Probing Neutrino Magnetic Moment at the Jinping Neutrino Experiment

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JHEP08(2021)068 ) eff ν µ Springer July 9, 2021 : June 15, 2021 March 24, 2021 : August 16, 2021 : : Kr in the liquid 85 , at 90% C.L. . With Kr) and the intrinsic Revised Accepted B 85 Received µ Published C and 11 MM searches at a different 14 − and ν 10 pp × 1 . 1 < Published for SISSA by https://doi.org/10.1007/JHEP08(2021)068 1 effective neutrino magnetic moment ( B a,b, ) with µ e ν 11 MM) is an important property of massive neutri- µ − ν [email protected] 10 MM is highly correlated with the systematic uncer- , ν × 2 . at 90% C.L. with 10-year data taking of solar neutrinos. 2 B ∼ and Jiajie Ling µ 1 11 a, − 10 Kr) can help to improve sensitivities below these levels and reach . × 3 85 2 . Kr. Reducing systematic uncertainties ( 1 85 2102.12259 < Jiajun Liao The Authors. C and a c and Neutrino Detectors and Telescopes (experiments) 14

Neutrino magnetic moment ( , pp [email protected] can reach eff ν Corresponding author. 1 µ Cr installed at Jinping neutrino detector for 55 days, it could give us a sensitivity to Beijing 100084, China E-mail: [email protected] School of Physics, SunNo. Yat-sen University, 135, Xingang Xi Road,Key Guangzhou, Laboratory of 510275, Particle P.R. & China Radiation Imaging (Tsinghua University), Ministry of Education, MM measurement with 4 kton fiducial mass at Jinping neutrino experiment (Jinping) b a Open Access Article funded by SCOAP Keywords: ArXiv ePrint: the region of51 astrophysical interest. With a 3the mega-Curie electron (MCi) neutrino artificial neutrino magneticthe source moment combination ( of those twomoment measurements, can the be flavor also structure probed of at the Jinping. neutrino magnetic of Besides the abundance ofscintillator, the we intrinsic find low the energy sensitivitytainties background to of background ( collaboration might indicate a from solar neutrinos. Therefore, itexperiment is to essential to confirm carry out orν the exclude such ausing electron hypothesis. recoil data from We both study natural the and artificial feasibility neutrino of sources. The doing sensitivity Abstract: nos. The recent anomalous excess at few keV electronic recoils observed by the XENON1T Baobiao Yue, Probing neutrino magnetic momentneutrino at experiment the Jinping JHEP08(2021)068 ]. ], 16 14 13 ], it – (1.1) order 8 [ 22 , B ν µ 21 m [ 18 − B µ 10 14 − 10 , B µ eff ντ ν µ eV m MM is less than ]. According to general consider- ν 18 19 – ), − 15 10 1.1 MM greater than , 2 2 ν [ × 2 B . 10 3 µ – 1 – ≈ 12) B ∼ ] is closely related to the neutrino mass 15 7 µ – ν (10 is the Fermi coupling constant and the Bohr mag- 2 1 − m F F 2 10 G G √ e 2 3 MM) [ π 10 m . According to eq. ( ν 4 3 Cr source e MM should have a model-independent and “naturalness” upper ~ 51 e = ν πm 4 ν µ = 5 6 11 B 13 1 . Hence if any observation of µ 14 B µ ], the Dirac 14 is the electron mass, − Cr neutrino signals yields 20 MM and the neutrino mass can be written as , e ν 51 neutrinos 10 B 19 m µ . MM with artificial neutrino source MM measurement with solar neutrinos flux calculation for 3.1 3.2 Sensitivity 3.3 Combined analyses with 55-day artificial neutrino source and 10-year solar 2.1 Jinping neutrino2.2 experiment Solar neutrino2.3 signals Background 2.4 Sensitivity ν ν MM should theoretically exist. Under the standard electroweak theory, the correlation (MSM) suggest that ifmoments neutrinos would are be Majorana at particles, theations the level [ magnitude of of theirlimit magnetic would be evidence of new physics and implies that neutrinos might be Majorana particles. where neton using the upper bound ofHowever, the some current experimental theoretical measurement of extensions the beyond neutrino mass the [ Minimally Extended Standard Model Neutrino magnetic moment ( and neutrino oscillation experimentsν have verified that thebetween neutrino mass is non-zero, so 1 Introduction 4 Conclusions A Electron scattering signal distribution and the effective neutrino B An effective neutrino magnetic moment mixing 3 Contents 1 Introduction 2 JHEP08(2021)068 ] ]. B < ]. µ 32 24 with ]. In 11 (90% eff B 40 , − µ 32 eff ν B 39 10 µ µ 11 × − 9 ]. Compared . MM reported 4 10 41 ν × MM measurement 9 . ]. Gemma experi- ν Cr neutrino source. MM in XENON1T. 2 ν 23 51 < (90% C.L.)) from solar neutri- ] at low electron recoil energy, ] B MM) with 26 MM with a µ e ], which is a commonly used source ν ¯ ν 11 38 − – 10 33 depicts the study on × MM measurement at Jinping neutrino ex- 2 ν ], located in one of the deepest underground Cr [ 8) [ . 32 51 2 . event excess [ , – 2 – 4 4 . σ (1 ∈ energy resolution. In addition, we also assume the ] enough to rule out the abnormal eff ν µ ] among the terrestrial experiments. 31 – 25 presents the research on (MeV) 28 3 MM ( E ν p / 5% . 4 (90% C.L.) [ (90% C.L.) [ (90% C.L.) with the SuperK-I solar neutrino data [ ], which, however, does not reach the sensitive region of B µ B 27 B µ 11 µ − 12 10 − − 10 10 10 MM measurement with solar neutrinos × The paper is organized as following. Section A high-precision measurement of solar neutrinos is proposed by the Jinping neutrino Recently, XENON1T observed a 3 A previous measurement at Super-Kamiokande reported an upper limit of ν 8 × × . 2 2 1 . this study, we chooseapproximately the median, to 500 PE/MeV,detector as has the 4 default kton fiducial setup,to target which Borexino, mass corresponds Jinping out is ofmuon expected 5 rates to kton and be total much mass more larger based sensitive detector on because mass. [ of a much lower cosmic-ray laboratories with 2400including m solar vertical neutrinos, rock-overburden, geoneutrinosultralow aims and cosmic-ray supernova to muon neutrinos rate. study with Thein MeV-scale the target which neutrinos, great material is benefit Cherenkov water-based of lightscintillation liquid are scintillator light (LS), sensitive can to beassumed the used three flight for different direction the light of energy yields and charged (200, event particles 500 vertex while and reconstruction. 1000 PE/MeV) Ref. in [ its calculation. In 2 2.1 Jinping neutrino experiment The Jinping neutrino experiment (Jinping) [ A combined anlysis for solarthe and end, artificial conclusions neutrino are source shown is in also section shown in this session. In periment through solar neutrinos. Besides,MCi-scale we electron-capture also neutrino consider source, the physicsin study scientific of study deloying and a can release sub-MeV neutrinos, as proposedusing by solar references sources. [ Section < However, the anomaly still needsdue to to be the large verified uncertainties by in future astrophysical sensitive measurements. terrestrial experiments experiment in China, andthis the study accuracy we explore is the expected possibility of to carrying reach sub-percentage level [ which could be caused by nos. Shortly afterwards, PandaX-II performed(90% a C.L.) similar study [ andby reported XENON1T. On the other hand, astrophysical observations have given tighter limits 1 ment bounds electron antineutrino magneticC.L.) moment using ( a highUp purity to germanium now, detecor the placed Borexino< collaboration close reported to the a most powerful stringent upper reactor limit core on [ JHEP08(2021)068 i ), B = = ' φ 8 10 ) A e W (2.3) (2.2) (2.1) ), ν N 10 ϑ (¯ 1 8 e . g 2 × ρ 10 } LS = is the fine ν × 1 ) 006) E . In the low + sin α e . V ρ , the electron 1 ν . In addition, 0 1 2 ( 2 2 − 11) − LS MM detection. g . = s ± − ν e ρ 0 2 e 1 cm T − dE , = N ) ± e and 46 ) 98(1 MM cm 2 . {z ν − 5 ,T σ µ,τ ( 73 ν In this study, we simply ν 10 . 88(1 ν (¯ B 2 . E 0 solar neutrino source. 1 g µ µ 4 ( pp × α ' th = σ i 06 2 e ) 2 ) . ν W α dr , m ) 88 µ,τ E ϑ π | solar neutrinos propagating from ν MM can be expressed as ν , the LS density ( 2 ( 1 ν ' T g i eα is the th + ), CNO ( i 2 e 9 r, E P } i # ) in the unit of ( MM cross section term, m 3 e is the kinetic energy of recoil electron, 10 π + sin . 2 F ν

