application/xmlCan ICARUS and OPERA ντ appearance experiments detect new flavor physics?Toshihiko OtaJoe SatoPhysics Letters B 545 (2002) 367-372. doi:10.1016/S0370-2693(02)02625-4journalPhysics Letters BCopyright © 2002 Elsevier Science B.V. All rights reserved.Elsevier B.V.0370-26935453-410 October 20022002-10-10367-37236737210.1016/S0370-2693(02)02625-4http://dx.doi.org/10.1016/S0370-2693(02)02625-4doi:10.1016/S0370-2693(02)02625-4http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/JournalsS300.3PLB19163S0370-2693(02)02625-410.1016/S0370-2693(02)02625-4Elsevier Science B.V.PhenomenologyFig. 1The left plot represents the phase dependence of the contour which denotes 1σ deviation of the event number from that with the standard expectation when the magnitudes of all the exotic couplings, |ϵμτs,m,d| are assumed to be 0.01 in the case of ICARUS-A. The right plot shows the expected difference of the number of events due to new interactions from standard case, NNPτ in the presence of the new physics couplings |ϵμτs,d|=0.01 and ϵμτm=0.01i in ICARUS-A. This plot is almost the same as that of ϵμτm=0. In the region around the (−π/2, −π/2) and (π/2, π/2), the deviation from the standard case becomes significant beyond the error indicated in Table 1.Fig. 2Expected event number arising from the new physics couplings |ϵμτs|=0.01 and |ϵμτm,d|=0 in ICARUS-A. The horizontal axis represents the complex phase of ϵμτs, and the vertical axis indicates the event number deviation from the standard model expectation, NτNP.Table 1The experimental parameters and the total error for ICARUS and OPERA. Here, we assume Npot=5×4.5×1019 pots. Total errors are given by the left-hand side of Eq. (9)Mdeteffσ2sysNτSMTotal errorICARUS-A5 kt0.0811140.47.4ICARUS-B0.0471.523.55.2OPERA1.8 kt0.0910.7516.34.3Can ICARUS and OPERA ντ appearance experiments detect new flavor physics?ToshihikoOtaatoshi@higgs.phys.kyushu-u.ac.jpJoeSatobjoe@rc.kyushu-u.ac.jpaDepartment of Physics, Kyushu University, Hakozaki, Higashi-ku, Fukuoka 812-8581, JapanbResearch Center for Higher Education, Kyushu University, Ropponmatsu, Chuo-ku, Fukuoka 810-8560, JapanEditor: T. YanagidaAbstractIn this Letter we explore the notion of whether it is possible to observe a flavor-changing effect in the τ appearance experiments, ICARUS and OPERA.PACS13.15.+g14.60.Pq14.60.StThe atmospheric neutrino anomaly [1] and the solar neutrino deficit [2] are well described by the neutrino oscillation. Accordingly, many experiments have been designed to observe the oscillation directly, and some of them are currently in the process of being carried out [3]. For example, the atmospheric neutrino anomaly could be explained by the νμ→ντ oscillation and the direct measurement of this oscillation (transition) is being attempted at CERN by two experiments, ICARUS [4] and OPERA [5], which aim to observe tau neutrino appearance events. These experiments will start to produce data in 2005 [6,7].Moreover, it is expected that almost all the oscillation parameters will be determined by oscillation experiments within the near future (for example, see [8]). Although in the above experiments the main concerns continue to be how well they can determine the oscillation parameters, it is also apparent that a long baseline experiment can probe new types of flavor-changing interactions using the oscillation manner [9–12]. Among such new effects, probing the μ–τ flavor-changing effects is most important since large μ–τ flavor-changing interactions are included in many of the models which attempt to explain a large mixing for νμ↔ντ oscillation. In our previous study [12], we investigated the feasibility of observing such exotic interactions in oscillation experiments and we showed that the νμ→ντ channel works most effectively for exploring the μ–τ flavor-violating interactions.11In Ref. [12] we also proposed the νμ→νμ disappearance channel in the search for the same interaction, however, it is obvious that the appearance channel will have an advantage over the disappearance channel because of the statistical margin of error. Fortunately, ICARUS and OPERA both use this channel and hence in this work we examined the performance of ICARUS and OPERA in the