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JHEP05(2018)066 Springer ). Scalars 6 May 4, 2018 May 9, 2018 b − : : April 18, 2018 : (10 February 21, 2018 4 : − Revised Accepted Published , Received and Xun-Jie Xu b Published for SISSA by https://doi.org/10.1007/JHEP05(2018)066 [email protected] [email protected] Werner Rodejohann , , b . 3 Manfred Lindner, a 1802.05171 The Authors. c Beyond , Neutrino

Large neutrino event numbers in future experiments measuring coherent elastic , [email protected] Institute for Research in FundamentalP.O. Sciences Box (IPM), 19395-5531, Tehran, Iran Max--Institut f¨urKernphysik, Postfach 103980, D-69029 Heidelberg, Germany E-mail: [email protected] b a Open Access Article funded by SCOAP ArXiv ePrint: We also outline UV-complete underlyingto models for that both include a number light violating scalar and with conservingKeywords: coupling coupling to neutrinos. and violating interactions are considered.probe It is for shown scalar that current (future)with of experiments masses a can around few the MeV neutrinospectrum couplings energy down shape allow to distortion. to the determinefrom Our level their of present 10 via evolution, and a Big future characteristic Bang limits nucleosynthesis are and compared neutrinoless with double constraints . Abstract: neutrino nucleus scattering allow precision measurementsanalyze of the standard and current new and physics.and prospective We quarks, limits using of COHERENT and a CONUS light as scalar examples. Both coupling to conserving neutrinos Yasaman Farzan, Probing neutrino coupling tocoherent a neutrino light scattering scalar with JHEP05(2018)066 ], 20 ]. Mostly it 2 29 – S) by the CO- ], TEXONO [ 26 , νN 19 20 ]. 16 ]. In the near future, – 25 6 4 14 18 , 13 -cleus [ 11 ν NS ν ], and 24 ], searches for a of the ], or for neutrino exotic interactions, be it NS, including CONUS [ 3 9 ν – 6 19 – 1 – 21 ], Ricochet [ 23 15 2 GEN [ ν ], ] or of other Lorentz-invariant types [ ] has opened a new window to probe Standard Model and beyond 22 1 17 13 3 – 10 1 , 11 2 ], parameters [ 2 ], for light sterile neutrinos [ ], MINER [ 5 , 21 4 In the present paper we focus on new neutrino physics caused by a new light scalar. 4.1 CONUS 4.2 COHERENT 2.1 New scalar2.2 interactions Cross section 2.3 From the fundamental couplings to the effective couplings modify the nuclear recoilwell spectrum as heavy in one. a Mostis characteristic of of manner, course our motivated both study by will for thecoherent focus lack neutrino-nucleus a of on scattering light signals the have in scalar been light colliderwas mentioned scalar as experiments, used before case. that and [ light its Light physics consequences does new in not physics suffer from limits on neutrino non-standard interactions neutrino [ the vector type [ more experiments will beCONNIE able [ to observe CE Such a particle can participate in coherent neutrino-nucleus scattering, and interestingly The observation of CoherentHERENT experiment Elastic [ neutrino-Nucleus Scatteringthe (CE Standard Model physics.low energies Those [ include the determination of the Weinberg angle at 1 Introduction 6 Summary and concluding remarks A Suggestions for underlying electroweak symmetricB models Calculation of the cross section 4 Constraints and future sensitivities from CE 5 Interpretation of the results 3 Existing bounds from particle and astroparticle physics Contents 1 Introduction 2 Light scalar interactions in coherent neutrino-nucleus scattering JHEP05(2018)066 ν φ C (2.3) (2.1) (2.2) ]. Discov- 31 we write the , ], indicating al- 30 N 29 , 26 , . ., 14 c c . . + H + H L L ν S could provide strong constraints R Cν ¯ ν T L φ νN φ, ν , we present the framework of a light φν y N ν 2 2 ψ y we discuss and interpret the implications = with the whole nucleus 5 Nφ φ νφ Γ c = . ) N , we summarize our findings. The calculational 5 and γ – 2 – ψ 6 4 ν + H which couples to neutrinos. There are two possi- , the hermicity of the Lagrangian implies that ≡ φ L iD φ ν c Nφ + L S have been discussed in refs. [ ¯ ν L ν φ C ν νN ( 2 y ¯ ν ≡ ≡ LNV can in general be a complex number. LNC L ν L as well. For real . For simplicity, throughout this paper we implicitly assume that y ν φ iD − ν C = , we discuss the constraints on such scalar from various particle and as- are real. Note that the couplings have flavor indices, suppressed here for clarity. ν 3 y ν D The same scalar field can couple to quarks. Since in coherent neutrino scattering we This paper is organized as follows: in section In both Lagrangians are concerned withLagrangian the as: effective coupling of valid for a complex and The lepton number violating form of the interaction can be written in analogy as couplings. The latter possibility requires the presence of right-handed neutrinos: where is a real field but most discussion and overall behavior of the bounds and limits remains nuclei) mediated by a lightof scalar coherent neutrino-nucleus scattering. and then discuss the2.1 corresponding cross section New scalarWe interactions consider a scalar fieldbilities denoted for by such coupling, namely lepton number violating (LNV) and conserving (LNC) details and outlines for UV-complete gauge invariant models are2 presented in appendices. Light scalar interactionsIn in this coherent section, neutrino-nucleus scattering we first introduce the possible interactions of neutrinos with quarks (or scalar with couplings to neutrinosand and include quarks, discuss a the discussion coherentsection scattering of cross form section factors whentroparticle physics the observables. coupling In sections toof various possible is observations. considered. In section In use reactor antineutrinos to probespectrum coherent shape scattering. for The light characteristicstruct scalars distortion the of with scalar the masses mass, around whichexisting the we ones neutrino explicitly from energy demonstrate. a allowsmodels variety We to of also that recon- sources compare may our in be limits particle behind with and the astroparticle existence physics. of such UV-complete light scalar particles are also outlined. ery limits on light particles inready CE before the observation by COHERENTon that CE light mediators. In ourobtain work, the as current mentioned limits before, from COHERENT we onalso focus its consider on mass explicit a and coupling future new with scalar realizations SM particle of particles. and this We experiment and also of CONUS, which will from high energy scattering experiments such as CHARM-II, as stressed in [ JHEP05(2018)066 , N ): C (2.6) (2.7) (2.8) (2.9) (2.4) (2.5) B We can . ν 1 E 2 ν E + 2 2 M to be real numbers. ) = N ν , D E (  , 2 2 ν N and max T E ψ T ) to the effective coupling ( N N  q ψ C O D . , M , + 5 q where φ − C . iγ 2 ν , 2 dT 2 dσ | , we present examples in which couplings N Thus, one can separate the cross section E φ  ν MT 2 φ D y + A 2  | m 2 2 + T 2 max N ). The masses of the scalar and nucleus are ) 1 2 SM T A 2 φ C N dT – 3 – 2.2 − C dσ m − 2 ≡ 1 A ], there is no interference in neutrino scattering between vec- ≡ + 4 = Nφ 4  32 Y L 2 Nφ  dσ dT + MT Γ MY . In appendix Z ) or eq. ( ) (2 νφ M ]. π 2 W 4 2.1 s 13 4 = and )) leads to -flipping scattering which will not interfere − L ⊃ L φ φ π 2.2 (1 m 4 dT dσ − N  hermicity of the Lagrangian demands φ M ) or eq. ( 2 F 2.1 G can be either eq. ( is the Dirac of the nucleus, assuming it is a -1/2 particle. — see the appendix in [ = is the coupling of the scalar with the nucleus, whose connection to the fundamental denotes the recoil energy. The SM cross section, assuming full coherence is given νφ N 2 N L ψ T ] SM C /M dT In summary, the Lagrangian (in addition to the SM) responsible for coherent neutrino 2 ν 33 ) will be discussed later. Note that we here consider both scalar and pseudo-scalar The actual spin of the nucleus can take other valuesMore but generally, as the it difference has of been the studied cross in section [ is suppressed dσ E 1 2 N Here couplings is discussed in the next subsection.by The division by the atomictor number (or axial-vector) form interactions and other forms of interactions, including (pseudo-)scalar and tensor. where we have defined The coherent scatteringscalar mediated interaction by is the of the light LNC scalar, or LNV independent form, of is whether (the derivation the is new given in appendix where by [ The first thing(either to eq. notice ( iswith that chirality-conserving the SM weak Yukawa interactions. interactioninto two of parts both containing the LNC pure and SM and LNV the forms new physics contributions: where respectively denoted by to neutrinos and quarks can be embedded2.2 in electroweak symmetric models. Cross section interactions. In what follows, theessentially latter only contribution the is scalar usually contribution very is much what suppressed, . and scattering is write Again, for real The conversion from fundamental quarkD couplings ( where JHEP05(2018)066 ) u to are ) in , is and φ n 2.19 q (2.10) (2.11) (2.12) (2.14) (2.13) B.6 f Z MT with the , ,  and φ )], we focus p q 011 2 φ 011 . . f 0 2.9 m 0 — see eq. (   2 ν 2 E T ] for the details and 2 043 043  . . 34 . 2 N # S [cf. eq. ( = 0 /C ], the form factors are: = 0 q n because the pseudo-scalar q 2 N n p s s f m 37 D νN N q C D 1 + are quark masses; q , on q , f , f X n , " 3 m , C n ) 066 0014 0015 Z . m . 066 . . 0 quark from [ 0 0 0 − = is actually qqφ, s ≈   term. This is in analogy to dark q . n A ≈  2 ) ν 2 C ν  ) n s E 2 p ν s + ( f ,C /E q f 0189 – 4 – 2 0208 p by ∼ X . has no effect on CE # . /E − T q − q 2 p q 6 MeV are masses of and ; n N u p . f u ZC C T m = 0 f O = 0 f D originate from fundamental couplings of q L ⊃ MT p n = u u − C − O N n N d p d q f D = 939 f C X " − n − , f , f p m and (1 (1 m . Taking the fundamental scalar interaction of quarks with 2 is related to ] and the data for the 2 N 27 27 0028 0027 = N . . C N p 0 0 C ≈ 36 ≈ , makes it almost independent of the type of nucleus — cf. eq. ( C C n   p t t 35 f f Y ≈ ≈ ], where an effective scalar interaction, corresponding to 3 MeV and . 0411 0451 p n . . b b 13 f f ). The cross section has little dependence = 0 ≈ = 0 ≈ p p = 938 n n d c d c 2.20 f f f f p are proton and neutron numbers in the nucleus; quarks from [ m d Since the pseudo-scalar coupling Obviously scalar interactions lead to a spectral shape different from that in the SM Z The explicit form of the negligible term 3 − the appendix. the scalar form factorsand in and . According to the updated data for the Here A the effective coupling where the couplings to protons and neutrons are on the scalar coupling, be of the form The effective couplings quarks. The connection between thebeen effective well couplings studied and in the spin-independent fundamentalto couplings dark know has matter the direct scalar detection. formsummarize factors Essentially, the of one relevant quarks needs results in below. the nuclei. We refer to [ case, see e.g. [ considered. For a light scalarthe under spectrum discussion are here we possible, seethan in that the particular additional typical if modifications of the transfer scalar mass is2.3 of the same From order the or fundamental smaller couplings to the effective couplings and eq. ( contribution is suppressed bydirect the detection where darkwell known matter to be interactions suppressed. mediated by a pseudo-scalar is in the definition of JHEP05(2018)066 ]: . and 41 (2.18) (2.19) (2.20) (2.15) (2.16) (2.17) Z A − 130), we A , . , ) ), in terms ) , 4 4 ) (Ge) ) (CsI) ) for Ge and − t t − 2.9 , C C 10 10 2 2 2 GeV Z,A × − − . × 6 6 . 10 10 6) and (54 . . in eq. ( 3 3 × × , , . (as in the case that the 72 2 2

