Constraints on general neutrino interactions with exotic fermion from neutrino-electron scattering experiments
CConstraints on general neutrino interactions with exotic fermion fromneutrino-electron scattering experiments
Zikang Chen, ∗ Tong Li, † and Jiajun Liao ‡ School of Physics, Sun Yat-Sen University, Guangzhou 510275, China School of Physics, Nankai University, Tianjin 300071, China
Abstract
The couplings between the neutrinos and exotic fermion can be probed in both neutrino scattering exper-iments and dark matter direct detection experiments. We present a detailed analysis of the general neutrinointeractions with an exotic fermion and electrons at neutrino-electron scattering experiments. We obtainthe constraints on the coupling coefficients of the scalar, pseudoscalar, vector, axialvector, tensor and elec-tromagnetic dipole interactions from the CHARM-II, TEXONO and Borexino experiments. For the flavor-universal interactions, we find that the Borexino experiment sets the strongest bounds in the low mass regionfor the electromagnetic dipole interactions, and the CHARM-II experiment dominates the bounds for otherscenarios. If the interactions are flavor dependent, the bounds from the CHARM-II or TEXONO experimentcan be avoided, and there are correlations between the flavored coupling coefficients for the Borexino ex-periment. We also discuss the detection of sub-MeV DM absorbed by bound electron targets and illustratethat the vector coefficients preferred by XENON1T data is allowed by the neutrino experiments. ∗ [email protected] † [email protected] ‡ [email protected] a r X i v : . [ h e p - ph ] F e b . INTRODUCTION The phenomenon of neutrino oscillations has been well confirmed by various neutrino ex-periments in the last two decades [1]. Since the explanation of neutrino oscillations requiresnonvanishing neutrino masses, which cannot be accounted for by the Standard Model (SM), theobservation of neutrino oscillations provides a strong motivation to search for new physics beyondthe SM that are associated with neutrinos. Moreover, the existence of dark matter (DM) throughabundant cosmological and astrophysical observations is one of the most plausible evidences ofnew physics beyond the SM. The DM direct detection experiments have pushed the limit on thecross section of DM scattering off nucleus close to the neutrino floor for weak scale DM. Thecouplings between the neutrinos and sub-GeV DM through the scattering off nucleus have beenstudied in Ref. [2–9]. There are also plenty of novel models and signatures proposed to search forsub-GeV DM through the scattering off electrons [10–15].Recently, the XENON collaboration reported an excess of electronic recoil events with the en-ergy around 2-3 keV [16] and the event distribution has a broad spectrum for the excess. Theycollected low energy electron recoil data from the XENON1T experiment with an exposure of0.65 tonne-years and analyzed various backgrounds for the excess events. Although a small tri-tium background fits the excess data well, the solar axion explanation or the solar neutrinos withmagnetic moment can also provide a plausible source for the peak-like excess. However, both ofthe two scenarios have tension with stellar cooling constraints [14, 17–21]. Some studies insteadproposed to explain the XENON1T excess through the electron recoil by solar neutrinos with thesterile neutrino DM in the final states of inelastic scattering [10–12]. On the other hand, the inverseprocess in which the incoming fermionic DM is absorbed by bound electron targets and emits aneutrino is sensitive to the DM with mass below MeV [13]. The two kinds of signals are governedby the same interactions between SM