2 T ν eα e A e 10 1 2 e,µ,τ P × E 2G T X ) N = m × r ES with Be neutrinos dominate the measurement of α MM cross section from neutrino magnetic 2 = ( = . In ν 7 i ) g ν 06) ) . 0 ν 1 F e 23 30) 0 g σ , they obey . . ν E – 3 –

(¯ 2 0 0 ( and − g is the normalized energy spectrum of each solar R ± , which indicates lowing detector energy threshold µ,τ

i 0 ) 2 ± ¯ ν ' Z S ν

i pp = S ν e ) Z W 93(1 /E , the exposure time e i . T E ϑ ) = SM ν and satisfies {z 98(1 1 4 ( . 1 φ σ ν V 2 ( MM is generally detected through the neutrino-electron 0 g 7 − − E ( ν i σ e ( µ,τ 1 X ν i eα pep /T T = sin 2 2 P hep e (1 g ]. Other types of solar neutrinos can be ignored. ) ), yields N 9 + 2 25 µ,τ g ν 10 2 1 (¯ 1 ) = g ) and g e × " 6 ES). The cross section of T ], which predict different solar neutrino fluxes. is the oscillation probability of the e ν ( 0 = and 10 ) σ 42 m ) 06) | 1 ν . pre × g . Whereas for 0 E µ,τ N ( , ν 23 ( e ) = 2 ± . i 12) ¯ eα ν ν with the total volume g . (mol/g) and the Avogadro constant 0 is the total electron number of the fiducial volume, yielding P 0 e 33 ,E e ' ρ e ± 93(1 and and . N 10 T ( W 4 e e × The signal from the electron and solar neutrino elastic scattering can be calculated In terrestrial experiments, ϑ ν is the neutrino energy, and 27 σ We checked that the choice of metallicity has negligible effect on the sensitivity of T . 2 46(1 1 d . d 35 0 ν MM according to ref. [ . Be ( 5 and birth location in the sun. The oscillation probability can be expressed as 1 density is the corresponding neutrinoneutrino. flux. the Sun to the earth, which has taken into account the distributions of energy spectrum with the following formula where 7 ( energy region, the contributions from ν Since Jinping laboratorymajor is neutrino far source away at fromstandard MeV solar nuclear energy models reactor region. (SSM) are plants,metallicity constructed Based (LZ) solar in [ on two neutrinos the flavors: is solar highchoose metallicity the the surface (HZ) neutrino metallicity, flux and the prediction low based on HZ hypothesis with structure constant. Moremoment is importantly, proportional the to can significantly boost the detection capacity. 2.2 Solar neutrino signals In the standard model (SM)E cross section term, for sin − elastic scattering ( JHEP08(2021)068 . 1 Be Be 1 pep 7 7 MM MM MM ] as a ν ν ν 43 and pp M M M M M M M