Y = 96 MeV = 173 5 7 , . . q ν − − t s y m 10 10  + 2 + 4 p ∝ × × , . b b ]. The form factors computed | | C q 5 5 C C ν ν for the heavy quarks are of the . . 38 ) as (32 C 1 9 y y 1 1 A Z . . q ) ) , , p p C 2 2 + C C : − − + 1 + 1 Z,A n q c c , m C 44 42 C 10 10 , m . . C C . Z × × 5 3 . . CsI 9 9 + 0 + 0 A − . . Y n n 4 4 (10%). If + 3 + 6  A 2 MeV 18 GeV  on the , , S experiments using different targets, we will C C to the [ . . ≈ t s s t O n p t t  ] agree well with the above results. Notice that – 5 – 42 42 φ

C C f N f m m 56 58 . . Ge = νN . . 5 7 = 2 = 4 0 0 C . . , s 40 Y , | b , , , (0 (0 u b b n n | | p b b 1 9 = . . f f 39 m m 8 8 q q | /C ν ) , , , , p y c 2 0 c ≈ ≈ n ) + (54 ) + (30 p . . c c A C N u u f f m m ) can be present. The definition of (8 (9 C C C 3 Ge − CsI | , , Y 1 1 Y ≈ ≈ s s . . n n p s s r (10 2. For example, taking the average values of ( f f C m m , m / ( O , m | ≡ + 1 + 6 , , d d u on the types of targets is weak because for heavy nuclei, u n p u Y u C C f f m m ) or Y 1 3 2 . . , , 7 MeV 27 GeV . . d d (1 (6 n p d d (10 f f m m × × O = 4 = 1  3 2  c are approximately the same for the heavy quarks because their contributions d p n 10 10 m m m m ( c, b, t = f N C are typically close to 1 coupling to the quarks comes from the mixing of a scalar singlet with the SM Higgs), the Z A When comparing the sensitivitiesignore of the CE small difference and assume The dependence of CsI targets, we get This means that from theby a fundamental coupling factor to of theof effective the coupling fundamental an couplings, amplification can be rewritten as can evaluate the explicit dependence of For Ge and CsI targets, taking the average values of ( we obtain negligible due to suppression byφ their masses. However, if contribution from all flavors will be comparable. Taking the following quark masses [ come from heavy quark loopsby that the couple effective field theorydespite in the different refs. quark [ content,out the to couplings be of proton almostsame and equal: order neutron of to magnitude the as scalar for turn the light quarks, then the contributions of heavy quarks are where JHEP05(2018)066 2 / 1 ) ]: (3.1) 2 eα . The | ) from 47 ν ν νφ y y | can cause n , of course + Ge double l α φ C e 76 + P → Cν − e T e + on ( π + φν 3 − − or e ) but the bounds on ]. Notice that as long n + p νφ D 45 + + in the mass range of our l p → . → 2 ν + (comparable to nuclear ). n D or on their product ( 03 MeV comes from . 3 K + ] (not on 2 ν − + n y . nφ 2 ν 5 < , − C n [Γ ). φ g cm n C 10 R = m 14 D 2 < | = 10 ν 10 sec after collapse, the core has a radius of if the new light boson couples to neutrinos, a LNV coupling of form value of the decaying nucleus. From double y ee n come from low energy neutron scattering off | ) ∼ . The difference originates from the fact that ∼ C ν 2 – 6 – ν Q n ρ y light particles coupled to neutrinos and neutrons ( C D (not to ] in the form of n + 46 C 2 ν value of 2.4 MeV the following bound is found [ C Q = S, since in these setups the nuclei are non-relativistic, their 2 ]. In the first | νN ν 49 y | have been found from different modes [ from neutron nucleus scattering: 2 is much smaller than the mass the bound is independent of / is lighter than the from meson decay: Xe with a 1 n ) φ ν φ ]. 136 C y 2 µα ], in particular using Pb as target. The effect of a new scalar would be | 48 ν 44 y – | α 42 P 10 MeV. The core can be hypothetically divided into the inner core with a radius . Moreover, the bound similarly applies for the LNV and LNC cases. In the LNC ∼ few 10 km and a matter density of φ consult the textbook [ ∼ However, because of the highbefore, pressure, neutrinos are most trapped of inside theof the nucleons core are and free. are thermalized As with mentioned a temperature Supernova bounds and limits: can affect the dynamics ofimpact a proto-neutron of our in particular several scenario ways.structure on of Before supernovae, the discussing let core the us of very awhen briefly proto-neutron neutrinos review star are the in overall the trapped firstmuch inside few smaller 10 the seconds than core after (i.e., explosion the the supernova mean core free radius). path of neutrinos For is more details, the reader can A more recent andbeta a bit decay [ weaker bound for Bounds from doubleneutrinoless beta : decay [ provided that beta decay of the absence of a signaland for ( such decay modes, boundsas of the order mass 10 of m case, sensitivity is to the combination that like the case of CE dominant sensitivity is only to Bounds on it can open newscalar decay will modes eventually for decay into a such as neutrino pair appearing as missing energy. From Bounds on interest, the strongest boundsnuclei [ on to provide a Yukawa-type scattering potential whose effect can be constrained. Notice • • • • In this section wevarious review observations the and relevant experiments bounds otherbounds on than on coherent scattering. the hadronic Asneutrino we couplings couplings shall are are see, on on the while nuclei in the considered setups are non-relativistic, neutrinos are ultra-relativistic. 