Probing Nonstandard Neutrino Physics at T2KK
N. Cipriano Ribeiro, T. Kajita, P. Ko, H. Minakata, S. Nakayama, H. Nunokawa
aa r X i v : . [ h e p - ph ] J a n Far Detector in Korea for the J-PARC Neutrino Beam 1
Probing Nonstandard Neutrino Physics at T2KK
N. Cipriano Ribeiro , T. Kajita , P. Ko , H. Minakata , S.Nakayama , and H. Nunokawa (1) Departamento de F´ısica, Pontif´ıcia Universidade Cat´olica do Rio de Janeiro, C. P.38071, 22452-970, Rio de Janeiro, Brazil(2) Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, andInstitute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa, Chiba 277-8582, Japan(3) School of Physics, KIAS, Seoul 130-722, Korea(4) Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397,Japan(5) Kamioka Observatory, Institute for Cosmic Ray Research, Univ. of Tokyo,Higashi-Mozumi, Kamioka-cho, Hida, Gifu 506-1205, Japan Abstract
Having a far detector in Korea for the J-PARC neutrino beam in addition toone at Kamioka has been shown to be a powerful way to lift neutrino parameter(∆ m and mixing angles) degeneracies. In this talk, I report the sensitivity ofthe same experimental setup to nonstandard neutrino physics, such as quantumdecoherence, violation of Lorentz symmetry (with/without CPT invariance), andnonstandard neutrino interactions with matter. In many cases, two detector setupis better than one detector setup at SK. This observation makes another supportfor the two detector setup.
1. Introduction
The neutrino mass induced neutrino oscillation has been identified as a dom-inant mechanism for neutrino disappearances through a number of the neutrinoexperiments: the atmospheric [1], solar [2], reactor [3], and accelerator [4] exper-iments. After passing through the discovery era, the neutrino physics will enterthe epoch of precision study, as the CKM phenomenology and CP violation in thequark sector. The MNS matrix elements will be measured with higher accuracy,including the CP phase(s), and the neutrino properties such as their interactionswith matter etc. will be studied in a greater accuracy.In recent years [5, 6], the physics potential of the Kamioka-Korea two detectorsetting which receive an intense neutrino beam from J-PARC was consideredin detail, and it has been demonstrated that the two detector setting is powerfulenough to resolve all the eight-fold parameter degeneracy [7, 8, 9], if θ is in reachof the next generation accelerator [10, 11] and the reactor experiments [12, 13].The degeneracy includes the parameters θ , δ and octant of θ , and it is doubledby the ambiguity which arises due to the unknown sign of ∆ m . The detectorin Korea plays a decisive role to lift the last one. For related works on Kamioka-Korea two detector complex, see, for example, [14, 15, 16, 17]. This observationwas the main motivation for this series of workshops, and a lot of speakers gavetalks about physics potential at the Kamioka-Korea two detector setup in the pastthree workshops.During the course of precision studies, it will become natural to investigatenonstandard physics related with neutrinos. In this talk, I will show that the c (cid:13) Kamioka-Korea identical two detector setting is also a unique apparatus for study-ing nonstandard physics (NSP), by demonstrating that the deviation from theexpectation by the standard mass-induced oscillation can be sensitively probedby comparing yields at the intermediate (Kamioka) and the far (Korea) detectors.In this talk, I discuss the potential of the Kamioka-Korea setting, concentratingon ν µ − ν τ subsystem in the standard three-flavor mixing scheme, and focus on ν µ disappearance measurement. We consider three different types of nonstandardneutrino physics: • Quantum decoherence (QD) [18, 19, 20] • Tiny violation of Lorentz symmetry with/without CPT [21, 22, 23] • Nonstandard neutrino interactions of neutrinos with matter due to somenew physics [24, 25]The first two cases go beyond the conventional quantum field theory framework,whereas the last case is strictly within the conventional QFT.In analyzing the nonstandard physics, we aim at demonstrating the power-fulness of the Kamioka-Korea identical two detector setting, compared to othersettings. For this purpose, we systematically compare the results obtained withthe following three settings (the number indicate the fiducial mass): • Kamioka-Korea setting: Two identical detectors one at Kamioka and theother in Korea each 0.27 Mton • Kamioka-only setting: A single 0.54 Mton detector at Kamioka • Korea-only setting: A single 0.54 Mton detector at somewhere in Korea.Among the cases we have examined Kamioka-Korea setting always gives the bestsensitivities, apart from two exceptions of violation of Lorentz invariance in aCPT violating manner, and the nonstandard neutrino interactions with matter.Whereas, the next best case is sometimes Kamioka-only or Korea-only settingsdepending upon the problem.This talk is organized as follows. In Sec. 2., we illustrate how we can probenonstandard physics with Kamioka-Korea two detector setting, with a quantumdecoherence as an example of nonstandard neutrino physics. In Sec. 3., we dis-cuss quantum decoherence. In Sec. 4., we discuss possible violation of Lorentzinvariance. In Sec. 5., we discuss non-standard neutrino matter interactions, andthe results of study is summarized in Sec. 6.. This talk is based on the work [26],where one can find more plots and detailed discussions covered in this talk.