1400 O

p e N p e B 7 p C p , which is the best fit of is the cross section of B MM signal-to-background α µ i ν σ 1200 B 11 0 − 1 ]. In order to measure 2 p e 10 neutrino distribution [ p e 44 B is similar to the one from 7 p CNO p Total × th 2 i . pp 1000 = 2 ]. The SM electron recoil of the eff ν µ r 45 K is the oscillation probability of a neutrino ES from 5 8 ν ) 800 ν o P neutrino flux can play an important role in the 0 – 4 – 1 2 r, E is the weight of ( pp ) Visible Energy [keV]

eα r ( P i Be neutrino accurately. The fluxes of CNO and neutrino can be mainly limited by the radiochemical 600 7 F pp ]. and detected at the Earth. Since the energy of 26 C ν 4 <1 MeV), the matter effects from the Earth can be ignored. 1 E 400 MM from all solar neutrinos. The SM ES signal is also background for ν max ν E takes no account of the day-night effect. from gallium experiments [ in the Sun, and ) ν r 5% 200 energy resolution has been considered. The dashed lines correspond to the contri- r, E ( with energy MM. The flux of 5 4 3 2 1 0 0

0 0 0 0 0 0 ν r eα

1 1 1 1 1 1

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c is the radius of the Sun, 1 -ﬂavor neutrinos. . Energy distribution from various solar neutrino components and backgrounds. (MeV) α

E R p / In this study, we assume 100% detection efficiency in the fiducial volume. Figure 5% ES for MM. The yellow band represents the regionMM hypothesis with in the XENON1T relative [ large . constraints with neutrino gives a clearhelps “shoulder” to structure determine in the thecould flux energy be of region measured from of the is 900 500 negligible. to to 1300 700 keV keV, region, which where the signal contribution from The input oscillation parameters areprecisely, taken it from is PDG crucial 2020 to evaluate [ accuratelyis all the components between most 250 sensitive andGiven 300 region keV, the which fact of that interest the energy (ROI)ES spectrum as signal, of an shown SM external with constraintdetection the on of yellow the band in figure Therefore, ν shows the energy spectrum for each solar neutrino component and also for backgrounds. where function of radius produced at neutrino is very low ( butions of the magneticelectronic moment recoil from caused their by sourcesν with the sameratio color. shown in The the target subplotν signal for is all the neutrinos, assuming Figure 1 4 JHEP08(2021)068 in Po (2.4) MM. 210 ν g/g 18 − , Po could be 10 C spectrum. Kr and 14 × 210 85 7 . ]. 2 Bi, 46 cpd/kton ]. Due to large abun- 210 48 remains a challenge due C, is the total target mass of 28000 14 pp Po piling up with external . For the low energy study, particle from ≈ C pile-up as TV 1 C of LS is 210 α 14 δt M 14 7 C- × ) 14 10 MM measurement. The cosmogenic C and × . To be conservative, we still consider TV ν 68 ± 14 175 2600 M e 456 . × C. With 200 ns charge integration window 3 C 14 Rate [cpd/kton] 14 C itself does not severely leaked above 150 keV – 5 – C- R FV ( 14 14 M × ) MM research, the internal Bi C Po Kr FV ν ES process becomes the intrinsic background to 14 85 210 210 ν M × Background C 14 -rays can be predicted with an exponential scaling factor accord- R γ ( . Background rates taken from Borexino Phase-II [ C. For the ideal study, we temporarily ignore the shape uncertainty ] after purification. The intrinsic × 14 46 2 C- MM, the SM ], other pile-up events, mainly C could be measured independently as Borexino [ Be neutrinos. However, the measurement of ≈ ν 7 14 Table 1 47 14 Po is the dominant background in the 350–550 keV range, which can be 210 is the target mass in the fiducial volume and and pile-up C below 150 keV, signal detection at such low energy region is infeasible. Thanks ]. R pp FV 14 49 ]. We assume the internal radioactive background can reach the same level as M Bi in the region from 700 to 1000 keV and its large quantity, they can be properly 32 C[ The rate of ) assumed, we can roughly estimate the rate of the 14 Po as a background in this study. Because of the signature of “shoulder” structure 210 -rays, are negligible. δt clearly fitted with a gaussiandiscriminated distribution. with scintillation In pulse210 addition, shape the from of measured through spectrum fitting. dance of to the good enegyto resolution affect at Jinping, to the pile-up of of where full volume. The energyAccording spectrum ref. is generated [ withγ self-convolution of the we also consider the( pile-up effect from Borexino Phase-II [ Borexino. The external ing to the distanceof from the the self-shielding edge effect of frombackground the the for fiducial large this detector volume analysis. size toradioactivities of the For are Jinping, detector the we surface. major can safely backgrounds Because ignore as this shown in table duced by cosmic-ray muons,for internal the and study external of radioactiveCosmogenic backgrounds. background In has addition, smallbackground induced impact by on cosmic-ray the ino muons [ is about 200 times lower than that in Borex- 2.3 Background In general, three types of background should be considered: cosmogenic background in- JHEP08(2021)068 , 2 α in χ σ 2 (2.5) pep . In this Rb delayed ] calculated truth 46 . Thus, good 85m eff ν to convert the µ )/BG Kr- MM measurement. Kr can significantly 85 2 ν χ 85 truth 1 2 − , 2 Po is selected as the ROI of MM and any other parameter, α α 210 is the penalty term to constrain in LS experiments. In figure δ ν σ = exp 2 decay rate of ) ], which requires a likelihood func- L pp α α bin of the prediction and the obser- BG=(BG-BG α δ Kr. σ 50 δ X 4% [ ( flux is constrained to 5% by Gallium . 85 th C and 0 i + away from its prior center value and 14 pp 2 α . Therefore, we could fix CNO and ]. . The background parameters are shown as emcee i Kr quantity in-situ. Borexino [ obs 51 pep 85 N – 6 – truth i obs − function as N /φ

