Dark Sectors and Kaon physics
Maxim Pospelov Perimeter Institute, Waterloo/University of Victoria, Victoria Kaon 2016
1 Outline of the talk
1. Introduction. Intensity Frontier. Portals to light new physics. 2. “Golden mode” of NA62, Kà π + missing energy – a potential for future discovery. Dark photons + light dark matter, Higgs portal scalar. 3. Radiative decays of Kaons, and sensitivity to new physics: K à µν l+l-; K à π+π0 e+e- 4. Beam dump mode ? 5. 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.)
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 ……….
4 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 (?)
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 gA 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.gA ) 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 ∆ ge/(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). At
3 “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.
8 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 (+Fermi, AMS2) positron rise. 5. Too-big-to-fail etc problems of CDM + solution via a DM re- scattering with a light mediator. 6. Other motivations (most recently, a claim of new particles in the decay of the 18.15 MeV state in 8Be).
9 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. 10
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 scrutiny11 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 2 102 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 104 aΜ,2 Σ MAMI Orsay 103 BaBar E774 APEX MAMI 5 U70 Test Runs 10 ae 6 CHARM DarkLight MESA 10 APEX Ε Ε VEPP3 7 4 E141 10 E137 10 LSND 8 10 Orsay HPS 109 5 SN 10 10 10 U70 11 10 3 2 1 103 102 101 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- 12 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]. − 13 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 aNP = aexperiment aSM theory (32) µ µ − µ aNP = aexperiment aSM theory (32) µ µ − µ = Y E (L Φ†)+h.c. (33) Lmass × R L = Y E (L Φ†)+h.c. (33) Lmass × R L 0 + (LΦ)=νLφ eLφ (34) (LΦ)=ν−φ0 e φ+ (34) L − L 1 eff = (LΦ1)(LΦ)(35) L eΛff = (LΦ)(LΦ)(35) L Λ
MN M mass = Y =NYR(LNΦ)+(LΦ)+NNN NN+(h.c.+(h.c.)(36))(36) L Lmass× × R 2 2
1 1 (Y )2(Y )2 = = (37)(37) Λ −Λ M−N MN
0 Y Φ 2 0 Y Φ = m1 (Y2 Φ ) /MN ; m2 MN at Y Φ MN (38) Y Φ M=N m1⇒ (Y−Φ ) /M N ; m2 MN at Y Φ MN (38) Y Φ MN ⇒ −
Y Φ mν(observed) Yθ Φ mν(observed) (39) θ ≈ MN ≈ MN (39) ≈ MN ≈ MN 1 µν 1 ψFµνσ ψ (40) ψF 2 σµνψ (40) 2 µν 1 ψF σµνiγ5ψ (41) 2 µν Sensitivity1 toµ νa light5 Higgs-mixed ψFµνσ iγ ψ (41) 2 1 scalar ψF˜ σµνψ (42) 2 µν Example: new particle1 admixedµν with a Higgs. ψF˜µνσ ψ (42) 2 1 2 1 2 2 = (∂ S) m S ASH†H (43) LHiggs portal 2 µ − 2 S − 1 1 After (Higgs Field = vev +2 fluctuation2 2 h), the actual Higgs boson Higgs portal = (∂µS) mAvSS ASH†H (43) Lmixes with S. 2 θ−=2 − (44) m2 h Av Mixing angle: θ = (44) m2 h
The model is technically natural as long as A not much larger than mS Low energy: new particle with Higgs couplings multiplied by θ New effects in Kaon and B-decays.
14 4
4 signal, and does not presuppose any hierarchy of gauge couplings as α! can be taken of order α.Therefore,thismodelappearsthemostnaturalcandidatefor MeV-scale secluded dark matter, having the chance to explain the 511 keVlinefromthegalactic center.