3 Existing bounds from particle and astroparticle physics JHEP05(2018)066 e is in to ν are α e e . In ν e ν ν λ n ν and/or e ν decreases and , where erg. 300 cm, which e e ν ν 53 n ' cm, which is much λ  2 ) τ φ ¯ ν , which roughly speak- n in the outer core, where /λ /m e 2 = ν R τ ν (with energy of 200 MeV) are n few 10 km). The consequences and ¯ e ). Considering the high density = ν ∼ e π µ ν are zero and their temperatures are ¯ ν (4 n / τ 2 ν ν (10 sec). Neutrinos diffusing out of the = E O µ 2 F few 10 km. The diffusion time, given by 10 MeV)(5 MeV ν and / G n ∼ ) because of a shorter mean free path φ µ ν ∼ E will increase dramatically. Conversion of  /λ R ( , it can have profound effect on the Equation 2 ) µ 2 – 7 – e σ which annihilates with inside the core. τ ) ¯ ν ν | ( R n ν µ are almost equal. Notice that the average energies + (1 sec) to y ν e | e O / ν 5 or ¯ − ) τ and ¯ ( µ e ν . In the outer core, the chemical potential of and therefore the diffusion time ν α , λ e ν ν particles can decay into a neutrino pair. The decay length is evalu- φ , the temperature of µ ν and their throughout the core are given by their temperature τ ), is therefore of order of ν , µ will lead to the production of R/λ ν ( e ¯ smaller than the radiusof of new the interactions proto-neutron on star supernovachange ( explosions of can equation be of categorized state in intoof case three of right-handed effects: LNV (anti)neutrino (1) interaction; (2) emissionthe new in cooling duration modes case of because neutrino of emission LNC ( interaction; (3) prolonging of State (EoS) inconverted to the inner core.ν For example, if In our case the ated to be approximately (10 tween an upper bound andfree a path lower of bound. neutrinos Newing interactions can coincides also with affect the theThis mean observable sets another duration limit. ofconvert Finally, neutrino if it emission there to is from any a a of new supernova. ¯ process that can remove Still, if the newcan particles contribute are to supernova stable, cooling. theyin Considering can however the diffuse the theoretical evaluation out uncertainty of and,energy along total carried with binding away, neutrinos, energy suchconsideration, contributions and within can the present be observational uncertainties, can tolerated. uncertainty only on rule Thus, the out supernova a cooling range of coupling be- affect this picture. First, letaction us of discuss the the new impact particleinside on is the supernova very core cooling. feeble, it it If can cannot theno exit be inter- energy without trapped. for hinderance Thus, and neutrinos if take toupper energy it bound show out is on up of produced the as the coupling the coreis of observed leaving large the enough events new of to particles. trap SN1987a. On the This the new other sets particles, hand, an the if impact the on coupling cooling will not be dramatic. is much smaller thanR the core radius core carry out the binding energy ofLet the us star now which see is how of order new of light 10 particles coupled to neutrinos and matter fields can of which is of orderthe of chemical few potential 10 MeV. vanishes, Thethe are energies inner also of core of is theoff of same nucleons order order with of but a theof chemical the cross nucleons, potential, energy section the 200 of of MeV. mean The free path neutrinos for scatter neutrinos will be of order of is about 200 MeV whichdegenerate. is much The larger chemical potentials than of theirequal. temperature, Thus, implying inside that thethe inner number core density of the number of of 10-15 km and the outer core. Within the inner core, the chemical potential of the JHEP05(2018)066 . 4 α ν will (3.4) (3.2) (3.3) ττ ) ν y . # will be signifi- 1, a significant and ( 2 φ & m /λ µτ 2 ν 2 , ) has a LNV coupling + ν E R 2 φ diffusion”, and holds y e 4 2 ν , m ν 2 ν ν E 1 ,( + E 4 2 ν 4 100, the produced sterile & µµ E can be converted into ¯ )(10 sec) ) 4 − n & ν e 2 φ y ν − 2 ν R m , 2 φ ) as “SN E ρ/m } 2 φ n m ( + 5 2 φ exchange becomes comparable to both for LNV and LNC cases can + m (10 sec) σ 2 ν 2 m ν between these two limits are there- φ . The number density of nucleons is φ E E × ρ/m 4 n n and 4 ( e, µ, τ n C σ C 4 ρ ν m log log ), the diffusion time y ∼ ∈ { " π × 4 ν √ -nucleon scattering should be more impor- u t v u α 2 y n ) 2 ν (4 ν 7 / n C − due to non-zero ( 2 ν 2 in the inner core will convert into antineutrinos, | – 8 – πE + τ 10 E ν e ν y α ν 16 2 F | × ¯ ν trapping”, respectively. G 2 , where R α → and ¯ ν ) = > n µ n n Cν ν + T e C + ) e to ¯ eα − ν φν ν ( ) ( τ ν eα ν σ y → ) ( ν n y p + and 200 MeV, the equation of state of the supernova core has to be re- ) µ − ν ( ν are expected to be the same and their chemical potentials to be zero, ∼ ( e τ σ ν ν E and of the form ( -nucleon scattering cross section if ν µ φ ν nos which is theneutrino-nucleon typical scattering energy cross for section allthe due neutrinos standard to in weak the cross outer section cantly affected. core. This In limit case isfor that shown both in the the figures LNC and LNV cases. generates an upper limitneutrinos on will the be coupling. trapped.fore If The excluded values by of supernova coolingas considerations. “SN The energy limits loss” are and denoted in “SN Drawing figure these figures we have assumed a nominal temperature of 30 MeV for neutri- not change the equation of state. When the interaction ishanded antineutrinos) LNC, into sterile scattering right-handed will neutrinoswhich (left-handed convert antineutrinos), do left-handed not neutrinos participatefraction (right- in weak of interactions. the If active (anti)neutrinos will convert into sterile ones. Avoiding this in which considered. In subsequent plotsthe associated that limit summarize to theof avoid limits this on feature our as scenario,conversion “SN of we core call EoS”. Since the temperatures a significant fraction of degenerate drastically changing the equation of state. That is, for to The produced antineutrino will be trapped. However, if The scattering cross section for sterileLet (anti)neutrinos us is discuss the given three by effects the mentioned same above one formula. by one. If indices, we find thatthe the neutrino-neutrino scattering crosslarger section than is that comparable to oftant. neutrinos, The thus cross the sectionbe of estimated the as scattering due to all these three effects, the neutrino scattering plays a key role. Neglecting flavor JHEP05(2018)066 . , φ 4 (3.6) (3.7) (3.5) process -nucleus -channel t R n ν , production. R ν , φ  . Our simplified → ) 5 distributions. At x ] which solves the =3 MeV 1 MeV. Lighter L T ν channel diagrams it