2 i pre φ χ N = Kr is hidden beneath all the other components of the Kr have the largest correlation with e

85 85 i T φ X Bi spectrum can mimic them in the low energy region, while = 210 and 2 Kr is generally difficult. are constrained with 0.54% and 0.24% respectively according to χ 85 Be in the ROI. That is to say, the residual pp Kr can accordingly improve the capability of 7 2 21 85 are the event numbers in the m ∆ i obs uncertainty. Kr can make corresponding improvement on the detection sensitivities of N σ 85 and MM could also bias the measurement of presents multi-parametric scatter plots of MCMC using 10-year data taking ν or 12 and MM measurement. Therefore, good liquid scintillator purification and indepen- θ 2 represents the deviation of parameter ν 2 pp i pre α δ sin N Figure Since multiple components are overlapping with each other at different visible energy As we mentioned above, the region between as we expect in the analyses of previous subsection. From another point of view, the Bi has strong correlation with CNO and eff ν MM measurement. However, MM component from µ existence of 210 the following study because having little effect on the results. the relative deviation of thestudy, background truth rates: the prediction of futureexperiments JUNO and experiment all [ background parametersMCMC are sampling free without plot, constraints.priors As of shown in the into likelihood for MCMC. at Jinping, showing bothdistributions. the correlation The for solarthe each neutrino standard pair HZ related of flux parameters parameters model: are and R shown their as posterior the ratio relative to regions, Markov Chain Monte Carloamong (MCMC) multi parameters, technique especially is the usedwhile relations to simultaneously between study obtaining the theMCMC correlations is individual based posterior on distribution ation Python to of package guide each named Monte component. Carlo sampling. Therefore, we use vation with visible energy fromsystematic 150 to terms, 1500 such keV, and as solarwhich, neutrino oscillation parameters andstandards solar for neutrino 1- flux. In For the sensitivity study, we build a where However, purification of coincidence signal can bethat used to it measure canmeasurement be to picked put out a 4% with constraint an on2.4 the efficiency rate of of 18%, Sensitivity which allows 10-year independent ν ROI, making it difficultν to measure. Inaffect addition, the It is almostdent free measurement to of mimic the shape of

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1 1 f f e . MCMC results on fitting parameters with 10-year data taking in Jinping. The solid, 4 0 1 2 0 1 2 5 8 4 4 1 Figure 2 dashed and dotted lines represent1-d 1- distribution of eachparameters. parameter. To fit Off-diagonal the plots plotcorner in show of one the this page, page. posterior we 2-d move the distribution bottom of right two triangle plots to the upper right JHEP08(2021)068 . 3 12 3 θ eff ν fix 2 µ free sin Po free free 210 MM from the ν ) Bi 35 V free free e MM is obtained for 210 ) ]. Gallium experiments ν M ( % Kr. The green line means 51 E 4 ( 85

Kr 30 99% C.L. 90% C.L. r free free 85 K % (90% C.L.), which is already 5 8 Standard HZ bound 3 Sta. only B C µ 14 free free 25 MM hypothesis about the recent 11 ] is bounded by Gallium experiments ν − B constraint on pp 10 . The sensitivities to fix pep free × × 3 4% 2 20 2 1 . 1 0 fix < 1 free [ CNO shows the fitting or sampling conditions of all are fixed,

– 8 – 15 2 come from the future JUNO [ pep Be 12 free free 7 θ 10 and MM between fixing solar oscillation parameters ( pp 5% 5% ν 2 21 MM measurement at Jinping with 10-year data taking. The blue , as shown in figure m ν , CNO and 5 eff ν ∆ 2 21 µ 12 ) to confirm or exclude the minimizer are consistent with each other. We find that there is fix θ σ m also have no effect on the sensitivity. The standard case in figure 0.24% 2 ∆ χ (3 , pep 0 energy resolution. The deep pink line is the statistics only case. 12 2 21 σ 5 0 θ m 10 25 20 15 fix 2

neutrino ﬂux with about 5% in both MCMC and Minuit.

based minimizer, Minuit, is used. The sensitivity of 2 ∆ 0.54% , the standard case can reach sin 2 3 pp (MeV) χ E ) and constraining them with JUNO reactor measurement. Similarly fixing or . The sensitivity of p 2 21 . The condition of parameters in MCMC and Minuit. Minuit specifies the standard case. / m 3% ∆ Tool In figure In order to study the influence of different inputs on the sensitivity to the measurement MM, a MCMC ν Minuit-Std parameters in Minuit and MCMC. significantly better than otherhas terrestrial experiments. more Furthermore, than weexcess 5 find in that Jinping XENON1T in 10 years (4 years) for the standard case as shown in figure no difference in sensitivityand to releasing CNO and assumes that and other parameters are all free. Table of different input values of MCMC method and Table 2 In MCMC, the constraints of constrain the fuchsia line presents the standard casethe with standard additional case withwith additional HZ model flux constraint. The purple line is the standard case Figure 3 line is the standard case with only the radiochemical constraints from Gallium experiments. The JHEP08(2021)068 C, C, 14 14 MM MM . By ν ν 1 , we find 4 40 Be fluxes, can improve 35 7 MM. Furthermore, we (90% C.L.). Any further , high light yield LS. As ν B 99% C.L. 90% C.L. and µ 12 30 pp − (MeV) MM detection sensitivity if the E ν 10 (90% C.L.). A more than 1000-fold × p ] MM with increased abundance of / 0 B 25 . B ν 6 µ Bi could hardly improve the sensitivity. 3% (90% C.L.). Kr measurement can further boost the × 12 < 210 2 − 85 B 1 µ 20 10 11 0 × 1 − [ – 9 – 0