(c) φ-mediator, mX >mφ:Inthisscenario,itisadvantageoustohaveafermionic dark matter candidate ψ with scalar (rather than pseudoscalar) couplings to φ.The annihilation ψψ → φφ proceeeds in the p-wave and can always be tuned to the required −6 level with a typical choice λψ ∼ 10 .Sincemψ ∼ few MeV, this value of the Yukawa coupling isSensitivity natural. The subsequent to decaya light of φ due Higgs-mixed to mixing with the Higgs is highly suppressed by the electron Yukawa coupling, scalar λ v2 2 m 2 m λ v2 2 Γ ∼ 1 × e × φ > sec−1 =⇒ 1 > 10−8. (24) Kàφ + missingm2 energyv – a potential8π ∼ for future discovery.m2 ∼ π ! h " ! EW " ! h " The naturalness§ Underlying requirement quark-W for theloopφ-mass for s wouldà d + impose Scalar a significantis enhanced constraint by here. 2 2 If we consider themt contribution/mW factor. from Higgs mixing in (17), λ1v/mh <∼ mφ/v,thisclearly favors§ a longAboveφ-lifetime di-muon (∼ 1sec)andasmallmixingparameter.Eventhen,onemustthreshold, recent LHCb searches of B à K + ensure that the “missing energy” decay K+ → π+ + φ is within the allowed range. At muon pair of fixed invariant mass provide a dominant constraint. the quark level, the amplitude for the process is given by a Higgs penguin (see, e.g. [34]): § Below mS = 210 MeV, the decays are displaced – in fact very long 2 2 2 ∗ outside of the NA62λ1v detector,3gW ms becausemt VtdVts of the small Yukawa for Leff = d¯LsRφ +(h.c.), (25) 2m2 2 64π2m2 v electrons. ΓS = !θ (mh e"/v) /(8π) mWS. leadingResult to the (see (non-SM) e.g. MP, missing Ritz, energy Voloshin decay,, 2007) λ v2 2 3m2V V ∗ 2 m3 Γ % 1 t td ts K . (26) K→π+φ−mediator m2 16π2v2 64πv2 ! h " ! " RequiringConstraint: that this (mixing width not angle) exceed2 < 2 the×10 observed-7, in the missing technically energy natural decay range branching +1.3 −10 + ratio Brof =mixings. 1.5−0.9 × 10 [35] associated with the SM process K → πνν¯,resultsin15 the following constraint on φ − h mixing:
λ v2 2 1 < 2 × 10−7. (27) m2 ! h " This cuts out a significant part of the parameter space, but together with (24) still leaves a relatively narrow interval for the mixing parameter, 10−7 − 10−8,wherethe model survives all constraints (although not without a modest amount of fine-tuning of the mediator mass) and thus can be the dominant dark matter component while still accommodating the positron signal through a combination of annihilation and decay. The constraints remain essentially the same for a pseudoscalar coupling of φ to the fermion ψ,iftheHiggssectorinSMisassumedtobeminimal,inwhichcase the mixing constant λ1 is CP-violating. The additional processes: s-wave annihilation ψψ → e+e− through a virtual φ,andalsoψψ → φφφ if kinematically allowed, are too weak in comparison with the p-wave annihilation ψψ → φφ to affect the constraints discussed above. In principle, with an extended Higgs sector, φ could also mix in a
12 3.1 Radiative Kaon decays
In this paper we will consider two important processes,
A: K+ → π+V [K+ → π+l+l−](10) B: K+ → l+νV [K+ → l+ν,K+ → l+νl+l−], where the SM processes are shown inside square brackets. The branchings for the SM processes with l+l− are small, on the order of O(10−7 − 10−8)dependingonparticular process of interest. For the semileptonic decays A, the SM rates were estimated in Ref. [22], where the starting point was the chiral perturbation theory together with the experimental input for the K+ → π+π−π+ vertex. This analysis results in the prediction for the q2- proportionalSensitivity vertex of K − π transition to with a virtuallight photon. vector In terms of this vertex, in the notation of Ref. [22], the expression for the amplitude is
