We present new constraints on the mass $m_{\nu_\tau}$ of the tau neutrino and
its mixing with a fourth generation neutrino. From an analysis of the partial
widths of tau lepton decays we obtain the following bounds at the 90%
confidence level: $m_{\nu_\tau} < 32$ MeV and $\sin^2\theta < 0.007$, where
$\theta$ describes the Cabibbo-like mixing of the third and fourth generation
neutrinos.Comment: 2 pages, no figures. Submitted to Phys. Rev. 

Swain, John

Taylor, Lucas

English

arXiv

We present new constraints on the mass $m_{\nu_\tau}$ of the tau neutrino and its mixing with a fourth generation neutrino. From an analysis of the partial widths of tau lepton decays we obtain the following bounds at the 90% confidence level: $m_{\nu_\tau} < 32$ MeV and $\sin^2\theta < 0.007$, where neutrinos.We present new constraints on the mass $m_{\nu_\tau}$ of the tau neutrino and its mixing with a fourth generation neutrino. From an analysis of the partial widths of tau lepton decays we obtain the following bounds at the 90% confidence level: $m_{\nu_\tau} < 32$ MeV and $\sin^2\theta < 0.007$, where $\theta$ describes the Cabibbo-like mixing of the third and fourth generation neutrinos

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arXiv:hep-ph/9712383v1  15 Dec 1997New constraints on the tau neutrino mass and fourth generation mixingJohn Swain and Lucas TaylorDepartment of Physics, Northeastern University, Boston, USA(December 20, 2013)We present new constraints on the mass mντ of the tauneutrino and its mixing with a fourth generation neutrino.From an analysis of the partial widths of tau lepton de-cays we obtain the following bounds at the 90% confidencelevel: mντ < 32MeV and sin2 θ < 0.007, where θ describesthe Cabibbo-like mixing of the third and fourth generationneutrinos.14.60.Pq, 13.35.DxI. INTRODUCTIONIn a previous paper we derived constraints on the massof the third generation neutrino ν3 and its mixing witha heavy fourth generation neutrino ν4 [1]. In this pa-per we update this analysis using recent experimentalmeasurements. We determine significantly more strin-gent constraints on the mass mν3 and the Cabibbo-likemixing angle θ, where the tau neutrino weak eigenstateis given by the superposition of two mass eigenstates|ντ 〉 = cos θ|ν3〉+sin θ|ν4〉. We compare the precise mea-surements of the τ partial widths for the following de-cays1 : τ− → e−ν¯eντ , τ− → µ−ν¯µντ , τ− → π−ντ , andτ− → K−ντ , with our theoretical predictions, as func-tions of mν3 and sin2 θ to obtain upper limits on boththese quantities.II. THEORETICAL PREDICTIONSThe theoretical predictions for the branching fractionsBℓ for the decay τ− → ℓ−ν¯ℓντ (XEM), with ℓ− = e−, µ−and XEM = γ, γγ, e+e−, . . ., are given by:Btheoryℓ =(G2Fm5τ192π3)ττ(1− 8x− 12x2lnx+ 8x3 − x4)×[(1−α(mτ )2π(π2 −254))(1 +35m2τm2W)]×[1− sin2 θ] [1− 8y(1− x)3 + · · ·](1)1Throughout this paper the charge-conjugate decays are alsoimplied. We denote the branching ratios for these processes asBe,Bµ,Bπ,BK respectively; Bℓ denotes either Be or Bµ whileBh denotes either Bπ or BK .where GF = (1.16639 ± 0.00002) × 10−5GeV−2 is theFermi constant [2]; ττ = (290.55 ± 1.06) fs is the taulifetime [3]; mτ = (1776.96+0.18+0.25−0.21−0.17)MeV [4] is the taumass, determined by BES from the τ+τ− productionrate near threshold which has no dependence on thetau neutrino mass; and x = m2ℓ/m2τ . The first termin brackets allows for radiative corrections [5–8], whereα(mτ ) ≃ 1/133.3 is the QED coupling constant [8] andmW = 80.400 ± 0.075GeV is the W mass [9]. The sec-ond term in brackets describes mixing with a fourth gen-eration neutrino which, being kinematically forbidden,causes a suppression of the decay rate. The third term inbrackets parametrises the suppression due to a non-zeromass of ν3, where y = m2ν3/m2τ and the ellipsis denotesnegligible higher order terms [1].The branching fractions for the decays τ− → h−ντ ,with h = π/K, are given byBtheoryh =(G2Fm3τ16π)ττf2h |Vαβ |2 (1− x)2×[1 +2απln(mZmτ)+ · · ·] [1− sin2 θ]×[1− y(2 + x− y1− x)√1− y(2 + 2x− y)(1− x)2](2)where x = m2h/m2τ , mh is the hadron mass, fh arethe hadronic form factors, and Vαβ are the CKM ma-trix elements, Vud and Vus, for π− and K− respectively.From an analysis of π− → µ−ν¯µ and K− → µ−ν¯µdecays, one obtains fπ|Vud| = (127.4 ± 0.1)MeV andfK |Vus| = (35.18±0.05)MeV [10, and references therein].The ellipsis represents terms, estimated to be O(±0.01)[10], which are neither explicitly treated nor implicitlyabsorbed into GF , fπ|Vud|, or fK |Vus|. The second termin brackets describes mixing with a fourth generationneutrino while the third