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neutrinos have long been a rich hunting ground for physics beyond the standard model ( bsm ) . in fact , neutrino mass is so far the only bsm physics that has been established in laboratory experiments . astrophysical evidence of dark matter suggests the existence of bsm particles , which have nevertheless not been observed yet . among all feasible candidates , weakly interacting massive particles ( wimps ) are theoretically rather appealing . these may be observable through their interactions within detectors , as the earth moves through the sea of wimps . this possibility has triggered a cornucopia of experimental efforts of direct dark matter detection  @xcite .    in this letter we examine the physics potential of combining a liquid xenon ( lxe ) detector , designed to search for wimp dark matter , with an intense electron - capture neutrinos source in order to look for neutrino magnetic moments ( @xmath1 mm ) and other new physics in @xmath2 elastic scattering . the idea of looking for new physics in the neutrino sector using dark matter detectors has been proposed before in the literature , see for instance refs . direct dark matter detection relies on observing nuclear recoils with electron - equivalent energy down to @xmath3  kev . due to the small values expected for the dark matter interaction cross section , large detector masses and low background levels are also required . a lxe time projection chamber ( tpc ) can provide a large volume , low detection thresholds ( sub - kev ) and a very low background rate at the energies of interest . at the same time the electron density is higher in xenon than in any other stable noble gas , thus providing the largest possible target density in any given volume near the source . the idea of using liquid noble gas detectors to search for @xmath1 mm was first suggested by vogel and engel  @xcite , but never developed . as a by - product we also find non - negligible sensitivity to sterile neutrino oscillations in the @xmath41  ev@xmath5 range suggested by recent terrestrial experiments  @xcite . when a nucleus decays via electron - capture almost all of the available energy goes into a mono - energetic neutrino . among possible nuclei which decay via electron - capture , @xmath6cr  offers several practical advantages : it is readily produced by thermal neutron capture  @xcite , has a mean lifetime of 39.96  days and produces two mono - energetic neutrino lines at 750  kev ( 90% ) and 430  kev ( 10% ) . mega - curie - scale @xmath6cr  sources have been produced in the past and used to calibrate the gallium radiochemical solar neutrino detectors gallex  @xcite and sage  @xcite . in the presence of a @xmath1 mm , the differential cross section for @xmath2 elastic scattering can be written as @xmath7 where @xmath8 is the electron mass , @xmath9 is the electron recoil energy , @xmath10 is the neutrino energy and @xmath11 is the @xmath1 mm in bohr magnetons ( @xmath12 ) . the term proportional to @xmath11 produces an increase in the number of events at low electron recoil energies . this makes two - phase lxe tpcs  @xcite , with their low - energy detection threshold , ideal detectors for such a search . currently , the lowest bounds on @xmath1 mm come from astrophysical observations  @xcite : @xmath13 . the best constraint from terrestrial experiments , on the other hand , has been obtained by the gemma experiment , @xmath14 at 90% cl  @xcite . in the sm , @xmath1mms are expected to be many orders of magnitude below present bounds , yet many extensions of the sm produce an enhancement of the @xmath1 mm , see for instance ref . @xcite and references therein .        for our sensitivity estimate , we assume a data taking period of 100  days , using a @xmath6cr  source with initial strength of 5  mci . our choice for the strength of the source is based on simulations conducted for the sox experiment  @xcite of the gallex enriched @xmath15cr material  @xcite irradiated in the high flux isotope reactor at oak ridge national laboratory . we consider a generic lxe detector , but for definiteness we chose a design similar to the proposed lz detector  @xcite . we assume a cylindrical fiducial volume with equal diameter and height , @xmath16  m , which contains @xmath17  tons of lxe , and we assume that the radioactive source is placed 1  m below the fiducial volume , along the central axis of the cylinder . neutrinos are detected via electron elastic scattering in the detector , see eq . [ eq : xsecmu ] . under these assumptions , a total of @xmath18 signal events are expected for a 100  day run . regarding backgrounds , we have considered contributions from solar neutrino interactions , @xmath19rn  and @xmath20kr  decay , and the @xmath21xe  @xmath22  decay . following ref . @xcite , the solar neutrino background is estimated to be 1.05 counts per ton and day for @xmath23 neutrinos and 0.51 counts per ton and day for @xmath24be neutrinos . the @xmath20kr  and @xmath21xe  backgrounds have been taken directly from fig .  