2. Basic ideas
Let me first describe the basic strategy of our analysis adopted in the followingsections. For the purpose of illustration, we consider quantum decoherence (QD),for which the ν µ survival probability is given by P ( ν µ → ν µ ) = P ( ν µ → ν µ ) = 1 −
12 sin θ (cid:20) − e − γ ( E ) L cos (cid:18) ∆ m L E (cid:19)(cid:21) , (1)with γ ( E ) = γ/E as an illustration. The ν µ survival probability is the same asabove, assuming CPT invariance in the presence of QD. Then one can calculatethe number of ν µ and ν µ events observed at two detectors placed at Kamiokaand Korea, using the above survival probability and the neutrino beam profiles.For simplicity, let us consider the number of observed neutrino events both at Kamioka and Korea, for each energy bin (with 50 MeV width) from E ν = 0 . E ν = 1 . ν µ event spectra at detectorslocated at Kamioka and Korea for the pure oscillation γ = 0 (the left column)and the oscillation plus QD with two different QD parameters, γ = 1 × − GeV/km (the middle column) and γ = 2 × − GeV/km (the right column). ∗ One observes the spectral distortion for non-vanishing γ . In particular, thespectral distortions are different between detectors at Kamioka and Korea due tothe differect L/E values at the two positions.
Fig. 1
Event spectra of neutrinos at Kamioka (the top panel) and Korea (the bot-tom panel) for γ = 0 (the left column), 1 × − GeV/km (the middle column),and γ = 2 × − GeV/km (the right column). The hatched areas denote thenon-quasi-elastic events.
Assuming the actual data at Kamioka and Korea are given (or well described)by the pure oscillation with sin θ = 1 and ∆ m = 2 . × − eV , we could claimthat γ = 1 × − GeV/km (shown in the middle column), for example, wouldbe inconsistent with the data. One can make this kind of claim in a more properand quantitative manner using the χ analysis, which is described in details inRef. [26]. ∗ In order to convert this γ in unit of GeV/km to γ defined in Eq. (2), one has to multiply0 . × − .