search for new interactions within the three-generation framework.First, we briefly review the key idea for exotic interaction search in an oscillation experiment. We then consider only the μ–τ flavor-violating effects. In a long baseline experiment, what we really observe are signals caused by secondary charged particles, such as muons. That is, we do not observe the neutrinos themselves. In other words, neutrinos are unobserved intermediate states. Therefore, if there are some kinds of new interactions that can induce the same final states as the standard model, then interference between these two amplitudes takes place. This means that the effect of new interactions appears not with the strength of the square of the exotic coupling, but with the strength of the exotic coupling itself.The contribution of the new interactions can be divided into three stages, neutrino beam production, its propagation, and its detection. First, we refer to the production process. The neutrino beam of the CNGS [6] facility is produced by pion decay. In this case we can parametrize the effect of the exotic interactions in pion decay as the shift in the muon neutrino state from a pure flavor eigenstate, |να〉, to a mixed state, |ναs〉 [9], because the helicity states of the muon and the neutrino are fixed in this decay: (1)νμs=Uμαs|να〉,Uμαs=0,1,ϵμτs, where ϵμτs denotes the ratio of the coupling of the exotic decay of pions, π+→μ+ντ, to the standard decay. Next, during the beam propagation from CERN to GranSasso, the neutrinos feel the matter effect not only due to the ordinary interaction, but also due to the new interactions, which can be interpreted as a shift in the potential [10]: (2)Hmatterαβ=a2Eν10000ϵμτm0ϵm∗μτ0, where a≡22GFneEν is the standard matter effect whose origin is the weak interaction, ne is the electron number density, and Eν is the neutrino energy. Finally, at the detection process, neutrinos are also affected by the new flavor-changing interactions. Parametrizing these effects, in principle, is very complicated since we have to deal with the hadronic process. However, in this Letter, we assume for simplicity that the neutrino state at the detection process is a flavor-mixed state, |ναd〉 [9], just like the source state, (3)ντd=Uταd|να〉,Uταd=0,ϵμτd,1. If more precise treatment in the detection process is required, we have to take into account the parton distribution and give ϵd's energy dependence [12]. Note that all ϵ's are complex numbers, i.e., ϵs,m,dμτ=|ϵs,m,dμτ|eiφs,m,d[9].Then, we estimate the shift in the total event number induced by new physics in ICARUS and OPERA, and consider the condition wherein a difference from the standard model becomes significant, since we cannot expect to observe the energy spectra in these two experiments.We set the condition that the criterion to guarantee the observation of new physics that the deviation in the number of events caused by the new interactions, |NτNP|, is greater than the error for the number of events expected by the standard interaction, NτSM. Here NτSM and NτNP are (4)NτSM=C∫dEνfνμ(Eν)Pνμ→ντSM(Eν)σντ(Eν)eff(Eν), and (5)NτNP=C∫dEνfνμ(Eν)Pνμ→ντ(Eν)−Pνμ→ντSM(Eν)σντ(Eν)eff(Eν), with fνμ being the muon neutrino flux and σντ being the charged current cross section for tau neutrino, and they are given in Ref. [6]. C is defined as NpotMdet[kt]NA×109, where NA is the Avogadro's number, Npot is the total number of protons on target in the beam production, and Mdet is the detector mass. Incidentally, ICARUS has a mass of 5 kt, while that of OPERA is 1.8 kt. The standard oscillation probability without exotic interactions, Pνμ→ντSM and that with the new physics effects, Pνμ→ντ can be approximated as (6)Pνμ→ντSM=sin22θ23cos4θ13δm3124EL2,(7)Pνμ→ντ=Pνμ→ντSM+2sin2θ23cos2θ23cos2θ13Reϵμτs−Reϵμτdδm3124EL2−2sin2θ23cos2θ13Imϵμτs+Imϵμτdδm3124EL+4sin32θ23cos2θ13Reϵμτma4ELδm3124EL, where θij's are the lepton-mixing angles defined by the following mixing matrix (8)U=1000c23s230−s23c23c130s13eiδ010−s13e−iδ0c13c12s120−s12c120001,δm231 is the larger mass difference, and L is the baseline length, 732 km. To derive Eq. (7), we treat δm212 and ϵ as the perturbations and adapt the high-energy approximation δm312L⪡Eν, which is now an