. 10 Po and 1 MM with different individual reductions of 15 ν × 210 < 8 Kr backgrounds, which is impossible with the current . 0 0 0 85 0 0 0 0 0 0 0 0 1 1 0 < 1 1 0 0 10 1 1 0 0 × × 1 1 × × 1 1 i i × × o o MM at Jinping with 10-year data taking. The blue line is the × × r r P P B B × × ν l l C C K K 0 0 0 0 (90% C.L.) as well as l l C and neutrino flux is the dominant systematic uncertainty affecting 4 4 5 5 1 1 1 1 1 1 8 8 2 2 2 2 A A Standard 14 5 MM. Additional 4% B pp ν µ , 11 3 − Bi with simple background reductions. We find that the reduction at 90% C.L. assuming the background level as shown in table MM down to 0 10 Bi background, respectively. And the black line is for all above background. ν B 5 0 210 and × µ 25 20 15 10

210

2 Kr would not help. Therefore, in order to reach the astrophysical limits, C background to reach 2 1 12 Kr background could at most reach Kr could significantly improve the sensitivity to 85 − 14 85 85 10 . The sensitivity to Po and × Po and 9 210 . 210 3 C and On the other hand, we also study the variation of In order to evaluate the effect of different background abundances on sensitivity to 14 < Kr, Kr, MM, we calculate the sensitivity to we have to heavily reduce technology. However, any reduction of abundance of backgrounds increases bythat a even factor if of each background 10 is or increased 100. by 100 As times shown individually, the in detection figure sensitivity investigate how much reductiondetection of sensitivity background of abundance astrophysical isreduction on observations. needed to It matchreduction would the in take more thanreduction 10,000-fold in the sensitivity on ν 85 of is comparing this with the standardaffect case, the we know sensitivity systematic to upper uncertainties limit can significantly to shown in figure the final sensitivity. Additional HZ flux bound, particularly fuchsia and red85 lines represent the sensitivityThe to solid (dotted) detect line refers a 100 (10) fold increase in theWithout background. considering systematic uncertainties, the statistical-only case shows that Figure 4 standard case with only the radiochemical constraints from Gallium experiments. The green, cyan, JHEP08(2021)068 ) and 1% ] can be placed 40 (90% C.L.) with a ), 432 keV ( B µ 81% . We obtain the effective 11 − , with a 27.7-day half-life. A e Cr source [ ν 10 51 MM hypothesis in XENON1T. × ν 1 V + . 2 51 ), 747 keV ( Outside < 9% −→ (90% C.L.). Moreover, if the abundance R − B e shows the cartoon sketch of the proposed µ MM can also be probed with artificial neu- dR ν 11 5 − ], – 10 – Cr + 10 51 40 ], we assume a 3 MCi , × 38 6 39 . R Inside 1 Cr is dR sensitivity to validate the < 51 σ MM would reduce to ν , the distance from event vertex position to the artificial source, for both , it still has 3 R 1 ) respectively. 9% . The cartoon sketch about the source positions. The sizes of them are not proportional Cr neutrino signals 51 MM with artificial neutrino source We calculate the energy spectra of signal, background and event vertex distribution ν MM can still reach at least ν The monoenergetic neutrino energies427 are keV ( 752 keV ( as function of cases based. Detail of this calculation is shown in the appendix 3.1 According to the BEST experimentat [ two possible locations:or outside inside with 1 at meter thesource away from positions. center the of The edge detector. decay of of the Figure fiducial volume largely reduce the experimentalThe time largest to challenging achieve for the suchshielding similar kind for sensitivity of those as experiment strong solar is radioactivebility sources. the neutrinos. of production, such In experiment transportation the instead current and of paper, worrying we about focus the on technique the details. capa- 3 As pointed out bytrino previous or study antineutrino [ sources. The great benefit of such kind measurement is that it can shown in table However, the sensitivity to 100-fold increase in all backgroundcontrol the with background respect abundance to of Borexino. Jinping Therefore, within it 10 is times advisable that to of Borexino. Figure 5 to the actual sizes. to of all those four backgrounds deteriorate to 10 times that of Borexino background level JHEP08(2021)068 2 ]. ], R χ G 25 B and 20

− 20 MM 52 (3.1) + , ν e µ

e ν

T r 25

, r a l e C o 1 15 ν 15 5 S Cr source is Cr source is ] 51 51 m [ MM should be

e 10 R 10 Cr and the solar ν MM will be more e presents the event 51 respectively. Given ν τ 6 ν 5 5 µ Cr can only contribute . MM with , ν 51 µ ν Inside Outside µ 0 0

, Event profile Event e ν signal from C.L. upper limits at Borexino [ Cr source for both cases as µ e 51 ν M 90% M ] (Inside) ] (Outside) M 1 1 e M − − e e MM shown as dashed line in blue color

s s r r τ

, assuming ideal position reconstruction. 2 2 r r a a ν l l ) to study C C − − o o R 1 1 . 5 5 BG Total S S 2.5 1 [cm [cm Cr neutrino source could be precisely counted. – 11 – 51 10 9 1400 , the individual ] MM and 10 10 B Cr can significantly break the structure of µ µ Inside ν × × Cr shows a prominent “shoulder” structure between 51 Outside 11 1200 51 − 27 79 . . . However, the neutrino source , 10 τ 1 4 MM, ν 6 × e function as eq. ( ( 1000 ν MM shown as dashed line in fuchsia color from 2 e = 8) [ χ . ν and 5 eff , µ 800 8 φ ν . 5 , e , 9 ν for both locations. Because of mixing, solar neutrinos contain the . 600 6 Visible Energy [keV] energy resolution has been considered. Right: the normalized event profile with ) = (3 from the source. The position resolution of reconstruction is not considered. τ 400 ν R (MeV) . Left: the event number of each component by 55-day data taking with the assumption (visible energy only) one-dimensional fitting. Therefore, a two-dimensional , µ E µ E ν MM. Therefore, the signal of T p 200 e / In the left plot of figure 3 1 5 3 1 5 ν , µ magnetic moment in solar neutrinos, which was also presented previously in [ 0 0 0 0 0 0 e

