Dark matter and exotic neutrino interactions in direct detection searches

Journal of High Energy Physics, Apr 2017

We investigate the effect of new physics interacting with both Dark Matter (DM) and neutrinos at DM direct detection experiments. Working within a simplified model formalism, we consider vector and scalar mediators to determine the scattering of DM as well as the modified scattering of solar neutrinos off nuclei. Using existing data from LUX as well as the expected sensitivity of LUX-ZEPLIN and DARWIN, we set limit on the couplings of the mediators to quarks, neutrinos and DM. Given the current limits, we also assess the true DM discovery potential of direct detection experiments under the presence of exotic neutrino interactions. In the case of a vector mediator, we show that the DM discovery reach of future experiments is affected for DM masses m χ ≲ 10 GeV or DM scattering cross sections σ χ ≲ 10−47 cm2. On the other hand, a scalar mediator will not affect the discovery reach appreciably.

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Dark matter and exotic neutrino interactions in direct detection searches

Received: February matter and exotic neutrino interactions in direct Enrico Bertuzzo 0 1 2 4 5 Frank F. Deppisch 0 1 2 3 5 Suchita Kulkarni 0 1 2 5 Yuber F. Perez Gonzalez 0 1 2 4 5 Renata Zukanovich Funchal 0 1 2 4 5 London WC 0 1 2 5 E 0 1 2 5 BT 0 1 2 5 U.K. 0 1 2 5 E-mail: 0 1 2 5 0 1 2 5 Open Access 0 1 2 5 c The Authors. 0 1 2 5 0 Working within a simpli ed 1 Nikolsdorfer Gasse 18 , 1050 Wien , Austria 2 R. do Mata~o 1371, CEP. 05508-090, S~ao Paulo , Brazil 3 Department of Physics and Astronomy, University College London 4 Departamento de F sica Matematica, Instituto de F sica, Universidade de S~ao Paulo 5 nuclei. Using existing data We investigate the e ect of new physics interacting with both Dark Matter (DM) and neutrinos at DM direct detection experiments. model formalism, we consider vector and scalar mediators to determine the scattering of DM as well as the modi ed scattering of solar neutrinos o from LUX as well as the expected sensitivity of LUX-ZEPLIN and DARWIN, we set limits on the couplings of the mediators to quarks, neutrinos and DM. Given the current limits, we also assess the true DM discovery potential of direct detection experiments under the presence of exotic neutrino interactions. In the case of a vector mediator, we show that the DM discovery reach of future experiments is a ected for DM masses m . 10 47 cm2. On the other hand, a scalar mediator will cInstitut fur Hochenergiephysik; Osterreichische Akademie der Wissenschaften 1 Introduction The framework Vector mediator Scalar mediator Introduction Scattering at direct detection experiments Neutrino and dark matter scattering Recoil events induced by DM and neutrino scattering Background free sensitivity in the presence of exotic neutrino interactions Current and future limits on DM-neutrino interactions Sensitivity to DM-nucleon scattering in presence of exotic neutrino inThe Standard Model (SM) of particle physics, despite its enormous success in describing experimental data, cannot explain DM observations. This has motivated a plethora of Beyond the Standard Model (BSM) extensions. Despite intense searches, none of these BSM extensions have been experimentally observed, leaving us with little knowledge of the exact nature of DM. The lack of an experimentally discovered theoretical framework that connects the SM degrees of freedom with the DM sector has led to a huge activity in BSM model building. Among various DM scenarios, the Weakly Interacting Massive Particle (WIMP) DM remains the most attractive one, with several experiments actively searching for signs of Within this paradigm, DM is a stable particle by virtue of a Z2 symmetry under which it is odd. The WIMP interactions with the SM particles can be detected via annihilation (at indirect detection experiments), production (at collider experiments) and scattering (at direct detection experiments). If the WIMP idea is correct, the Earth is subjected to a wind of DM particles that interact weakly with ordinary matter, thus direct detection experiments form a crucial component in the experimental strategies to At direct detection experiments, WIMP interactions are expected to induce nuclear recoil events in the detector target material. These nuclear recoils can be in most detectors, discriminated from the electron recoils produced by other incident particles. Depending on the target material and the nature of DM | SM interactions, two di erent kind of DM interactions can be probed: spin-dependent and spin-independent DM | nucleus scattering. The current limits for spin-independent DM-nucleus interactions are considerably more stringent, and the next generation of direct detection experiments will probe the spin-independent interactions even further by lowering the energy threshold and increasing A signal similar to DM scattering can also be produced by coherent neutrino scattering nuclei (CNSN) in DM direct detection experiments [1{3], hence constituting a background to the WIMP signal at these experiments. Unlike more conventional backgrounds such as low energy electron recoil events or neutron scattering due to ambient radioactivity and cosmic ray exposure, the CNSN background can not be reduced. The main sources contributing to the neutrino background are the uxes of solar and atmospheric neutrinos [4], both fairly well measured in neutrino oscillation experiments [5, 6]. Within the SM, CNSN originates from the exchange of a Z boson via neutral currents. Given the minuscule SM cross-section CNSN < 10 39 cm2 for neutrino energies < 10 MeV, and the insensitivity of the existing DM detectors to this cross-section, CNSN events have yet to be experimentally observed. The minimum DM | nucleus scattering cross-section at which the neutrino background becomes unavoidable is termed the neutrino oor [7]. In fact, the neutrino oor limits the DM discovery potential of direct detection experiments, so diminishing the uncertainties on the determination of solar and atmospheric neutrino uxes as well as the direct measurement of CNSN is very important. Fortunately, dedicated experiments are being developed to try to directly detect CNSN [8, 9] in the very The absence of any WIMP signal at the existing direct detection experiments has resulted in the need for next generation experiments. It