ν 50 is not possible. Pro- & L 4 ν / u φ φ 1 m ! and ¯ → ) ) will be quite different so and log(1 + 2 x ν ]), we find eff t νν − decays away before the onset 51 ) [ δN φ x . x eff φ 1, we find from BBN with that from ) m . Combining this bound with the one δN (1 + < ) log(1 + 2 MeV x 1 + 2 2 φ ν x x 9 ) can lead to contributions at loop level production. The y 2 − /m  R 3 (3 MeV is the temperature at neutrino 2.2 . 1 MeV, this bound does not apply because at the BBN or the CMB era. Thus, within 2 10 ν 2 0 1 T (1 + 2 x =1 MeV > (1 + 2 × 2 eff T . 2 φ x | φ 5 N − and ¯ 4 1 = 2 | – 9 – by warming up the ) m can take place but are suppressed. The − ν < R x πm x y 1 MeV, although | ν | H ν eff is the energy of colliding neutrinos in the center-of- exist so we should only check for the ) 32 y < | ) or in eq. ( φ N =3 MeV ν as one scalar degree of freedom if they enter thermal R νNφ . For T (1 + φ E ν the contribution from the LNC and LNV cases to the 7 | x ) = 2.1 → 1 eff − → 2 R − N ¯ ν 2 φ 10 νν < m T R ( m × νN σH ν σ ν can lead to 5 ν

n or will be produced at high temperatures but it will decay before n → 5 R are in MeV and , in which ¯ − ν L φ 2 φ ¯ νφ 1 MeV ¯ R ν Y < . T 10 ν ν L ν /m × ( 2 ν → → 7 σ and . E ¯ ν L 1 φ 1 MeV, ¯ ν ν L m = 2 < & ν ν x from neutron-Pb scattering gives the limit denoted “BBN + n scat.” in figure φ y n m = 1 MeV, combining the above bound on C decays into neutrinos before from the plasma. That is why the φ in which on where mass frame. Taking decoupling and 0.3 is the bound from CMB on process can also take placehas but a because smaller of cross cancelation section. between The cross section of the dominant production mode is bound denoted “BBN + nanalysis scat.” seems appears to as be afull vertical in line Boltzmann excellent in equations. agreement figure with the resultsii) LNC of case: [ incesses this like case, the production of scalars via Notice that for 0 of BBN it stillm contributes to scattering, yields φ the present uncertainties, therein is turn, no can bound contribute from to equilibrium. BBN Taking for additional number of relativistic degreesin of the freedom following, ( we address themi) separately. LNV case: inFor this case, no neutrino decoupling without affecting BBN and CMB bounds: The effective couplings in eq. ( • to neutrino mass. Beforesymmetric evaluating UV-complete the models contributions, thatcan let at provide us low mass notice energies for thatA, neutrinos give the the at rise electroweak tree to tree level, these level too. effective contribution coupling In to the neutrino models mass summarized turns in out appendix to be given by these effective JHEP05(2018)066 ) φ 1 ]). At 52 . couplings. The 5 ν y   )). The contribution (as shown in figure cut 2.2 φ cut Λ Λ 100 GeV arise. In these figures, the 100 GeV  2  . 2 6    . The induced effective mass will L 5 5 ν − N − R ν 10 Y 10 Y × × 8 or ¯ (as in case of eq. ( 8  c L  ν V V e Cν e 6 φ T 8 – 10 – − ν − )) or 10 q N 2.1 × ρ = 10 ν m ν ) to neutrino mass, one should bear in mind that these = 2 cut y 2 φ Λ N m 2.2 3 5 cut . One-loop contribution to neutrino mass. C ) 3 ) denote quarks and the lines without an arrow attached to 2 Λ 2 ), ( 3 π 0 2 ) q Y 2 ( Y 2.1 π (16 2 F G and ∼ Figure 1 (16 (as in case of eq. ( ν q ∼ R m ν ν m couplings will then have the same pattern. In evaluating the loop contribution ν y 100 GeV. Neutrino mass term is a helicity-flipping operator so the loop diagram ∼ Figure 1: One-loop contribution to neutrino mass Let us now discuss the effects of forward scattering off nuclei due to the new interaction cut on neutrino propagation in matterbe composed of of chirality nuclei, flipping form as follows Both these contributions are tooin small to case be of discernible LNV at coupling) beta in decay experiments experiments or searching (even for neutrinoless double beta decay. and the other one can be estimated as loop level, the contribution comeswhich, from as a usual, tadpole can contributionthe be to three canceled loop by level, alines contributions counter-term marked such (see as with for the examplelines ones sec can in 11.2 denote figure of [ from the first diagram can be estimated as from couplings in eqs.couplings ( are valid onlyΛ at energies belowproviding electroweak neutrino mass scale has so to involvedirect the an odd result natural number of of UV this helicity cutoff flipping is is that there is no two loop contribution to neutrino mass and at one couplings times the VEVvalue of to be a consistent new with scalarmass the and measured in neutrino the masses. model. The flavor The structure of VEV neutrino can take an arbitrary e week JHEP05(2018)066 , . ], 2 ν 0. 1 ) φ /E (4.1) 2 ν /m T > ) is the m , we find T 3 − − ) − . ν ) φ ) E ν ν ( ν )(5 MeV E ) is the range of ( 5 T − max T,E T ( max 10 ′ T / + = 150 g cm + ∆ q ( q p l i 8 MeV) and decay dσ dT ρ θ ] and COHERENT [ C ) . S experiments require in- ,T )( 19 i T 5 ν T − − E νN NS • • ) 10 ν ν / 0 and 1 for ν E . More detailed discussion can be y ( so we can write the effective mass ν ν p T < max . One may wonder why forward scat- eV ( /m ν T 2 /m − which has to be compared with ( 12 p ) m θ ν − /m ν C ) † 2 ν E ν 10 ' ( m E = × N Φ( max ν – 11 – ν 0 T /m γ dE N T . Data collection started in 2017 and first results are ν 2 C − is the number of Ge nuclei, ( 8 MeV cm and 0 5 ) is the reactor neutrino flux, and 1 Z Ge n ν − s N E dT S experiments: reactor neutrinos ( 13 q Am 50 MeV) neutrino fluxes. Two types of neutrino sources can be T 10 . ' νN +∆ p × i i T 5 . T ). Taking for example the density of the as Z Am p Ge ' 50 MeV). Two on-going experiments, CONUS [ ρ/m N tN )( . m ].