parametrises the effects of a non-zero mν3 [1].The fourth generation neutrino mixing affects all thetau branching fractions with a common factor whereas anon-zero tau neutrino mass affects all channels with dif-ferent kinematic factors. Therefore, given sufficient ex-perimental precision, these two effects could in principlebe separated.III. RESULTSWe use the recently updated world average values forthe measured tau branching fractions [3]:1Be = (17.786± 0.072)%; (3)Bµ = (17.356± 0.064)%; (4)Bπ = (11.01± 0.11)%; (5)BK = (0.692± 0.028)%. (6)Substituting in equations 1 and 2 for the measured quan-tities we find that bothmντ and sin2 θ are consistent withzero.We therefore derive constraints onmντ and sin2 θ froma combined likelihood fit to the four tau decay chan-nels. The likelihood is constructed numerically followingthe procedure of Ref. [11] by randomly sampling all thequantities used according to their errors. The CLEOmeasurement of the τ mass was used to further con-strain mν3 . From an analysis of τ+τ− → (π+nπ0ν¯τ )(π−mπ0ντ ) events (with n ≤ 2,m ≤ 2, 1 ≤ n +m ≤ 3),CLEO determined the τ mass to be mτ = (1777.8±0.7±1.7)+[mν3(MeV)]2/1400MeV [12]. The likelihood for theCLEO and BES measurements to agree, as a function ofmν3 is included in the global likelihood.The fit yields upper limits ofmν3 < 38MeV (7)sin2 θ < 0.008 (8)at the 95% C.L. ormν3 < 32MeV (9)sin2 θ < 0.007 (10)at the 90% C.L. These results improve on our previousdeterminations of mν3 < 42MeV and sin2 θ < 0.014 at90% C.L. [1]IV. DISCUSSIONThe limit on mν3 can be reasonably interpreted as alimit on mντ , since the mixing of mν3 with lighter neu-trinos is also small [2]. The best direct experimental con-straint on the tau neutrino mass is mντ < 18.2MeV atthe 95% confidence level [13] which was obtained usingmany-body hadronic decays of the τ . While our con-straint is less stringent, it is statistically independent.Moreover, it is insensitive to fortuitous or pathologicalevents close to the kinematic limits, details of the reso-nant structure of multi-hadron τ decays, and the absoluteenergy scale of the detectors. Since LEP has completedrunning on the Z it is unlikely that significantly improvedconstraints on mντ , using multi-hadron final states, willbe forthcoming in the foreseeable future.Future improved measurements of the tau branchingfractions, lifetime, and the tau mass from direct recon-struction would enable significant improvements to bemade in the determinations of both mντ and sin2 θ. IfCLEO and the b-factory experiments were to reduce theuncertainties on the experimental quantities by a factorof approximately 2, then the constraints on mντ fromthe technique we have described would become the mostcompetitive. Were a tau-charm factory to be built, thenthe determination of mντ by direct reconstruction wouldagain become the most sensitive technique.Our upper limit on sin2 θ is already the most stringentexperimental constraint on mixing of the third and fourthneutrino generations.ACKNOWLEDGEMENTSWe would like to thank the Department of Physics,Universidad Nacional de La Plata for their generous hos-pitality and the National Science Foundation for financialsupport. J.S. gratefully acknowledges the support of theInternational Centre for Theoretical Physics, Trieste.[1] J. Swain and L. Taylor, Phys. Rev. D 55, 1R (1997).[2] R. M. Barnett et al., Phys. Rev. D54, 1 (1996).[3] W. Li, Invited talk at the XVIII International Sympo-sium on Lepton Photon Interactions, Hamburg, July 28– August 1, 1997, (unpublished).[4] J. Bai, Phys. Rev. D53, 20 (1996).[5] S. M. Berman, Phys. Rev. 112, 267 (1958).[6] T. Kinoshita and A. Sirlin, Phys. Rev. 113, 1652 (1959).[7] A. Sirlin, Rev. Mod. Phys. 50, 573 (1978).[8] W. J. Marciano and A. Sirlin, Phys. Rev. Lett. 61, 1815(1988).[9] L. Taylor, in Proceedings of the XVIIth InternationalConference on Physics in Collision, edited by H. Heath(World Scientific, Singapore, 1997), in press.[10] W. J. Marciano, Phys. Rev. D45, R 721 (1992).[11] J. Swain, and L. Taylor, Numerical Construction of Like-lihood Distributions and the Propagation of Errors, hep-ex/9712015 (1997). To appear in Nucl. Instrum. &Methods.[12] R. Balest et al., Phys. Rev. D47, R3671 (1993), the neu-trino mass dependence quoted in this paper is in errordue to a typographical oversight (A. Weinstein, privatecommunication). This does not, however, affect any othernumbers in the paper.[13] L. Passalacqua, Nucl. Phys. B (Proc. Suppl.) 55C, 121(1997).2

New constraints on the tau neutrino mass and fourth generation mixing

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