is expected that these experiments will eventually reach the sensitivity to measure solar (and perhaps atmospheric) neutrinos from the neutrino oor. It thus becomes important to analyse the capacity of these experiments to discriminate between DM and neutrino scattering events. It has been shown that a su ciently strong Non-Standard Interaction (NSI) contribution to the neutrino | nucleus scattering can result in a signal at direct detection experiments [10{13]. Several attempts have been made to discriminate between DM scattering and neutrino scattering The cases considered so far involve the presence of BSM in either the neutrino scattering or the DM sector. However, it is likely that a BSM mediator communicates with both the neutrino and the DM sector, and the DM and a hidden sector may even be responsible for the light neutrino mass generation [17]. In such cases, it is important to consider the combined e ect of neutrino and DM scattering at direct detection experiments. In this work we analyse quantitatively the e ect of the presence of BSM physics communicating to both the neutrinos and the DM sector on the DM discovery potential at future direct detection experiments. The paper is organized as follows. In section 2 we de ne the simpli ed BSM models we consider while section 3 is dedicated to calculational details of neutrino scattering and DM scattering at direct detection experiments. Equipped with this machinery, in section 4, we describe the statistical procedure used to derive constraints for the existing and future experiments. We consider the impact of the BSM physics in the discovery potential of direct detection experiments in section 5. Finally, we conclude in section 6. The framework Working within the framework of simpli ed models, we consider scenarios where the SM is extended with one DM and one mediator eld. The DM particle is odd under a Z2 symmetry, while the mediator and the SM content is Z2 even. The symmetry forbids the decay of DM to SM particles and leads to 2 ! 2 processes between SM and DM sector which results in the relic density generation, as well as signals at (in)direct detection To be concrete, we extend the SM sector by a Dirac DM fermion, , with mass m and consider two distinct possibilities for the mediator. In our analysis we will only specify the couplings which are relevant for CNSN and DM-nucleus scattering, namely, the couplings of the mediator to quarks, neutrinos and DM. We will explicitly neglect mediator couplings to charged leptons, and comment brie y on possible UV-complete models. Vector mediator In this scenario, we extend the SM by adding a Dirac fermion DM, , with mass m a real vector boson, V , with mass mV . The relevant terms in the Lagrangian are: where the currents are Lvec = V (Jf + J ) + f = Af are the vector and axial-vector couplings of SM fermions to the vector mediator V , while g A de ne the vector and axial-vector couplings between the mediator V and . The Lagrangian contains both left-and right-handed currents, thus implicitly assuming the presence of an extended neutrino sector either containing sterile neutrinos or right-handed species. We will not go into the details of such an extended neutrino sector, simply assuming the presence of such left-and right-handed currents and dealing with their phenomenology. Following the general philosophy of simpli ed DM models [18, 19], we write our e ective theory after electroweak symmetry breaking (EWSB), assuming all the couplings to be independent. This raises questions about possible constraints coming from embedding such simpli ed models into a consistent UV-completion. The case of a U(1) gauge extension has for example been studied in [20], where it has been shown that, depending on the vector-axial nature of the couplings between the vector and the fermions (either DM or SM particles), large regions of parameter space may be excluded.1 In our case we allow 1Even without considering the additional fermionic content which may be needed to make the model the possibility of di erent couplings between the members of weak doublets, i.e. terms with isospin breaking independent from the EWSB. As shown in [21], such a possibility to be very small. Moreover, we expect a non-trivial contribution of the isospin breaking sector to electroweak precision measurements, in particular to the T parameter. Since the analysis is however highly model dependent, we will not pursue it here. We brie y comment here on collider limits for the new neutral vector boson. For mV < 209 GeV, limits from LEP I [22], analyzing the channel e+e its mixing with the Z boson has to be < 10 3, implying the new gauge coupling to be < 10 2. This limit can be evaded in the case of a U(1) gauge extension, if the new charges , impose that are not universal and the new boson does not couple (or couples very weakly) to muons or by small U(1) charges in extensions involving extra scalar elds (See, for instance, eq. (2.5) of ref. [23]). For mV > 209 GeV, there are also limits from LEP II [24], Tevatron [23] and the LHC [25{27]. Since these limits depend on the fermion U(1) charges, they can be either avoided or highly suppressed. Scalar mediator For a scalar mediator, we extend the SM by adding a Dirac fermion DM, , with mass m and a real scalar boson, S, with mass mS. The relevant terms in the Lagrangian with the associated currents are Lsc = S @ The couplings gSf and gS de ne the interaction between the scalar and the SM and the DM sectors, respectively. Similar to the vector mediator interactions, the presence of an extended neutrino sector is assumed in the scalar mediator Lagrangian as well. Since in this work we will focus on the spin-independent cross-section at direct detection experiments, we consider only the possibility of a CP even real scalar mediator. For a scalar singlet it is easier to imagine a (possibly partial) UV-completion. Take, for example, the case of a singlet scalar eld S added to the SM, which admits a quartic dimension 6 operators such as S2`LHeR are generated (with `L and eR being the SM lepton doublets and singlets), which after spontaneous symmetry breaking and for energies HS jHj2S2 and takes the vacuum expectation value (VEV) vS. Non local = 21 arctan( HS vvS=(m2S m2H )) and yf is the fermion Yukawa coupling. The coupling with neutrinos can be arranged for example in the case of a neutrinophilic 2HDM [28, 29]. Typical values of gSf