Light scalar dark matter at neutrino oscillation experiments

Journal of High Energy Physics, Apr 2018

Abstract Couplings between light scalar dark matter (DM) and neutrinos induce a perturbation to the neutrino mass matrix. If the DM oscillation period is smaller than ten minutes (or equivalently, the DM particle is heavier than 0.69×10−17 eV), the fast-averaging over an oscillation cycle leads to a modification of the measured oscillation parameters. We present a specific μ − τ symmetric model in which the measured value of θ13 is entirely generated by the DM interaction, and which reproduces the other measured oscillation parameters. For a scalar DM particle lighter than 10−15 eV, adiabatic solar neutrino propagation is maintained. A suppression of the sensitivity to CP violation at long baseline neutrino experiments is predicted in this model. We find that DUNE cannot exclude the DM scenario at more than 3σ C.L. for bimaximal, tribimaximal and hexagonal mixing, while JUNO can rule it out at more than 6σ C.L. by precisely measuring both θ12 and θ13.

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Light scalar dark matter at neutrino oscillation experiments

HJE Light scalar dark matter at neutrino oscillation Jiajun Liao 0 1 3 Danny Marfatia 0 1 3 Kerry Whisnant 0 1 2 0 2323 Osborn Drive , Ames, IA, 50011 U.S.A 1 2505 Correa Rd. , Honolulu, HI, 96822 U.S.A 2 Department of Physics and Astronomy, Iowa State University , USA 3 Department of Physics and Astronomy, University of Hawaii-Manoa , USA Couplings between light scalar dark matter (DM) and neutrinos induce a perturbation to the neutrino mass matrix. If the DM oscillation period is smaller than ten minutes (or equivalently, the DM particle is heavier than 0:69 10 17 eV), the fast-averaging over an oscillation cycle leads to a modi cation of the measured oscillation parameters. We present a speci c symmetric model in which the measured value of 13 is entirely generated by the DM interaction, and which reproduces the other measured oscillation parameters. For a scalar DM particle lighter than 10 15 eV, adiabatic solar neutrino propagation is maintained. A suppression of the sensitivity to CP violation at long baseline neutrino experiments is predicted in this model. We nd that DUNE cannot exclude the Neutrino Physics; Beyond Standard Model; Solar and Atmospheric Neutrinos DM scenario at more than 3 C.L. for bimaximal, tribimaximal and hexagonal mixing, while JUNO can rule it out at more than 6 C.L. by precisely measuring both 12 and 13. 1 Introduction The model 2 3 E ects on neutrino oscillation parameters Tests of the model in future neutrino experiments Summary A Second-order corrections B A general treatment of oscillation probabilities 10 22 eV has attracted much attention recently since it can resolve the small scale crisis for standard cold DM due to its large de Broglie wavelength; see ref. [3] and references therein. Constraints on fuzzy DM can be obtained from Lymanforest data and a lower limit of 20 10 22 eV at 2 C.L. has been set from a combination of XQ-100 and HIRES/MIKE data [4], although a proper handling of the e ect of quantum pressure and systematic uncertainties may relax the limit [5]. Nevertheless, light scalar DM candidate of mass below a few keV are generally expected in many extensions of the Standard Model (SM). Examples include a QCD axion [6{8], moduli [9{12], dilatons [13, 14], and Higgs portal DM [15]. Constraints on hot DM require that light scalar DM cannot be produced thermally in the early universe. A popular production mechanism for generating light scalar DM is the misalignment mechanism, in which the elds take on some initial nonzero value in the early universe, and as the Hubble expansion rate becomes comparable to the light scalar mass, the DM eld starts to oscillate as a coherent state with a single macroscopic wavefunction [16]. The properties of light scalar DM can be probed if they are coupled to SM fermions, which induce a time variation to the masses of the SM fermions