neutrino and the exotic fermion. The relevant interactionsare inevitably constrained by the precision measurements in neutrino experiments [14, 15]. In thiswork we study the constraints on general neutrino interactions with sub-GeV exotic fermion fromneutrino-electron scattering experiments.The large volume detectors enable precise measurements of neutrino properties. The largeneutrino detectors like Borexino can be used to place constraints on general neutrino interactions.The Borexino experiment, located at the Laboratori Nazionali del Gran Sasso, was built witha primary goal of measuring solar neutrinos from the pp chain [22]. We employ the Borexinomeasurements of low energy solar neutrinos to set limits on the neutrino-electron scattering withan outgoing fermion χ νe → χe , (1)where χ could be sterile neutrino or other possible exotic fermions. The results apply for the exoticfermion χ being either DM candidate or not. We restrict the general neutrino interactions cate-gorized by dimension-5 dipole operators and dimension-6 four-fermion operators. They respectLorentz invariance and the gauge symmetries SU (3) c × U (1) em . The scattering cross section from2he magnetic and electric dipole operators is inversely proportional to the recoil energy and thusthe experiments with low energy threshold are sensitive to them. For the four-fermion interac-tions, all Lorentz-invariant operators (scalar, vector, pseudoscalar, axialvector and tensor) will beexplored in the neutrino-electron scattering. As the produced solar electron neutrinos oscillateinto muon and tau neutrinos, we can also place limits on the general interactions of all neutrinoflavors. In addition, accelerator neutrinos with the energy being several tens of GeV can be usedto exploit large χ mass region. We thus take into account the constraints from the CHARM-IIexperiment [23, 24] as well as reactor neutrino using TEXONO [25] data.This paper is organized as follows. In Sec. II, we discuss the effective Lagrangian of an exoticfermion interacting with neutrino and electron. Then we display the amplitudes and differentialcross sections of neutrino-electron scattering with the outgoing exotic fermion. In Sec. III, weconsider three neutrino-electron scattering experiments: CHARM-II, TEXONO and Borexino,and show the constraints on the general neutrino interactions. Finally, we discuss the detection ofsub-MeV DM absorbed by bound electron targets and summarize our conclusions in Sec. V. II. THE GENERAL NEUTRINO INTERACTIONS WITH EXOTIC FERMION AND NEUTRINO-ELECTRON SCATTERING
We consider a Dirac fermion χ and its general interactions with neutrino and electron. The ef-fective Lagrangian including both dim-5 dipole operators and dim-6 four-fermion operators readsas L ⊃ G F √ (cid:34)(cid:88) a ¯ χ Γ a ν α ¯ e Γ a ( (cid:15) aα + ˜ (cid:15) aα γ ) e + v H √ χσ µν ( (cid:15) Mα + (cid:15) Eα γ ) ν α F µν (cid:35) + h.c. , (2)where α ≡ { e, µ, τ } , v H (cid:39) GeV is the vacuum expectation value of the SM Higgs, F µν is theelectromagnetic field strength tensor and Γ a ≡ { I, iγ , γ µ , γ µ γ , σ µν ≡ i [ γ µ , γ ν ] } correspond tothe scalar ( S ), pseudoscalar ( P ), vector ( V ), axialvector ( A ) and tensor ( T ) operator, respectively.The four-fermion operators are analogous to those in Ref. [26]. Here the dimensionless parameters (cid:15) Mα , (cid:15) Eα , (cid:15) aα and ˜ (cid:15) aα are in general complex. The presence of new interactions of Eq. (2) will giverise to the tree-level neutrino-electron scattering, as shown in Fig.1.In the SM, the neutrino-electron scattering is governed by both the weak neutral current (NC)and charged current (CC). The effective Lagrangian for the SM NC is