can be inferred from the speci c realization of the simpli ed model, but in the remainder of this paper, we will remain agnostic about realistic UV-completions in which the simpli ed models we consider can be embedded, focusing only on the information that can be extracted from CNSN. We stress however that, depending upon the explicit UVcompletion, other constraints apply and must be taken into account to assess the viability of any model. For example, in generic BSM scenarios with a new mediator coupling to fermions, the dijet and dilepton analyses at the LHC put important bounds, as has been exempli ed in [30, 31]. In this paper we aim to concentrate only on the constraints arising from direct detection experiments. Scattering at direct detection experiments Neutrino and dark matter scattering Let us now remind the reader about the basics of CNSN. In the SM, coherent neutrino nuclei is mediated by neutral currents. The recoil energy released by the neutrino scattering can be measured in the form of heat, light or phonons. The di erential cross-section in terms of the nuclear recoil energy ER reads [7] = (QSVM)2F 2(ER) G2F mN with the SM coupling factor SM = N + (4s2W Here, N and Z are the number of neutrons and protons in the target nucleus, respectively, F (ER) the nuclear form factor, E the incident neutrino energy and mN the nucleus mass we use the nuclear form factor [32] F (ER) = 3 j1 (q(ER)rN ) exp exchanged during the scattering, mn ' 932 MeV the nucleon mass, s 0:9 the nuclear In the case of the vector model de ned in eq. (2.1), the di erential cross-section gets modi ed by the additional V exchange. The total cross-section should be calculated as a coherent sum of SM Z and vector V exchange, and reads GV = 1 + 2 QV g Here, the coupling factor QV of the exotic vector boson exchange is given by [33] QV = (2Z + N )gVu + (2N + Z)gVd ; and q2 = 2 mN ER is the square of the momentum transferred in the scattering process. To obtain eq. (3.4), we assumed that the neutrino production in the sun is basically una ected by the presence of NP, in such a way that only LH neutrinos hit the target. As expected, the interference term proportional to gV gA can give both constructive and destructive interference; in particular, remembering that q2 negative, we have constructive interference for gV < gA. For a detailed discussion of the interference e ects at direct detection using e ective theory formalism, see [34]. As a last remark, let us notice that, due to the same Dirac structure of the SM and NP amplitudes, the correction to the di erential cross-section amounts to an overall rescaling of the SM one. For the simpli ed model with a scalar mediator de ned in eq. (2.3), the di erential cross-section has a di erent form, GS = jgSjQS In this case, the modi ed di erential cross-section is not simply a rescaling of the SM amplitude, but due to the di erent Dirac structure of the S vertex with respect to the SM vector interaction, it may in principle give rise to modi cation of the shape of the distribution of events as a function of the recoil energy. However, as we will see, for all practical purposes the impact of such modi cation is negligible. Using the analysis presented in [33], the coupling factor for the scalar boson exchange is given by QS = Zmn 4 q=c;b;t mq 5 The form factors fTpq; fTnq capture the e ective low energy coupling of a scalar mediator to a proton and neutron, respectively, for a quark avor q. For our numerical analysis we use fT u = 0:0153, fTpd = 0:0191, fTnu = 0:011, fTnd = 0:0273 and fTp;sn = 0:0447, which are the p values found in micrOMEGAs [35]. A more recent determination of some of these form factors can be found in refs. [36, 37], we have used this estimation to determine the e ect of the form factors on our nal result (see section 5). of purely SM interactions with no additional contributions from exotic interactions. For the scalar case, the situation is much di erent. GS includes QS, a quantity dependent on the target material. For LUX, QS couplings, hence for jgSj 1362 gSq, considering universal quark-mediator 100 GeV, natural values of GS are Turning now to DM, its scattering o the nucleus can give rise to either spin-independent or spin-dependent interactions. In our analysis we will consider only the spin-independent scattering,2 as the next generation experiments sensitive to this interaction will also be sensitive to neutrino scattering events. The spin-independent di erential cross-section in 2For the mediators we consider here, the spin-dependent cross-section is in fact velocity suppressed by v2, see for instance [38]. each of the two simpli ed models is given by = F 2(ER) (gS )2Q2S with the energy E of the incident DM particle and all other variables as previously de ned. Recoil events induced by DM and neutrino scattering Given the detector exposure, e ciency and target material, the above speci ed di erential cross-sections can be converted into recoil event rates. We rst look at the recoil event rate induced by neutrino scattering, where the di erential recoil rate is given by = N =dER is the di erential cross-section as computed in eqs. (3.4){(3.6) for the vector and scalar mediator models, respectively. For our numerical analysis, we use the neutrino uxes from [3]. Integrating the recoil rate from the experimental threshold Eth up to 100 keV [7], one obtains the number of neutrino events Ev = "(ER) dER ; to be computed for either the scalar or the vector mediator models. Here, Eth is the detector threshold energy and "(ER) is the detector e ciency function. For the DM scattering o nuclei, the di erential recoil rate also depends on astrophysical parameters such as the local DM density, the velocity distribution and it is given as = N mN m velocity, vmin(ER) is the minimum DM speed required to cause a nuclear recoil with energy ER for an elastic collision and f (v) the DM velocity distribution in the Earth's frame of reference. This distribution is in principle modulated in time due to the Earth's motion around the Sun, but we ignore this e ect here as it is not relevant for our purposes. If the detector has di erent target nuclides, one has to sum over all their weighed contributions as, for instance, is done in ref. [39]. In what follows we will assume a Maxwell-Boltzmann distribution, given as f (v) = <> Nesc (2 taken from [33]. eq. (3.12) as In order to constrain only the DM-nucleon interaction