due to the oscillation of { 1 { the DM eld. Here we consider the couplings between the light scalar DM and the SM neutrinos, which were rst studied in ref. [17] by using the nonobservation of periodicities in solar neutrino data. Constraints on light scalar DM couplings were also considered in refs. [18, 19] by using the data from various atmospheric, reactor and accelerator neutrino experiments. In general, the interactions between DM and neutrinos provide a small perturbation to the neutrino mass matrix; a generic treatment of small perturbations on the neutrino mass matrix is provided in refs. [20, 21]. If the DM oscillation period is much smaller than the periodicity to which an experiment is sensitive, the oscillation probabilities get averaged, and a modi cation of the oscillation parameters can be induced if the data are interpreted in the standard three-neutrino framework. Evidence of time varying signals has been searched for in many neutrino oscillation experiments. Super-Kamiokande nds no evidence for a seasonal variation in the atmospheric neutrino ux [22], and the annual modulation of the atmospheric neutrino ux observed at IceCube is correlated with the upper atmospheric temperature [23]. Monthlybinned data from KamLAND indicate time variations in reactor powers [24]. Tests of Lorentz symmetry via searches for sidereal variation in LSND [25], MINOS [26{28], IceCube [29], MiniBooNE [30], Double Chooz [31], and T2K [32] data, are negative. Also, Super-Kamiokande [ 34 ] and SNO [35, 36] nd no signi cant temporal variation in the solar neutrino ux with periods ranging from ten minutes to ten years. We therefore take the DM oscillation period to be smaller than ten minutes. In this work, we study the modi cation of neutrino oscillation parameters due to light scalar DM-neutrino interactions. Since the predictions are avor structure-dependent, we present a speci c symmetric model in which the symmetry is broken by light scalar DM interactions thus generating a nonzero mixing angle 13. We rst examine the e ects of this model on data from various neutrino experiments. We then study the potential to distinguish this model from the standard three-neutrino oscillation scenario at the future long-baseline accelerator experiment, DUNE, and the medium-baseline reactor experiment, JUNO. The paper is organized as follows. In section 2, we present a model in which symmetry is broken by the DM interactions. In section 3, we examine the implications of this model for the measured neutrino oscillation parameters. In section 4, we simulate future neutrino oscillation experiments to study the potential to distinguish this model from the standard scenario. We summarize our results in section 5. In appendix A we calculate how the scalar DM interactions with neutrinos a ect neutrino mass and mixing parameters, and in appendix B we determine how the DM oscillations cause a shift in the e ective neutrino oscillation parameters measured in experiments. 2 The model The Lagrangian describing the interactions between light scalar DM and neutrinos can be written in the avor basis as [18, 19] 1 2 m0 c L L 1 2 c L L + h.c. ; (2.1) { 2 { = e; ; , m0 is the initial neutrino mass matrix, and is the coupling constant matrix. Since the light scalar DM can be treated as a classical eld, the nonrelativistic solution to the classical equation of motion can be approximated as [17] (x) ' p2 (x) m cos(m t ~v ~x) ; (2.2) (2.3) (2.4) (2.6) (2.7) where U0 is the initial mixing matrix, mi0's are the initial neutrino eigenmasses, and the elements of the perturbation matrix are E = p2 m = 0:0021 eV We consider a model in which the initial mixing angle 103 = 0 and the measured 13 value is generated by the DM interactions. In order to simplify our calculations, we specialize to models in which the DM interactions only a ect the masses at higher orders in the perturbation, leaving them e ectively unchanged. From the generalized perturbation results of ref. [21], we nd that the most general perturbation satisfying the