# Presentation: 202723

## New Prospects for SSA Measurements in PHENIX:How can we separate out the various contributions to SSA at RHIC?

- Mickey Chiu
- University of Illinois at Urbana-Champaign
- RBRC SSA Workshop 2005

## Sivers Fcn from Back2Back Analysis

**Boer and Vogelsang, Phys.Rev.D69:094025,2004, hep-ph/0312320**

- Non-Zero Sivers function means that there is a left/right asymmetry in the kT of the partons in the nucleon
- For a positive Siver’s function, there will be net parton kT to the left (relative to direction of proton, assuming spin direction is up).
- 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

## Unpolarized Results from Run03 p+p

- anti-aligned

- aligned

- Asymmetry
- numerator is difference between aligned and anti-aligned  dist’s, where aligned means trigger jet and spin in same direction
- 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)

- Run03 -charged dn/d

- Boer and Vogelsang, PRD69:094025,2004

## 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).
- Assumed Poisson statistics
- 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

- -

## AN Reduction 1: Polarization

- Polarization P < 1 just reduces AN by P

- 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)

- 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

- ST

- j1

- j2

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

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

- up
- down
- unpolarized

- away side parton

- AN

- 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).
- 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

## x, pT coverage

- Vogelsang et al

- Boer-Vogelsang paper considers pT ~ 10 GeV jets
- x coverage here slightly lower
- gluon dominated region

## “Radial” Running Modes

- ST

- SL

- ST

- Could run in “radially” transverse mode
- Preferred mode for this analysis
- There could be a transverse component during longitudinal running
- Coexist with longitudinal running
- Have to worry about longitudinal asymmetry contribution

## Measuring Collins in p+p?

- Important test of Universality and Scale Evolution
- Collins needs to be known in p+p to get transversity from SSA
- p+p is much more complicated
- Intrinsic kT as well as radiative effects
- Many other diagrams
- t-channel “dominates” over s-channel
- At LO, this is a dilution of 10-3
- ~5% cos(2h) modulation at Belle becomes 0.5x10-4 modulation at RHIC
- unpolarized beam required: ~ 300/pb (200 GeV), 980/pb (500 GeV)

**~**

- e+e-

- p+p

- Belle
- cos(2h) method
- Seidl

- h

## Summary & Observations

- It could already be that transversity and Collins are not important in p+p, and that gluon Sivers = 0.
- Would be important to verify this independently with techniques that are a priori theoretically unambiguous
- Given 0.35/pb of data, we should be able to get 1% statistical significance in AN using gamma-charged measurements of jet 
- Expected raw AN could be 3.5%
- Could also be as low as 0.5%, or as large as 10%
- Effects from P=0.5, jet angle not aligned with transverse polarization, and fragmentation to dihadrons reduces raw AN to ~1.0%
- Can Collins be directly measured at RHIC?
- Contribution is whatever remains?

- Sivers

- Collins

- Higher Twist