3. Quantum Decoherence (QD)
When a quantum system interacts with environment, quantum decoherence(QD) could appear. A classic example is a two-slit experiment with electronbeams. If we do not measure which hole an electron passes through, one observesan interference pattern. On the other hand, if we try to determine which holean electron passes through using some device, the interference pattern will bedistorted. As the disturbance becomes stronger, the interference will be distortedmore, thus it eventually disappears.It has been speculated for some time that there may be a loss of quantum coher-ence due to environmental effect or quantum gravity and space-time foam, etc..Although quantum decoherence (QD) due to rapid fluctuation of environment isconceivable, QD due to quantum gravity is still under debate among theoreticians.In this talk, I present our phenomenological study of QD, namely how this effectcan be probed by the Kamioka-Korea setting. rather than discuss the ground onthe origin of QD within quantum gravity. For previous analyses of decoherence inneutrino experiments, see e.g., [19, 27, 28].As discussed in Sec. 1. we consider the ν µ − ν τ two-flavor system. Since thematter effect is a sub-leading effect in this channel we employ vacuum oscillationapproximation in this section. The two-level system in vacuum in the presenceof quantum decoherence can be solved to give the ν µ survival probability Eq. (1)[19, 20]. Notice that the conventional two-flavor oscillation formula is reproducedin the limit γ ( E ) →
0. Since the total probability is still conserved in the presenceof QD, the relation P ( ν µ → ν τ ) = 1 − P ( ν µ → ν µ ) holds.Nothing is known for the energy dependence of γ ( E ) from the first principleincluding quantum gravity. Therefore, we examine, following [19], several typicalcases of energy dependence of γ ( E ), which are purely phenomenological ansatzs: γ ( E ) = γ (cid:18) E GeV (cid:19) n (with n = 0 , , −
1) (2)In this convention, the overall constant γ has a dimension of energy or (length) − ,for any values of the exponent n . We will use γ in GeV unit in this section. Inthe following three subsections, we analyze three different energy dependences, n = 0 , − , First, let me consider the case with n = − γ ( E ) ∝ E . It turns out thatthe correlations between ∆ m and sin θ at three experimental setups. Notethat there are strong correlations between sin θ and γ for the Kamioka-only andKorea-only setups, and the slope of the correlation for the Kamioka-only setup isdifferent from that for the Korea-only setup (see Fig. 2 in Ref. [26]). Therefore theKamioka-Korea setup can give a stronger bound than each experimental setup.This advantage can be seen in Fig. 2, where we present the sensitivity regions of γ as a function of sin θ (left panel) and ∆ m (right panel).We can repeat the same analysis for other cases n = 0 and n = 2. In Table 1, wesummarize the bounds on γ at 2 σ CL achievable by three different experimentalsettings, along with the upper bounds on γ at 90% CL obtained by analyzing theatmospheric neutrino data in [19], for the purpose of comparison.In the case of E dependence of γ ( E ), the sensitivity to γ in the Kamioka-Koreasetting is better than the Korea-only and the Kamioka-only settings by a factor ν ν – γ ( × -23 GeV) t r ue s i n θ true ∆ m = 2.50 × -3 eV Kamioka + KoreaKamiokaKorea ν ν – γ ( × -23 GeV) t r ue ∆ m ( × - e V ) true sin θ = 0.960Kamioka + KoreaKamiokaKorea Fig. 2
The sensitivity to γ as a function of sin θ ≡ sin θ (left panel) and∆ m ≡ ∆ m (right panel). The case of 1/E dependence of γ ( E ). The red solidlines are for Kamioka-Korea setting with each 0.27 Mton detector, while the dashedblack (dotted blue) lines are for Kamioka (Korea) only setting with 0.54 Mton detec-tor. The thick and the thin lines are for 99 % and 90 % CL, respectively. 4 years ofneutrino plus 4 years of anti-neutrino running are assumed. The other input valuesof the parameters are ∆ m = +2 . × − eV (with positive sign indicating thenormal mass hierarchy) and sin θ =0.5. The solar mixing parameters are fixed as∆ m = 8 × − eV and sin θ =0.31. greater than 3 and 6, respectively. Also all the three settings can improve thecurrent bound almost by two orders of magnitude. This case demonstrates clearlythat the two-detector setup is more powerful than the Kamioka-only setup.For n = 0 (the case of an energy independent constant γ ( E )), we find that thesensitivity to γ in the Kamioka-Korea setting is better than the Korea-only andthe Kamioka-only settings by a factor greater than 3 and 8, respectively. AlsoKamioka-Korea two detector setting can improve the current bound by a factorof ∼ n = 2 with γ ( E ) ∝ E , the sensitivity to γ in the Kamioka-Koreasetting is better than the Korea-only and the Kamioka-only settings by a factorgreater than 3 and 5, respectively. On the other hand, the current bound imposedby the atmospheric neutrino data surpasses those of our three settings by almost ∼ γ ( E ). In a sense, the current Super-Kamiokande experiment is already a powerfulneutrino spectroscope with a very wide energy range, and could be sensitive tononstandard neutrino physics that may affect higher energy neutrinos such as QDwith γ ( E ) ∼ E .