given by L NC = G F √ νγ µ (1 − γ ) ν ¯ eγ µ ( g V − g A γ ) e , (3)where g V = − + 2 sin θ W and g A = − . The CC Lagrangian can be transmitted as L CC = G F √ νγ µ (1 − γ ) ν ¯ eγ µ (1 − γ ) e . (4)3 IG. 1. The tree-level Feynman diagrams for the ν α + e − → χ + e − process, where the circular bulb(square) represents the effective dim-5 dipole (dim-6 four-fermion) interaction. The CC current only contributes to the scattering of ν e . The differential cross section of neutrino-electron scattering in the SM is [26] dσ SM αβ dE R = G F m e π (cid:104)(cid:16) g Lαβ (cid:17) + (cid:16) g Rαβ (cid:17) (cid:16) − E R E ν (cid:17) − g Lαβ g Rαβ m e E R E ν (cid:105) , (5)where α ( β ) denotes the flavor of the neutrino in the initial (final) states, E ν is the neutrino energy, E R is the electron recoil energy and (cid:16) g Lαβ , g
Rαβ (cid:17) = (2 sin θ W + 1 , θ W ) , α = β = e ; (2 sin θ W − , θ W ) , α = β = µ, τ ; , α (cid:54) = β . (6)We then calculate the differential cross section of ν α + e → χ + e by following the proceduregiven in the appendix. Here we show the differential cross sections for different operators: dσ Sν α dE R = G F m e π (cid:20) | (cid:15) Sα | (cid:18) E R m e (cid:19) + | ˜ (cid:15) Sα | E R m e (cid:21) (cid:18) m e E R E ν + m χ E ν (cid:19) , (7) dσ Pν α dE R = G F m e π (cid:20) | (cid:15) Pα | E R m e + | ˜ (cid:15) Pα | (cid:18) E R m e (cid:19)(cid:21) (cid:18) m e E R E ν + m χ E ν (cid:19) , (8) dσ Vν α dE R = G F m e π (cid:20)(cid:0) | (cid:15) Vα | + | ˜ (cid:15) Vα | (cid:1) (cid:18) − E R E ν + E R E ν − m χ E ν m e + m χ E R E ν m e (cid:19) − (cid:0) | (cid:15) Vα | − | ˜ (cid:15) Vα | (cid:1) (cid:18) E R m e E ν + m χ E ν (cid:19) − Re [ (cid:15) Vα (˜ (cid:15) Vα ) ∗ ] E R E ν (cid:18) − E R E ν − m χ E ν m e (cid:19)(cid:21) , (9) dσ Aν α dE R = G F m e π (cid:20)(cid:0) | (cid:15) Aα | + | ˜ (cid:15) Aα | (cid:1) (cid:18) − E R E ν + E R E ν − m χ E ν m e + m χ E R E ν m e (cid:19) + (cid:0) | (cid:15) Aα | − | ˜ (cid:15) Aα | (cid:1) (cid:18) E R m e E ν + m χ E ν (cid:19) − Re [ (cid:15) Aα (˜ (cid:15) Aα ) ∗ ] E R E ν (cid:18) − E R E ν − m χ E ν m e (cid:19)(cid:21) , (10) dσ Tν α dE R = 2 G F m e | (cid:15) Tα − ˜ (cid:15) Tα | π (cid:20) − E R E ν + E R E ν − E R m e E ν − m χ E ν (cid:18)
12 + 2 E ν m e − E R m e (cid:19)(cid:21) , (11) dσ EM ν α dE R = 2 √ α EM G F | (cid:15) Eα − (cid:15) Mα | m e (cid:104) m e E R − m e E ν − m χ E ν E R (cid:18) − E R E ν + m e E ν (cid:19) − m χ E ν E R (cid:18) − E R m e (cid:19) (cid:105) , (12)4here α EM (cid:39) / is the electromagnetic fine structure constant. Here we assume each of thescalar, pseudoscalar, vector, axialvector, tensor and electromagnetic dipole operators dominates ata time. The differential cross sections of ¯ ν α + e → ¯ χ + e are the same as those of ν α + e → χ + e except for the cross term of the axialvector operator in Eq. (10) changed sign. From theabove equations, we realize that the the bounds on { ˜ (cid:15) Sα , ˜ (cid:15) Pα , ˜ (cid:15) Vα , ˜ (cid:15) Aα , ˜ (cid:15) Tα , (cid:15) Eα } will be the same as { (cid:15) Pα , (cid:15) Sα , (cid:15) Aα , (cid:15) Vα , (cid:15) Tα , (cid:15) Mα } if we consider only one (cid:15) parameter at a time. III. NEUTRINO-ELECTRON SCATTERING EXPERIMENTS
In our analysis, we consider three neutrino-electron scattering experiments: CHARM-II, TEX-ONO and Borexino. Other neutrino-electron scattering experiments such as GEMMA [27] andLSND [28] can be also used to constrain the parameter space. However, we find their sensitivitiesare weaker compared to those from CHARM-II, TEXONO and Borexino experiments. Here wepresent the detailed analysis of the CHARM-II, TEXONO and Borexino experiments below.
