Tau Production and its Decay via Neutrino

1. Tau Production and its Decayvia Neutrino Kentarou Mawatari (Kobe U.) with M. Aoki, K. Hagiwara （KEK）, and H. Yokoya (Hiroshima U.) “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 KEK NuFact04@大阪 K. Mawatari (Kobe)

2. Contents • CERN-to-GranSasso …motivation • Our message • The decay distributions of tau leptons • The polarization of tau produced via neutrino(presented in NuInt04@GranSasso) • The decay of tau in the lab. frame • Summary NuFact04@大阪 K. Mawatari (Kobe)

3. ν π,e,μ… 1. CERN-to-GranSasso …motivation CERN • In 2006 two long baseline experiments, OPERA and ICARUS, will start. 　　　　　↓ντappearance • We study on tau production and its decay via neutrino. 730km GranSasso νμ→ντ τ (CERN) (GranSasso) NuFact04@大阪 K. Mawatari (Kobe)

4. 2. Our message • Tau polarization isquite 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 NuFact04@大阪 K. Mawatari (Kobe)

5. 3. The decay distributions of tau leptons τ-→πντ-→e-νν • in the tau rest frame π,e τ θ* z left-handed right-handed • The decay particle distributions significantly depend on tau polarization. NuFact04@大阪 K. Mawatari (Kobe)

6. 4. The polarization ofτproduced viaν • Kinematics τ k=(Eν, 0, 0, Eν) p =(M, 0, 0, 0) k’=(Eτ, pτsinθ, 0 , pτcosθ) q=k-k’, W2=(p+q)2 k’ N ντ θ k p in the lab. frame QE(Quasi-elastic scattering) W=M RES(Δresonance production) M+Mπ<W<1.4GeV DIS(Deep inelastic scattering) 1.4GeV<W • Spin density matrix(λ: tau helicity in the lab. frame) NuFact04@大阪 K. Mawatari (Kobe)

7. The spin polarization vector of tau in the tau rest frame : • Spin polarization of tau P : the degree of polarization P =1 fully polarized P =0 fully unpolarized • The polarization vector is related with the spin density matrix Rλλ’ : NuFact04@大阪 K. Mawatari (Kobe)

8. Total cross section • Kinematical region Eν=10 GeV tau momentum scattering angle incoming neutrino energy NuFact04@大阪 K. Mawatari (Kobe)

9. Polarization of tau produced via neutrinoντ+ N →τ- + X Eν= 10 GeV scattering angle QE RES DIS polarized unpolarized τenergy right-hand left-hand NuFact04@大阪 K. Mawatari (Kobe)

10. θP Brief summary of the polarization of tau produced via neutrino scattering angle τmomentum contour of cross section in DIS • Tau produced via neutrino has high degree of polarization • and the non-trivial spin direction. NuFact04@大阪 K. Mawatari (Kobe)

11. 5. The decay of tau in the Lab. frame τ-→πνEν=10GeV NuFact04@大阪 K. Mawatari (Kobe)

12. τ-→e-νν Eν=17GeV NuFact04@大阪 K. Mawatari (Kobe)

13. τ-→πν Eν=17GeV τ-→e-νν Eν=17GeV Out In In NuFact04@大阪 K. Mawatari (Kobe)

14. Brief summary of the decay of tau produced via neutrino • We considered the energy, polar angle, and azimuthal angle dependence of the decay particle, pion and electron, from tau leptons produced via neutrino. • The decay distributions depend on the tau polarization, especially τ→πνmode has the strong dependence. • For the neutrino case we can see the In-Out asymmetry in terms of the azimuthal angle, while for the anti-neutrino case there is no such asymmetry. NuFact04@大阪 K. Mawatari (Kobe)

15. 6. Summary • Tau polarization isquite important in the decay of tau produced by neutrino-nucleon scattering. NuFact04@大阪 K. Mawatari (Kobe)