K. Mawatari (Kobe)1 Decay distribution of tau produced by neutrino-nucleon scattering Kentarou Mawatari (Kobe U.) with M. Aoki, K. Hagiwara （ KEK ）, and H. Yokoya (Hiroshima U. & RIKEN BNL) “Tau polarization in νN scattering” NPB668(2003)364 “Pseudoscalar form factors in νN scattering” PLB591(2004)113 “The decay of tau produced in νN scattering” in progress

K. Mawatari (Kobe) Ⅰ. The CNGS project … motivation The recent experiments on neutrino oscillation have a grate impact on not only particle physics but also astrophysics and cosmology. In the forthcoming neutrino experiments, ν τ appearance which is the positive evidence of the ν μ →ν τ oscillation is the one of main subjects, as well as precise measurements of the oscillation parameters and unknown θ 13 or CP phase measurement. τ ν μ →ν τ ( CERN ) ( GranSasso ) In 2005, the CNGS (CERN Neutrinos to Gran Sasso) project, OPERA and ICARUS experiments, will start. ⇒ aim to observe ν τ appearance We study on tau production and its decay via neutrino. CERN730km GranSasso ν(+ν ） π,e,μ…

K. Mawatari (Kobe) I.The CNGS project …motivation II.The decay distributions of tau leptons III.The polarization of tau produced via neutrino IV.The decay of tau in the lab. frame V.Conclusions ◆ Contents ◆

K. Mawatari (Kobe) Ⅱ. The decay distributions of tau leptons Tau leptons immediately decay into several particles, thus its decay distributions are important.  The decay particle distributions significantly depend on tau polarization. θ*θ* π,e left-handed right-handed τ-τ- z It is necessary to get information on the spin polarization of tau leptons in order to identify the tau production by neutrino. (in the tau rest frame)

K. Mawatari (Kobe) Ⅲ. The polarization of tau produced viaν QE W=M RES M+M π <W<W cut DIS W cut <W Kinematics k =(E ν, 0, 0, E ν ) p =(M, 0, 0, 0) k’=(E τ, p τ sinθ, 0, p τ cosθ) q=k-k’, W 2 =(p+q) 2 ντντ τ θ k k’ p N  in the lab. frame Produced tau will be partially polarized due to its heavy mass. (If tau were massless, it would have the fully left-handed polarization because of the V-A interaction.) In the long baseline experiments, three processes mainly contribute to tau production; quasi-elastic scattering (QE), resonance production (RES), and deep inelastic scattering (DIS). hadronic invariant mass

K. Mawatari (Kobe) Physical region Total cross section tau momentum scattering angle incoming neutrino energy The QE and RES contributions are significant, as well as DIS, especially around production threshold regions.

K. Mawatari (Kobe) Spin polarization vector and spin density matrix Spin polarization vector and spin density matrix P : the degree of polarization P =1 fully polarized P =0 fully unpolarized The polarization vector is related with the spin density matrix R λλ’ (λ: tau helicity in the lab. frame) : The spin polarization vector of tau in the tau rest frame : The spin polarization vector of tau in the tau rest frame : Calculation of the spin density matrix Calculation of the spin density matrix hadronic tensor leptonic tensor ν τ W

K. Mawatari (Kobe) QE (quasi-elastic scattering) The hadronic tensor The hadronic weak current W(q) The six form factors F(q 2 ) are decided theoretically and experimentally. Note that the pseudoscalar form factor F p plays an important role for the polarization of tau produced by neutrino since its contribution is proportional to the lepton mass and it has the spin-flip nature, although it is not known well. (We discussed it in PLB591(2004)113.) with n(p) p(p’)

K. Mawatari (Kobe) RES (Δ resonance production) The hadronic tensor The hadronic weak current N(p) Δ(p’) W(q) The eight form factors C(q 2 ) are decided theoretically and experimentally. with the spin 2/3 particle wave function the Breit-Wigner factor

K. Mawatari (Kobe) DIS (deep inelastic scattering) The hadronic tensor (the quark-parton model) The quark tensor N(p) W(q) q(p q ) X q’ ξ : the momentum fraction of quark and nucleon (p q = ξp ) f q : the parton distribution function (PDF)

K. Mawatari (Kobe) Polarization of tau produced by neutrino Polarization of tau produced by neutrino polarized unpolarized right-hand left-hand τenergy scattering angle E ν =10 GeV

K. Mawatari (Kobe) Summary of the polarization of τ produced by ν Summary of the polarization of τ produced by ν θPθP τmomentum scattering angle contour of cross section in DIS Tau produced via neutrino has high degree of polarization and the non- trivial spin direction.  Tau produced via neutrino has high degree of polarization and the non- trivial spin direction. This feature can be understood by considering This feature can be understood by considering the helicity amplitudes in the CM frame of the scattering particle the helicity amplitudes in the CM frame of the scattering particle the effects of Lorentz boost. the effects of Lorentz boost.

K. Mawatari (Kobe) Ⅳ. The decay of tau in the Lab. frame τ - →πν E ν =10 GeV ντντ τ θ N θ* π

K. Mawatari (Kobe) The event distribution in the CNGS project

K. Mawatari (Kobe) Ⅴ. Conclusions We considered the energy and angular dependence of the decay particle, pion and electron, from tau leptons produced via neutrino in the CNGS project. We considered the energy and angular dependence of the decay particle, pion and electron, from tau leptons produced via neutrino in the CNGS project. The decay particle distributions are significantly affected by the tau polarization, especially The decay particle distributions are significantly affected by the tau polarization, especially τ→πν mode has the strong dependence. Rather strong azimuthal asymmetry of Rather strong azimuthal asymmetry of π - about the tau momentum axis is predicted.  Tau polarization is quite important in the decay of tau produced by neutrino-nucleon scattering.