# Presentation: 388523

## 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

## Contents : 

-  Introduction : W-jet production
-  Parity-odd asymmetry in W-jet events
-  Phenomenology and Simulation
-  Summary

## Introduction

-  High-qT W-boson productions at Hadron Collider

- UA1, UA2 Collaborations @ CERN

- CDF, D0 Collaborations @ FNAL Tevatron

- have been measured by

## qT-distributions  - Experiments - 

- CDF (’91)

- D0 (’98)

-  Measurements in Tevatron Run-I

- qT-distributions  - Experiments -

## qT-distributions  - Theory -

- qT-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

## Lepton 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

## 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.

## Lepton Angular Distributions

- 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 :

## Recent 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.

## Parity-odd asymmetry 

## Parity-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

## Parity-odd asymmetry

-  β-decay of polarized nucleus :

- P

## Parity-odd asymmetry

-  Parity transformation :

-  Parity-odd observables :

-  with spin :

-  without spin :

## Parity-odd and Naïve-T ( T )-odd

-  T-transformation :
-    (anti-unitary)

- ~

-  P-odd observables without spins are interesting,
-   because these are at the same time T-odd.

- ~

- ~

## Unitarity and T-odd quantity

- Time-reversal violation

-  T-odd quantity

- → proportional to the absorptive parts of scattering amplitude

- ~

- ~

- absorptive part

## One-loop calculation

- Hagiwara,Hikasa,Kai(’84)

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

## One-loop calculation

- with CTEQ6M

- Hagiwara,Hikasa,Kai(’84)

## Phenomenology and Monte Carlo Simulation

## 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.

## Two-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

## Realistic Observables

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

- Laboratory frame

-  qT is observable,
-   from jet transverse momentum

## Monte-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

## Effective Higher-Order enhancement

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

-  good as well, for P-even distributions

- Mirkes,Ohnemus (’94)

- setting
- absorb the H.O. enhancement
- into LO result, approximately

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

- Kidonakis,Vera(’04)

## Results : 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

## Results : 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

## RHIC 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

## RHIC case : 

-  W+, one-lepton flavor

- # of events ~ 11,000.

-  Left-right asymmetry  →

## Summary

-  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

## Slide 29