2 φ φ φφ ν 53 = ∆ . Three loop contributions to neutrino mass. The dots denote charged current weak is the running time, E /m i ν t N y

ν ν p C Figure 1: Three loopinteraction contribution vertices. to neutrino mass. The dots denot Here ∆ recoil energy in eachHeaviside bin, theta Φ( function, equal to 0 for The CONUS experiment uses anear very low a threshold nuclear detector powerantineutrino setting flux plant 17 is m (3.9 2 away GWexpected soon. thermal To power) study the in sensitivity Brokdorf, of CONUS, Germany. we compute the The event numbers total given by at rest ( adopt these two sources respectively.experiments on In light this scalar section, . we study the sensitivities4.1 of the two CONUS 4 Constraints and futureTo sensitivities collect from large CE statistics attensive and coherent low-energy scattering ( energies,invoked CE to carry out CE reason lies in the differentaction Lorentz induces structure a of contribution the ofIn form induced the operators. ¯ case The of vectorialand scalar, inter- should the be matter compared effects tofound have the in the mass [ operatorial splitting, form ∆ as the mass themselves as ( a shift in the masswhich of is neutrinos completely of negligible order comparedtering of to due 3 ∆ to a possibleimpact on new neutrino gauge propagation boson in with matter, similar while mass the present and case coupling of has a such scalar a does large not. The Figure 2 interaction vertices. Notice that Figure 1: One-loop contribution to neutrino mass JHEP05(2018)066 ). N 4.3 (4.2) (4.3) ) does . The 8 MeV 05 keV 40 1 MeV, . ν . 3 > at 8 MeV, ν = 0 = 0 ν T,E in eq. ( E ( φ E T f 30 m = 1%. We also σ dσ dT ], and normalize f 1 MeV) . 54 σ = 100 GeV) = 30 MeV) = 3 MeV) = 0 φ φ φ φ . , m , m , m , m 2 5 5 5 ) − − − − 20 kg). The threshold of , i 10 10 10 10 · × × × × 4 3 3 5 . . . . Recoil energy T/keV = 1 year, ∆ bkg = 4 = 5 = 4 = 3 N to the event number in each t , Y Y Y Y keV 2 a 2 · is the SM expectation, and + , i 10 a σ SM+( SM+( SM+( SM+( i ) in CONUS. 0 2 bkg + N N − ( N

2 (day

f

0 ]

i / 20 15 10 05 00 N

σ 0

cm . . . . . i

SM ,i

1 1 1 1 1

i 1 i /N

N = 2% takes care of the uncertainty in N SM = − 2 sys s where a ,i − σ . We take ∆ σ i 0 13 ) because the cross section sys + N ) and its dependence on the fundamental quark 10 ) ,i 4.1 , σ . a < T N/N φ × – 12 – , i 2 stat ) 2.18 5 m ν σ . bkg E [(1 + ( N i + 5 . max X i 1 T N = 1 MeV) function in ( . 2 p = 100 GeV) = 30 MeV) = 10 MeV) = 0 θ φ φ φ φ χ = , m , m , m , m ). For comparison, the event numbers of the SM signal are also shown. 2 5 6 6 0 − − − − . ,i 1 10 10 10 10 is defined in eq. ( , corresponding to 4 kg natural Ge (with average atomic number × × × × with an uncertainty of 2.17 5 4 0 8 . . . . stat 25 Y σ a = 3 = 1 = 7 = 5 ), we use a recent theoretical calculation of the flux [ Y Y Y Y ν 10 ), we compute the event numbers for several examples ( E Recoil energy T/keV 5 SM+( SM+( SM+( SM+( × . 0 4.1 ], 32 . 13 = 3 . Event excess caused by light scalar bosons in CONUS (left) and COHERENT (right).

0 6). For Φ(

i . 05 00 N 20 15 10

. . . . .

