2004/9/16Tau04@Nara K. Mawatari (Kobe)1 Decay distribution of tau produced by neutrino-nucleon...

　　　　　　　　　　　2004/9/16Tau04@Nara K. Mawatari (Kobe) 1

Decay distribution of tau Decay distribution of tau produced by neutrino-nucleon produced by neutrino-nucleon

scatteringscatteringKentarou Mawatari (Kobe U.)Kentarou Mawatari (Kobe U.)

with M. Aoki, K. Hagiwara with M. Aoki, K. Hagiwara （（ KEKKEK ）） ,,and H. Yokoya (Hiroshima U. & RIKEN BNL)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

2004/9/162Tau04@Nara K. Mawatari (Kobe)

ⅠⅠ. The CNGS project …motivation. 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.

τνμ→ντ

(CERN)(GranSasso)

In 2005, the CNGS (CERN Neutrinos to Gran Sasso) project, OPERA and ICARUS experiments, will start. 　　　　⇒ aim to observe ντ appearance

We study on We study on tau productiontau production and and its decayits decay via neutrino. via neutrino.

CERNCERN

730km730km

GranSassoGranSassoν(+ν ）

π,e,μ…


Today I show that …Today I show that … Tau polarizationTau polarization is is very very importantimportant in the in the

decay of tau produced by neutrino-nucleon decay of tau produced by neutrino-nucleon scattering.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

I. The CNGS project …motivationII. The decay distributions of tau leptonsIII.The polarization of tau produced via neutrinoIV. The decay of tau in the lab. frameV. Conclusions

◆ ◆ Contents Contents ◆◆


ⅡⅡ. The decay distributions of tau . The decay distributions of tau leptonsleptons

Tau leptons immediately decay into several particles, thus its decay distributions are important.

The decay particle The decay particle distributions significantly distributions significantly depend on depend on tau polarizationtau polarization..

θ*

π,e

left-handed right-handed

τ-

z

It is necessary to get information on the spin It is necessary to get information on the spin polarization of tau leptons in order to identify polarization of tau leptons in order to identify the tau production by neutrino.the tau production by neutrino.

(in the tau rest frame) e


ⅢⅢ. The polarization of tau . The polarization of tau produced viaνproduced viaν

QE W=MRES M+Mπ<W<Wcut

DIS Wcut<W

KinematicsKinematics k =(Eν, 0, 0, Eν)p =(M, 0, 0, 0)k’=(Eτ, pτsinθ, 0 , pτcosθ)q=k-k’, W2=(p+q)2

ντ

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


Physical regionPhysical region Total cross sectionTotal cross section

tau momentumscattering angle incoming neutrino energy

The QE and RES contributions are significant, as well as DIS, especially around production threshold regions.


Spin polarization vector and spin density matrixSpin 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 The polarization vector is related with the spin density matrix RRλλ’λλ’

(λ: tau helicity in the lab. frame) (λ: tau helicity in the lab. frame) ::

• The spin polarization vector of tau in the The spin polarization vector of tau in the tau rest frame :tau rest frame :

Calculation of the spin density matrixCalculation of the spin density matrix

hadronic tensorleptonic tensor

*'

jj

ν

τ

W

j

*'' MMR


QE QE (quasi-elastic scattering)(quasi-elastic scattering) pn

The hadronic tensor

The hadronic weak current

W(q)

J

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.)

with

n(p)

p(p’)


RESRES (Δ resonance production) (Δ resonance production) // pn

The hadronic tensor

The hadronic weak current

JN(p)

Δ(p’)W(q)

The eight form factors C(q2) are decided theoretically and experimentally.

with

the spin 2/3 particle wave function

the Breit-Wigner factor


DISDIS (deep inelastic scattering) (deep inelastic scattering) 'qq

The hadronic tensor (the quark-parton model)

The quark tensor

N(p)

W(q)

q(pq)

X

q’

ξ : the momentum fraction of quark and nucleon (pq= ξp )fq : the parton distribution function (PDF)


Polarization of tau produced by Polarization of tau produced by neutrinoneutrino

polarized

unpolarized

right-hand

left-hand

τenergy

scattering angleXN Eν=10 GeV


Summary of the polarization of τ Summary of the polarization of τ produced by νproduced by ν

θP

τmomentum

scattering angle contour of cross section in DIS

Tau produced via neutrino has high degree of Tau produced via neutrino has high degree of polarizationpolarization and the non-trivial spin direction. 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 the helicity amplitudes in the CM frame of the scattering particlescattering particle• the effects of Lorentz boost.the effects of Lorentz boost.


ⅣⅣ. The decay of tau in the Lab. . The decay of tau in the Lab. frameframe

τ-→πν 　　 Eν=10 GeV

ντ

τ

θN

θ*

π


ii

i

ii

i

ddE

d

ddE

dddEPEdEA

ddE

dN

1

coscos)(

The event distribution in the CNGS project


ⅤⅤ. Conclusions. Conclusions

We considered the energy and angular dependence of the We considered the energy and angular dependence of the decay particle, pion and electron, from tau leptons produdecay particle, pion and electron, from tau leptons produced via neutrino in the CNGS project.ced via neutrino in the CNGS project.

The decay particle distributions are significantly affected The decay particle distributions are significantly affected by the tau polarization, especially 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 polarizationTau polarization is is quitequite important important in the decay of in the decay of tau produced by neutrino-nucleon scattering.tau produced by neutrino-nucleon scattering.

2004/9/16Tau04@Nara K. Mawatari (Kobe)1 Decay distribution of tau produced by neutrino-nucleon...

Documents

Transcript of 2004/9/16Tau04@Nara K. Mawatari (Kobe)1 Decay distribution of tau produced by neutrino-nucleon...