1 1 1 1 1 1

5% V e k [ s t n u o c

] τ . 1 µ 3.2 Sensitivity We need to build a similar the energy spectrum and(visible event energy vertex and difference event vertex) between two signalfrom dimensional fitting and is backgrounds, much better than the sensitivity almost equal to thefrom sum solar of neutrinos forbetter than both other cases. neutrino flavorthe magnetic That same moment. is as The the to ROI solar of say, neutrino the case sensitivity in figure to The position information canneutrinos be or background, used which to are separate uniformly distributed the inside the500 detector. and 600 keV, withMoreover, which the the amount flux of of the ν when combined with solar neutrinosensitive signal. than In the this other case, twoprofile the neutrino in probing flavors. of the The right different plot slices in as figure a function of The distributions of energy andleft vertex plot position of for figure signal andcontribution background are from shown in the 4 respect to neutrino flux relative to the solar neutrinos with 55-day Figure 6 ( JHEP08(2021)068 . bin. (3.2) e,µ,τ 4 fix ν R . With µ τ ν µ Po free 210 and 10 τ ν neutrino flux, the µ Bi e ν reconstructed free 210 , th j 2 8 99% C.L. 90% C.L. Kr free Cr comes from the independent 85 α α δ σ 51 can be achieved with the source is the C e ν j α 14 free ] X µ B e 6 + 2 × fix pep ]. Gallium experiments constrain the flux of 1 signal statistics in the inside-detector case 1 i,j obs 38 is also a background for e , 0 ν N e i,j 1 obs ν fix 36 [ MM for different neutrino flavors. The sensitiv- − ,

– 12 – CNO N 4 ν 35 i,j pre N Be free 7 MM components using 55-day data taking. The solid (dashed) Cr case. j , because R ν X τ 51 ]. Other parameters are consistent with the standard case . ν pp e 5% 2 i µ T 3 X 38 are from the collected solar neutrinos during 55 days of data , = τ , the fitter has an extra fit parameter due to the neutrino flux and Cr ν 2 36 1% , τ 51 χ 2 bin from 150 to 1500 keV and ν 35 µ [ e and is the most sensitive one among all neutrino flavors due to the presence Cr. In the following analysis, we assume the uncertainty of neutrino T 12 0 µ fix e θ 51 5 0 ν ν 1%

th source. Since there is more 25 20 15 10

µ i 2 e 2 21 ν presents the sensitivities of m Cr is fix as shown in table 7 ∆ 51 2 is the MM for . The sensitivity with each . The status of parameters in Minuit. The constraint of ν i Figure neutrinos with about 5%. Tool Minuit of the strong than the outside-detector case, thedeployed best in sensitivity the to centerweaker of sensitivity detector. to On the55-day other data taking, hand, we the obtain stronger the results with 90% C.L. upper limits shown in table flux from in section ities of taking. Clearly, where Compared with section uncertainty from lines represent the inside (outside) function is used in the following study as Figure 7 Table 3 measurements by calorimeter techniquepp in [ JHEP08(2021)068 . . ) e e µτ B ν ν eff ν and µ µ µ µ from from e 11 τ ν τ − 2 ν ν 4 µ and µ µ 10 e 51 ν . × , which is a µ and 3 Cr data could . eff ν + 0 µ 1 51 3 µ ν 99% C.L. 90% C.L. µ ] µ 2 ν < B ( µ × 49 B . for different cases. The 1 µ 1 0 2 11 µτ 0 ' eff ν − 1 τ [ µ 2 ν

e 10 5.1 5.0 Cr is more sensitive to µ µτ 51 × improves significantly, which is , a mixing of and eff ν presents the sensitivity for 1 µ 9 e µ µτ e . ν 8 ν ν eff ν 0 5.1 5.0 µ µ µ µ < e ν 0 to 1.1 1.5 µ 5 0 e MM with 55-day data taking. 25 20 15 10

ν ] 2 µ B µ 6 – 13 – 11 −

Cr r Cr a 51 l 10 e 51 o 5 c × S r

[ u r o a . 55-day data taking of s e

] τ y r 4 B - ν after marginalization with other parameters. The gray band is C 0 Inside 1 µ 1 e 5 Outside Xenon1T 1 Combination 1 ν shows the two dimensional 90% C.L. contours for µ 0 plane. The right plot of ﬁgure 8 3 Cr source, the sensitivity on 1 and 90% C.L./ × µτ 51 [ eﬀ ν

µ e ν space, 10-year solar neutrinos could exclude a lot possible parameter . 90% C.L. upper limits of µ 2 µ e ν , e and ν Cr case. The combination stands for combing the data of 10-year solar neutrinos µ e 1 . ν 51 Table 4 µ Cr source. B 51