cross-section n at zero momentum transfer, which is independent of the type of experiment, it is customary to write = N 2 2n m n = Z 2 2N v2=mN d SI (ER = 0) as a function of energy thresholds in the range 10 4 keV 102 keV, varied in logarithmic steps. For each threshold we then compute the background-free exclusion expression analogous to eq. (3.11), explicitly Ev = "(ER) dER : Background free sensitivity in the presence of exotic neutrino interactions The presence of CNSN at direct detection experiments highlights the existence of a minimal DM - nucleon scattering cross-section below which CNSN events can not be avoided and in this sense the direct detection experiments no longer remain background free. This minimum cross-section is di erent for di erent experiments, depending on the detector threshold, exposure and target material. Using the de nition given in eq. (3.15), it is possible to represent the CNSN in the (m ; n) plane introducing the so-called one neutrino event contour line. This line essentially de nes the DM mass dependent threshold/exposure pairs that optimise the background-free sensitivity estimate at each mass while having a background of one neutrino event. The presence of additional mediators will modify this minimum cross-section with respect to the SM and hence, modify the maximum reach of an experiment. In this section, we show how the one neutrino event contour line changes due to the additional vector and scalar mediators considered in eq. (3.4) and (3.6). To compute the one neutrino event contour line we closely follow ref. [7]. Considering, for instance, a ctitious Xe target experiment, we determine the exposure to detect a single E (Eth) = Ev = 1 V = 0.3 V = 2.3 V = 3.6 S = 29.2 S = 52.3 S = 82.8 detector. We show on the left (right) panel three examples for the vector (scalar) mediator. We also show the SM one neutrino event contour line (in blue) for comparison. The red star is a point for which we will show the energy spectrum. The green region is excluded by LUX at 90% of C.L. [41]. limits, de ned at 90% C.L. as the curve in which we obtain 2.3 DM events for the computed n = If we now take the lowest cross-section of all limits as a function of the DM mass, we obtain the one neutrino event contour line, corresponding to the best background-free sensitivity achievable for each DM mass for a one neutrino event exposure. Let us stress that the one neutrino event contour line, as de ned in this section, is computed with a 100% detector e ciency. The e ect of a nite detector e ciency will be taken into account in section 5 when we will compute how the new exotic neutrino interactions can a ect the discovery potential of direct detection DM experiments. Comparing eq. (3.18) with eqs. (3.12) and (3.15), we see that the simpli ed models introduced in section 2 can modify the one neutrino event contour line. In fact, such modi cations have been studied in speci c models with light new physics e.g. in [10]. We show in gure 1 some examples of a modi ed "one neutrino event contour line for our models, xing the values of the parameters GV and GS as speci ed in the legends. These parameters have been chosen to be still allowed by current data, see sections 4 and 5. The left panel of the gure describes changes in the one-neutrino event contour line in presence of a new vector mediator. As will be explained below, it is possible to have cancellation between SM and exotic neutrino For the vector case the one-neutrino event contour line is e ectively a rescaling of the SM case. Figure 1 (right panel) on the other hand shows modi cation of the contour line for a scalar mediator. Note that unlike in the vector scenario, the factor GS has a di erent normalization. No signi cant change in the one-neutrino event contour line is expected in the scalar case. reduction of the CNSN cross session according to eqs. (3.19) and (3.20). There are a few remarks we should make here. First, it is possible, in the context of the vector mediator model, to cancel the SM contribution to CNSN and completely eliminate the neutrino background. For mediator masses heavy enough to neglect the q2 dependence of the cross-sections, this happens when, cf. with eq. (3.4), A = QV SM GF m2V = where for the last equality we assume gVu = g Vd = g V is a numerical value that depends only on the target nucleus. We show in table 1 the values of aV for various nuclei. Second, in the case of the scalar scenario, it is possible to compensate for only part of the SM contribution to the CNSN. Inspecting eqs. (3.1) and (3.6) we see that the positive in an e ective increase of the cross-section. This is accomplished for gS = QV SM GF m2S = where again aS is a numerical value that depends only on the target nucleus. Its value for di erent nuclei are shown in table 1. We show in the right panel of gure 1 an example Finally, we should note that the one neutrino event contour line only gives us a preliminary estimate of the minimum cross-sections that can be reached by a DM direct detection experiment. It is worth recalling that this estimate is a background-free sensitivity. Interactions modifying both neutrino and DM sector physics will lead to a non-standard neutrino CNSN background which should be taken into account. Furthermore, the compatibility of the observed number of events should be tested against the sum of neutrino and DM events. In this spirit, to answer the question what is the DM discovery potential of an experiment? one has to compute the real neutrino oor. This will be done in section 5, which will include a more careful statistical analysis taking into account background uctuations and the experimental e ciency. Current and future limits on DM-neutrino interactions When new physics interacts with the DM and neutrino sector, the limits from direct detection experiments become sensitive to the sum of DM and neutrino scattering events. A natural question to ask is the capacity of current experiments to constrain this sum. The aim of this section is to assess these constraints and derive sensitivities for the next generation of direct detection experiments. For the analysis of the current limits we consider the results of the Large Underground Xenon (LUX) [41] experiment. This choice is based on the fact that this experiment is at present the most sensitive one probing the m region on which we focus. On the other hand, for the future perspectives