Measuring Transversity In P+P

Anselm Vossen

Hadrons

Quark

�� Hadrons

CIPANP 2012

2

The three leading order, collinear PDFs

Parton Distribution Functions

q(x)f1

q (x)

q(x) g1

q(x)

Tq(x)h1

q(x)chiral odd, poorly knownCannot be measured inclusivelyExtract from semi-inclusive measurements

unpolarized PDFquark with momentum x=pquark/pproton in a nucleon well known – unpolarized DIS

helicity PDFquark with spin parallel to the nucleon spin in a longitudinally polarized nucleon known – polarized DIS

transversity PDFquark with spin parallel to the nucleon spin in a transversely polarized nucleon

• We can connect observables to first order calculations on the lattice– First step: Tensor charge gT , can come from lattice and experiment– First order calculations need connection to experiment– Parton distributions on the light-cone compare moments

• Why p+p?: High xBj (forward), Q2, test understanding of p+p

Extracting Transversity from Data and the Lattice

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Chiral odd-cannot be measured inclusively

ACollins ∝∑𝑞𝑒𝑞

2 h1𝑞 (𝑥 )∗𝐻 1

⊥

∑𝑞𝑒𝑞2 𝑞1

𝑞 ( 𝑥 )𝐷𝑞h (𝑧 )

GlobalFit with FFs fromBelle

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Why is so hard to measure?

• Boost suppresses transverse spin vector• Semi-classic picture: Rotating charge

• Leptonic probe is ‘too fast’ to see transverse spin• To probe: knock out quark and use effect generated by angular

moment conservation

–

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Artru Model for Collins Fragmentation

π+ picks up L=-1 tocompensate for thepair S=1 and is emittedup.

u-quark absorbsphoton/gluon and flips it’s Spin.

Proton spin is pointing up!

String breaks anda dd-pair with spin1 is inserted.

A simple model to illustrate that spin-orbital angularmomentum coupling can lead to left right asymmetries in spin-dependent fragmentation:

L = -1

In Di-hadron measurements: Can have relative angular momentumAdvantage: Collinear framework applicable

6

Collins Effect In Jets

Aexp 2 N sin(C )dc

PBeamN

Φh

–pbeam

pbeamS⊥

pπ

PJET

jT

ΦS Look for spin dependent azimuthal distributions of charged pions inside the jets! First proposed by F. Yuan in Phys.Rev.Lett.100:032003.

Measure average weighted yield:

d dUU 1 AN sin(h s)

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More Correlation Measurements: of Pions in Jets

What about predictions, also for di-hadrons?

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The RHIC Polarized Collider

Versatility:• Polarized p+p Sqrt(s) collisions at 62.4 GeV, 200 GeV and 500 GeVRecent Spin Runs:• 2011 500 GeV, longitudinal at Phenix, transverse at STAR ~30 pb^-1 sampled• 2012 200 GeV, Phenix and STAR, transverse ~20 pb^-1 sampled (at STAR: ~x10 statistics)

ANDY/ BRAHMS

STAR

PHENIX

AGS

LINAC BOOSTERPol. H- Source

Spin Rotators(longitudinal polarization)

Siberian Snakes

200 MeV Polarimeter

RHIC pC PolarimetersAbsolute Polarimeter (H jet)

AGS pC PolarimeterStrong AGS Snake

Helical Partial Siberian Snake

Spin Rotators(longitudinal polarization)

Siberian Snakes

E-Lens and Spin Flipper

EBIS

See http://www.phy.bnl.gov/cnipol/fills/

Full azimuth spanned with nearly contiguous electromagnetic calorimetry from -1<h<4

approaching full acceptance detectorPID (Barrel) with dE/dx, in the future: ToF pi/K separation up to 1.9 GeV 9

• Central Region (-1<eta<1)• Identified Pions, eta• Jets

• Endcap (1<eta<2)• Pi0, eta, (some) jets

• FMS (2<eta<4)• Pi0, eta

FMS

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First Step: Mid-rapidity Collins analysis

Run 12 Projections

z: fractional momentum of the hadronjT: transverse momentum from the jet-axis

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b

X

1f p

a

X

1hSp,

Using Hadron Pairs:

Interference Fragmentation Function in p-p

c

0 /

H

D0 /

( ) sin( )S R UT S RA

S

R-S

: Angle between polarisation vector and event plane

𝐴𝑈𝑇 ∝h1 ∙𝐻1¿

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Transversity from di-Hadron SSA

UTUT

UU

A

Physics asymmetry

IFF + Di-hadron FFmeasured in e+e-

Transversityto be extracted

Hard scatteringcross sectionfrom pQCD

Unpolarized quark distribution Known from DIS

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Results or IFF at (z1x m1) Binning

A. V.. et. al, PRL 107, 072004(2011)

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NEW: STAR shows significant Signal!

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Decay Angle Distributions

17Additional precision data from this years run+ increased kinematic reach

+/-+/-

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Summary & Outlook

• First signal of transversity in p+p collisions in single and di-hadron Correlations observed

• p+p: high scale, high xBj

• 2012 Data will allow precision measurement, comparison with SIDIS (e.g. factorization in Collins)

• Future measurements– 0 combinations– (more) forward measurements– Additional modulations of cross-section

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Backup

Belle detectorKEKB

• KEK-B: asymmetric e+ (3.5 GeV) e- (8 GeV) collider:-√s = 10.58 GeV, e+e-U(4S)BB-√s = 10.52 GeV, e+e- qqbar (u,d,s,c) ‘continuum’

• ideal detector for high precision measurements: - tracking acceptance θ [17 °;150°]: Azimuthally symmetric - particle identification (PID): dE/dx, Cherenkov, ToF, EMcal, MuID• Available data:

~1.8 *109 events at 10.58 GeV, ~220 *106 events at 10.52 GeV

21/18

Measurements of Fragmentation Functions in e+e- at Belle

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q1

quark-1 spin

Interference effect in e+e-

quark fragmentation will lead to azimuthalasymmetries in di-hadron correlation measurements!

Experimental requirements: Small asymmetries very large data sample! Good particle ID to high momenta. Hermetic detector

Measuring transverse spin dependent di-Hadron CorrelationsIn unpolarized e+e- Annihilation into Quarks

electron

positron

q2

quark-2 spin

( )

z1,2 relative pion pair momenta

z2 z1

( )

21221111 m,zHm,zHA cos

1

2

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Results or IFF at (z1x m1) Binning

AV et. al, PRL 107, 072004(2011)

Origin of Single Spin Asymmetries

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),(

)(ˆ)(),( ,

21

3

2,121

3

. Thqlkji

Tqi pzFFdxdx

qqqqdxGkxq

dzdxdxXppd

lk

fragmentationfunction

pQCD Proton Structure

small spindependence

Can initial and/or final state effects generate large transverse spin

asymmetries? (AN ~10-1)

h

X’

q

fb

fa

σ

FFq

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Transverse Spin Structure FunctionsTransversity correlation between transverse proton spin and quark spin

Sp– Sq coupling

xqxqxq

),()( 221

kzHxq

Collins FFQuark transversespin distribution

J. C. Collins, Nucl. Phys. B396, 161 (1993)

• One of three collinear parton distribution functions needed to describe the spin structure of the nucleon at leading order

• Chiral odd quantity: needs chiral odd partner-> FF• Inaccessible in inclusive measurements: poorly known

Anselmino et. al., PRD75 054032

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Di-Hadron Correlations

1 2

1 2

1 2

p+p c.m.s. = lab frame

, : momenta of protons

, : momenta of hadrons

( ) / 2

: proton spin orientation

A B

h h

C h h

C h h

B

P P

P P

P P P

R P P

S

1hP

2hP

100 GeVAP

100 GeVBP

CP

BS

pp hhX

1 2hadron plane: ,

scattering plane: ,

h h

C B

P P

P P

: from scattering plane to hadron planeR : from polarization vector

to scattering plane S

2 CR

Bacchetta and Radici, PRD70, 094032 (2004)

( ) sin( )S R UT S RA

1 1UTA h H

: Angle between polarisation vector and event plane