Ge

1 1 SM 1 1 1

i 25) corresponds to 1.2 keV recoil energy. The reactor neutrino flux at

i /N

N . N SM To study the sensitivity of CONUS on light scalar bosons, we adopt the following Using eq. ( 0 -function [ = 72 2 ≈ introduce a background inbin. our calculation by The adding backgroundionization energy in detection CONUS in CONUS( is is 0.3 about keV, which 1 ifhas count divided negligible by the contributions quenching and factor also large uncertainties, so we set a cut of The pull parameter the normalization originating fromsupply or various the sources uncertainty of such thethat fiducial as may mass the change and distance. variation theHere Other of shape we systematic nuclear of uncertainties assume fuel the they are event proportional spectrum to are the parameterized event by numbers and take with contains the additional contributionsthat of the shape light of scalar the bosons. spectrumdifferent, when in we One particular include can the for scalar see low contribution values from can of be the dramatically figure χ A it to meet the total antineutrino flux (2 10 MeV, 30 MeV andsignal 100 strength GeV) is and quantified compare by them the with ratio the SM value in figure couplings is given by eq. ( It is necessary tonot insert automatically the vanish when and Figure 3 The effective coupling JHEP05(2018)066 . , + 2 ν 3 π E ) = f 6 6 6 6 ∼ − − − − , σ a 10 10 10 10 σ MT × × × × =30 MeV) 7 5 3 8 φ ∼ . . . . 2 φ m 16 14 13 11 ( m ). As a result, in observation of the Y σ 2.7 while the second and 1 keV. We assume the µ . ν . Because the first decay 6 6 6 6 e ] a 6.7 + − − − − ν 1 + + 10 10 10 10 µ µ × × × × =10 MeV) ν → φ 5 9 0 4 . . . . + + 9 7 7 6 m + ( π e Y → + the most optimistic bounds together with for the LNC and LNV cases respectively. µ 6 6 6 6 5 5 − − − − 10 10 10 10 with blue dashed lines. If the flux uncertainties – 13 – =5 MeV) × × × × 5 φ , 1 4 9 3 . . . . 4 m 5 4 3 3 ( and figure and figure S experiments are independent of the LNC/LNV cases, Y 4 4 νN 6 6 6 6 − − − − ). It can in fact be used to determine the value of the mass. In 10 10 10 10 2.8 =1 MeV) × × × × φ 3 8 5 0 . . . . m . The first is produced in the decay ( e ν Y . , and ) Y µ f 1%). This will be possible if the reactor neutrino flux is better understood due to ν . σ decay at rest. In its recent groundbreaking publication [ . Uncertainties of the reactor neutrino flux assumed in CONUS100 and the corresponding ) we only sum over the bins from 1.2 keV to 1.75 keV. we show the potential of CONUS100 for determining the mass and coupling of the , 0 , µ , + a 6 ν . Since we care about to what extent the CONUS bound could be improved in the fu- , we assume several different flux uncertainties and compute the corresponding bounds 4.2 σ µ As mentioned above, the shape information for light scalar masses is noteworthy in The result is shown in figure We also study future improved sensitivities of CONUS by assuming a 100 kg Germa- ( Y 1 5% particle assuming two characteristic examples. As long as the mass of the scalar is not . (2.0%, 1.0%) 3 (1.0%, 0.5%) 2 (0.6%, 0.3%) 2 (0.5%, 0.1%) 2 and SM coherent scattering was announced.flux, There are three typesthe of third neutrinos are in produced the in neutrino is the a subsequent two-body decay decay and the pion is at rest, the produced neutrinos will be monochromatic much larger than the neutrino energyreconstruction or of the typical the momentum mass exchange, is possible. 4.2 COHERENT The COHERENT experiment uses a CsI to detect neutrinos produced by the upcoming (realistic) bounds so that other possibilities fallthe into spectrum, the see gap eq. betweenfigure them. ( φ can not be reduced toupcoming such bound an (blue optimistic solid level,ble curve) then and the the constraint optimistic shouldon be bound between (blue the dashed curve).ture, we In prefer ta- to present in figure nium detector as thecorresponding target systematic and uncertainties an are improved(0 threshold also down reduced to toimproved 0 a theoretical models matching and level, measurements.of ( The data forecast taking for is CONUS100 also with shown 5 in years figures Although the constraints of CE the other constraints dependWe on therefore present the the two of cases the separately. interaction, as explained in section Table 1 bounds on which corresponds to abouteq. 1.75 ( keV recoil energy according to eq. ( JHEP05(2018)066 3 PE n flux, (4.8) (4.4) (4.5) (4.6) (4.7) 130). ]: µ , 7 keV. , . 55 ν ), so we # ) and the ν 13 ) y beam with ν 5. This im- ] which can ≈ 4.8 1 µ = < ν ) = (54 ), ( T,E ]). This number αβ /M ( PE ) 1 2 ν 4.7 ν n Z,A E y 7 keV but does not dσ dT 2 ; (ii) for the . I / )) 13 ≈ ν Cs T ≤ E N ( T ), we also compute the ratio . Note that there is a kink , max , ) 3 ,  4.7 0 as well. Since reactor neutrinos  ν µ ν µ T,T ν 5 E m ( , E m θ ) − T,E 0  ]: 8 MeV . ( − . and ) ν 1 1 2 ν E 3 4 4 29 T  E dσ dT keV is replaced with  ( − 2 ν ≈ e 2 ν ν )) ν 3 µ E 17 3 µ 0 Ge 2 µ . φ E E ν 1 m ( m N m π E 64 192 δ – 14 – ( ≈ ) + 2). The event numbers are computed by 0 0 0 − m ν / φ φ φ 2 57 MeV are the and pion masses, respectively. 2 π µ . E PE max ( = m n µ , m ν ) = ) = e , and becomes approximately zero for ν = beam generates events with ν ν φ T,T ( φ = 139 0 E E µ PE ν ( ( θ ν ν π n 0 µ µ E ) has been integrated out. For simplicity, we assume that ν ν φ is about 4 keV in COHERENT. Using eqs. ( m dE φ φ " 2 4.4 T ) except that (i) / µ dT m 4.1 T 0 Z +∆ i + i T ]. The result is shown in figures T 1 66 MeV and Z . I / Cs ]) on light scalar bosons. The SM expectation is also provided by [ 1 20, the signal acceptance fraction is about 70% (cf. figure S9 of [ = 105 should be in the range (0 tN 8 MeV, which corresponds to the maximal recoil energy > µ ν . in COHERENT, shown in the right panel of figure E m PE = ∆ 0 In the COHERENT experiment, the recoil energy of the nucleus is converted to multi- n i = 29 N ν plies that the threshold for signal acceptance fraction data, we canfigure study 3 the of constraint [ of the COHERENTbe data used (from to compute theties total provided normalization by factor. [ We directly use the relevant uncertain- is approximately proportional to the recoil energy [ For drops down quickly for smaller Therefore, the monochromatic contribute to signals witharound higher 14 recoil keV. energies. Consequently, a kink appears inple figure photoelectrons and eventually detected by PMTs. The number of photoelectrons We also assume thattake the equal couplings cross of section neutrinos forN/N all are neutrino flavor flavors. universal Using (( around eq. 14 keV ( in theE event spectrum. This is caused by the monochromatic which is similar to eq.the ( delta function inCs eq. and I ( have approximately the same proton and neutron numbers, ( where where Remembering that the muon also decays at rest, the neutrino fluxes are given by [ with energy: JHEP05(2018)066 n C ν y √ couplings ' Y Y particle, as- φ . Since the beam 100). Again, the 2 µα × ) ν y 100 kg of data taking, ( to neutrinos is taken to α × fluxes, it will be sensitive φ P e ν . -Pb scattering and meson decay and n and 2 eα ) µ shows the potential of the assumed ν ¯ ν y Yue.pdf 6 ( µ α ν from the P 4 kg and 5 year ν assuming the uncertainties (both systemat- y × 5 20, plus a prolonged running for few years, at – 15 – and ∼ n C , the spectral distortion due to the scalar exchange is 3 including 30 kg liquid , 10 kg high purity Ge, and and figure 4 4 show the constraints and limits on the relevant combination of 5 and 4 http://webhome.phy.duke.edu/˜schol/COHERENT S with different targets, can be improved by a factor of 2. The blue solid and dashed lines are the upper In the future, the COHERENT experiment will further develop the detection of See: Y νN 4 experiment (a factor 10on smaller uncertainties) isbounds shown by that dashed CONUS blackrespectively. can line; set As the seen bound with from 1 these year figures, CONUS can improve the bound by one or two experiments. As seen fromfrom the COHERENT figures, shown by this aThe bound solid bounds is black from relatively line weak. meson isat already decay The well are the present below sensitive COHERENT bound this to experiment combinedto bound. is similar composed flavor of composition. Our forecast for the future bound by the COHERENT interactions, respectively. To drawbe these flavor lines universal. the Eachstart coupling limit by of is discussing however the sensitivenumber bounds to conserving which a interactions. apply different The for flavorfrom red-dashed structure. combining both lines the lepton show Let upper the number bounds us constraint violating on on and lepton to experiments based on reactor neutrinos. 5 Interpretation of theFigures results versus the mass of the scalar for lepton number conserving and lepton number violating less dramatic as forthe CONUS. momentum This exchange is and mostly nuclearfuture caused recoil. by COHERENT the version Figure larger forsuming energy determining of two the the characteristic mass neutrinos, examples. andbecause coupling Due of of to the the the smaller larger statistics, energy the of reconstruction COHERENT, potential and is also less promising compared a black dashed curveical in and figure statistical) arethe reduced liberty by to a denotedetermination factor this of of the potential mass 10. situation ofneutrino the as For energy. scalar COHERENT the particle As (stat. sake is seen possible of in if definiteness, figure its mass we lies take below the typical this paper. Considering thatkg the CsI) total will fiducial bebest mass increased the compared by statistics to a may the factorof be current of the increased value statistical by (14.6 uncertainties athe by factor uncertainties a of of factor 100, future of measurement whichshow 10. will corresponds the It be to sensitivity is reduced a of by therefore reduction future a reasonable COHERENT factor to between versions assume 1 on that and the 10. light To scalar coupling, we plot to the -type couplings, whereas COHERENT will also haveCE muon-type neutrinos. 185 kg NaI crystal.including all A the complete different targets study and on different detection the technology future is sensitivities beyond the of scope future of COHERENT provide much larger event numbers, CONUS limits will be better, though of course limited JHEP05(2018)066 ). 2.2 (stat.×100) (stat.×100) trapping R COHERENT COHERENT SNν diffusion 0νββ+n scat. CONUS CONUS100 SN core EoS BBN+n scat. COHERENT COHERENT BBN+n scat. SNν diffusion SNν CONUS CONUS100 SN energy loss Meson+n scat. Meson+n scat. 2 2 10 10 . ) for a lepton number conserving 3 φ Y, m – 16 – 5 years (light-blue) respectively. Various other limits 1 1 × 10 10 (MeV) (MeV) ϕ ϕ S experiments on ( m m but for lepton number violating interactions, see eq. ( νN 4 ). The black, dashed black, blue, and dashed blue curves correspond to 0 0 2.1 10 10 1 year, and CONUS 100 kg . Similar to figure × -3 -4 -5 -6 -5 -6 -3 -4