A. CHARM-II
The CHARM-II experiments measured the high energy ν µ and ¯ ν µ beam from the Super ProtonSynchrotron (SPS) at CERN [23, 24]. The mean neutrino energies of the ν µ and ¯ ν µ beam are23.7 GeV and 19.1 GeV, respectively. The unfolded differential cross sections from the measure-ment have been given in Ref. [23], and the data points are shown in Fig. 2. Our SM predictionsare consistent with those given in the Ref. [23]. Therefore, we consider the following χ functionin our analysis for new physics: χ CHARM-II = (cid:88) i ( dσ/dE R ) i − s i ) σ i + ( ν µ → ¯ ν µ ) , (13)where s i and σ i are the measured differential cross section and its corresponding uncertaintiestaken from Ref. [23]. B. TEXONO
The cross section of ¯ ν e scattering on electrons has been measured by the TEXONO experimentutilizing electron antineutrinos produced by the Kuo-Sheng Nuclear Power Reactor with a CsI(Tl)scintillating crystal detector [25]. The detector is placed at a distance of 28 m from the 2.9 GWreactor core. The range of recoil energy used in the analysis is from 3 MeV and 8 MeV, respec-tively. The measured event rates and uncertainties have been given in Ref. [25], which are shownin Fig. 3. As seen from the red and blue dashed curves in Fig. 3, our SM predictions agree quitewell with those given in the Ref. [25]. Therefore, we consider the following χ function in our5 .0 0.2 0.4 0.6 0.8 1.00.00.51.01.52.0 E R / E ν d σ / d E R ( a . u . ) E R / E ν d σ / d E R ( a . u . ) FIG. 2. The differential cross sections of the ν µ (left) and ¯ ν µ (right) scattering on electrons at CHARM-II.The black data points and the blue dashed SM prediction curve are taken from Ref. [23]. The red curvecorresponds to our best-fit prediction in the SM. analysis for new physics: χ TEXONO = (cid:88) i ( R i − R i (1 + α )) σ R,i + (cid:18) ασ α (cid:19) , (14)where R i ( R i ) and σ R,i are the predicted (measured) event rates and corresponding uncertaintiesin the i th recoil energy bin. Here σ α is the normalization uncertainty, and we take it to be for conservation. Both the measured event rates and uncertainties are taken from Ref. [25]. Thepredicted event rate in the i th recoil energy bin is calculated by R i = N e (cid:90) dE ν φ ¯ ν e ( E ν ) (cid:90) i dE R dσ ¯ ν e dE R , (15)where N e = 2 . × is the number of target electrons in the CsI detector per kilogram, φ ¯ ν e ( E ν ) is the reactor antineutrino flux taken from Ref. [25] and the total flux is normalized to . × cm − s − . C. Borexino
The Borexino experiment measured solar neutrinos at the Laboratori Nazionali del Gran Sasso.Only ν e are produced in the core of the Sun. However, after adiabatic propagation in the sun,the solar neutrinos arrive at the the Earth contain all three flavors: ν e , ν µ and ν τ . The survivalprobability of solar neutrinos is given by [29] P ee ≈ s + c ( c cos θ m + s sin θ m ) , (16)6 - ( MeV ) E ve n t R a t es ( d ay - k g - M e V - ) FIG. 3. The event rates of ¯ ν e − e − scattering in the TEXONO experiment. The black data points andthe blue dashed SM prediction curve are taken from Ref. [25]. The red curve corresponds to our best-fitprediction in the SM. where s ( c ) denotes sin θ ( cos ) , θ is the vacuum mixing angles in the PMNS matrix. Here θ m is the effective mixing angle at the production point in the Sun, which is given by θ m = 12 arctan sin 2 θ cos 2 θ − ˆ Ac , (17)with ˆ A ≡ √ G F N Se E ν /δm and N Se being the number density of electron at the productionpoint in the Sun. Here we ignore the small corrections due to the day-night asymmetry in theBorexino measurement [30]. We consider the pp , Be and pep spectra measured in the Borex-ino phase-I [31–33] and phase-II [22, 34], and the B data collected between January 2008 andDecember 2016 [35]. The expected event rate at Borexino is given by R i pre = N e (cid:90) dE ν Φ i ( E ν ) (cid:2) P iee σ e ( E ν ) + (1 − P iee ) σ µ ( E ν ) (cid:3) , (18)where N e = 3 . × / ton is the density of target electrons in the Borexino detector [22],and i indicates solar neutrino sources pp , Be , pep and B . Φ i ( E ν ) is the corresponding solar neu-trino flux taken from the standard solar model (B16-GS98-HZ) [36]. P iee is the survival probabilitygiven in Eq. (16). The cross section in Eq. (18) is calculated by σ α = (cid:90) dE R dσ α dE R η ( E R ) , (19)where α = e, µ , dσ α dE R is the differential cross section, and η ( E R ) is the detection efficiency. Weextract the detection efficiency for B from Fig. 2 in Ref. [35] and take it as unity for other neutrino7 ource Measurement (cpd/100 t) SM prediction (cpd/100 t) Percentage error pp ± +6 − . ± . Be ± . +1 . − . (phase I), . ± . +0 . − . (phase II) . ± . pep . ± . ± . (phase I), . ± . +0 . − . (phase II) . ± . B . +0 . − . ± .
