New Prospects for
Transverse Physics with
the PHENIX detector
JPS/DNP, Maui 2005
Mickey Chiu
University of Illinois at Urbana-Champaign
September 18, 2005
Sivers and Why it is Interesting
pp  X at s  19.4 GeV
J=1/2
E704
<LZ> = ?
1
S  ( P  kT )
f ( x, kT , ST )  f ( x, kT )  N f ( x, kT ) T
2
ST P kT

•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
Sivers Fcn from Back2Back Analysis
Boer 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
h
(either aligned or anti-aligned to ST)
•Trigger doesn’t have to be a leading particle,
j1
but does have to be a good jet proxy
•Then look at  distribution of away side
particles
2
0
ST
j2
Unpolarized Results from Run03 p+p
Boer and Vogelsang, PRD69:094025,2004
•Asymmetry
   
AN  
 
1/Ntrig dN/d (au)
Ng = Nd (E704)
Run03 -charged dn/d
anti-aligned
aligned
•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)
Estimated AN from Run03 p+p
Ng = Nd (E704)
parametrized AN
-
|x|
 x 0.5 2 2 2
 x 0.5 2 2 2
e
) , A=0.08, =0.8
•Parametrized AN with Axe (e
•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
AN Reduction 1: Polarization
•Polarization P < 1 just reduces AN by P



P( N   N  ) PN   (1  P)( N   N  )  PN   (1  P)( N   N  )
AN 



N N
N  N
•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)
AN ()   d j1 cos( j1 ) AN ( j1 , )
•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
 4
P

 

4
d j1 cos( j1 )
 4


4
d j1
 0.9
j1
ST
j2
AN Reduction 2: Di-Hadron vs. Di-Jets
AN
away side parton
up
down
unpolarized
di-hadron
di-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).
ANdihad (  ) 


dijet
(
N
(
x
)

N
(
x
))
A
dijet
N ( x ) g ( x ' ) ( x ' (   x )) dxdx'
 dijet


(
N
(
x
)

N
( x )) g ( x' ) ( x'(   x )) dxdx'
dijet
dijet

•The effect broadens and lowers (by just a little bit) the asymmetry
Combined Effects
Full di-jet Sivers
Reduced by lower <P>, di-hadron smearing
Run03 p+p gamma-charged, 0.35/pb
process contribution to 0
•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…)
Run05 Prospects
(LR) BLUE (AN = 6.24%)
(LR) YELLOW (AN = 5.27%)
Commisioning Period
PHYSICS Period
ST
M. Togawa
SL
Blue
(TB)
: 10.3%  3.9%
(TB)
Yellow : 21.5%  5.3%
•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.
Prospects (Continued)
Run05
Run06?
Full di-jet Sivers
Reduced by lower <P>, di-hadron smearing
Run03 p+p gamma-charged, 0.35/pb, P=0.5
Run05 expectation, 3.8/pb, P~0.06
Run06, 9.5/pb, P = 0.6
Radial vs Vertical Transverse Running
private communication, Boer and Vogelsang
1 = /2
Boer and Vogelsang, PRD69:094025,2004
1 = 0
ST
ST
AN | pT ,1 | sin(  ) | pT , 2 | sin( 2 )
1 = /2 :
1 = 0
:
AN | pT ,1 |  | pT , 2 | cos()
AN   | pT , 2 | sin( )
1  cos(
~
 sin( 
    (   )
pT 1 ~ pT 2
Collins Effect?
PHENIX Acceptance
R. Seidl, Belle Collaboration
0
N()/N0
edge on view
distribution of hadrons around away side hadron
Collins Effect averages to 0 in back-to-back d di-hadron measurement.
Summary
•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 Ng = Nd (E704)
•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…
Backup Slides
Single Spin Asymmetry of 0 and NonIdentified Charged Hadrons at xF ~ 0 vs pT
process contribution to 0
AN for both charged hadrons and neutral pions
consistent with zero at midrapidity.
h-
Data taken 0.15 pb-1 and 15 % beam polarization
More statistics needed to map
out pT x  g/q dependence
A Prediction for Sivers at Mid-Rapidity
•LO calculation
•How valid is the framework?
•Would be nice to have a measurement that is
less reliant on theoretical assumptions
Umberto D’Alesio, RIKEN BNL SSA Workshop ‘05
process contribution to 0