2 in ref . @xcite and rescaled according to our run length and detector mass , while for @xmath19rn  we assume that a goal of 0.1  @xmath25bq / kg can be achieved  @xcite , about a factor of 30 reduction with respect to what has been achieved for exo-200  @xcite . finally , an important source of background could come from the source itself . in 10% of @xmath6cr decays there is a 320  kev gamma , which can easily be shielded with just a few cm of tungsten . however , impurities present in the chromium prior to irradiation , can lead to the production of mev gamma emitters  @xcite . these will require significant additional shielding to be reduced down to an acceptable level . we base our calculation of this background on the measured gamma activity of the gallex source  @xcite . our source is assumed to be shielded by a 17  cm thick tungsten layer , which , when combined with 70  cm of lxe ( present between the tungsten shield and the edge of the detector ) , provides an attenuation of @xmath26 for a 1.5  mev gamma . nevertheless , with @xmath27 gammas emitted per day ( in all directions ) , we expect about 10 to pass through the shielding and compton scatter in the detector fiducial volume . most of these would deposit energy in excess of the maximum from a @xmath6cr  neutrino , though . further suppression could come from a veto on mulit - site compton scattering events . we estimate the surviving background in the fiducial volume from source gammas to be less than 1 event per day at the start of the data taking , and , since @xmath2895% of mev gammas come from short - lived isotopes ( such as @xmath29cu , @xmath30ge and @xmath31na ) , this rate should rapidly decay with time . therefore , we will neglect these events in our analysis , but we note that care must be taken in the preparation of the @xmath15cr source material to ensure the required level of purity is reached .    to constrain the @xmath1 mm , the analysis is done in terms of the recoil energy of the electron only . the recoil energies are smeared on an event - by - event basis according to a gaussian with @xmath32 . generally , we find that the energy resolution does not have a significant impact on the @xmath1 mm sensitivity . a poissonian @xmath33 is constructed using 0.1  kev wide bins in @xmath9 , from 2  kev to 140  kev unless otherwise stated . in this energy range a total of @xmath34 signal events are expected , together with a total of @xmath35 background events . the distribution of signal and background events in electron recoil energy is shown in fig .  [ fig : mu ] ( left ) . reducing the backgrounds does not significantly improve the sensitivity to this observable since in the low - energy region , where the @xmath1 mm enhancement is expected , the background rate is already quite low . on the other hand , we find the low - energy threshold to be the most relevant parameter in this analysis ( as expected from eq . [ eq : xsecmu ] ) . [ fig : mu ] ( right ) shows the dependence of the sensitivity as a function of detector threshold . with a fairly conservative threshold of 2 kev the 95% cl bound is @xmath36 . such values would yield an improvement of a factor of 5 over the currently best terrestrial limit . a second possible application of the setup studied here would be the search for light sterile neutrinos . sterile neutrinos arise in most models of neutrino mass generation . searches for oscillations between active and sterile neutrinos have been conducted using many combinations of neutrino sources , detectors and oscillation channels  @xcite . experimental results are inconclusive , with strong tension between different data sets ( see , _ e.g. _ , refs . in particular , an analysis of gallex and sage data shows an apparent deficit of events which is consistent with oscillations involving a sterile neutrino with a squared mass difference with the active states @xmath37 and a mixing angle such that @xmath38  @xcite , which is commonly referred to as the _ gallium anomaly_. the smoking gun of a sterile neutrino would be to observe events following an oscillating pattern in @xmath39 , the distance traveled by the neutrino divided by its energy . a monochromatic neutrino source reduces the oscillating pattern to a pure function of @xmath40 . given the energy of the primary @xmath6cr  neutrino the oscillation length at @xmath41 would be @xmath42 90  cm and thus the oscillating pattern would be observable _ inside _ a meter - scale detector . the expected spatial resolution in lxe tpcs is at the sub - cm level , which makes them ideal candidates for such an experiment .    