006 0 . ± . sources. The measured event rates and our predicted event rates in the SM are given in Table I.We see that our SM predictions agree with the measured event rates. For new physics analysis, weemploy the following χ function [26]: χ Borexino = (cid:88) i (cid:2) R i exp − R i pre (1 + α i ) (cid:3) ( σ istat ) + (cid:18) α i σ i th (cid:19) , (20)where R i exp ( σ iexp ) are the central values (statistical uncertainties) of the i th measurement given inTable I, R i pre is the predicted event rates calculated in Eq. (18), and σ ith is the theoretical uncertain-ties given in the last column in Table I. IV. CONSTRAINTS FROM THE EXPERIMENTAL DATA
In this section, we present our results of the constraints on the coupling coefficients of thegeneral neutrino interactions with χ and electrons using the neutrino-electron scattering data fromthe CHARM-II, TEXONO and Borexino experiments. A. Flavor-universal bounds
We firstly consider the flavor-universal couplings, i.e. by setting (cid:15) iα ≡ (cid:15) i in Eq. (2), where i in-dicates the scalar (S), pseudoscalar (P), vector(V), axialvector (A), tensor (T) and electromagnetic(E or M) dipole operators. Here we also assume only one (cid:15) i ( ˜ (cid:15) i ) exists at a time. As mentioned be-fore, the bounds on { ˜ (cid:15) Sα , ˜ (cid:15) Pα , ˜ (cid:15) Vα , ˜ (cid:15) Aα , ˜ (cid:15) Tα , (cid:15) Eα } will be the same as { (cid:15) Pα , (cid:15) Sα , (cid:15) Aα , (cid:15) Vα , (cid:15) Tα , (cid:15) Mα } in this case.The 90% CL upper bounds on the magnitude of the coefficients (cid:15) i ( ˜ (cid:15) i ) as a function of m χ areshown in Fig. 4. From Fig. 4, we see that the CHARM-II experiment yields the strongest boundsfor the scalar, pseudoscalar, vector, axialvector and tensor interactions. For the electromagneticdipole interaction, the Borexino experiment has the best sensitivity for m χ below 1 MeV. Thereis an upper limit on m χ for the CHARM-II bounds due to the kinematic constraint. This canbe explained by Eq. (A6), from which we get m χ ≤ (cid:112) (2 E ν + m e ) m e − m e (cid:39) MeV for E ν = 23 . GeV. Also, the upper limits on m χ from the TEXONO and Borexino experiments are8uch smaller than the CHARM-II experiment due to low neutrino energies used in these two ex-periments. In addition, we see that the bounds become flat at small m χ , which can be understoodfrom Eqs. (7), (8), (9), (10), (11) and (12) since the differential cross sections are insensitive to m χ as m χ (cid:28) E ν . From Fig. 4, we find that for m χ (cid:46) MeV, the strongest bounds on the magnitudeof (cid:15)
S,P ( ˜ (cid:15) S,P ), (cid:15) V,A ( ˜ (cid:15) V,A ) and (cid:15) T ( ˜ (cid:15) T ) can reach 1.0, 0.5 and 0.2, respectively. The strongest boundson the magnitude of (cid:15) M,E can reach . × − for m χ (cid:46) . MeV.