appropriate assumption, and then extract the terms of O(ϵ,δm312). The details of this derivation are given in Refs. [12,13]. We use the detection efficiency, eff(Eν), estimated in Refs. [4,5]. The condition that we set at the beginning of this paragraph, that the number of events induced by new physics is larger than the error in the standard oscillation assumption, can be described as follows: (9)σsta2+∑α=1n∂NτSM∂λα2σpar2α+σsys2<NτNP. There are three kinds of errors of differing origins: (i) The statistical one, σsta, which is estimated by NτSM. (ii) Errors coming from the uncertainties of the oscillation parameters. These are represented as the second term in the square root of Eq. (9) according to the error propagation prescription, where λα is one of n parameters included in NτSM, and σparα is its uncertainty. Exactly speaking, this treatment works well only when NτSM depends linearly on all the parameters. In general, the dependence of λαs is not so simple. However, since the oscillation probability can be approximated here as sin22θ23cos4θ13(δm322L/4Eν)2 in almost all the energy regions referred to, by regarding sin22θ23cos4θ13(δm322)2 as one parameter included in NτSM, this method can be justified approximately. It is expected that the precision of sin22θ23, Δ(sin2θ23), becomes 1%, while that of δm312, Δ(δm312), is reduced to 3% in the next-generation experiments [8]. Moreover, the uncertainty of cos2θ13 does not affect the error estimation due to the smallness of θ13. From these considerations, σpar is calculated as (10)σpar2≃Δsin22θ23cos4θ13δm3222+2sin2θ23cos4θ13δm322Δδm322. (iii) The systematic error, σsys, which is given in Refs. [4,5,7]. The ICARUS Collaboration reports the relation between the detection efficiency and the background event rate, and some studies with different event selection rules are described in Ref. [4]. Among them, we picked out two cases, which we refer to as ICARUS-A and ICARUS-B. The efficiencies and errors for these cases are given in Table 1.Now, we present our results. Here, we presume that the CERN proton beam will achieve 4.5×1019 pots per year and we assume a total running time of 5 years. The total error in each experiment is indicated in Table 1. For numerical calculation, we use the following theoretical parameters: (11)sinθ12=1/2,sinθ23=1/2,sinθ13=0.1,δm312=3×10−3 eV2,δm212=5×10−5 eV2,δ=π/2. Since Eq. (7) is a good approximation in this context, we can expect that the numerical results do not depend on δm21, sinθ12, δ, or sinθ13.We firstly categorize the flavor-changing interactions into two classes by Lorentz and SU(2)L properties. The first one corresponds to the case where there exists an effective flavor-changing interaction of singlet/triplet type, say (12)l̄ττ2Cq̄qC†τ2lμ+h.c.and/orl̄ττaCq̄qC†τalμ+h.c.⊃ν̄τγσμd̄γσu+h.c., where l and q are the lepton and quark doublets, respectively, τa is the Pauli matrix, and C denotes charge conjugation. This type of interaction is induced by the exchange of SU(2)L singlet and/or triplet scalar [12,14]. New physics effects are expected to be of the same order of magnitude at the source, the matter and the detector for this case. In this case, there is a constraint for ϵ's from the SU(2)L counter part process of Eq. (12) such as τ−→μ−π0[14]. The isospin-breaking effect somewhat relaxes the limit. Nevertheless, we still have to set the ϵμτs≲O(10−2). Therefore, we set |ϵμτs,m,d|=0.01 for the new physics parameters. The left plot of Fig. 1 shows dependence of the region that satisfies the condition of Eq. (9). The inside of this contour represents the parameter region where we can observe the new physics effect at the 1σ confidence level. The right plot is a section of the left one at ϵμτm=0.01i, although in this case the contours denote the difference in the event number due to the new effect from the expected number with the assumption of standard oscillation. These behaviors can be clearly understood by Eq. (7). It strongly depends on the phases of the exotic interaction couplings. In some regions the total effect can exceed the range of the error.Next, we assume that |ϵμτs|=0.01 and that |ϵμτm,d|=0. This parameter set corresponds to the situation that the new interaction is doublet type, namely, (13)l̄τCd̄RqC†μR+h.c.