decaying invisibly2 eκmV V 2 M → = (k + p) $ W (m ), (11) K πV (4π)2m2 µ µ V K+à π+ + missing energy – a potentialK for future discovery of dark V photonwhere k decayingand p are the to light kaon anddark pion matter. momenta, $µ is the polarization of V -boson, and 2 2 −12 2 2 W (mV ) # 10 (3 + 6mV /mK)[22].Thelatterisinreasonableagreementwithexperi- mental determination via the K+ → π+e+e− decay [23] and with the rate of K+ → π+µ+µ− + + + 2 2 Kdecayà [24].π + Notice dark thephoton proportionality à π +χχ of the amplitude to mV that replaces q of the vir- tual photon and suppresses the rate for small mV $ mK.Thisamplitudegivesrisetothe followingThe rate branching for decay ratio: to a dark photon (MP, 2008):
2 2 2 2 ακ mV W −5 2 mV → → ΓK πV = 10 4 f(mV ,mK,mπ)=⇒ BrK πV # 8×10 ×κ . (12) 2 π mK 100 MeV ! " In this formula, dimensionless factor f(m ,m ,m )standsforthemassdependenceof Decouples as mV à0. V K π phase space and matrix element, and f is normalized to 1 in the limit mπ,V → 0whenmK is kept finite. The last relation in (12) is valid only when mV is much smaller than mK , Sensitivebut in practice probes for all ofm mixingV below 200 angles MeV. down to 10-3. In order to constrain (12), one has to know the subsequent fateofV .Itcandecayto lepton pairs or invisibly, if such channel is open. In case of the invisible decay, one could use the results of K+ → π+νν¯ search, but due to a rather restrictive kinematic window for pion momentum [25], this constraint is difficult to implement for arbitrary mV .Iftheinvisible16 decay is absent, K+ → π+V → πl+l− decays will contribute to the K+ → π+l+l− process. Given that there is still some uncertainty in the determination of W (q2)anditsshape,and without a dedicated search for a resonant part, one could still contemplate that ∼10% of the existing branching ratio for K+ → π+V → πe+e− may come from the resonance. Thus, we require (12) be less than 3 × 10−8,andarriveattheconstraintonmassversuscoupling plotted in Figure 2. As one can see, the constraint becomes stronger than (g − 2)µ for mV around 300 MeV. We also include a sensitivity line, up to whichthemodelcanbeprobed −9 if ∆Brres ∼ 6 × 10 can be achieved in the dedicated analysis of lepton spectra.
6 Constraints on invisibly decaying dark MiniBooNE sensitivity to vector portal DM photonsMiniBooNE sensitivity to leptophobic DM
20 NΧ"NΧ mΧ)10 MeV Κ)0POT)2+10 10&3
10&4
1000 MiniBooNE 10&5 90% C.L. 10 MiniBooNE [arXiv:1211.2258] 1 signal B Α
Dark 10&6 photon Baryonic MiniBooNE K!"Π!!invisible Unique sensitivity mediation vector Π0"Γ!invisible & over much of the 10 7 Monojet CDF parameter space! mediation Neutron Scattering J Ψ"invisible! "
10&8 10&1 # 1
mV GeV 24 23 BNL results can be significantly improved by NA62 ! " 17 Radiative decays
New particles could be coupled only to leptons proportionally to their mass. Or they can couple to quarks in such a way to prevent π0à V + γ. (Irvine group idea in connection with Be8 anomaly).
In that case studies of
K à µν l+l- K à π+π0 e+e- can shed light on these type of models.
18 4
φ S h H ψ
δ13/cβ sα/cβ cα/cβ − q δ23/sβ cα/sβ sα/sβ
W , Z δ13cβ + δ23sβ sin (β α) cos (β α) − − φ TABLE I. Values of ξψ for φ = S, h1, h2, ψ = , q, W , Z in the L2HDM+ . S Leptonic 2HDM + singlet scalar 1 preliminaries Consider 2HDM where one of the Higgses (Φ1) will mostly couple to φ We follow Brian’s notes and notation as closely as possible. leptons, andThe also potential mixes is with a singlet that is “light” relative to EW scale. Defined this way, ξψ,V = 1 is a coupling of SM Higgs strength. In Table I, we show these couplings in terms of V = V + V + V (1) 2HDM S portal + + + FIG. 1. Branching ratios for S γγ, e e−, µ µλ−, τ τ2− λas 2 the angles α and β. 2 2 2 1 2 V2HDM = m11Φ1†Φ1 + m22Φ2†Φ→2 m12 Φ1†Φ2 + Φ2†Φ1 + Φ1†Φ1 + Φ2†Φ2 (2) a function of mS . − 2 2 2 2 We assume that h has SM-like couplings to the gauge λ5 + λ Φ†Φ Φ†Φ + λ Φ†Φ Φ†Φ + Φ†Φ + Φ†Φ (3) 3 1 1 2 2 4 1 2 2 1 2 1 2 2 2 bosons and quarks, which means that cos (β α) 0 2 − 1 2 2 AS 3 λS 4 and cos α sin β. Furthermore, if tan β 1, then H VS = BS + m0S + S + S (4) relies exclusively on couplings2 2 to4 leptons, Eq. (3), comes and S will couple much more strongly to leptons