latter requirement is of the form, 0 0 E = BBp 2 s023 0 sin 2 203 2 c023 0 cos 2 203 1 p 0 c0osisn22 202033CAC : and v in where m is the mass of the scalar DM particle, 10 3 is the virialized DM velocity. Since v 0:3 GeV=cm3 is the local DM density, 1, we neglect the spatial variation for neutrino oscillation experiments. In the presence of scalar DM interactions, the e ective Hamiltonian for neutrino oscillations can be written as where Ne is the number density of electrons. The e ective mass matrix can be treated as the sum of an initial mass matrix and a small perturbation [21], i.e., H = 1 2E M yM + p 2GF Ne B@0 0 0C ; A 0 M = U0 B@ 0 m02 0 CA U0y + E cos(m t) ; As a further simpli cation, we assume the model is the perturbation becomes 0 0 E = B 0 { 3 { symmetric, i.e., 203 = =4. Then 13 23 12 CP p mj ; since the eigenmasses are not shifted at leading order, we drop the superscript `0' hereafter. In appendix A, we show that the leading order corrections have amplitudes (2.8) (2.9) (2.10) (2.11) (3.1) (3.2) (3.3) (3.4) Note that 12 is second-order in the 's and is therefore proportional to cos2(m t), while CP depends only on the phase of and is constant, i.e., it is not a ected by the DM oscillation. Both 23 are dependent linearly on cos(m t). 3 E ects on neutrino oscillation parameters In this section, we study how the neutrino oscillation parameters are modi ed in our model, assuming the period of the DM oscillation ( = 2 =m ) is short compared to the experimental resolution of periodicity. Here we use the superscript `0' to denote the initial oscillation parameters, and the superscript `e ' to denote the e ective parameters measured at neutrino oscillation experiments if the data are interpreted in the standard three-neutrino framework. For the parameters obtained after incorporating the DM perturbation, no superscript is used. 3.1 Short-baseline reactor experiments The leading oscillation probability for reactor antineutrinos (at a Daya Bay-like distance) is P = 1 13 and averaging over a DM oscillation cycle, we get as found previously in ref. [18]. If 103 = 0, then sin2 2 1e3 = 2( 13)2, so the angle being measured in these experiments is e 13 ' p 13= 2 : 3.2 Long-baseline appearance experiments For long-baseline experiments, the formulas are more complicated. From ref. [37], P ( P ( ! e) = x2f 2 + 2xyf g cos( 31 + CP) + y2g2 ; ! e) = x2f 2 + 2xyf g cos( 31 CP) + y2g2 ; { 4 { where x = sin 23 sin 2 13, y = A^), g = sin(A^ 31)=A^, A^ = jA= m231j, and A before averaging, = j m221= m231j, f; f = sin[(1 ^ where C = cos(m t). After averaging, the leading term for x2f 2 is which is similar to the reactor case, i.e., the e ective 13 is 13=p2. We can write yg as x f cos 203 sin 2 102. After explicitly putting in the perturbation, yg becomes Combining eqs. (3.5) and (3.7) and after averaging, the xyf g term is yg y0g 1 + 2C2 12 cot 2 102 is suppressed compared to the usual case since it is proportional to two factors of the 's (assuming 0), instead of just one | the term proportional to one factor of was linear in C and averaged to zero. For symmetry, 203 = =4 and the term vanishes completely. The upshot is that the e ect of the Dirac CP phase on P ( ! e) and P ( ! e) is suppressed in long-baseline neutrino oscillation appearance experiments. Also, as shown in appendix B, this model predicts a suppression of the sensitivity to CP violation in all types of neutrino oscillation experiments. 