we will consider two Xe target based detectors: the one proposed by the LUX-ZonEd Proportional scintillation in LIquid Noble gases (LUX-ZEPLIN) Collaboration [42] and the one proposed by the DARk matter WImp search with liquid xenoN (DARWIN) Collaboration [43]. Current bounds. LUX is an experiment searching for WIMPs through a dual phase Xe time projection chamber. We will consider its results after a 3:35 104 kg-days run presented in 2016 [41], performed with an energy threshold of 1:1 keV. We also use the e ciency function "(ER) reported in the same work. In order to assess the constraining power of current LUX results for the two models presented in eqs. (2.1){(2.3), we compute the total number of nuclear recoil events expected at each detector as parameter space. Evtotal = Ev + Ev : Using this total number of events, we compute a likelihood function constructed from a Poisson distribution in order to use their data to limit the parameters of our models, L(^jN ) = P (^jN ) = where ^ indicates the set of parameters of each model, N the observed number of events, b the expected background and (^) is the total number of events Evtotal. According to [14] Maximizing the likelihood function we can obtain limits for the di erent planes of the In the case of the vector model, we performed a scan of the parameter space in the 500 GeV, 710 GeV and 103 GeV. while we always choose g limits in gure 2 for gV =m2V = 10 6 GeV 2,3 and 4 GeV 2 (right), which 2 = p limit. In each case, we show the results for three values of the DM mass, m = 10 GeV (violet), 15 GeV (red) and 50 GeV (green). We see that we can clearly distinguish two regions: for 2 = 10 6 GeV 2, when jgV 4 the DM contribution is the dominant one (in particular, as jgV at most the SM one), and sets jgV j < 2 gAj ! 0 the contribution to the neutrino = 10 (50) GeV. 100 GeV, 315 GeV, 10--610 -8 -6 -4 -2 0 2 4 6 8 10 Λ-V2 = 10-6 GeV-2, Current Limit Λ-V2 = 4 π GeV-2, Current Limit of the vector model. The coloured region can be excluded at 90% C.L. by current LUX data [44] (continuous lines) and by the future LUX-ZEPLIN [42] (dashed lines) and DARWIN [43] experiments (dotted lines). The plots are for m for two di erent cases: 2 = 10 6 GeV 2 (left) and 2 = p GeV 2 (right). For simplicity, in the latter case we only show the DARWIN future sensitivity, since the LUX-ZEPLIN results are qualitatively similar but a factor of 4-10 less sensitive. 2 = = 10 (50) GeV and jgV On the other hand, for larger values of jgV gAj, the number of neutrino events rapidly becomes dominant and no bound on the DM-mediator coupling can be set. For the extreme 4 GeV 2, one can set the limits jgV j < 4:3 Inspection of gure 2 shows two peculiar features: an asymmetry between the bounds on positive and negative values of gV gA, and the independence of these limits on the DM mass. We see from eq. (3.4) that the asymmetry can be explained from the dependence of ΛS-2 = 10-6 GeV-2, Current Limit ΛS-2 = 4 π GeV-2, Current Limit di erent cases: S 2 = 10 6 GeV 2 (left) and S 2 = p 4 GeV 2 (right). the scalar model. The coloured region can be excluded at 90% C.L. by current LUX data [44] (continuous lines) and by the future LUX-ZEPLIN [42] (dashed lines) and DARWIN [43] experiments (dotted lines). The plots are for m the interference term on the sign of gV gA. Such interference is positive for gV explaining why the bounds on negative gV gA are stronger. As for the independence of A bounds from the DM mass, this can be understood from the fact that when V becomes su ciently small we e ectively reach the gV ! 0 limit in which the DM mass is not relevant. Turning to the bounds that the current LUX results impose on the parameter space of the scalar model, we varied the parameters in the ranges 2 = Our results are presented in gure 3. On the top left (right) panel, xing 4 GeV 2), for m (green). From these plots we see that LUX can limit jgS j < 4:5 = 10 (50) GeV if jgSj < 0:5, when 4 GeV 2, we get the bound jgS j < 1:3 2 = 10 6 GeV 2 . For the limiting case = 10 (50) GeV 2 = 2 = 10 6 (= p As gS ! 0, the contribution to the neutrino oor tends to the SM one, except for a particular value of gS gSq, as discussed at the end of the previous section. In the opposite limit, i.e. where the neutrino oor dominates, gS ! 0, the current limit is jgSj < 0:7 (jgSj < . As in the vector case, we see that this bound does not depend on the DM matter mass, for the same reasons explained above. Future sensitivity. To assess the future projected LUX-ZEPLIN sensitivity, we will assume an energy threshold of 6 keV, a maximum recoil energy of 30 keV and a future exposure of 15:34 t-years [42]. According to the same reference, we use a 50% e ciency for the nuclear recoil. For DARWIN, we will consider an aggressive 200 t-years exposure, no nite energy resolution but a 30% acceptance for nuclear-recoil events in the energy range of 5{35 keV [43]. Let us now discuss the bounds that can be imposed on the parameter space of our models in case the future experiments LUX-ZEPLIN and DARWIN will not detect any signal. We scan the parameter space over the ranges of eqs. (4.3) and (4.4), obtaining the exclusion at 90% C.L. The results are presented in the bottom panels of gure 2 ( gure 3) for the vector (scalar) model. In the region in which the DM events dominate, we see that LUX-ZEPLIN will be able to improve the bound on jgV j and jgS j by a factor between 2 and 10 depending on the DM mass, while another order of magnitude improvement can typically be reached with DARWIN. However, we also see that, somehow contrary to expectations, the bounds on the neutrino couplings are expected to be less stringent than the present ones. While the e ect is not particularly relevant in the vector case, we can see that in the scalar case the LUX-ZEPLIN sensitivity is expected to be about a factor of 4 worse than the current LUX limit. This is due to the higher threshold of the experiment, that limits the number of measurable solar neutrino events. As such, a larger jgS j is needed to produce a su ciently large number of events, diminishing the constraining power of LUX-ZEPLIN. While in principle this is also true for the DARWIN experiment, the e ect is compensated by the aggressive expected exposure. Sensitivity to DM-nucleon scattering in presence of exotic neutrino In section 3, we computed the background-free sensitivity of direct detection experiments in presence of exotic