than particle couples toV leptons= S withA Φ†Φ a coupling+ A Φ†Φ strength+ A Φ†Φ on+ Φ†Φand sensitivity levels to light(5) scalars coupled to leptons portal 11 1 1 22 2 2 12 1 2 2 1 themostly order of from the SM low lepton and Yukawa medium couplings, energy which processes, in that areand independent does from the UV completion (result- to quarks. This can be accomplished by choosing α 0 4 thenot case use of the any muonΦ1 and of is theΦm2 canµ/v additional be decomposed4 10− , as the particles muon g brought2 ing muon in by decays, the leptonic kaon decays, electron beam Calling the the lightest × scalar particle S−, one takes a large tan beta + (and negative) and β π/2. In this case, we can make problem can be solved. Thus we are motivated to study+ dumps and high-intensity e e− colliders). In Sec. 4 we φa UVregime, completion. and considers We present an effective theΦa = second, low-energymodel dependentLagrangian, (6) h arbitrarily SM-like, consistent with the observations of the effective Lagrangian of an elementary scalar(vSa ,+ ρa + iηa/ √analyze2 the set of constraints tied to the specific way group of constraints in the next Section. of UV-completing the model. These include rare B and the ATLAS and CMS experiments, while allowing mH 1 1 = (for∂ aS=1)2 , 2. vm1 =2 Svc2β,+v2 = vsβ. gΦ1Shas, Yukawa(3) couplingsHiggs toS leptons decays. and WeΦ2 to reach quarks. our conclusions in Sec. 5. and tan β to vary (ignoring questions of fine tuning for AlthoughLeff 2 µThe we mass− introduced2 matrixS for neutral the CP-even notation scalars isg = ξ m/v in l=e,µ,τ describing a particular UV completionM 2 inM 2 Sec.M 2 2, weρ will now). 1 h11 h12 h13 1 M 2 M 2 M 2 ρ withmakewheregl m usel/v it asis of aimportant thispromising parameterization phenomenologicalthatM = 1. (ρS1 ρcan2 S) be model. when hlight,12 h22 presenting2. hcouples23 2 mostly re- to leptons,(7) Given this pattern of masses and couplings, we can find ∼ L −2 2 2 2 2. LEPTONIC HIGGS PORTAL Given that S is not the SM Higgs boson,S the interactionMh13 Mh23 Mh33 S sultsproportionally in this Section to their on massesξ , i.e.. normalizingThis leads to gan on effective the SM “reweighting” the singlet mixing angles, terms in (3) maywith seem to contradict the SM gauge in- variance.Higgsof the Thus, Yukawa traditional at the coupling. very e-mV minimum parameter Eq. (3) space requires for allIn effect this section, involving we discuss leptons. a concrete UV-completion of 2 2 2 2 2 vA vA m a proper UV completion, probably in theMh11 form= m12 tan ofβ new+ λ1v costheβ low-energy Lagrangian(8) in Eq. (3). A simple starting 12 12 h h 2 2 2 2 M = m cot β + λ v sinpointβ to couple a singlet field(9) to the SM is through the δ13 2 , δ23 2 1+ξ 1 2 cot β, particles at the EW scale charged underh the11 SM12 gauge 2 m m m 2 2 S − H − h − H group. On the other hand, if a UV-completeMh33 = m0 model is Higgs portal, (10) 2 2 2 Mh12 = m12 + λ345v cos β sin β (11) (24) found that representsA. Lifetimes a consistent and generalization decay− of modes (3), of S 2 2 =(A + λ )H†H, (4) the light scalar solution to the muon g Mh213 = problemv (A11cβ + de-A12sβ)(12)int −2 L S S or serves additional attention. Another impetusMh23 = v for(A22 study-sβ + A12cβ)(13) where H is the SM Higgs doublet and A, λ are coupling ing veryWe light will beyond-SMThe concentrate mass eigenstates scalars comeson are related the from mass to the these existing range by from 1 MeV to S vA12 discrepancy of the muon- and electron-extracted charge constants. The trilinear term induces mixing between the ξ tan β, (25) a few GeV for mS. (A region from 200 keV to 2me 1 2 ρ1 sα cα δ13 singleth and the ordinary Higgs boson h after electroweak −m radius of the proton [12]. ∼− H MeV may represent an interrestingρ2 = c ”blindα sα δ23 spot”symmetryH [27, breaking, 28], where(14)H =(v + h)/√2. The mixing This works presents a detailed study of the light scalars 2 but is