4. Violation of Lorentz Symmetry
Lorentz symmetry is one of the cornerstones of the quantum field theory, whichis a mathematical tool for high energy physics nowadays. Therefore it is importantto test this symmetry experimentally as accurately as possible. There may be
Table 1
Presented are the upper bounds on decoherence parameters γ defined in (2)for three possible values of n . The current bounds are based on [19] and are at 90%CL. The sensitivities obtained by this study are also at 90 % CL , and correspondto the true values of the parameters ∆ m = 2 . × − eV and sin θ = 0 . n Curent bound Kamioka-only Korea-only Kamioka-Korea n = 0 < . × − < . × − < . × − < . × − n = − < . × − < . × − < . × − < . × − n = 2 < . × − < . × − < . × − < . × − a small violation of Lorentz symmetry, which would modify the usual energy-momentum dispersion relations. In such a case, neutrinos can have both velocitymixings and the mass mixings, which are CPT conserving [21]. Also there could beCPT-violating interactions in general [21, 22, 23]. Then, the energy of neutrinoswith definite momentum in ultra-relativistic regime can be written as mm † p = cp + m p + b, (3)where m , c , and b are 3 × c is dimensionless quantity, b has dimension ofenergy. For brevity, we will use GeV unit for b .Within the framework just defined above, we can work in the ν µ − ν τ twoflavor subsystem, and derive the ν µ survival probability, which depends on sixparameters. We further assume that three matrices m , c and b are diagonalizedby the same unitarity transformations with the same mixing angles: namely, θ m = θ c = θ b ≡ θ . Then the ν µ survival probability is given by : P ( ν µ → ν µ ) = 1 − sin θ sin (cid:20) L (cid:18) ∆ m E + δb δcE (cid:19)(cid:21) , (4)and we recovers the case treated in [29]. Here, δb ≡ b − b and δc ≡ c − c , where c i =1 , and b i =1 , , are the eigenvalues of the matrix c and b . Note that we still have4 parameters, θ , ∆ m , δb and δc . The survival probability for the anti-neutrinois obtained by the following substitution: δc → δc, δb → − δb (5)The difference in the sign changes signify the CPT conserving vs. CPT violatingnature of c and b terms. As pointed out in [30], the analysis for violation ofLorentz invariance with δc term is equivalent to testing the equivalence principle[31]. The oscillation probability in (4) looks like the one for conventional neutrinooscillations due to ∆ m , with small corrections due to the Lorentz symmetryviolating δb and δc terms. In this sense, it may be the most interesting case toexamine as a typical example with the Lorentz symmetry violation. Note that thesign of δb and δc can have different effects on the survival probabilities, so thatthe bounds on δb and δc could depend on their signs, although we will find thatthe difference is rather small. For ease of analysis and simplicity of presentation, we further restrict our anal-ysis to the case of either δb = 0 and δc = 0 (CPT conserving), or δb = 0 and δc = 0 (CPT violating).Let me first examine violation of Lorentz invariance with CPT conservation,namely δb = 0 and δc = 0. Unlike the case of quantum decoherence, the sensitiv-ities to δc achieved by the Kamioka-Korea setting is slightly better than those ofthe Korea-only and the Kamioka-only settings but not so much. The sensitivityis weakly correlated to θ , and the best sensitivity is achieved at the maximal θ .There is almost no correlation to ∆ m .Next we consider the CPT and Lorentz violating case ( δc = 0 and δb = 0).In this case, unlike the system with decoherence, the sensitivity is greatest inthe Kamioka-only setting, though the one by the Kamioka-Korea setting is onlyslightly less by about 15 − ν µ and ν µ survival probabilities. In this scenario, theeffect of the nonvanishing δb appears as the difference in the oscillation frequencybetween neutrinos and anti-neutrinos, if the energy dependence is neglected. Inthis case, the measurement at different baseline is not very important. Thenthe Kamioka-only setup turns out to be slightly better than the Kamioka-Koreasetup. This case is also unique by having the worst sensitivity at the largest valueof ∆ m . Also, the correlation of sensitivity to sin θ is strongest among the casesexamined in this paper, with maximal sensitivity at maximal θ . (See the rightand the left panels of Fig. 5 of Ref. [26] for details.)I summarize the results in Table 2, along with the present bounds on δc and δb ,respectively. We quote the current bounds on δc ’s from Ref.s [32, 33] which wasobtained by the atmospheric neutrino data, | δc µτ | . × − . (6)We note that the current bound on δc µτ obtained by atmospheric neutrino data isquite strong. The reason why the atmospheric neutrino data give much strongerlimit is that the relevant energy is much higher (typically ∼
