.063 0.009 fm [4], 3 c f 1/2 f ￿ ￿ → 512 π mf − ± ￿ ￿ ￿ f ￿ one obtains a relation between mφ and ￿. Thus, for ￿￿ ￿ 2 8 ￿ ￿ mφ =0.5 MeV, the anomaly suggests ￿ 1.3 10− . ￿ 2 2 ￿ + ￿ × where Qf is the fermion charge, τf mφ/4mf , and For mφ > 2me,theφ e e− process is highly con- ≡ → 2 strained by searches for light Higgs bosons [1], so we A1/2(τ)=2τ − [τ +(τ 1) arcsin √τ]. (8) consider the mφ < 2me region, which is relatively uncon- − strained. Since ge gp,theφ e coupling is suppressed An approximate proportionality to particle masses en- relative to that of￿ a massive photon-like− particle, so pre- sures that couplings to neutrinos are negligible. cision measurements of α and (g 2)e do not constrain Processes (5), (7) define the gross features of φ- this scenario. − phenomenology in cosmological and astrophysical set- The astrophysical and fixed-target constraints depend tings. The ensuing constraints are summarized as fol- on the cross section for eφ eγ conversion, which for lows: m m with a stationary→ electron target is φ ￿ e Energy loss in stars via eγ eφ (red giants, white 2 2 • dwarfs etc) is exponentially→ suppressed for m > dσ π(ge/e) α (E me) 2 φ = 4 − 2 E(Q EQ 2meQ Tstar. In practice, it means a strong bound on mass, dE meQ (Q E + me) − − − ￿ mφ > 250 keV, for the fiducial range of couplings. 2 2 2 ∼ 2me)+me(3Q +3Qme +2me) , (5) − The decay of φ in the early Universe at T mφ ￿ • results in a negative shift of the “effective∼ num- where E is the electron recoil energy and Q is φ energy. ber of neutrinos.” For mφ > 250 keV the shift is At Q me, this leads to the total cross section of ￿ moderate, Neff 0.5 [11], and can be easily com- 2 2 2 ∼− π(ge/e) α 5 MeV ge pensated by the positive contributions from other σeφ = 13 mbn , (6) ￿ 2meQ × Q × e light particles (e.g. sterile neutrinos). ￿ ￿ Conclusions 1. Light New Physics (not-so-large masses, tiny couplings) is a generic possibility. Some models (dark photon, scalar coupled Higgs portal) are quite natural, and helpful in explaining a number of puzzles in particle physics and astrophysics.

2. Some of the original motivations for light dark photons are weakened, but some new ideas (e.g. connection to 750 GeV) appear. Concerted effort in “dark photon” case rules out minimal model as a cause of g-2 discrepancy. Other possibilities remain.

3. Light dark matter via production & scattering is an appealing physics goal. Currently searched at the MiniBoone.

4. Future: more experimental possibilities. 37