Decay distribution of t au produced by neutrino-nucleon scattering

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 Tau04@Nara K. Mawatari (Kobe)

2. CERN 730km ν(+ν） GranSasso π,e,μ… 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,ντ appearance which is the positive evidence of the νμ→ντ oscillation is the one of main subjects, as well as precise measurements of the oscillation parameters and unknown θ13 or CP phase measurement. In 2005, the CNGS (CERN Neutrinos to Gran Sasso) project, OPERA and ICARUS experiments, will start. 　　　　⇒ aim to observe ντ appearance τ νμ→ντ (CERN) (GranSasso) We study on tau production and its decay via neutrino. Tau04@Nara K. Mawatari (Kobe)

3. Today I show that … Tau polarization isvery important in the decay of tau produced by neutrino-nucleon scattering. • The decay particle distributions significantly depend on tau polarization. • Tau produced via neutrino has high degree of polarization and the non-trivial spin direction. K. Hagiwara et al., NPB668 (2003) 364 ◆ Contents ◆ • The CNGS project …motivation • The decay distributions of tau leptons • The polarization of tau produced via neutrino • The decay of tau in the lab. frame • Conclusions Tau04@Nara K. Mawatari (Kobe)

4. Ⅱ. The decay distributions of tau leptons • Tau leptons immediately decay into several particles, thus its decay distributions are important. (in the tau rest frame) π,e τ- θ* z left-handedright-handed • The decay particle distributions significantly depend on tau polarization. It is necessary to get information on the spin polarization of tau leptons in order to identify the tau production by neutrino. Tau04@Nara K. Mawatari (Kobe)

5. τ k’ N ντ θ k p QEW=M RESM+Mπ<W<Wcut DISWcut<W Ⅲ. The polarization of tau produced viaν • 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). • in the lab. frame • Kinematics k=(Eν, 0, 0, Eν) p=(M, 0, 0, 0) k’=(Eτ, pτsinθ, 0 , pτcosθ) q=k-k’, W2=(p+q)2 hadronic invariant mass Tau04@Nara K. Mawatari (Kobe)

6. Physical region • Total cross section scattering angle incoming neutrino energy tau momentum The QE and RES contributions are significant, as well as DIS, especially around production threshold regions. Tau04@Nara K. Mawatari (Kobe)

7. τ ν W • The spin polarization vector of tau in the tau rest frame : • 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 Rλλ’(λ: tau helicity in the lab. frame) : • Calculation of the spin density matrix hadronic tensor leptonic tensor Tau04@Nara K. Mawatari (Kobe)

8. QE (quasi-elastic scattering) W(q) • The hadronic tensor p(p’) n(p) • The hadronic weak current with The six form factors F(q2) are decided theoretically and experimentally. Note that the pseudoscalar form factor Fp 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.) Tau04@Nara K. Mawatari (Kobe)

9. RES (Δ resonance production) W(q) • The hadronic tensor Δ(p’) N(p) the Breit-Wigner factor • The hadronic weak current with the spin 2/3 particle wave function The eight form factors C(q2) are decided theoretically and experimentally. Tau04@Nara K. Mawatari (Kobe)

10. DIS (deep inelastic scattering) • The hadronic tensor (the quark-parton model) W(q) q’ q(pq) N(p) ξ : the momentum fraction of quark and nucleon (pq= ξp ) fq: the parton distribution function (PDF) X • The quark tensor Tau04@Nara K. Mawatari (Kobe)

11. Eν=10 GeV Polarization of tau produced by neutrino scattering angle polarized unpolarized τenergy right-hand left-hand Tau04@Nara K. Mawatari (Kobe)

12. Summary of the polarization of τ produced by ν contour of cross section in DIS scattering angle θP τmomentum • Tau produced via neutrino has high degree of polarization and the non-trivial spin direction. • This feature can be understood by considering • the helicity amplitudes in the CM frame of the scattering particle • the effects of Lorentz boost. Tau04@Nara K. Mawatari (Kobe)

13. Ⅳ. The decay of tau in the Lab. frame τ-→πνEν=10 GeV τ θ* ντ N π θ Tau04@Nara K. Mawatari (Kobe)

14. The event distribution in the CNGS project Tau04@Nara K. Mawatari (Kobe)

15. 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. • The decay particle distributions are significantly affected by the tau polarization, especially τ→πν mode has the strong dependence. • Rather strong azimuthal asymmetry of π- about the tau momentum axis is predicted. • Tau polarization isquite important in the decay of tau produced by neutrino-nucleon scattering. Tau04@Nara K. Mawatari (Kobe)