1

Parity-Odd Asymmetry in W-Jet Events

Hiroshi Yokoya (Niigata U.)

RBRC workshop, June 18-23, 2006

“RHIC physics in the Context of the Standard Model”

Ref. K.Hagiwara, K.Hikasa, N.Kai, Phys.Rev.Lett.52(1984)1076;

K.Hagiwara, K.Hikasa, HY, hep-ph/0604208

2

Contents :

• Introduction : W-jet production

• Parity-odd asymmetry in W-jet events

• Phenomenology and Simulation

• Summary

3Introduction

• High-qT W-boson productions at Hadron Collider

UA1, UA2 Collaborations @ CERN

CDF, D0 Collaborations @ FNAL Tevatron

have been measured by

4

CDF (’91)D0 (’98)

• Measurements in Tevatron Run-I

qT-distributions - Experiments -

5qT-distributions - Theory -

• High-qT (qT ~ MW)perturbation is good

complete NLO calc. Arnold,Reno(’89);Gonsalves,Pawlowski,Wai(’89)

(NNLO is modest ) Kidonakis,Vera (’04)

c.f.) small-qT (qT ≪ MW)

Arnold,Kauffman(’91),Ellis,Ross,Veseli(’98),,,

K ~ 1.3, flat behavior

log corrections → qT-resummation

6Lepton Angular Distributions

P-even

P-odd

• Rich information on the polarization of W-boson, i.e.the details of production mechanism can be investigated

Fi : structure functions

7

Collins-Soper frame

(W-rest frame)

W-jet c.m. frame

(parton c.m. frame)

Notice : Both frames are NOT constructible from observables, because of missing neutrino momentum.

Collins-Soper Frame

8

P-even parts :LO (tree-level)Chaichian,Hayashi,Yamagishi(’82)

Mirkes,Korner,Schuler(’91),Mirkes(’92)NLO (one-loop)

P-odd parts :LO (one-loop)Hagiwara,Hikasa,Kai(’84)

• pQCD calculation :

Lepton Angular Distributions

9Recent Results from CDF [hep-ex/504020]

• Some of the P-even distributions are measured at Tevatron Run-I, in good agreement with the pQCD prediction in NLO.

• In Run-II, measurements of P-odd distributions may be possible.

We study the simple and practical observables of the P-odd asymmetry, and perform a realistic Monte-Carlo simulation.

10

Parity-odd asymmetry

11Parity-odd asymmetry

"for their penetrating investigation of the so-called parity laws which has led to important discoveries regarding the elementary particles"

T.D. Lee and C.N. Yang

The Nobel Prize in Physics 1957

12

• β-decay of polarized nucleus :

P

Parity-odd asymmetry

13Parity-odd asymmetry

• Parity transformation :

• Parity-odd observables :

with spin :

without spin :

14

• T-transformation :

• T-transformation : (anti-unitary)

Parity-odd and Naïve-T ( T )-odd

~

• P-odd observables without spins are interesting,

because these are at the same time T-odd.~

~

15

• Unitarity of S-matrix

Time-reversal violation

• T-odd quantity

→ proportional to the absorptive parts of scattering amplitude

Unitarity and T-odd quantity~

~

absorptive part

16One-loop calculation

Hagiwara,Hikasa,Kai(’84)

• one-loop calculation in pQCD on the absorptive part of scattering amplitude

17

with CTEQ6M

Hagiwara,Hikasa,Kai(’84)

One-loop calculation

18

Phenomenology and Monte Carlo Simulation

19

Collins-Soper frame

(W-rest frame)

W-jet c.m. frame

(parton c.m. frame)

Notice : Both frames are NOT constructible from observables, because of the missing neutrino momentum.

Collins-Soper Frame

20Two-fold ambiguity

• (longitudinal) neutrino momentum is not observable

→ Two-fold ambiguity in

determining

• W-jet c.m. frame

• Collins-Soper frame

Advantage of CS frame : only the sign of cosθ can’t be determined.

sinθ and φ can be determined.

　

Laboratory frame

21Realistic Observables

• Pseudo-rapidity difference of lepton and jet, instead of

Laboratory frame

• qT is observable,

from jet transverse momentum

22Monte-Carlo simulation

• Tevatron Run-II :Luminosity :

• “standard” CDF cuts :

• W → lepton detection : • jet identification :

W’s transverse mass :

Jet cone size :

• qT minimum cut :

CDF hep-ex/504020

23Effective Higher-Order enhancement

LO Matrix Elements with “effective” H.O. enhancement

• good as well, for P-even distributionsMirkes,Ohnemus (’94)

settingabsorb the H.O. enhancement into LO result, approximately

• not confirmed for P-odd, because NLO is not known.

Kidonakis,Vera(’04)

24Results : Event yield

• Total number of events for one lepton-flavor ~ 50,000.

c.f.) for Run-I we get: # ~ 16,000.

: 12,676.: 6,941.

CDF

25Results : Observable P-odd asymmetries

• Left-right asymmetry

more than 5σ deviation from zero-asymmetry is expected

• sign(sin2φ) asymmetry

(combining all Δy and qT)

～ 5% at large Δη

+

+

-

-

①

②

④

③

26RHIC case :

• looser cut for qT minimum to use more events

→ perturbation works well?

Perhaps, we need qT-resummation for the azimuthal

angular distributions D.Boer and W.Vogelsang, hep-ph/0604177

pp collision

27RHIC case :

• W+, one-lepton flavor

# of events ~ 11,000.

• Left-right asymmetry →

28Summary

• High-qT W-boson production at Hadron colliders

• P-odd asymmetries in decay-lepton angular distributions

• Monte-Carlo simulation for Tevatron Run-II and RHIC

• well-described by (NLO) pQCD

• lepton angular distributions are measured at

Tevatron

• naïve-T-odd as well• arise from the absorptive part of scattering amplitudes• new test of the pQCD prediction

• two-fold ambiguity → realistic observables

• we proposed observable asymmetries

29