100 GeV) than theone we are considering ( ∼ δb , Barger et al. [34] argue that | δb µτ | < × − GeV (7)from the analysis of the atmospheric neutrino data.Let me compare the sensitivity on δb within our two detector setup with thesensitivity at a neutrino factory. Barger et al. [34] considered a neutrino factorywith 10 stored muons with 20 GeV energy, and 10 kton detector, and concludedthat it can probe δb < × − GeV. The Kamioka-Korea two detector setupand Kamioka-only setup have five and six times better sensitivities compared withthe neutrino factory with the assumed configuration. Of course the sensitivity ofa neutrino factories could be improved with a larger number of stored muons anda larger detector. A more meaningful comparison would be possible, only whenone has configurations for both experiments which are optimized for the purposesof each experiment. Still we can conclude that the Kamioka-Korea two-detectorsetup could be powerful to probe the Lorentz symmetry violation.
Table 2
Presented are the upper bounds on the velocity mixing parameter δc and theCPT violating parameter δb (in GeV). The current bounds are based on [32, 33, 34]and are at 90% CL. The sensitivites obtained in this study are also at 90 % CL, and correspond to the true values of the parameters ∆ m = 2 . × − eV andsin θ = 0 . | δc | < × − . × − . × − . × − | δb | (GeV) < . × − . × − . . × − . . × −
5. Nonstandard Neutrino Interactions with Matter
In the presence of new physics around electroweak scale, neutrinos might havenonstandard neutral current interactions with matter [24, 25, 35, 36], ν α + f → ν β + f ( α, β = e, µ, τ ), with f being the up quarks, the down quarks and electrons.In such a case, the low energy effective Hamiltonian describing interaction betweenneutrinos and matter is modified as follows: H eff = √ G F N e ε ee ε eµ ε eτ ε µe ε µµ ε µτ ε τe ε τµ ε ττ (8)where ǫ ’s parameterize the nonstandard interactions (NSI) of neutrinos with mat-ter. Here, G F is the Fermi constant, N e denotes the averaged electron numberdensity along the neutrino trajectory in the earth.In this work we truncate the system so that we confine into the µ − τ sectorof the neutrino evolution, which is justified when ǫ ’s are sufficiently small. Then,the time evolution of the neutrinos in flavor basis can be written as i ddt ν µ ν τ ! = " U ∆ m E ! U † + a ε µτ ε τµ ε ττ − ε µµ ! ν µ ν τ ! , (9)where U is the flavor mixing matrix and a ≡ √ G F N e . In the 2-2 element ofthe NSI term in the Hamiltonian is of the form ε ττ − ε µµ because the oscillationprobability depend upon ε ’s only through this combination. In the following, weset ε µµ = 0 for simplicity, and study the sensitivity on ε ττ . At the end, the resultshould be interpreted as ε ττ − ε µµ . The evolution equation for the anti-neutrinosare given by changing the signs of a and replacing U by U ∗ .Since we work within the truncated 2 by 2 subsystem, we quote here only theexisting bounds of NSI parameters which are obtained under the same approxima-tion. By analyzing the Super-Kamiokande atmospheric neutrino data the authorsof [37] obtained | ε µτ | . . , | ε ττ | . . , (10)at 99 % CL for 2 degrees of freedom. † † A less severe bound on | ε ττ | is derived in [38] by analyzing the same data but with ε eτ andwithout ε µτ In Fig. 3, presented are the allowed regions in ε µτ − ε ττ space for 4 yearsneutrino and 4 years anti-neutrino running of the Kamioka-only (upper panels),the Korea-only (middle panels), and the Kamioka-Korea (bottom panels) settings.The input values ε µτ and ε ττ are taken to be vanishing.As in the CPT-Lorentz violating case and unlike the system with decoherence,the Korea-only setting gives much worse sensitivity compared to the other twosettings. Again the Kamioka-only setting has a slightly better sensitivity than theKamioka-Korea setting. However we notice that the Kamioka-only setting hasmultiple ε ττ solutions for sin θ = 0 .