not treated in this paper.)S Inδ31 thisδ32 mass1 angle range,h is given the by S vA12 h mh with enhanced coupling to leptons, and UV-completes ξq 1+ξ 1 cot β. (26) We assume that the elements in the 3rd column and row are much smaller than those in the − m2 − m2 Eq.dominant (3) via the decay “leptonic modes Higgs of portal”.S are It to also leptons, ex- with partial Av h H plores a great varietyfirst 2. of Then phenomenological the masses of the heavy consequences higgs (h is the lighter of the 2) are θ = , (5) width given by m2 m2 of the model. The phenomenology of1 a light scalar cou- h Recall that the Yukawa couplings of S are g = m2 M 2 + M 2 (M 2 M 2 )2 +4M 4 (15) − S ,q pled to leptons in many ways resemblesh,H 2 theh11 darkh22 photon∓ h11 − h22 h12 S 3/2and the coupling of the light, mostly singlet scalar S to ξ,qm,q/v. phenomenology, but with couplings to individual flavors2 2 mS 4m SM fermions is simply their SM Yukawa coupling times proportional to their masses. As a result, at any given1 We can re-express the shift of the mass of the light- ΓS = g 1 2 this. mixing(28) angle. Low mass singlets are constrained by energy the production→ of such a× scalar8π is most− effimcient est scalar from Eq. (19) due to electroweak symmetry S B and K meson decays (see, e.g. a collection of theoret- using the heaviest kinematically accessible lepton. We ical and experimental studies in Refs. [14–21]), and for breaking in terms of its more physical parameters, identify the most important search modes for the scalar Depending on the coupling strength andm the< boost4 GeV the of mixing angle is limited to θ < 10 3. that could decisively explore its low mass regime. Our S − 2 Significant further advances in sensitivity to θ| are| possi- S mainproduced conclusionS is, that the an decay elementary length scalar of withS can cou- be macroscopic, 2 2 mH ξ ble with the planned SHiP experiment [22]. Therefore, m m . (27) plingor to rather leptons, prompt., scaling as Form can example, be very effi atcientlym =1GeVthe S 0 S there is no room for accommodating θ O(1), and con- − tan β probed, and in particular the whole mass range consis- proper decay length is sequently no large correction to the muon∼ g 2 is allowed tent with the solution of the muon g 2 discrepancy can 2 2 in this simple model. − Strong cancellation between δm and m to obtain a be accessed through the analysis of existing− data and in S 0 2To circumvent this obstacle, we modify the SM not upcoming experiments. 1 GeV-scale value of mS represents a (mild) fine-tuning 6 only by adding a singlet but also introducing a second Our fullc modelτ(mS is= based 1GeV) on the lepton-specific3 10− cm two Higgs , (29) in this theory. We have checked that the hierarchy of × × ξS Higgs doublet that mixes with the singlet. In particu- doublet model with an additional light scalar singlet. The lar, we are interested in the so-called “lepton-specific” the mass scales, mS mh,Hl is indeed possible without mixing of the singlet with components of the electroweak representation of a generic two Higgs doublet model doubletsand the results decay in the is effective very Lagrangian prompt. of Eq. (3). It inducing an instability of the corresponding minimum in (L2HDM) [23–26]. Calling the two doublets with SM also gives us the possibility to include additional observ- the scalar potential. The γγ channel may become noticeable (upHiggs to charge20% assignments Φ and Φ , we assume that ables and constraints due to the fact that S receives small 1 2 Φ couples∼ exclusively to leptons, while Φ couples to butjust nonvanishing below couplingsmS =2 tom theµ) SM due quarks to and the gauge loop-induced1 cou- 2 quarks. Moreover, we assume that all physical compe- bosons.pling We to note photons. that the In UV our completion model, presented the scaling in g m al- nents of Φ are at the weak scale or above. Taking this work is not unique. For an alternative way