Transverse Single-Spin Asymmetries

Understanding the Proton:One of the fundamental building blocks of

ordinary matter!

Spin decomposition of proton still not understood. Expected contributions from parton spin and orbital angular momentum.

Transverse spin structure cannot be deduced from longitudinal (helicity) structure

• Spatial rotations and Lorentz boosts don’t commute!• Relationship between longitudinal and transverse structure provides information on relativistic nature of partons within proton.

Measurement of the Transverse Single-Spin Asymmetry for Mid-rapidity Production of Neutral Pions in Polarized p+p

Collisions at 200 GeV Center-of-Mass EnergyChristine A. AidalaColumbia University

Measurement of the Transverse Single-Spin Asymmetry for Mid-rapidity Neutral Pions

at PHENIX

Obtaining Spin-Dependent Yields, Relative Luminosity, and Polarization

Handling Background

Results

Studying Proton Spin Structure via Spin Asymmetries

Difference in spin-dependent cross sections for particle production as a fraction of the total cross section

At high energies, can understand particle production in terms of factorization in perturbative QCD.

Why at RHIC?The first and only polarized proton collider in

the world.

Various equipment to maintain and measure the polarization through acceleration and storage.

Advantages of a polarized hadron colliderHigh energy factorization, new probes (W’s)Polarized hadrons g+q, g+g collisions

left

right

Versus

Left

NA

LLA

21

gqLG 21

21gq

STLxqdx )(

21

21

Hard Scattering Process

2 2x P

1 1x P

s

qgqg

)(0

zDq

X

q(x1)

g(x2)

1P

2P

Fragmentation function (FF)

Partonic cross section

Partonic distribution function (pdf)

Left-right asymmetries up to ~30% observed in forward particle production from collisions of unpolarized with vertically polarized protons.

Mechanism remains unclear, but various ideas proposed…

Large asymmetries observed!

Tpp kpS

hTjetq kpS

q(x)

Sivers effect: kT-dependent pdf, collinear FF

Collins effect: collinear pdf, kT-dependent FF

Can’t be parallel Importance of kT!

L=1proton

scattered q that fragments

Transversity distribution

E704 at Fermilab4.19s GeV

pT = 0.5-2.0 GeV/c

Transverse-momentum-dependent factorization in pQCD

Collinear factorization—assumes parton momentum collinear to parent hadron.• pdf’s and FF’s integrated in partonic transverse momentum, kT

Keep kT dependence several possible new pdf’s and FF’s.

21 ppSAN

Invariant mass (GeV/c2)

rrAAA

bkgN

bkgN

N

1

00

LeftRightRightLeft

LeftRightRightLeftBeamN

NNNN

NNNN

PA 1

09.1,1

,,

,,

LLR

RNNRNN

PA

LeftLeft

LeftLeft

BeamLeftN

35.0||

2001-02 data—First polarized proton run at RHIC!15% average polarization0.15 pb-1

Measure particle production on one side of the beam for spin up vs. down

ORMeasure particle production to the left vs. right for a

single spin direction

Versus OR

June 2006

Mathematically exact. Must know relative luminosity (R) of bunches with spin up vs. down.

Excellent mathematical approximation for cross check. Uses equivalence of spin-up, beam-left and spin-down, beam-right. Luminosity effects cancel.

Obtain polarization for each beam fill by fill from RHIC proton-carbon polarimeter• Both beams polarized at RHIC. Consider spin states of one beam, average over spin states of other.

• 35% relative polarization uncertainty

• Calculate asymmetry of (signal + background) in the 0 mass integration region.• Calculate asymmetry of bkg around peak as estimate of asymmetry of bkg under peak.• Subtract asymmetries, weighted by fraction of background under peak (r).

0 Measure photon pairs in electromagnetic calorimeter (EMCal).Eliminate as much background as possible using EMCal cluster shower shape cut and charged track veto.

Beam-beam counters as min-bias trigger and to measure R • 3.0 < || < 3.9

• 2 azimuthal coverage: essential to avoid bias in transverse collisions, where azimuthal asymmetries expected!

Fill index

Polarization-corrected asymmetries obtained fill by fill, then averaged over all fills.

AN 0PRL 95, 202001 (2005)

xF~0.0

AN of mid-rapidity neutral pions consistent with zero within a few percent. No large asymmetry observed as for forward production.

Current measurement dominated by gluon-gluon and quark-gluon scattering.

• Collins effect diluted/suppressed

• Constrains gluon Sivers pdf(Bianconi + Radici, PRD 73, 034018 (2006))

Partonic contributions to pion production

left

right

Only for quarks!