B. Flavor-dependent bounds
Since only ν µ ( ¯ ν µ ) are measured at the CHARM-II experiment and only ¯ ν e are measured atthe TEXONO experiment, the bounds from these two experiments can be avoided if the couplingcoefficients are flavor non-universal. To illustrate the flavor dependence of these bounds, we showthe 90% CL allowed regions in the ( (cid:15) e , (cid:15) µ ) plane for the scalar and vector interactions in Fig. 5.Here we fixed m χ = 1 MeV, and assume the coupling coefficients are real for simplicity. We alsoassume (cid:15) τ = (cid:15) µ for the Borexino experiments. As seen from Fig. 5, the CHARM-II experimentis not sensitive to (cid:15) e , and the TEXONO experiment has no sensitivity to (cid:15) µ . The solar neutrinoexperiment at Borexino can impose constraints on both (cid:15) e and (cid:15) µ due to the flavor transition in theSun. We also show the allowed regions of the combined data from these three experiments as thegray shaded regions in Fig. 5. From Fig. 5, one can see that the sensitivity of the combined datamainly comes from the CHARM-II and TEXONO experiment. V. DISCUSSION AND CONCLUSION
As stated in the Introduction, the exotic fermion χ could or could not be a DM particle. Here webriefly discuss the detection of DM hypothesis and the XENON1T excess. If we reverse the aboveprocess and interpret the exotic fermion χ as DM particle, the incoming DM χ can be absorbed bybound electron targets and emit a neutrino χe → νe . (21)For the DM elastic scattering off the electron, to explain the XENON1T excess, the key point ishow to produce abundant DM particles with high velocity v DM (cid:38) . [37]. In contrast, Ref. [13]proposed the above DM absorption scenario in which a DM particle deposits its mass energy ratherthan kinetic energy and it is sensitive to sub-MeV fermionic DM. For the DM absorption with freeelectrons χe → νe , analogous to the case with nucleus absorbing the DM [4, 5], the total eventrate is naively given by R = ρ χ m χ σ e N T Θ( E R − E th ) , (22)where N T is the number of target nuclei per detector mass, the local DM density is ρ χ (cid:39) . / cm , Θ is the Heaviside theta function, E th is the experimental threshold, E R = m χ / m e .001 0.010 0.100 1 10 100 10000.010.10110100 m χ ( MeV ) | ϵ S | ( | ϵ ˜ P | ) m χ ( MeV ) | ϵ P | ( | ϵ ˜ S | ) m χ ( MeV ) | ϵ V | ( | ϵ ˜ A | ) m χ ( MeV ) | ϵ A | ( | ϵ ˜ V | ) m χ ( MeV ) | ϵ T | ( | ϵ ˜ T | ) - - m χ ( MeV ) | ϵ M | ( | ∈ E | ) CHARM - IITEXONOBorexino
FIG. 4. The 90% CL upper bounds on the magnitude of coupling coefficients as a function of m χ forthe scalar, pseudoscalar, vector, axialvector, tensor and electromagnetic dipole interactions. We assumethat the couplings are flavor universal and only one (cid:15) i ( ˜ (cid:15) i ) exists at a time. The gray, blue and red shadedregions are excluded by the CHARM-II, TEXONO and Borexino experiment, respectively. The bounds on | ˜ (cid:15) Sα | , | ˜ (cid:15) Pα | , | ˜ (cid:15) Vα | , | ˜ (cid:15) Aα | , | ˜ (cid:15) Tα | , and | (cid:15) Eα | are the same as | (cid:15) Pα | , | (cid:15) Sα | , | (cid:15) Aα | , | (cid:15) Vα | , | (cid:15) Tα | , and | (cid:15) Mα | , respectively. for a free electron absorbing the DM, and σ e is the absorption cross section per electron. For theXENON1T experiment, we have N T (cid:39) × / tonne and E R (cid:39) keV giving m χ (cid:39) keV.10 - - - ϵ eS ϵ μ S BorexinoTEXONO CHARM - II - - - - ϵ eV ϵ μ V BorexinoTEXONO CHARM - II FIG. 5. The 90% CL allowed regions in the ( (cid:15) e , (cid:15) µ ) plane for the scalar (left panel) and vector (right panel)interactions. Here we assume m χ = 1 MeV and the coupling coefficients are real with (cid:15) τ = (cid:15) µ . Theregion enclosed by the black, blue and red curves correspond to the CHARM-II, TEXONO and Borexinoexperiments, respectively. The gray shaded regions correspond to the allowed regions of the combined datafrom these three experiments. With the total exposure being 0.65 tonne · years, XENON1T observed 285 events