of UV ∝ 1,2 3. CONSTRAINTS ON LIGHT SCALAR DUE lows for unambiguous determinations of theΦ correspond-/ Φ tan β very large as well as arranging for completing the same model with the use of vector-like 2 1 TO ITS COUPLINGS TO LEPTONS the physical ≡ bosons of Φ to be heavier than those of fermionsing branching at the weak ratios. scale see We Ref. plot [13]. theWhile branching many ratios of S 1 Φ , we arrive at the “almost SM-like” limit, but with aspectsas a of function the low-energy of its phenomenology mass in Fig. based 1 noting on the that2 the decay is the set of heavier Higgses that couple to leptons with effective Lagrangian (3) are similar in both approaches, We subdivide all possible constraints on light scalar always dominated by the heaviest kinematicallycouplings allowed enhanced by tan β.Thenthemixingterm the UV-dependent effects are markedly different (espe- S into two groups. The first, model independent, group lepton pair. A (Φ†Φ + Φ†Φ ) will most efficiently mix with Φ , cially for the flavor-changing observables). 12 1 2 2 1 S S 1 This paper is organized as follows. In the next sec- resulting in the light scalar S coupling to leptons with tion we discuss light scalars coupled to leptons and a strength possbile UV completion of such models via the leptonic m g = tan β θ , (6) Higgs portal. In Sec. 3 we group the set of constraints v × × 2 3 10 3 3 10 10 10 Μ Μ Μ Μ 3 100 B s 10 100 B s 100 2 hh h 4 hh h 10 10 10 B K 10 B K ! " HPS Σ HPS Σ 2 ! " ! " 2 2 Μ 5 2 Μ
GeV g 10 eff g
Ξ Ξ 1
1 " ! Κ 1 " ! ! ! ! " ! " 12 tan Β200$ $ tan Β200 # # A ! !" 6 ! !" 10 0.1 mh126 GeV 0.1 mh126 GeV 0.1 ! ! E137 mH200 GeV E137 mH200 GeV
7 10 0.01 0.01 mH 300GeV 0.01 mH 300 GeV ! ! ! 8 ! ! 3 103 10 103 " 10 0.01 0.1 1 10 100 ! 0.01 0.1" 1 !10 100 ! " mh GeV mh"GeV
!" !"
“Effective” mixing angle for electronsS FIG. 1. Left panel: Constraints on the coupling to leptons (in terms of both ξ = g(v/m)andeff = ge/e)asafunctionofthescalar Figure 1:mass, Allowed based purely regions on the effective with theory parameters in Eq. (3). The region fixed where (g as2)µ describedis discrepant at 5σ inis shaded the in text. red, while On the green the left, the shaded band shows where the current discrepancy is brought below 2σ.WeshowconstraintsfromthebeamdumpsE137,Orsay,andE141.− right handThe axis projected is sensitivities given fromby µκeff3e,NA48/2,NA62,HPS,analysesofexistingdatafromCOMPASSandmeξ/ev. On the right, the right-handB-factories, axis as well is as aA12 related projected sensitivity at BELLE II are→ also≡ shown. (See Section 3 for details.) Right panel: Constraints on the L2HDM+ϕ UV completion of the effective theory in Eq. (3), as described in Sec. 2. Model independent results are as in the left panel. In addition, for this particular to ξ as in the text. The get the E137 and HPS regions, we( ) just+ use the+ values taken from UV completion, there are constraints on the model from searches for h SS 2µ2τ, B K ,andBs µ µ .Wehaveset → → → ∗ − → − tan β =200,Onem Hcan= m still=500GeV,and “fix”m 12the=1TeV.(SeeSection4fordetails.) g-2 discrepancy with such the standard κ vs. mHV± kinetic mixing plot. scalar. particle couples to leptons with a coupling strength on flavors are non-universal and proportional to the mass. the order of the SM lepton Yukawa couplings, which in As a result, at any given energy the production of such Batell, Lange, McKeen4 , 4Pospelov, Ritz, 2016. the case of the muon is mµ10/v 4 10− , the muon g 2 a scalar is most efficient using the heaviest kinematically problem can be solved. Thus we are× motivated to study− accessible lepton. We identify the most important search B-factorythe effective Lagrangian signal of from an elementary the scalarassociatedS, perturbativitymodes τ+τ for- the+ scalarScalar that could à decisively τ+τ- exploreµ+µ- its low mass regime. Our main conclusion is that an elementary 1 2 1 2 2 = (∂ S) m S + g S, (3) scalar with coupling to