5 4 3 2 1 0 6

Cr source neutrinos. In this study, we deﬁne

[ ] . The left plot shows 90% C.L. upper limits on B

0 1 ×

f f e 1 1 51 neutrinos . We reproduce the XENON1T anomalous excess with 90% C.L. band of The left plot of figure µτ eff ν even more sensitive than 10-yearexclude data most taking of from the solar neutrinos.space in 55-day both The combination could only(90% weakly C.L.) improve for inside case (outside case). solar neutrino mixing. Thethe value of appendix this mixed variable µ for comparison. With a 10-year data taking ofcombination of solar neutrinos couldTo reach give a a better sensitivity, sensitive55-day we search combine the for measurement of 10-year solar neutrinos and inside (outside) with 55-day 3.3 Combined analyses with 55-day artificial neutrino source and 10-year solar Figure 8 right one is thethe sensitivity corresponding to area based on 90% C.L. in XENON1T. The solid (dashed) lines represent the JHEP08(2021)068 ], × × 3 1 25 . MM 1 ν < MM hypothesis (90% C.L.). In Cr to determine ν energy resolution B 51 . The left segment MM hypothesis in µ ν 9 Neutrino flux is the to validate the 11 MM. The HZ model − σ Cr source compared to ν pp (MeV) 10 51 E MM and the sensitivities of × p ν ]. The right segment presents 8 / level at 90% C.L. with 10-year . 53 0 B 3% µ < 11 MM has been constrained to the MM can be measured with − ν e (90% C.L.). ν 10 Kr or B × 85 µ 2 . 11 1 , Jinping could validate the − effective neutrino magnetic moment. We have 9 < 10 C could significantly improve the sensitivity to B – 14 – Kr only has a limited improvement. On the other µ 14 × 85 11 bound on 0 Be could lead to . ] and red clump stars [ − 7 1 ], also with the astrophysical observations: cooling of 31 10 MM measurement at Jinping neutrino experiment with 4% < ν can reach 27 × and 2 eff ν . Cr neutrino source, .A 2 µ pp 51 σ ∼ ) at 90% C.L. for inside (outside) the detector in 55 days. We have B ]. As shown in figure µ from this work compared to terrestrial experiments: Borexino [ 24 11 ], white dwarfs [ − eff ν µ 30 10 × ] and PandaX-II [ 5 Cr source. . 26 1 51 shows < level at 90% C.L. by many terrestrial neutrino experiments. However, XENON1T ( 9 B B µ µ In the end, we present the current several best results of With respect to 3 MCi We find the sensitivity of 11 11 − − MM detection, while the reduction of MM measurement plays an important role in determining the intrinsic nature of neutrinos discussion for the Jinping Neutrino Experiment.National Key Jiajie R&D Ling program acknowledges of the China supportScience under from Foundation grant of NO. China 2018YFA0404013, National underImaging, Natural Grant NO. Ministry 11775315, of Key Education. LabNatural Jiajun of Science Particle Liao Foundation of & acknowledges China Radiation the (Grant No. support 11905299), from Guangdong the Basic National and Applied strength of Acknowledgments We would like to express the gratitude to Shaomin Chen and Zhe Wang for their insight and globular clusters [ the electronic neutrino magneticGemma experiment moment [ from thisas work suggested by with XENON1T in theby future. reducing It the could systematic reach uncertainties the and region of the astrophysical intrinsic interest background or by enriching the the neutrino magnetic moment induced by different neutrino flavors. both solar neutrino and artificialof neutrino figure sources at JinpingXENON1T in [ figure within 10 times thathypothesis of in Borexino. XENON1T. In this case, Jinping still has10 3 also considered the combination of 10-year solar neutrino and 55-day dominant systematic uncertaintyconstraints that on affects the the fluxesaddition, sensitivity of we to find thatν the reduction of hand, to be conservative, it is advisable to control the background abundance of Jinping calculated the feasibility of doing both natural and artificial neutrino sources. data taking from solarXENON1T neutrinos by at more than Jinping,could 5 which improve can the validate sensitivity the to ν and probing new physics in10 the neutrino sector. The recently reports a hint of a 4 Conclusions

JHEP08(2021)068

e e B / ] [ , ) ) i 2 0 2 0 1 R R, t 1 1 1 (A.1) (A.2) ( − R 2 φ ) ) 0 0 0 R, t, E R x i ( 1 1 1 + + E 2 0 ψ ) ( R x

2( +

e ) e d i s t u O ( r C 0

1 5 R , ( ) = ) i

−

) e d i s n I ( r

C ,T 1 1 5 i neutrino branch with E in the shell, π , is the decay rate initial- R, t, E (

(

) th α ) e R a m m e G i e t ψ σ ( ) i ,T ) = 2 i Cr E R and E 51 ( ( ( ) R e S eα R σ P ( and the )

S Jinping HZ bound HZ Jinping t e,µ,τ X

α Jinping standard Jinping R, t, E ) ( i , time branch and ψ

i th Red clump stars clump Red as i is expressed by X – 15 – ) ) R, t, E R (

R R d

( ( ψ White dwarfs White e S i N X

) Globular clusters Globular R ) = ( e Cr source e with the area of the shell

51 N

A PandaX-II . This formula can also be used for the light sterile neutrino i N R, t, T e ) = E ( ρ e

and a thickness

is the fraction of the N XENON1T LS ]. In our case, there is almost no neutrino oscillation. Therefore, it ) R ρ i is also proposed and studied by Z. Ye et al. simultaneously. We predict the signal event in diﬀerent interfacial shell centered on the ) 53 E

( R R, t, T

( ( Borexino f During preparing this paper, we notice an independent and similar study S . N ) t is the total electron number density as a function of ( 2 ) ) = Cr πR R R 51 4 ( ( . The current status (90% C.L.) of the neutrino magnetic moment and the sensitivities of 22 11 00 e e R 11 11 11 ) N N i ﬂux calculation for E 00 00 00