in our analysis , we have adopted a phenomenological approach based on a 3 + 1 framework , where there is only one extra sterile state at the ev scale . in this framework , the @xmath0 disappearance oscillation probability can be expressed in terms of one mixing angle and one mass squared splitting only , as : @xmath43 where @xmath10 is the neutrino energy , @xmath40 is the distance between the source and the interaction point in the detector , @xmath44 and @xmath45 is an effective mixing angle . the sensitivity to sterile neutrino oscillations is computed using the distance between the source and the interaction point ( @xmath40 ) as the main variable in the analysis . a binned gaussian @xmath33 is built using 3  cm wide bins . the detector is assumed to have a constant spatial resolution of 1  cm ; however , the largest uncertainty in @xmath40 comes from the shape and size of the radioactive source itself . in the present work , we assume that the source will be a cylinder with both height and diameter equal to 14  cm . to achieve such a compact source will require that the chromium material be enriched to @xmath2895% in @xmath15cr . this is much higher than what was achieved by gallex  @xcite , but similar to what was reached by sage  @xcite . a smearing function was generated , by a monte carlo calculation , that simultaneously accounts for the finite source size and the detector resolution . two nuisance parameters are added to the @xmath33 for signal and background normalization uncertainties . a gaussian penalty term ( or pull - term ) is added to the @xmath33 for the background uncertainty and marginalization is performed over both nuisance parameters . unless otherwise stated , no constraint is assumed for the flux normalization and it is therefore left completely free during the fit . for the backgrounds , an uncertainty of 0.5% is assumed . we expect this could be achieved by using the data collected during the source - free operation of the detector corresponding to the the dark matter search . the process is repeated for each point in the @xmath46 parameter space . since the low - end threshold for the electron recoil energy is not expected to have a great impact on the sterile neutrino analysis , it is set to 5  kev in this case . the results for the sterile neutrino sensitivity are shown in fig . [ fig : sterile ] . since the sensitivity mainly comes from a shape analysis , this measurement is far from being limited by systematics . we find the main limiting factor to be the @xmath21xe  background . the expected number of background events ( across the full energy range ) is around 51,130 , from which around 44,000 are from @xmath21xe  @xmath22  decays . this background can be reduced by using lxe depleted in @xmath21xe , though . the sensitivities for both possibilities are shown in fig . [ fig : sterile ] ( left ) . for contrast , we also compare the lxe sensitivity to that of borexino / sox  @xcite using a comparable , 5  mci @xmath6cr  source ( the sox proposal is based on 10  mci ) . the complementarity in @xmath47 coverage of the two experiments is evident . in the case of lxe , the relatively high spatial resolution improves sensitivity at high @xmath47 , while for sox , the relatively large detector volume , or range in @xmath40 , improves the reach at low @xmath47 . it is remarkable that , for a depleted xe experiment , most of the region favored by the gallium anomaly is covered with _ shape information alone_. therefore , if the gallium anomaly is correct this configuration would , with high likelihood , confirm it by a clear observation of the oscillatory pattern . both the sterile neutrino and @xmath1 mm searches are statistics limited and would be improved by repeated redeployments of the @xmath6cr  source . repeated deployment has a precedent in gallex , which irradiated and deployed the same source material twice  @xcite . we will consider five deployments , each identical in source strength and duration to our previously considered single deployment .    