and the expectedevent number is ± . This gives the total scattering cross section σ e (cid:39) × − cm .In fact, the absorbing electron in a shell with a binding energy would be ionized with recoilenergy [38, 39]. In Eq. (22) there should also appear the ionization form factor of an elec-tron in a certain shell and the total differential ionization rate is obtained by summing overall possible shells of the absorbing target electrons. The recoil energy of a free electron ab-sorbing the DM E R is then shifted. The best fit to the XENON1T data was found to be ( m χ = 56 . , σ e = 1 × − cm ) [13]. We take the vector interaction for illustration.The total scattering cross section σ e for vector operators is σ Ve = G F m χ ( m χ + 2 m e ) π ( m e + m χ ) (cid:104) | (cid:15) V | (2 m e + 4 m e m χ + 3 m χ ) + | ˜ (cid:15) V | (6 m e + 8 m e m χ + 3 m χ ) (cid:105) . (23)By transforming the above best fit to the parameterization in our context, one essentially obtains | (cid:15) V | , | ˜ (cid:15) V | (cid:39) . which is allowed by the neutrino scattering experiments.The decaying DM scenario usually faces the requirement of stability. The corresponding life-time of χ should be longer than the age of the Universe, i.e. t Universe = 4 . × sec [40].Requiring the DM being stable at the Universe time scale would set a very stringent bound on thecoupling and/or the DM mass. For the vector interaction in our effective framework, the leadingdecay process is χ → νγ with one photon radiated from the closed electron loop. The constraintwould be quite stringent if only electron is involved in the calculation of the above decay width. In11 realistic UV model in Ref. [13] with χ only coupled to right-handed neutrino, the decay χ → νγ is suppressed by the insertion of neutrino mass. The decay of χ into νγγ is forbidden and theleading decay becomes χ → νγγγ which leads to a quite weak constraint. We refer the detaileddiscussion of the sub-MeV DM absorption by electrons to Ref. [13] and future studies.In this work we study the constraints on general neutrino interactions with sub-GeV exoticfermion χ from neutrino-electron scattering experiments. The general neutrino interactions arecomposed of dimension-5 dipole operators and dimension-6 four-fermion operators. We em-ploy the measurements of CHARM-II, TEXONO and Borexino experiments to set limits on theneutrino-electron scattering with an outgoing fermion χ . We find that the bounds are dominatedby the CHARM-II experiment in most of the parameter space for the flavor-universal interactionsand m χ below 155 MeV, while the Borexino experiment sets the strongest bounds in the low massregion for the electromagnetic dipole interactions. The limits are found to be | (cid:15) S,P | ( | ˜ (cid:15) S,P | ) < , | (cid:15) V,A | ( | ˜ (cid:15) V,A | ) < . , | (cid:15) T | ( | ˜ (cid:15) T | ) < . for m χ (cid:46) MeV and | (cid:15) M,E | < . × − for m χ (cid:46) . MeV. If the coupling coefficients are flavor non-universal, the bounds on (cid:15) e ( (cid:15) µ ) can be avoidedfor the CHARM-II (TEXONO) experiment, and there are correlations between the bounds on thecoupling coefficients from the Borexino experiment. Finally, as an example, we discuss the de-tection of sub-MeV DM absorbed by bound electron targets. By transforming the best fit to theXENON1T data in our parameterization, we obtain the preferred coefficients for vector interac-tions as | (cid:15) V | , | ˜ (cid:15) V | (cid:39) . which is allowed by the neutrino experiments. ACKNOWLEDGMENTS
TL is supported by the National Natural Science Foundation of China (Grant No. 11975129,12035008) and “the Fundamental Research Funds for the Central Universities”, Nankai University(Grant No. 63196013). JL is supported by the National Natural Science Foundation of China(Grant No. 11905299), Guangdong Basic and Applied Basic Research Foundation (Grant No.2020A1515011479), the Fundamental Research Funds for the Central Universities, and the SunYat-Sen University Science Foundation.