(

11 11 11

] [ f

f f e where = ized with 3 MCi. The area of the shell where is the neutrino fluxdifferent as monoenergetic a functionstudy of such as radius ref.can [ reduce to Outside source. source with a radius Note added. arXiv:2103.11771 A Electron scattering signal distribution and the effective neutrino Figure 9 Jinping both with solar neutrinos and artificial source. Basic Research Foundation (GrantFunds for No. the Central Universities, 2020A1515011479), and the the Sun Fundamental Yat-Sen Research University Science Foundation. JHEP08(2021)068 ) so , . e , B.2 ) 0 Cr (B.3) (B.2) (B.1) (A.6) (A.3) (A.4) (A.5) e e R eff 51 , ,T R i ) dEdT e i + 2 E 0 ( dEdT x ,T ) e R i e x σ ) E to ν +2 i ( 1 with respect to x e E e x E E,T σ ( ( ln ) eff − f i , 2 0 φ ) can be modified as µτ 3 0 ) e (1 m) is the shortest , E R i 1 e σ ( R ) T dEdT from . Therefore, eq. ( X ) − , x , we obtain 2.2 e f )) 2 x t . Moreover, remove the ) ,T τ ) 1 eff ντ i t R + 2 ν x E ,T i ν ( ! 0 i ( µ ν E 1 µ + X 2 1 E ( R 0 E Cr i E eτ e and Be ( T R 2( 51 σ 7 ( P e − τ eτ − ) B ν R Cr σ R i P e e ) µ µ − 1 1 eff 51 i A T E T Be (862 keV) dominates the pro- ) + + ( 2 0 7 R E N 1 f R E = 55 days, it reduces to ( ) e µ A 2 2 ( 2 ν h ρ f E i N T µ ! i ( eµ π e 3 X LS i 8 i P ρ µτ B Be ρ eτ . Therefore, eq. ( X µτ B eff ν T 7 µ eff ν eµ τ ) P # µ ) µ = LS ν t to compare with the solar neutrino fluxes. µ P r 0 ρ ( µ + ) + (

R eff # 2 e ' during Cr − 2 Cr e 2 with the integral by 0 φ α m x 0 2 eff 51 ) 51 e and R Cr + 2 π µ R R R E T – 16 – B ν ( ) E,T µ eff 51 ( x x µτ . In this study, A 2 µ ν ( µ = eff ν r τ + 2 i e Cr R eτ µ N ν µ ln + σ e eff 51 P x and . With an integral by 0 µ ) ) ρ 2 0 MM R t R E E ln rR 3 R LS A ( ( µτ ) + ) + 2 0 Be ρ ν µτ i 2 N 0 and ee i x 7 − eµ at ROI, the yellow band in figure eτ E e σ R R ( P 2 ) µ P ( P ρ + ) ν π i x µτ − ) = eµ

0 4 x ) µ eff ν Bq. Moreover, an effective neutrino flux LS e + ) 2 P ρ + µ R ) E + = E , and ( 16 Be 0 x ) ( 2( 0 Cr decay rate 7 eµ

in i R

i 10 eﬀ E + ) = R P 51 S MM τ ( R, t, T e ( S φ 2( 0 ν ( × T

2 e i µτ 2 µ ( R ν − µτ N S ( α m σ 0 e 2 N ZZ 2 With the same calculation strategy, the signal event in different spherical π 005 i − R α . m + and φ " 0 as an effective mixing of π µ 2 1 R i SM ν µτ = 6 10.4 m) is the radius of the fiducial volume sphere and ZZ " µτ X σ µ can be split into eff ν i e ∼ 1 2 MM contributions from the event number, resulting in µ Cr φ ( ZZ e ) = = N µτ is the radius (0.5 m) of the sphere source shielding. In addition, we obtain an i e ν eff 51 0 eff ν i φ r = R X µ R µτ ) = e t, T σ i ( = T X pre ( N N N where portions of can reduce to SM and with effective neutrino flux B An effective neutrinoWe define magnetic moment mixing which is an uniform distribution of where the whole fiducial volume canas to be compare written with as the fluxes ofInside solar source. neutrinos. shell yields If utilizing an effective where distance from the sourceevent to number as the a edge function of of the time fiducial volume. So far, we obtain the total where JHEP08(2021)068 τ 2 ν Be ap- µ 7 ] 24 51 (1982) . Be 44 7 eα 26 25 P + 0 (1982) 3152 µ 2 ν 26 µ 49 . ]. Phys. Rev. D 0 , ' Phys. Rev. D Constraining Majorana arXiv:1909.06048 Phys. Rev. D ]. , 2 [ , SPIRE ]. IN Sov. J. Nucl. Phys. µτ [ , Phys. Rev. D eff ν SPIRE , ]. µ SPIRE IN IN ][ ][ ]. SPIRE ]. IN (2019) 221802 (1982) 359 ]. SPIRE ]. ]. 123 206 SPIRE IN 44 [ IN ]. Electromagnetic Properties of Neutrino and Neutrino Electrodynamics and Possible Effects [ SPIRE SPIRE IN (1986) 446 [ IN arXiv:1403.6344 SPIRE – 17 – hep-ph/0208132 [ [ [ 64 IN (1988) 64 [ keV), the probability from the densest point of (1980) 963 Nucl. Phys. B 213 , Phys. Rev. Lett. 45 Majorana Neutrinos and Magnetic Fields , Resonant Spin-Flavor Precession of Solar and Supernova (1982) 283] [ Neutrino electromagnetic interactions: a window to new ), which permits any use, distribution and reproduction in = 862 Radiative Decays of Massive Neutrinos (2015) 531 (2003) 376 (1988) 1368 The Magnetic Moment of a Massive Neutrino and Neutrino (2003) 35 25 E 87 , 37 Improved Upper Limit on the Neutrino Mass from a Direct ). Further more, the average oscillation probability 648

563 R ]. 2.3 Sov. Phys. JETP ]. , 06 Phys. Lett. B . CC-BY 4.0 , Study of the neutrino electromagnetic properties with prototype of Borexino Resonant Amplification of Neutrino Spin Rotation in Matter and the Solar Phys. Rev. Lett. SPIRE = 0 This article is distributed under the terms of the Creative Commons , SPIRE Electromagnetic Properties and Decays of Dirac and Majorana Neutrinos in a Erratum ibid. IN ]. r Electromagnetic Properties of Majorana Neutrinos IN [ [ ( Majorana Neutrinos and their Electromagnetic Properties Phys. Rev. D collaboration, , eα Phys. Lett. B Nucl. Phys. B ]. ]. obeys eq. ( Rev. Mod. 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