neutrino interactions. However, what is the true 3 discovery potential given the exotic neutrino interactions background remains unanswered. In this section, we perform a detailed statistical analysis, taking into account the estimated background and observed number of events and comparing these against the DM and neutrino interaction via a pro le likelihood analysis. To assess the DM discovery potential of an experiment we calculate, as in ref. [45], the minimum value of the scattering cross-section n as a function of m that can be probed by an experiment. This de nes a discovery limiting curve that is the true neutrino of the experiment. Above this curve the experiment has a 90% probability of observing a DM detection. This is done by de ning a binned likelihood function [46, 47] where we have a product of Poisson probability distribution functions (P) for each bin i ux normalization, L( j ) [47]. The neutrino (Ev ) and DM (Ev ) number of events were computed according to eqs. (3.11) and (3.16), respectively. For each neuuxes from solar and atmospheric neutrinos are denoted by is a collection of the extra parameters (gVq;S, gV;S, etc.) to be taken into account in the model under consideration. Since we will introduce the discovery limit in the DM cross-section, note that we will keep the DM-mediator coupling gV;S free. For this study, we considered only the contribution of the 8B and hep solar and atmospheric neutrinos, due to the thresholds of the considered experiments. For a xed DM mass, we can use eq. (5.1) to test the neutrino-only hypothesis H0 against the neutrino+DM hypothesis H1 constructing the ratio times, Z90, given by where ^ and ^ n are the values of the uxes and DM cross-section that maximize the each mass m and cross-section n we build a probability density function p(ZjH0) of the test statistics under H0, the neutrino only hypothesis. This is performed by constructing 2 ln (0) [45{47]. Finally, we compute the signi cance that can be achieved 90% of the p(ZjH0) dZ = 0:90 : Therefore, the minimum value for the cross-section for which the experiment has 90% probability of making a 3 DM discovery is de ned as the value of n that corresponds to Z90 = 3. In gure 4 we can see the neutrino oor considering only the SM contribution to the CNSN (dark blue) as well as the result for some illustrative cases, in the vector mediator scenario, for the LUX-ZEPLIN experiment with two di erent energy thresholds. The case V = 0.3 V = 2.3 V = 3.6 V = 0.3 V = 2.3 V = 3.6 coupling was obtained considering V 2 = 10 6 GeV2. results are for the LUX-ZEPLIN experiment with two di erent energy thresholds: a very low one, SM neutrino oor (dark blue) is shown, along with the most extreme case still allowed for the vector 2 = p 4 GeV 2. Above this curve a 3 can be achieved by the experiment, while below this curve it is di cult to discriminate between a DM signal and a non-standard (vector mediated) contribution to the neutrino with the opposite sign to the SM one, so it actually cancels some of the standard signal. same phenomenon noticed in the literature: close to a DM mass of 6 GeV, the discovery limit is substantially worsened because of the similarity of the spectra of 8B neutrinos and the WIMP, see, for instance [45]. However, the minimum cross-section that can be probed is di erent for each parameter GV , due to the contribution of the vector mediator. For the limit according to the value of GV . In gure 5 we can see the neutrino oor considering only the SM contribution to the current limit on jgSj ( < 2 10 7) for 2 = p CNSN (dark blue) as well as the result for some illustrative cases, in the scalar mediator scenario, for the LUX-ZEPLIN experiment with two di erent energy thresholds. Here the 4 GeV 2. In the case of the lower threshold, we see that the point where the discovery limit is highly a ected due to the 8B neutrinos is displaced close to a mass of 7 GeV. This shift of the distribution is provoked by the extra factor that appears in the scalar case with respect to the SM (see eq. (3.6)). For the Therefore, we see that contrary to the vector case, the scalar contribution does not a ect S = 58.4 S = 82.8 S = 58.4 S = 82.8 very much the discovery reach of the experiment as compared to the one limited by the standard CNSN. In gure 6 we show the behavior of the number of CNSN events as a function of the energy threshold of the detector and for a detector e ciency varying from 40% to 60%. of the LUX experiment for the vector and scalar mediator models, the number of neutrino events for Eth 1 keV are basically the same and both about 10 times larger than the SM contribution. However, for the choices Eth 0:1 keV (lower threshold) and Eth (higher threshold) used in gures 4 and 5, the number of CNSN events for the vector model is about 4 times larger than that for the scalar model, explaining the di erence in sensitivity for the vector and scalar models at those thresholds. We see again that the SM and the vector mediator model number of CNSN events di er simply by a scale factor, independent of the energy threshold, as expected from eq. (3.4). On the other hand, for the scalar case there is a non-trivial behavior with respect to the SM due to the extra term threshold low energy 8B neutrinos become accessible. However, the di erence between the SM and the scalar mediator cross-sections diminishes more with lower Eth than it increases with lower E so the number of CNSN events di ers only by a factor 3. For the higher threshold only atmospheric neutrinos are available, both SM and scalar contributions are expected to be of the same order as the extra scalar contribution is suppressed by E 2 also see that a detector e ciency between 40% to 60% does not a ect the above discussion and consequently we do not expect the neutrino oors we have calculated in this section to be very di erent had we chosen to use in our computation 40% or 60% e ciency instead of the 50% we have used. We have also performed an estimation of the e ect of the uncertainty on the form factors fTp;qn on the results of our calculation and concluded that they can a ect the neutrino V=3.6 S=82.8 threshold. In red we show the predictions for the SM and in blue (green) for the vector (scalar) e ciency of 50% corresponding to the red star in gure 5, respectively. The di erent contributions are shown separately: DM only (green), standard CNSN (black), non-standard CNSN (blue) as well