45. The fake solutions are nearly eliminatedin the Kamioka-Korea setting.The sensitivities of three experimental setups at 2 σ CL can be read off fromFig. 3. The approximate 2 σ CL sensitivities of the Kamioka-Korea setup forsin θ = 0 .
45 (sin θ = 0 .
5) are: | ǫ µτ | . .
03 (0 . , | ǫ ττ | . . . . (11)Here we neglected a barely allowed region near ǫ ττ = 2 .
3. The Kamioka-only orKamioka-Korea setup can improve the current bounds on ε ’s by factors of 8 (8)and 60 (16), which are significant improvement.There are a large number of references which studied the effects of NSI and thesensitivity reach to NSI by the ongoing and the various future projects. We quotehere only the most recent ones which focused on sensitivities by superbeam andreactor experiments [39] and neutrino factory [40], from which earlier referencescan be traced back.By combining future superbeam experiment, T2K [10] and reactor one, Double-Chooz [13], the authors of [39] obtained the sensitivity of | ǫ µτ | to be ∼ ǫ ττ isexpected. The same authors also consider the case of NO ν A experiment [11]combined with some future upgraded reactor experiment with larger detector asconsidered, e.g., in [41, 42] and obtained ǫ µτ sensitivity of about 0.05 which iscomparable to what we obtained.While essentially no sensitivity of ǫ ττ is expected by superbeam, future neutrinofactory with the so called golden channel ν e → ν µ and ¯ ν e → ¯ ν µ , could reach thesensitivity to ǫ ττ at the level of ∼ ǫ µτ by neutrino factory was not derived in [40], from Fig. 1 of this reference, one cannaively expect that the sensitivity to ǫ µτ is similar to that of ǫ ee which is ∼ ǫ µτ is not bad.
6. Conclusion
The Kamioka-Korea two detector system for the J-PARC neutrino beam wasshown to be a powerful experimental setup for lifting the neutrino parameterdegenracies and probing CP violation in neutrino oscillations. In this talk, Ipresented the sensitivities of the same setup to nonstandard neutrino physicssuch as quantum decoherence, tiny violation of Lorentz symmetry, and nonstan-dard neutrino interactions with matter. Generally speaking, two detector setup ismore powerful than one detector setup at Kamioka, not only for lifting the neu-trino parameter degeneracies, but also probing/constraining nonstandard neutrinophysics. The sensitivities of three experimental setups at 90% CL are summarizedin Table 1 and Table 2 for quantum decoherence and Lorentz symmetry violationwith/without CPT symmetry, respectively. We can say modestly that futurelong baseline experiments with two detector setup can improve the sensitivitieson nonstandard neutrino physics in many cases, in addition to lifting the neu-trino parameter degeneracies. It would be highly desirable to make such neutrinophysics facilities realitic in the near future. -2-1.5-1-0.500.511.52-2-1.5-1-0.500.511.52 ε ττ -2-1.5-1-0.500.511.52-0.3 -0.2 -0.1 0 0.1 0.2 0.3 ε µτ -0.2 -0.1 0 0.1 0.2 0.3 ε µτ Fig. 3
The allowed regions in ε µτ − ε ττ space for 4 years neutrino and 4 years an-ti-neutrino running. The upper, the middle, and the bottom three panels are forthe Kamioka-Korea setting, the Kamioka-only setting, and the Korea-only setting,respectively. The left and the right panels are for cases with sin θ ≡ sin θ = 0 . σ , 2 σ , and 3 σ CL, respectively. The other input values of the parametersare idential to those in Fig. 21
PK is grateful to the organizers of the workshops for inviting him for the talk.
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