leptons scaling as m can be productionLeff 2 willµ − test2 S the model below mS ~ 3.5GeV. Kaon decay studies 3 l=e,µ,τ very efficiently probed, and in particular the whole mass 10 + - range consistent with a solution of the muon g 2 dis- are also warranted (K à µν l l including low m ) − with gl ml/v as a promising phenomenological model. crepancy can be accessedee through an analysis of existing ∼ Given that S is not the SM Higgs boson, the interac- data and in upcoming experiments. tion terms in (3) may appear to contradict SM gauge Our full UV-complete model is based on the lepton- invariance. Thus, at minimum, Eq.E137 (3) requires an ap- specific two Higgs doublet model with an additional light
propriate UV completion,Β generically in the form of new scalar singlet. Theh mixingh h of the singlet with compo- particles at the electroweak100 (EW) scale charged under the tan nents of the electroweak doublets results in the effective SM gauge group. On the other hand, if a UV-complete Lagrangian of Eq. (3). The model also induces addi- model is found that represents a consistent generalizationB K tional observables, and thus constraints, due to the fact of (3), the light scalar solution to the muon g 2 prob- that S receives small but nonvanishing couplings to the lem deserves additional attention. Another impetus− for B Μ Μ SM quarks and gauges bosons. We note that the UV studying very light beyond-the-SM (BSM) scalars comes completion presented in this work is not unique. For from the existing discrepancy10 of the muon- and electron- an alternative UV completion of the same model utiliz- extracted charge radius of the proton [13]. mhing126 vector-likeGeV fermions at the weak scale, see Ref. [14]. This paper presents a detailed study of light scalars m While200 manyGeV aspects of the low-energy phenomenology with enhanced coupling to leptons, and provides a vi- H based on the effective Lagrangian (3) are similar in both able UV-completion of Eq. (3) through what we dub m 300 GeV Happroaches, the UV-dependent effects are markedly dif- the ‘leptonic Higgs portal’. We also analyze a variety of ferent (especially for flavor-changing observables). phenomenological consequences1 of the model. The phe- nomenology of a light scalar coupled0.01 to leptons resembles0.1 This1 paper is organized10 as follows.100 In the next section in many ways the phenomenology of the dark photon, but we discuss light scalars coupled to leptons and a possi- mh GeV with the distinct feature that the couplings to individual ble UV completiontan Β of200 such models via the leptonic Higgs
Figure 2: Allowed regions of tan β and mh with ξ fixed to the value that brings the theoretical prediction for (g 2)µ into agreement with experiment, i.e. we live in the green band in the above plots. We− also show the limit from the perturbativity of the τ coupling to the non-SM-like heavy higgs. The beam dump experiment E137 limits mh 50 MeV in this case.
10 Beam dump mode
Running the NA62 in the beam dump mode is also a good idea:
§ Unparallel (among existing experiments) sensitivity to the displaced decays of light particles.
§ Proton beam dump is also automatically a photon, electron and muon beam dump.
§ Sensitivity to models of light New Physics where g-2 of the muon is corrected via series of light “overlapping” new resonances, where search for a bump is not possible. (Chen, MP, Zhong in progress)
21
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. There is a strong sensitivity of NA62 to all underlying 2-body decay modes that give Kà p + missing energy. Models with very light scalars mixed via the Higgs portal. Models with dark photon decaying invisibly.
3. New radiative decay mode studies (K à µν l+l-) could constrain lepton-specific Higgs models with light particles. The observed K à π+π0 e+e- spectrum can be analyzed for presence of anomalies.
4. Beam dump run is a good idea (possible pre-amble for SHiP) 22