Appendix A: Calculation of the differential cross section
The amplitude for ν ( p ) e ( k ) → χ ( p ) e ( k ) is given by M = G F √ u χ ( p ) P L u ν ( p ) ¯ u e ( k )( (cid:15) S + ˜ (cid:15) S γ ) u e ( k )+ G F √ u χ ( p ) iγ P L u ν ( p ) ¯ u e ( k ) iγ ( (cid:15) P + ˜ (cid:15) P γ ) u e ( k )+ G F √ u χ ( p ) γ µ P L u ν ( p ) ¯ u e ( k ) γ µ ( (cid:15) V + ˜ (cid:15) V γ ) u e ( k )+ G F √ u χ ( p ) γ µ γ P L u ν ( p ) ¯ u e ( k ) γ µ γ ( (cid:15) A + ˜ (cid:15) A γ ) u e ( k ) G F √ u χ ( p ) σ µν P L u ν ( p ) ¯ u e ( k ) σ µν ( (cid:15) T + ˜ (cid:15) T γ ) u e ( k )+ iG F v H eQ e t ¯ u χ ( p ) σ µν ( (cid:15) M + (cid:15) E γ ) P L u ν ( p ) ¯ u e ( k ) γ µ t ν u e ( k ) , (A1)where the projector P L = (1 − γ ) / is inserted to force the incoming neutrinos to be left-handedand t = p − p . The amplitude for ν ( p ) e ( k ) → χ ( p ) e ( k ) is given by M = G F √ v ν ( p ) P R v χ ( p ) ¯ u e ( k )( (cid:15) S ∗ − ˜ (cid:15) S ∗ γ ) u e ( k )+ G F √ v ν ( p ) P R iγ v χ ( p ) ¯ u e ( k ) iγ ( (cid:15) P ∗ − ˜ (cid:15) P ∗ γ ) u e ( k )+ G F √ v ν ( p ) P R γ µ v χ ( p ) ¯ u e ( k ) γ µ ( (cid:15) V ∗ + ˜ (cid:15) V ∗ γ ) u e ( k )+ G F √ v ν ( p ) P R γ µ γ v χ ( p ) ¯ u e ( k ) γ µ γ ( (cid:15) A ∗ + ˜ (cid:15) A ∗ γ ) u e ( k )+ G F √ v ν ( p ) P R σ µν v χ ( p ) ¯ u e ( k ) σ µν ( (cid:15) T ∗ − ˜ (cid:15) T ∗ γ ) u e ( k )+ iG F v H eQ e t ¯ v ν ( p ) P R σ µν ( (cid:15) M ∗ − (cid:15) E ∗ γ ) v χ ( p ) ¯ u e ( k ) γ µ t ν u e ( k ) , (A2)where the projector P R = (1 + γ ) / is inserted to force the incoming anti-neutrinos to be right-handed. The differential cross section of neutrino-electron scattering ν (¯ ν ) + e → χ ( ¯ χ ) + e is dσ ( νe ) dE R = 132 πm e E ν |M| , (A3)where |M| is the spin-averaged amplitude square. The scattering angle is cos θ = E R ( E ν + m e ) + m χ / E ν (cid:112) E R + 2 m e E R . (A4)By requiring cos θ ≤ , we can get the bounds on E R as E min(max) R = 2 m e E ν − m χ ( m e + E ν ) ∓ E ν (cid:113) (2 m e E ν − m χ ) − m e m χ m e ( m e + 2 E ν ) , (A5)and the minimal energy to generate the elastic scattering is E min ν = m χ + m χ m e . (A6) [1] P. A. Zyla et al. (Particle Data Group), PTEP , 083C01 (2020).[2] V. Brdar, W. Rodejohann, and X.-J. Xu, JHEP , 024 (2018), arXiv:1810.03626 [hep-ph].[3] W.-F. Chang and J. N. Ng, Phys. Rev. D , 035028 (2020), arXiv:1903.12545 [hep-ph].
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