as the combined spectrum (red). To exemplify the di culty in discriminating between an energy spectrum produced by DM collisions from the modi ed neutrino oor, in the two cases studied in this paper, we show in gure 7 examples of the energy spectrum for the points corresponding to the red stars in gure 4 (vector) and gure 5 (scalar). We show explicitly the various contributions: the recoil spectrum produced by DM events only (green), by the standard CNSN (black), by the non-standard CNSN due either to the vector or scalar mediator (blue). In red we show the combined spectrum. In both cases, one would be able to discriminate the spectrum due to DM plus SM events (orange curve) from only CNSN events (black). However, if there is an extra contribution from non-standard interactions, increasing the neutrino background (blue), one cannot discriminate anymore this situation from the total spectrum which also contain DM events(red). Both points were chosen in a region where solar neutrinos dominate the background and are only achievable for a very low energy threshold. For the nominal threshold of the LUX-ZEPLIN experiment only the vector scenario will a ect the sensitivity of the experiment for do not present here our results for DARWIN as they are qualitative similar to those of Conclusions Coherent neutrino scattering o nuclei is bound to become an irreducible background for the next generation of dark matter direct detection experiments, since the experimental signature is very similar to DM scattering o nuclei. In this work we have considered the case in which new physics interacts with both DM and neutrinos. In this situation, it becomes important to compute the neutrino oor while taking into account the contributions from exotic neutrino interaction. This sets the true discovery limit for direct detection experiments instead of a background-free sensitivity. For de nitiveness, we have focused on two simpli ed models, one with a vector and one with a scalar mediator interacting with the DM and the SM particles. We calculated the bounds on the parameter space of the two simpli ed models imposed by the latest LUX data. These are presented in gures 2 and 3. The most interesting case is, however, the one in which some signal could be detected in a future DM direct detection experiments. In this case our models predict modi cations to the standard neutrino oor. The main result of our analysis is shown in and 5, in which we show that it is possible to nd points in the parameter space of the models in which not only the number of events produced by DM and by the modi ed CNSN are compatible, but in which also the spectra are very similar. This immediately implies that the modi ed CNSN can mimic a DM signal above the standard neutrino oor, challenging the interpretation of a DM discovery signal. We show that the problem is more signi cant for experiments that can probe m < 10 GeV or n < 10 47 cm2. Although a new scalar interaction will not, in practice, a ect the discovery reach of future experiments such as LUX-ZEPLIN or DARWIN, a new vector interaction can mimic DM signals in a region above the standard neutrino oor of those experiments, challenging any discovery in this region. It should be noted that the scenarios considered here lead to a variety of signatures apart from a modi cation of the CNSN at direct detection experiments. First and foremost, we did not account for any relic density constraints from DM annihilation. Throughout the analysis we have assumed that the DM relic density is satis ed. Secondly, the DM annihilation to neutrinos will generate signals at indirect detection experiments which will lead to additional constraints on the parameter space. Direct production of DM particles at the LHC, constrained by monojet searches will also be an additional signature of interest. Finally, exotic neutrino interactions themselves are constrained by several neutrino experiments and should be taken into account for a more complete analysis. Despite these possible extensions of the study, our analysis is new in the sense that it considers for the rst time the combined e ect of exotic neutrino and DM interactions at the direct detection experiments. We demonstrate the current limits on the combined parameter space for the DM and neutrino couplings and nally demonstrate the reach of direct detection experiments. Acknowledgments We are thankful to Achim Gutlein for several very useful discussions about neutrino oor calculations. We also would like to thank Genevieve Belanger for helpful discussions. SK wishes to thank USP for hospitality during her visit, where this work originated. SK is supported by the `New Frontiers' program of the Austrian Academy of Sciences. This work was supported by Fundac~ao de Amparo a Pesquisa do Estado de Sa~o Paulo (FAPESP) and Conselho Nacional de Ci^encia e Tecnologia (CNPq). This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 674896. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 55 (1985) 25 [INSPIRE]. D 33 (1986) 3495 [INSPIRE]. Phys. 11 (2009) 105011 [arXiv:0903.3630] [INSPIRE]. [4] A. Gutlein et al., Solar and atmospheric neutrinos: background sources for the direct dark matter search, Astropart. Phys. 34 (2010) 90 [arXiv:1003.5530] [INSPIRE]. [5] SNO collaboration, B. Aharmim et al., Combined analysis of all three phases of solar neutrino data from the sudbury neutrino observatory, Phys. Rev. C 88 (2013) 025501 [arXiv:1109.0763] [INSPIRE]. [6] Super-Kamiokande collaboration, R. Wendell et al., Atmospheric neutrino oscillation analysis with sub-leading e ects in Super-Kamiokande I, II and III, Phys. Rev. D 81 (2010) 092004 [arXiv:1002.3471] [INSPIRE]. reach of next generation dark matter direct detection experiments, Phys. Rev. D 89 (2014) 023524 [arXiv:1307.5458] [INSPIRE]. Charge coupled devices for detection of coherent neutrino-nucleus scattering, Phys. Rev. D 91 (2015) 072001 [arXiv:1405.5761] [INSPIRE]. Spallation Neutron Source, arXiv:1509.08702 [INSPIRE]. JCAP 07 (2012) 026 [arXiv:1202.6073] [INSPIRE]. baryonic currents, Phys. Rev. D 85 (2012) 113016 [arXiv:1203.0545] [INSPIRE]. oor, Phys. Rev. D 95 (2017) 051701 [arXiv:1607.01468] [INSPIRE]. neutrino background in direct dark matter detection experiments, Phys. Rev. D 93 (2016) 075018 [arXiv:1602.05300] [INSPIRE]. [15] T. Franarin and M. Fairbairn, Reducing the solar neutrino background in dark matter searches using polarized Helium-3, Phys. Rev. D 94 (2016) 053004 [arXiv:1605.08727] neutrino bound, Phys. Rev. D 90 (2014) 055018 [arXiv:1406.5047] [INSPIRE]. (2015) 093011 [arXiv:1412.2027] [INSPIRE]. 