Mickey ChiuUniversity of Illinois at Urbana-Champaign

JPS/DNP, Maui 2005

September 18, 2005

New Prospects for Transverse Physics with

the PHENIX detector

Sivers and Why it is Interesting

•Non-Zero Sivers function means that there is a left/right asymmetry in the kT of the partons in the nucleon•Probe of space-time structure of nucleon wave-function

•Testable kT dependence •Sivers and orbital angular momentum?

•Parton Shadowing causes kT asymmetry?•Red Shift/Blue Shift effects in peripheral regions?

•ST (P kT) is T-odd and naively thought to vanish•FSI effects found by Brodsky et.al. that allow T-odd function to be non-zero

J=1/2

<LZ> = ?

TT

TTT

NTTT kPS

kPSkxfkxfSkxf

)(),(

2

1),(),,(

GeV 4.19at sXpp E704

Sivers Fcn from Back2Back AnalysisBoer and Vogelsang, Phys.Rev.D69:094025,2004, hep-ph/0312320

•Boer and Vogelsang find that this parton asymmetry will lead to an asymmetry in the distribution of back-to-back jets

•There should be more jets to the left (as in picture to the left).

•Should also be able to see this effect with fragments of jets, and not just with fully reconstructed jets

•Take some jet trigger particle along ST axis (either aligned or anti-aligned to ST)•Trigger doesn’t have to be a leading particle, but does have to be a good jet proxy•Then look at distribution of away side particles

ST

j1

j2

0

2

h

Unpolarized Results from Run03 p+p

anti-alignedaligned

•Asymmetry

•numerator is difference between aligned and anti-aligned dist’s, where aligned means trigger jet and spin in same hemisphere•denominator is simply unpolarized distribution

•On left are some theoretical guesses on expected magnitude of AN from Siver’s•On right are gamma-charged hadron dist’s from Run03 p+p

•2.25 GeV gamma’s as jet trigger, 0.6-4.0 GeV charged hadrons to map out jet shape•Dotted lines are schematic effect on away side dist due to Siver’s Fn (not to scale)

NA

Run03 -charged dn/dBoer and Vogelsang, PRD69:094025,2004

1/N

trig

dN

/d

(a

u)

Ng = Nd (E704)

Estimated AN from Run03 p+p

•Parametrized AN with , A=0.08, =0.8•Used this to calculate AN using unpolarized gamma-charged Run03 p+p dN/d

•Put asymmetry into distribution and then calculate AN

•On right shows statistical significance from Run03 p+p (0.35/pb).•Note that area around =0 can be used as a systematic check (it should be flat)•Also note that AN from Boer/Vogelsang paper is idealized, and the real signal will be reduced

parametrized AN

)(2222 25.025.0|| xxx eeAxe

-

Ng = Nd (E704)

AN Reduction 1: Polarization•Polarization P < 1 just reduces AN by P

NN

NNPPNNNPPN

NN

NNPAN

))(1())(1()(

•Besides that, most of the time the jet is not aligned exactly along the polarization axis, which means AN=AN(j1,) and also the polarization is reduced by cos(j1)

),()cos()( 111 jNjjN AdA

•We can make a simple (though wrong) estimate for this effect by calculating the average polarization from a jet spread of /2 around the polarization axis

9.0)cos(

4

4 1

4

4 11

j

jj

d

dP

ST

j1

j2

AN Reduction 2: Di-Hadron vs. Di-Jets

updownunpolarized

away side parton AN

di-hadrondi-jet

•Since we don’t reconstruct jets fully, we have to use di-hadron correlations to measure jet . This smears out the di-hadron AN relative to the di-jet AN, with smearing function g (assumed here to be a gaussian, with jT=0.35).

•The effect broadens and lowers (by just a little bit) the asymmetry

'))('()'())()((

'))('()'()())()(()(

dxdxxxxgxNxN

dxdxxxxgxAxNxNA

dijetdijet

dijetNdijetdijetdihad

N

Combined EffectsFull di-jet SiversReduced by lower <P>, di-hadron smearingRun03 p+p gamma-charged, 0.35/pb

•Given 0.35/pb of data, we should be able to get 1% statistical significance in AN using gamma-charged measurements of jet dphi•Expected raw AN could be 3.5%

•Could also be as low as 0.5%, or as large as 10%•x-dependence of Sivers?

•Effects from P=0.5, jet angle not aligned with transverse polarization, and fragmentation to dihadrons reduces raw AN to ~1.0%•Have not evaluated systematic errors yet (underlying event…)

process contribution to 0

Run05 ProspectsBLUE (AN = 6.24%) YELLOW (AN = 5.27%) (LR)

(TB)

(LR)

(TB)

PHYSICS Period

•Short Transverse Run•0.15/pb, P~50% FOM = P2L = 0.075

•Mostly Running Longitudinally in Run05•Transverse component seems to systematically have a radial component•3.8/pb, PY~10%, PB~5% FOM=0.166•Vertical component seems ~ 0.

SL

ST

Commisioning Period

Blue : 10.3% 3.9% Yellow : 21.5% 5.3%

M. Togawa

Prospects (Continued)

Full di-jet SiversReduced by lower <P>, di-hadron smearingRun03 p+p gamma-charged, 0.35/pb, P=0.5Run05 expectation, 3.8/pb, P~0.06Run06, 9.5/pb, P = 0.6

Run05Run06?

Radial vs Vertical Transverse RunningBoer and Vogelsang, PRD69:094025,2004

STST

1 = 01 = /2

)sin(||)sin(|| 22,1, TTN ppA

1 = 0 : )sin(|| 2, TN pA 1 = /2 : )cos(|||| 2,1, TTN ppA

21 ~

)(

TT pp

sin(

cos(1~

private communication, Boer and Vogelsang

Collins Effect?

0

PHENIX Acceptance

edge on view

Collins Effect averages to 0 in back-to-back d di-hadron measurement.

distribution of hadrons around away side hadron

N()/N0

R. Seidl, Belle Collaboration

•By Using di-Hadron Correlations at mid-rapidity, the gluon Sivers function can be explored

•First unambiguous test for gluon Sivers function•Inclusive AN could have other contributions•No contamination from Collins effect

•Different effects can smear out the asymmetry•Jet fragmentation•Normal Intrinsic kT

•Radiative (e.g., Sudakov) effects•In run05, we can approach limits of (and ignoring Sudakov effects)•In run06, ~8X better limits if we get 9.5/pb radial transverse run with P~60%•Can also look at Muon Arm Correlations…

Summary

Ng = Nd (E704)

Backup Slides

Data taken 0.15 pb-1 and 15 % beam polarization

Single Spin Asymmetry of 0 and Non-Identified Charged Hadrons at xF ~ 0 vs pT

h-

AN for both charged hadrons and neutral pions consistent with zero at midrapidity.

process contribution to 0

More statistics needed to map out pT x g/q dependence

A Prediction for Sivers at Mid-Rapidity

Umberto D’Alesio, RIKEN BNL SSA Workshop ‘05

•LO calculation•How valid is the framework?

•Would be nice to have a measurement that is less reliant on theoretical assumptions

process contribution to 0