. Constraints from CE 10 10 10 10 10 10 10 10

Y Y Figure 5 Figure 4 interaction, see eq. ( the 95% C.L. constraintCONUS of 4 the kg recent COHERENTfrom data, particle the and sensitivities astroparticle of physics future are explained COHERENT, in section JHEP05(2018)066 -Pb n 3 MeV, denoted > 5 φ m and 4 with data taking time. Since 2 / 1 . CONUS with only one year of − in CONUS100 (left panels) and CO- t ee ) Y ν trapping considerations. y R ν denoted by “BBN + n scat.” shows the 4 scales as . φ 8 σ / – 17 – 1 and coupling − t φ m up to 2.4 MeV is the combined bound from the 5 will scale as Y -Pb scattering and BBN. As seen from the figure, for exchange being equal to that in the SM. As we discussed before, in n φ . Since the uncertainties of CONUS are mainly limited by statistics, the and from double beta decay on ( 4 100) (right panels) assuming the presence of a , with the true values / 1 n × ) C 2 eα | ν is ruled out by supernova cooling and y | . Measurements of the mass , the bound on 5 α 4 diffusion” show the limits resulting essentially from a neutrino-nucleon scattering Y P ν ( In the LNC case, the orange line in figure The violet curve in figure 2 ∝ / 1 n φ affected. As seen fromalready the probe figures, the all CONUS thisin experiment range. figure with The 1 green year of area data between taking solid can and dotted-dashedcombined green bound lines from scattering on data taking can provide a stronger“SN bound. The dashed green linescross in figures section due to the vicinity of this line supernova evolution and emitted neutrino flux will be dramatically orders of magnitudes. SinceC CONUS is abound reactor that neutrino it experiment, can itσ set can on only the probe cross section Figure 6 HERENT (stat. indicated by the green . JHEP05(2018)066 ) R ). is × 2 ν 2 ν ν 5 E Y E , parti- ∼ ∼ φ above the = 10 MeV MT eα φ MT | & ν m boson or Higgs . y 2 φ | , for true values n Z φ 2 m 6 C ) or (60 MeV provided that m 5 p − Y -channel, it is crucial s 100) loses its capability 10 ) for COHERENT (stat. with expected mass and turns out to have a mass , × 4 -channel signals is also a below the green solid line t φ φ − Y 10 , by our future versions of CONUS Y by CONUS will have drastic conse- φ and ) are (10 MeV -channel and φ s can significantly affect BBN. As seen from NS experiments. For ,Y m ν 5 ) or (60 MeV φ 5 − ). Even with larger couplings, COHERENT − m 10 5 10 scattering. As seen from the figure, a significant – 18 – -channel process. In the 100) are set to larger values to lead to similar × t × n 5 × . and + few 7 α 4 , ∼ ¯ ν , the equation of state in supernova inner core will dras- . In principle, there could be a scenario where the future ν 5 φ y → n , the mass and coupling can be determined with better than ) in the band between the black solid and dashed curves in ) as good as CONUS100. As shown in figure Y/m 5 + φ − e ν ,Y φ = 10 Y, m m 3) MeV and 10 MeV), then the coupling and the mass can be determined separately Y , − 4 but it has still reasonable precision in determining 5 . − φ -channel, however, depends rather on the high statistics and low thresholds, (1 t m displays the prospect of measuring ∈ 6 φ is found, the supernova cooling bounds tell us that interaction cannot involve ) = (10 m 4 φ . Since the band is too narrow, we cannot find such a scenario where the mass can 4 ) for CONUS100, and (10 MeV Discovering a positive signal for the effects of Figure = 10 MeV and 5 Y, m 100). Here for comparison, we choose the same masses for the two experiments. However, − φ quences for the analysisin of figure supernova evolution. Ifso a the value interaction of should bearound of lepton 2 MeV, number violating it form. willments. If be If, more however, double intriguing beta as decay it searches may fail be to discovered discover at double beta experi- to have the energy matchinformation the on the new mass boson and mass thecan coupling. to be get For precisely example, the the measured resonance, masses frommasses which of in the the provides the resonances useful observed inwhich colliders. is the The strength measurement of of CONUS. by the current COHERENTwe data can but only still choose withinfigure the ( sensitivity ofbe future determined. COHERENT, Besides,reason. the difference The between new scalar boson causes a maintain their sensitivity to COHERENT experiment is able toif determine ( the mass. Forby example, the as future we COHERENT have checked, excluded experiment. by However, such the a current large coupling COHERENT has data. already been To find a scenario which is not excluded large enough (close tois its larger present than bound). the typicalbut This energy-momentum is is transfer in understandable smaller the because thanAnother CONUS100 the ( reason energy-momentum is transfer theboth in better lose COHERENT statistics their ( in ability CONUS. to If determine the the mass mass and is the raised coupling to separately. 60 MeV, They then however precision as CONUS100 (cf.still figures cannot measure ( m 10% accuracy by CONUS100. In comparison,to COHERENT determine (stat. deduce that coherent scattering results may have dramatic impact on SNand and BBN COHERENT, physics. assuming true values10 of ( × the couplings in COHERENT (stat. cle with the figures this mass range candotted-dashed be green probed line by CE in figure tically change because of part of the parameter space above this line can be probed by CONUS. We can therefore the bound from COHERENT is already stronger. Both for LNC and LNV cases, a JHEP05(2018)066 , φ 4 νφ − + e 10 , where & → 2 N ν + 1 MeV will C y π 2 | < . If COHER- ) could be ex- eα 2 -Pb scattering 2 φ N | ) n ν C m eα 2 y ) | ( | ν and for y µα α ( ) | ν νφ P α y + ( | e P . In any case, in analyzing α / → eτ 2 | P ) + ν µα y ) ( K , ν -Pb measurements would be very y n eµ ( | ) ν , the chances of finding a signal for α y 5 , it may be possible that COHERENT ( | − P (close to the present bound) would imply µα  10 has to be taken into account. Comparing ) 4 ν − ee ∼ y Y ) ( 10 ν ], and new Y (i.e. on -Pb scattering experiments increase. If CONUS y – 19 – ∼ n 56 ν and if meson decay experiments find y n |  | 5 C eα − ) ν 10 y and ( | , making it difficult to see an effect on 5 6 with sizeable − , this means that signals for Y < − φ 5 10 − 10 m 10 < Y < × n 5 C ), the CONUS experiment will easily determine 5 couplings are large enough to be within the reach of COHERENT (that Y > − e , we conclude that because of the BBN bounds, discovery of ν 10 5 × . 5 6 and − 4 10 Y > We conclude this section by mentioning some possibilities on inferring the flavor struc- If CONUS and/or COHERENT finds < runs over all active flavors for the LNV case (over all light right-handed species for LNC ν Acknowledgments We thank Giorgio Arcadi, Tommy Ohlsson,ful Kate discussions. Scholberg and YF Stefan thanks Vogl for MPIK many Heidelberg help- where a part of this work was done for their are competitive withexperiments a such combination as of mesonbounds bounds decay probe from and areas BBN neutron-scattering inand experiments. and parameter supernova space evolution, from Moreover, that in variousversions these of can particular terrestrial the have for experiment important or leptonyet upcoming consequences number explored reactor for experiments violating areas such BBN in interactions. as parameter CONUS space. will Future reach not physics. Focussing here on the lightand case we future demonstrated coherent the discovery scattering potentialinteracting of with experiments current neutrinos on and quarks. the Theby mass shape the of and scalar the coupling nuclear interaction, recoil andis of spectrum is allows scalar around distorted even particles the to determine energy the of mass the of the scattered scalar, neutrinos. if its mass Even current limits by COHERENT will discover new effect but CONUS will report null results6 for new physics discovery. Summary and concludingCoherent remarks elastic neutrino-nucleus scattering can probe both new light as well as heavy α case). The information byENT COHERENT can alone then would determine becuts), able information on to flavor structure distinguish of tracted. the In flavor