in the case of the @xmath1 mm search , the sensitivity with increased statistics is remarkable . at 95% cl , assuming a low - energy threshold of 2  kev , the corresponding bound is pushed down to @xmath48 . if a lower threshold can be achieved , even the astrophysical limit would be surpassed . the sensitivity to sterile neutrino oscillations with increased statistics is shown in fig . [ fig : sterile ] ( right ) . in this case , we assume 90% depleted xe , and show sensitivities from both a shape - only analysis , and an analysis with the shape information plus a 2% uncertainty in the normalization . as can be seen in the comparison of the two bounds , no major improvement is expected from imposing the normalization constraint , since the information comes from observing the oscillating pattern in the detector . only in case of large @xmath49 , where the oscillation is averaged out , would a normalization constraint help . according to our results , after five deployments the full gallium anomaly as well as a sizable region of the reactor anomaly would be covered at 95% cl .    obviously , with 10,000 - 50,000 @xmath2 elastic scattering events with momentum transfers in the 100kev range a number of precision tests of the electro - weak sector of the sm become possible . assuming an absolute normalization at the 1% level and statistical errors at or below 1% , overall accuracies for the total cross section of 1 - 2% appear feasible , providing constraints on the weak mixing angle and its running . to summarize , our results indicate that the combination of a large liquid xenon detector , designed and built to search for dark matter , with a mega - curie scale electron capture neutrino source would provide excellent reach in the search for the neutrino magnetic moment , exceeding the current laboratory bounds by at least a factor of 5 . with repeated source deployments , such an experiment would even be competitive with the best astrophysical limits . moreover , this combination would allow a test of the reactor and gallium anomalies ; specifically , their interpretation as oscillations due to an ev - scale sterile neutrino . its reach would be complementary to other source proposals with sensitivity to the oscillating pattern over almost the entire interesting range of @xmath47 . clearly , a detailed technical feasibility study is required , but so far no major technological obstacles have been identified . this work has been supported by the u.s . department of energy under award numbers and . we would like to thank the authors of ref . @xcite for sharing with us their results for the global fit of the reactor and gallium anomalies . m.  pospelov , neutrino physics with dark matter experiments and the signature of new baryonic neutral currents , phys.rev . d84 ( 2011 ) 085008 . http://arxiv.org/abs/1103.3261 [ ] , http://dx.doi.org/10.1103/physrevd.84.085008 [ ] . m.  pospelov , j.  pradler , elastic scattering signals of solar neutrinos with enhanced baryonic currents , phys.rev . d85 ( 2012 ) 113016 . http://arxiv.org/abs/1203.0545 [ ] , http://dx.doi.org/10.1103/physrevd.85.113016 [ ] . m.  pospelov , j.  pradler , dark matter or neutrino recoil ? interpretation of recent experimental results , phys.rev . d89 ( 2014 ) 055012 . http://arxiv.org/abs/1311.5764 [ ] , http://dx.doi.org/10.1103/physrevd.89.055012 [ ] . j.  abdurashitov , et  al . , measurement of the response of the russian - american gallium experiment to neutrinos from a cr-51 source , phys.rev . c59 ( 1999 ) 22462263 . http://arxiv.org/abs/hep-ph/9803418 [ ] , http://dx.doi.org/10.1103/physrevc.59.2246 [ ] . v.  lebedenko , et  al . , limits on the spin - dependent wimp - nucleon cross - sections from the first science run of the zeplin - iii experiment , phys.rev.lett . 103 ( 2009 ) 151302 . http://arxiv.org/abs/0901.4348 [ ] , http://dx.doi.org/10.1103/physrevlett.103.151302 [ ] . l.  baudis , et  al . , neutrino physics with multi - ton scale liquid xenon detectors , journal of cosmology and astroparticle physics 2014  ( 01 ) ( 2014 ) 044 . 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in this letter we point out the possibility to study new physics in the neutrino sector using dark matter detectors based on liquid xenon . 
 these are characterized by very good spatial resolution and extremely low thresholds for electron recoil energies . when combined with a radioactive @xmath0 source , both features in combination allow for a very competitive sensitivity to neutrino magnetic moments and sterile neutrino oscillations . 
 we find that , for realistic values of detector size and source strength , the bound on the neutrino magnetic moment can be improved by an order of magnitude with respect to the present value . 
 regarding sterile neutrino searches , we find that most of the gallium anomaly could be explored at the 95% confidence level just using shape information .