3.3 Medium-baseline reactor experiments For KamLAND and JUNO, the oscillation probability is P ( e ! e) = 1 For 103 = 0, the angular factors after averaging over the DM oscillations are Equations (3.11) and (3.12) are identical to the standard case with sin2 2 13 replaced by 2( 13)2, the same as for short-baseline reactor and long-baseline accelerator experiments. In eq. (3.13), the sin2 2 102-dependent term on the right-hand side has a coe cient, 1 shift in the measured value of 12. To determine how the shift depends on sin2 2 102 + 2 sin 2 102 cos 2 102 12 = sin2 2 1e2 12=2, and what one measures in this type of experiment is be much larger than the time in which neutrinos travel through the Sun, which is about 2:3 seconds. This requirement restricts the mass of the scalar eld: m 1:8 10 15 eV. The three-neutrino survival probability for adiabatic propagation is 2 P ( e ! e) = cos2 13 cos2 13 cos2 m cos2 12 + sin2 m0 sin2 12 + sin2 13 sin2 13 = cos2 13 cos2 13 1 + cos 2 m cos 2 12 + sin2 13 sin2 13 ; where cos 2 m = q cos 2 12 ^ A0 (cos 2 12 A^0)2 + sin2 2 12 ; p with A^0 = 2 2GF Ne0E= m221, and Ne0 is the electron number density at the point in the Sun where the neutrino was created. Here ij = i0j + ij cos(m t) and ij = i0j + ij cos(m t + m t0) are the mixing angles at the production point in the Sun and at the Earth, respectively. They di er by a phase factor m t0, where t0 is the time traveled by neutrinos from the production point to the Earth. Since 103 = 0, expanding to the leading term, we have (3.14) (3.15) (3.16) (3.17) (3.18) (3.19) 1 2 1 2 1 2 F 2 1 2 123P0[cos2(m t) + cos2(m t + m t0)] : P P0 + 12[cos 2 102F cos2(m t) 2 sin 2 102 cos 2 m0 cos2(m t + m t0)] (3.23) and we see that reactor experiments. 3.5 Atmospheric neutrinos The survival probability of atmospheric neutrinos is : (3.21) (3.20) (3.22) (3.24) (3.25) (3.26) (3.27) (3.28) (3.29) Because there is no interference term between cos2(m t) and cos2(m t + m t0), we can average over them separately. Hence, hP i P0 + 12 By a similar calculation, the e ective shifts in 1e2 and 1e3 lead to P P0 + 1e2 (F cos 2 102 2 sin 2 102 cos 2 m0) 2( 1e3 )2P0 ; 13=p2, the same as for medium-baseline and the corresponding barred quantities can be obtained by replacing the phase m t with m t + m t0. Also, to the leading order, we have where cos 2 m0 has the same form as eq. (3.18), and F = q If P0 is the probability without the perturbation, i.e., then keeping the leading correction for each , we have For 103 = 0, after averaging, P ( ! ) = 1 (cos4 13 sin2 2 23 + sin2 23 sin2 2 13) sin2 Since the ( 23)2 term is doubly suppressed, we have 1e3 p 13= 2 and e 23 This also applies to the long-baseline survival probability. Also, as shown in appendix B, matter e ects do not change these results. e 23 From the analytic analysis of the last section, we see that the constraints on this model mainly come from the measurement of 1e3 and 1e2 . From eqs. (2.8) and (3.2), we have e and from eqs. (2.10) and (3.16), we have for the normal hierarchy, and for the inverted hierarchy. Since the correction to 23 is doubly suppressed in the oscillation probabilities in this model, 2e3 remains maximal. We rst study the sensitivity of long-baseline accelerator experiments to this model. Since the currently running experiments, T2K and NO A, have large experimental uncertainties, we consider the next-generation DUNE program. In our simulation, we use the GLoBES software [38, 39] with the same experimental con gurations as in ref. [40]. For the oscillation probabilities in the DM scenario, we modify the probability engine in the GLoBES software by averaging the probabilities over a DM oscillation cycle numerically. We also use the Preliminary Reference Earth Model density pro le [41] with a 5% uncertainty for the matter density. 23 = 4 To obtain the sensitivities to the DM parameters at future long-baseline neutrino experiments, we simulate the data with the SM scenario in the normal hierarchy. Since the sensitivity to the Dirac CP phase is suppressed at such experiments, we conservatively choose CP = 0. Also, due to the double suppression of the correction to 23, we choose , which is within the 1 range of the global t [42]. We also adopt the other mixing angles and mass-squared di erences from the best- t values in the global t, which are 203 = 4 and 103 = 0. For 102, we consider three benchmark values that are inspired by { 8 { (4.1) (4.2) (4.3) (4.4) TBM HG χ 6 4 2 0 correspond to 102 = 45 , 35:3 , and 30 , respectively. underlying discrete symmetries. Namely, 102 = 45 for bimaximal (BM) mixing [43{45], 0 0 12 = 35:3 for tri-bimaximal (TBM) mixing [46{48], and 12 = 30 for hexagonal (HG) mixing [ 49, 50 ]. Since the masses are not a ected at the leading order, we adopt the central values and uncertainties for the mass-squared di erences from the global t, i.e., m221 = (7:40 0:21) to account for constraints from the current global t, i.e., sin2 e Also, since the long baseline experiments are not sensitive to 12, we impose a prior on 1e2 12 = 0:307 0:013. We use eq. (4.2) to calculate the predicted value of 1e2 . Then for a given 102 and the lightest mass m1 (m3) for the normal (inverted) hierarchy, we scan over the magnitudes and phases of and 0. We nd that the phases of and 0 only have a small e ect on the 2 value, which agrees with the analytical expectation that the measurement of the CP violation is suppressed. We also marginalize over both the normal and inverted hierarchy for the tested DM scenario. We nd that the 2 value for the inverted mass hierarchy is always larger than that for the normal hierarchy for the same lightest mass. This is because the masses are not a ected at the leading order and the mass hierarchy can be resolved with high con dence at DUNE [51]. The minimum value of 2 as a function of m1 is shown in gure 1 for the three benchmark values of 102. As an illustrative example, we show the oscillation probabilities for 102 = 35:3 and m1 = 0:1 eV in the neutrino and antineutrino appearance channels in gure 2. We see that the DM oscillation curves overlap the SM curves su ciently in both modes that a clear discrimination is not possible. From gure 1 we see that DUNE alone cannot distinguish the DM scenario from the SM scenario at more than the 3 C.L. if m1 { 9 { HJEP04(218)36 are: 0 12 = 35:3 , m1 = 0:1 eV, for the other parameter values. = 0:0024 ei0:7502 eV and 0 = 0:00041 ei1:278 eV. See the text is greater than about 0.05 eV. We also see that as m1 decreases, 2 min increases. This can be understood from eqs. (4.1) and (4.3). For a smaller m1, the magnitude of required to explain the measured 13 becomes larger, and higher order corrections then break the degeneracies between the SM and DM scenarios. Since future medium-baseline reactor experiments can make a high precision measurement of both 12 and 13, we study the sensitivity reach at JUNO. We use the GLoBES software to simulate the JUNO experiment. The experimental con guration is the same as that in ref. [52], which reproduces the results of ref. [53]. We use the same procedure for the long-baseline accelerator experiments except with no prior on 1e2 , since JUNO can measure 12 more precisely than the current experiments. For the lightest mass between 0 and 0.2 eV, we nd that the minimum value of 2 at JUNO is 47.6, 46.9 and 57.0, with the initial mixing being BM, TBM and HG, respectively. Hence, JUNO can rule out this model with the three initial mixings at more than 6 C.L. 5 Summary We studied the e ects of light scalar DM-neutrino interactions at various neutrino oscillation experiments. For a light scalar DM eld oscillating as a coherent state, the coupling between DM and neutrinos induces a small perturbation to the neutrino mass matrix. We consider the case in which the DM oscillation period is smaller than the experimental resolution of periodicity, i.e., ten minutes. After averaging the oscillation probabilities over a DM oscillation cycle, the perturbation to the neutrino mass matrix leads to a modi cation of the e ective neutrino oscillation parameters if the experimental data are interpreted in the standard three-neutrino oscillation framework. Since the results depend on the avor structure of the initial mass matrix and the perturbation matrix, we presented a speci c symmetric model with DM interactions that do not a ect the eigenmasses at the leading order. We examined the e ects of this model on the e ective oscillation parameters measured at various neutrino experiments. If the mass of the scalar eld is lighter than 1:8 10 15 eV, then solar neutrinos propagate adiabatically. We nd that all existing neutrino oscillation