the content special of case the that events (e.g. by timing y ture or type of interactionlimits. that arise If due to the theis complementarity of if the various sources and in meson decay experiments asfinds well a as signal in for will be within reachinteresting. of next If generation CONUS [ we finds would conclude experiments. Similarly BBN, effects of suchfigures light indicate LNC interaction withfor light supernova right-handed evolution. neutrinos with immediate consequences coupling, we may draw a conclusion that ( JHEP05(2018)066 , L φ ]. ν NS , or 57 R = 0. ν 2.3 ∗ ¯ ν d (A.1) (A.2) q φ D βY U(1) that 5 MeV and × ∼ = sin φ d . To avoid a need m β 2 and Γ , sin ) . ∗ ). Moreover, the mixing u 2 Φ c ). For 5 . to nuclei should of course φ . m − β. c β Y . m φ ( − , naturalness (i.e., absence of (10 2 1 5 O ] sin Φ + H + H O − q m . As we have seen in section · = sin Y i Q † [ 10 0 q † qφ u I ) Φ H ∼ q ' h = R d / D ¯ φ d AφH q q 5 Γ d m D Y m iγ + ( ∼ 2 2 + u − | and q and Φ ), otherwise the rate of invisible decay mode 2 10 | ). The coupling of C 2 . and 2 2 ( c – 20 – m − . ¯ q m 2.2 | ∼ ' β ≡ . For Γ (10 + qφ 5 + H Φ ), ( 2 O Γ − | should be smaller than qφ φ m ] sin q 2.1 2 1 q 10 β Γ CQ ), 2 Y ¯ 2 1 q [ m considering first the LNC interaction, a mechanism similar T ∼ and the neutral component of Φ, we find the coupling of 5 sin (1) which in turn promises a rich phenomenology at the LHC. Φ m R β φ R Φ − O = ¯ u 2 2 m u Φ) = q , two scenarios can be realized: m Y C ( φ, / ( Cν i with neutral component of the Φ doublet. For a lepton number to be real, the coupling will be invariant and therefore T V H q φ between h Y φν quarks respectively to be given by Γ A β d quarks to be = d β ) will exceed the experimental limits. Combining these, we conclude that in and φφ and u with an electroweak doublet, Φ. Taking complex couplings of form u is taken to be the SM Higgs, → 1 TeV, this implies sin φ with SM Higgs cannot exceed φ (1). Taking In what regards neutrinos, Taking thus Φ to be a new doublet, its coupling to quarks can in principle be as large The most economic solution is to identify Φ with the SM Higgs. Remember that the ∼ H A model in which a scalar couples both to neutrinos and charged has been considered in [ ( O φ 5 to the Φ to the one describedthrough above can mixing provide of aviolating lepton coupling number conserving interaction of we obtain sin for fine-tuned cancelation m fine-tuned cancelation) requires the mass ofpling Φ to to be within the reach of the LHC and its cou- experiments. as couplings of the SM Higgsof to quarks of first generationBr are case the contributions from quarkswill of be different of generations the to same the order and coupling too of small a to nucleus lead to to discernable effects on current CE equivalently Notice that taking arise from its couplingscalar to quarks. The latter can originate from the mixing of theand singlet a mixing of φ In this section we showcan how one give can rise build to a effective toy coupling model of symmetric form under SU(2) as well as the ones shown in eqs. ( research and innovation programmeNo under 674896 the and No Marie 690575.support. Sklodowska-Curie YF grant WR is is agreement also supported grateful by to the DFG ICTP with associate grant office RO for 2516/6-1A in partial the financial Heisenberg program. Suggestions for underlying electroweak symmetric models hospitality. This project has received funding from the European Union’s Horizon 2020 JHEP05(2018)066 . L ∆ . As (A.3) 0 C ]. The y T 2 58 ) L Ψ /M and its decay . Naturalness i αβ H ) ++ h ν y m ( coupling to neutrinos = ( . ∝ φ R ν cross sections, assuming is suggested in [ Ψ C and neutrino mass matrix αβ ) C ν with a neutral component of ν Cν νN T R C T D φ Ψ ( , φ φν 0 and y αβ ) ν + ν νN C CL 2 scattering mediated by the new light scalar T 1 k . The cross section for the lepton number k H φ φ R νN can be obtained by this mechanism. Moreover, ¯ Ψ 1 3 y – 21 – p − 2 p NN ¯ ΨΨ + ν TeV without fine tuned cancelation) again implies that Ψ M ∼ . 2 ∆ = y m L  , we can integrate out Ψ and arrive at even as large as 10 φ ν m C coupling can be obtained by the mixing of ], 1 MeV  governed by 58 ∼ Ψ Cν L ν φ T M ¯ Ψ m φν develops a expectation value, an inverse for neutrino . The Feynman diagram of coherent → φ if mass generation will emerge andwill the flavor be structure similar. of H In this scenario, the SM Higgs will have an invisible decay mode neutrinos and requires a Dirac singlet Ψ with the following Lagrangian When shown in [ ∆ is not much heavierpromises than rich TeV phenomenology and at itsinto the coupling a LHC to same such leptons sign as are pair production of of of charged orderAnother ∆ leptons. of scenario that 1 can which providescenario coupling is of form very similar to the inverse seesaw mechanism for generating mass for The quantum numbers ofvacuum expectation ∆ should valuemechanism. be is Identifying responsible the these two, same for thewill as neutrino flavor be structure the mass determined of by the triplet in that(i.e., scalar of the neutrino whose type mass: tiny II ( seesaw The an electroweak triplet ∆ which couples to the left-handed lepton doublet as The discovery of a scalar field in coherent scattering experiments will therefore, at least • • in the models outlined here, hint towards rich newB collider phenomenology. Calculation of theIn cross this section appendix, wea give the lepton analytic number calculation conserving of interaction with Figure 7 boson. JHEP05(2018)066 ]. ]. νN (B.5) (B.6) (B.1) (B.2) (B.3) (B.4) SPIRE . and ]. SPIRE  IN IN T ][ νN ][ 2 N ) we can see D SPIRE . , IN B.4 ) ) )+ 2 2 ][ , p p T  ( ( ) because the initial r r 2 ν + 2 u u E T ) ) B.1 2 M  Nφ (2 Nφ 2 N Γ Γ 2 N hep-ex/0511042 i i arXiv:1710.02730 [ D C ). From eq. ( [  )( )( 2 2 + 2 in eq. ( k k M B.3 ( / 2 ( N 0 0 2 ) r r C 5  arXiv:1708.01294 case. The initial and final momenta u u γ L [ MT. 2 φ 2 φ 2 P ] + ) Average CsI neutron density distribution . νN m L m − i 2 i ν ] in eq. ( 2 ν P Observation of coherent elastic − (2006) 033005 − ) to − − D = E (2018) 072501 L Nφ νφ 2 MT 2 = (1 + 2 + P q q Γ 2 2 B.1 N )Γ ν ) 1 R ) 1 1 , q k C C 120 P (2017) 1123 D 73 ↔ 1 · k M k ( – 22 –  ( ( k 1 . The scattering amplitude of this diagram is γ 0 0 2 + R k s s ) · 7 2 − P v νφ u 357 2 φ p γ 1 ) ) Γ · p m R R 2 γ νφ νφ | P ( P + = Γ ν Γ 1 1 i i y p Phys. Rev. p q ( ), which permits any use, distribution and reproduction in ( | Nφ · · , L R γ γ M , )Γ MT  P P ) ) Phys. Rev. Lett. (2 1 tr tr[ 1 M , π p p 2 2 and ) we obtain ( ( + ) ) 4 s s 5 φ 2 φ 2 2 v u k = B.4 iγ m m · CC-BY 4.0 ν = = φ γ + + 1 1 D collaboration, D. Akimov et al., φ φ This article is distributed under the terms of the Creative Commons dT Prospects for measuring coherent neutrino-nucleus elastic scattering at a dσ + tr[( M M does not change the result so the cross sections are equal for MT MT i 1 2 i ν L C (2 (2 × P ≡ = = ↔ 2 scattering, one needs to change eq. ( νφ | φ R , if the initial antineutrino is left-handed, the amplitude automatically vanishes. We P neutrino-nucleus scattering stopped-pion neutrino source from COHERENT data COHERENT νN R M K. Scholberg, M. Cadeddu, C. Giunti, Y.F. Li and Y.Y. Zhang, i P | [2] [3] [1] Attribution License ( any medium, provided the original author(s) and source areReferences credited. which is the cross section for bothOpen neutrino and Access. antineutrino scattering. Consequently, one has tothat interchange scattering. From eq. ( For can therefore sum over all the spins and apply the trace technology: We have inserted a right-handedantineutrino projector produced by the chargedof current interaction should be right-handed. Because are denoted in the way shown in figure where Γ violating case is identical. Let us first focus on the JHEP05(2018)066 ] , ]. ] , D 96 ] (2018) Sensitivity SPIRE IN ]. (2015) 013011 ][ Accelerator and D 97 Probing neutrino ]. Phys. Rev. ]. SPIRE , ]. -prime and D 92 IN Z arXiv:1201.3805 arXiv:1511.02834 ]. ][ hep-ph/0702175 SPIRE [ [ ]. [ SPIRE IN SPIRE (2018) 451 IN ][ Phys. Rev. IN COHERENT enlightenment SPIRE , ][ ][ IN SPIRE Phys. Rev. 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