⊃ν̄τμRd̄RuL+h.c. This is induced by the SU(2)L doublet intermediation. From the relation [15], (14)ūγ5d=−imu+md∂σūγσγ5d, the doublet mediation amplitude gets the enhancement factor, mπ2/(mu+md), in the pion decay process. In contrast there is no such enhancement in the propagation or detection processes. Therefore, ϵμτs is much bigger than ϵμτm,d, and thus only ϵμτs can contribute to the oscillation phenomenon. This enhancement allows us to search for the smaller exotic coupling, which is included in the elementary process, by O(10−2) less than that in the singlet and triplet cases, Eq. (12). In this case, there is a constraint on the effective coupling from the SU(2)L counter process, τ−→μ−+π0, namely ϵμτs≲O(10−2). The results of this calculation are presented in Fig. 2. This is also clearly explained by Eq. (7). In the region around φs=±π/2, the gaps from the standard oscillation expectation become large. However, they do not reach the 1σ level of significance even if the events of ICARUS and OPERA are combined.Finally, we discuss the sensitivity for different oscillation parameters from Eq. (11). As we have noted again and again, Eq. (7) is a very good approximation in this context. It shows that the sensitivity does not depend on the sub-leading oscillation parameters, δm212, sinθ12, or δ at all, and that it is also independent of sinθ13, since all the terms depend only on cosθ13. Therefore, it is completely free from the choice of the solar parameters and θ13. According to the fact that the statistical error is dominant among the three kinds of errors, the condition in Eq. (9) reduces to Pνμ→ντ−Pνμ→ντSM>Pνμ→ντSM. From Eqs. (6) and (7), it is found that this inequality depends essentially on two parameters, δm312 and sinθ23. However, as long as the statistical error is dominant over the systematic error, the dependence on δm312 and θ23 is canceled out and hence the sensitivity is independent of these parameters. For example, even if δm312≃5×10−3 eV2, causing the event number itself to increase, we still have almost the same sensitivity as that with δm312=3×10−3 eV2. Note that here δm312L/4E⪡1. Of course, if the expected number is very small, then the error due to the parameter uncertainty and the systematic error become even more important. Therefore, in such a case, the plot for the sensitivity has a slightly different shape. For example, if δm312≃1×10−3 eV2, then the decrease in the event number will impair the sensitivity. Recent analysis [16] suggests that slightly smaller value, 2.5×10−3 eV2, as the best fit value for δm312 than that we applied. This small change does not affect the sensitivity.To conclude, we summarize the results of the Letter. We roughly evaluated the feasibility of examining new physics with ICARUS and OPERA, and we obtained the following conclusions. •There is a possibility of observing of the new interaction effects whose magnitude is |ϵμτs,m,d|≳O(10−2). This value is around the current limit.•The effects strongly depend on the phases of the couplings.•To explore much smaller ϵ, additional statistics is necessary. For this purpose, it is important to raise the efficiency, even if some of the background events contaminate the total tau events.AcknowledgementsThe authors are grateful to T. Morozumi for useful discussion. The work of J.S. is supported in part by Grants-in-Aid for Scientific Research from the Ministry of Education, Science, Sports, and Culture, of Japan, Nos. 12047221 and 12740157. The English used in this manuscript was revised by K. Miller (Royal English Language Centre, Fukuoka, Japan).References[1]Super-Kamiokande CollaborationY.FukudaPhys. Rev. Lett.8119981562[2]J.N.BahcallM.C.Gonzalez-GarciaC.Penã-Garayhep-ph/0111150[3]K2K Collaborationhep-ex/0110034K2K Collaborationhep-ex/0206037K2K Collaborationhep-ex/0206033K2K Collaborationhttp://neutrino.kek.jp/[4]ICARUS Collaboration, C. Rubbia, et al., LNGS-EXP 13/89 Add. 2/01, ICARUS-TM/2001-09ICARUS CollaborationThis article is available on the ICARUS web sitehttp://pcnometh4.cern.ch/ICARUS Collaborationhttp://www.aquila.infn.it/icarus/[5]OPERA Collaboration, M. 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