9-10 (2015) 8 [arXiv:1506.03116] [INSPIRE]. [18] J. Abdallah et al., Simpli ed models for dark matter searches at the LHC, Phys. Dark Univ. [19] A. De Simone and T. Jacques, Simpli ed models vs. e ective eld theory approaches in dark matter searches, Eur. Phys. J. C 76 (2016) 367 [arXiv:1603.08002] [INSPIRE]. gauge invariance for simpli ed dark matter models, JHEP 02 (2016) 016 [arXiv:1510.02110] [INSPIRE]. 115006 [arXiv:1104.4127] [INSPIRE]. energies and limits on an additional Z0 gauge boson, Z. Phys. C 65 (1995) 603 [INSPIRE]. Phys. Rev. D 70 (2004) 093009 [hep-ph/0408098] [INSPIRE]. Phys. C 38 (2014) 090001 [INSPIRE]. [arXiv:1209.2535] [INSPIRE]. distributions using pp collisions at p [hep-ph/0610253] [INSPIRE]. [27] ATLAS collaboration, ATLAS search for new phenomena in dijet mass and angular dark sectors with monojets and dijets, JHEP 07 (2015) 089 [arXiv:1503.05916] [INSPIRE]. vs. LUX constraints, JHEP 03 (2014) 134 [arXiv:1401.0221] [INSPIRE]. with primarily spin-dependent interactions with matter, arXiv:1003.1912 [INSPIRE]. candidates, Comput. Phys. Commun. 192 (2015) 322 [arXiv:1407.6129] [INSPIRE]. nucleon from e ective eld theory and phenomenology, Phys. Lett. B 730 (2014) 342 [38] J. Kumar and D. Marfatia, Matrix element analyses of dark matter scattering and annihilation, Phys. Rev. D 88 (2013) 014035 [arXiv:1305.1611] [INSPIRE]. LUX, lite and light, JCAP 03 (2014) 014 [arXiv:1311.4247] [INSPIRE]. Theoretical Advanced Study Institute in Elementary Particle Physics: Journeys Through the Precision Frontier: Amplitudes for Colliders (TASI 2014), June 2{27, Boulder, U.S.A. (2015), arXiv:1502.01320 [INSPIRE]. LUX exposure, Phys. Rev. Lett. 118 (2017) 021303 [arXiv:1608.07648] [INSPIRE]. arXiv:1509.02910 [INSPIRE]. 94 (2016) 063527 [arXiv:1604.03858] [INSPIRE]. [1] B. Cabrera , L.M. Krauss and F. Wilczek , Bolometric detection of neutrinos , Phys. Rev. Lett. [2] A.K. Drukier , K. Freese and D.N. Spergel , Detecting cold dark matter candidates , Phys. Rev. [3] L.E. Strigari , Neutrino coherent scattering rates at direct dark matter detectors , New J. [8] G. Fernandez Moroni , J. Estrada , E.E. Paolini , G. Cancelo , J. Ti enberg and J . Molina, [9] COHERENT collaboration, D. Akimov et al., The COHERENT experiment at the [10] R. Harnik , J. Kopp and P.A.N. Machado , Exploring nu Signals in Dark Matter Detectors , [11] M. Pospelov and J. Pradler , Elastic scattering signals of solar neutrinos with enhanced [12] D.G. Cerden~ o et al., Physics from solar neutrinos in dark matter direct detection experiments , JHEP 05 ( 2016 ) 118 [Erratum ibid . 09 ( 2016 ) 048] [arXiv:1604.01025] [13] J.B. Dent , B. Dutta , J.L. Newstead and L.E. Strigari , Dark matter, light mediators and the [14] J.B. Dent , B. Dutta , J.L. Newstead and L.E. Strigari , E ective eld theory treatment of the [16] P. Grothaus , M. Fairbairn and J. Monroe , Directional dark matter detection beyond the [17] W.-C. Huang and F.F. Deppisch , Dark matter origins of neutrino masses , Phys. Rev. D 91 [20] F. Kahlhoefer , K. Schmidt-Hoberg , T. Schwetz and S. Vogl , Implications of unitarity and [21] P.J. Fox , J. Liu , D. Tucker-Smith and N. Weiner , An e ective Z0 , Phys. Rev . D 84 ( 2011 ) [22] DELPHI collaboration, P. Abreu et al ., A study of radiative muon pair events at Z0 [23] M. Carena , A. Daleo , B.A. Dobrescu and T.M.P. Tait , Z0 gauge bosons at the Tevatron , [ 24 ] Particle Data Group collaboration , K.A. Olive et al., Review of particle physics, Chin. [25] ATLAS collaboration, Search for high-mass resonances decaying to dilepton nal states in s = 7 TeV with the ATLAS detector , JHEP 11 ( 2012 ) 138 [26] CMS collaboration, Search for heavy narrow dilepton resonances in pp collisions at ps = 7 s = 8 TeV, Phys . Lett . B 720 ( 2013 ) 63 [arXiv:1212.6175] [INSPIRE]. [28] S. Gabriel and S. Nandi , A new two Higgs doublet model , Phys. Lett. B 655 (2007) 141 [29] S.M. Davidson and H.E. Logan , Dirac neutrinos from a second Higgs doublet , Phys. Rev . D [30] M. Chala , F. Kahlhoefer , M. McCullough , G. Nardini and K. Schmidt-Hoberg , Constraining [31] G. Arcadi , Y. Mambrini , M.H.G. Tytgat and B. Zaldivar , Invisible Z0 and dark matter: LHC [32] J.D. Lewin and P.F. Smith , Review of mathematics, numerical factors and corrections for dark matter experiments based on elastic nuclear recoil, Astropart . Phys. 6 ( 1996 ) 87 [33] P. Agrawal , Z. Chacko , C. Kilic and R.K. Mishra , A classi cation of dark matter candidates [34] R. Catena , Phenomenology of dark matter-nucleon e ective interactions , J. Phys. Conf. Ser. [35] G. Belanger , F. Boudjema , A. Pukhov and A. Semenov , MicrOMEGAs4 .1: two dark matter [36] J.M. Alarcon , J. Martin Camalich and J.A. Oller , The chiral representation of the N scattering amplitude and the pion-nucleon sigma term , Phys. Rev. D 85 (2012) 051503 [37] J.M. Alarcon , L.S. Geng , J. Martin Camalich and J.A. Oller , The strangeness content of the [39] E. Del Nobile , G.B. Gelmini , P. Gondolo and J.-H. Huh , Update on light WIMP limits: [40] G.B. Gelmini , TASI 2014 Lectures: The Hunt for Dark Matter , in the proceedings of [41] LUX collaboration, D.S. Akerib et al., Results from a search for dark matter in the complete [42] LZ collaboration , D.S. Akerib et al., LUX-ZEPLIN (LZ) conceptual design report, [43] DARWIN collaboration , J. Aalbers et al., DARWIN: towards the ultimate dark matter detector , JCAP 11 ( 2016 ) 017 [arXiv:1606.07001] [INSPIRE]. [44] LUX collaboration, D.S. Akerib et al., Improved limits on scattering of Weakly Interacting Massive Particles from Reanalysis of 2013 LUX data , Phys. Rev. Lett . 116 ( 2016 ) 161301 [45] J. Billard , F. Mayet and D. Santos , Assessing the discovery potential of directional detection of Dark Matter , Phys. Rev . D 85 ( 2012 ) 035006 [arXiv:1110.6079] [INSPIRE]. [46] F. Ruppin , J. Billard , E. Figueroa-Feliciano and L. Strigari , Complementarity of dark matter detectors in light of the neutrino background , Phys. Rev. D 90 (2014) 083510 [47] C.A. O'Hare, Dark matter astrophysical uncertainties and the neutrino oor , Phys. Rev. D


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Dark matter and exotic neutrino interactions in direct detection searches, Journal of High Energy Physics, 2017, DOI: 10.1007/JHEP04(2017)073