results can be explained in this model with a shift of the e ective mixing angles | the measured value of 13 arises wholly from DM-neutrino interactions. The model also predicts a suppression of the CP violation at neutrino oscillation experiments. We then studied the potential of DUNE and JUNO to discriminate between this model and the standard three-neutrino oscillation scenario. We nd that DUNE cannot make a distinction at more than 3 C.L. for bimaximal, tribimaximal and hexagonal mixing, while JUNO can rule out the DM scenario at more than 6 C.L. by making high-precision measurements of both 12 and 13. Acknowledgments This research was supported in part by the U.S. DOE under Grant No. DE-SC0010504. A Second-order corrections For 203 = 45 and 103 = 0, the mass matrix can be rewritten as HJEP04(218)36 M = m1I + R203 BB m21c102s12 0 We diagonalize the above mass matrix by the unitary matrix, m21c102s102 m21(c102)2 0 p 2 m31 1 A 0 CC (R203)T : where Ri0j is the rotation matrix in the i j plane with a rotation angle i0j , U is and R102 is From eq. (A.1), the leading order corrections in the 1{3 and 2{3 sector are We see that after the rotations of R203, U and R102, the mass matrix in the 1{2 sector is 0 0 0 m21 ! 1 m31 2 2(c012)2 + 02(s012)2 p 2 0 sin(2 102) p 2 0 cos(2 102) + 2 22 02 sin(2 102) ! p 2 0 cos(2 102) + 2 22 02 sin(2 102) 2 2(s012)2 + 02(c012)2 p 2 0 sin(2 102) U = R203U R102R102 ; 0 U = B 0 1 13 23CA ; 0 1 (A.1) (A.2) (A.3) (A.4) (A.5) : (A.6) Hence, the next-to-leading order correction in the 1{2 sector is p 2 Since the DM perturbation potentially introduces additional complex phases in and 12, we must recast the parameters to put them in the standard form. We combine the initial rotation with the in nitesimal one to get (e.g., in the 2{3 sector), 23 ! = To rst order, the magnitude of the 1-1 element is Likewise for the o -diagonal element, Therefore the rotation in the 2{3 sector is now arg((R23)12) 023 ' cot 203 Im 23 : c23ei 23 where 23 includes a shift in Re( 23). Since j 23j similar manipulation can be done for R12, with j 12j; j 012j 23 1, 23 and 023 are small. A 1. In the 1{3 sector, we get R13 = 1 where 13 = arg( 13). Note that the cosine terms in R13 do not get a phase at rst order because their shifts are at second order (due to the fact that 103 = 0). Hence, the leading corrections to the three mixing angles are 12 (A.7) 23 (A.8) (A.9) (A.10) (A.11) (A.12) (A.13) (A.14) (A.15) (A.16) (A.17) Combining these 2-D rotations together in the full 3-D rotation matrix and making some phase changes in rows and columns so that the 1{1, 1{2, 2{3, and 3{3 elements are real we get 0 c13c12 c13s12 s12s23e i 012. This is not quite in the standard form, but we can multiply the second and third rows by e i and the third column by ei to get the standard form for U with CP = ( 13 + ). Since the phases in are all small, CP is primarily given by A general treatment of oscillation probabilities A general way to look at the oscillation probabilities is to do a Taylor series expansion about the standard expression: P P0 + + + 1 2 13C + 123C2 + 12 23C3 + 23C 223C2 Using hCi = 0, hC2i = 1=2, hC3i = 0, and hC4i = 3=8, where h i indicates averaging over the DM oscillation, and after averaging, On the other hand, the expansion in terms of e ective parameter shifts is P 223 + 2 12 1 2 1e2 + ( 1e2 )2 + 12 1e3 + e each ) hP i 12 + 1 4 123 + 1 4 223 ; (B.1) (B.2) (B.3) (B.4) and eq. (B.3) reduces to (again keeping only the leading correction for each ) P 1e2 + (neglecting the small, second-order correction to 23, which is acceptable since the leading order terms involving 23 are generally not zero). Note that since the period of DM oscillation considered here is much larger than the neutrino travel time at a terrestrial experiment, the expansions in eqs. 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Jiajun Liao, Danny Marfatia, Kerry Whisnant. Light scalar dark matter at neutrino oscillation experiments, Journal of High Energy Physics, 2018, 136, DOI: 10.1007/JHEP04(2018)136