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APPROXIMATION OF JET AXIS IN RAPIDITY SEPARATED DIHADRON CORRELATIONSJosh PerryIowa State UniversityPHENIX Collaboration

MEASUREMENT AT PHENIX Collide transversely polarized protons

2

Right

Left PA

RL

RLN

1

= particle yield to the left versus particle yield to the right

NA

Experiment

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ASYMMETRY SOURCES Sivers Effect

Initial state effect Proton spin and parton transverse momentum

are correlated

Right

Left

kT

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Sivers Effect Initial state effect Proton spin and parton transverse momentum are correlated

Final state quark momentum leaves asymmetrically Results in final state Left/Right asymmetry of fragmentation

hadrons

Right

Left

ASYMMETRY SOURCES

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ASYMMETRY SOURCES

Right

Left

Collins Effect (coupled with Transversity) Final state effect Final state quark leaves WITHOUT asymmetry but

inherits proton polarization (through transversity)

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ASYMMETRY SOURCES Collins Effect (coupled with Transversity)

Final state effect Final state quark leaves WITHOUT asymmetry but inherits proton

polarization (through transversity)

Quark spin and quark fragmentation shape are correlated Results in a final state Left/Right asymmetry of fragmentation hadrons

Right

Left

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MY RESEARCH Measure the Collins Effect independent of

Sivers Find a way to ignore initial state Sivers EffectCollins and Sivers (possibly

more)Collins alone, no Sivers

?

We’re going to need a place to collide protons and detect particle showers exiting the collision...

MPC Single Cluster Asymmetry

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RHIC Relativistic Heavy Ion Collider

200 GeV CMS ~60% Polarization Data I am analyzing is from Run12 (Spring of 2012)

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PHENIX (PIONEERING HIGH ENERGY NUCLEAR INTERACTIONS EXPERIMENT)

Central arms Forward arms

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PHENIX (PIONEERING HIGH ENERGY NUCLEAR INTERACTIONS EXPERIMENT)

Central arms Forward arms

MPC 3.1 < | η | < 3.9• Neutral Pions

Central Arms | η | < 0.35•Neutral Pions• Photons•Electrons•Etc.

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PHENIX CRAYON DRAWINGPHENIX Central Arm Detectors

PHENIX Forward EM Calorimeter (MPC)

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HARD SCATTERING 2 -> 2 scattering at leading order

Conservation of momentum Outgoing partons back-to-back in CM frame

G Gq q

G q

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HARD SCATTERING 2 -> 2 scattering at leading order

Conservation of momentum Outgoing partons back-to-back in CM frame

G Gq q

GHigher x

q

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HARD SCATTERING 2 -> 2 scattering at leading order

Conservation of momentum Outgoing partons back-to-back in CM frame

G Gq q

GHigher x

Lower xq

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KINEMATIC SELECTION

G

PHENIX Central Arm Detectors

PHENIX Forward EM Calorimeter (MPC)

Automatic bias of parton species from our detector positions (and kinematic selection)The goal is Collins: now we just need transversely polarized quarks so we can detect the fragmentation products.

q

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TRANSVERSITY DISTRIBUTION How often is a quark’s spin parallel to the

proton’s spin direction?

u-quark

d-quark

parallelantiparallel qqq

Spin 1/2

hep-ph/070100v3

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KINEMATIC SELECTION

G

PHENIX Central Arm Detectors

PHENIX Forward EM Calorimeter (MPC)

We now have set up a bias for mostly transversely polarized quarks to be headed toward our detector!

q

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KINEMATIC SELECTION

G

PHENIX Central Arm Detectors

PHENIX Forward EM Calorimeter (MPC)fragmention neutral pion

fragmention hadrons

After the collision, the forward-going quark and central-going gluon fragment into particle showers

q

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q

KINEMATIC SELECTION

G

PHENIX Central Arm Detectors

PHENIX Forward EM Calorimeter (MPC)fragmention neutral pion

Sum up central particle shower constituent momenta to reconstruct central gluon (jet) momentum.FastJet Anti-K_T algorithm applied

Reconstructed central jet direction

PHENIX does not have hadronic calorimetery, jet energy goes missing…

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P_RECO/P_JET CORRECTION Apply a momentum correction based on the

sampled longitudinal momentum fraction during fragmentation i.e.; momentum of the reconstructed jet divided by

the momentum of the jet in monte carlo

<z> = P_hadron/P_parton

p p

<z> P_reco/P_jetForward pion Central jet

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q

‘FLIP AND SWAP’

G

PHENIX Central Arm Detectors

PHENIX Forward EM Calorimeter (MPC)fragmention (neutral pion)/<z>

Reconstructed (central jet)/(P_reco/P_jet) direction

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q

‘FLIP AND SWAP’ Perform Lorentz boost to CM frame of central

jet and forward neutral pion

G

Reconstructed (central jet)/(P_reco/P_jet) direction

forward jet direction (unobserved)

fragmentation (neutral pion)/<z>

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q

‘FLIP AND SWAP’ Flip reconstructed central jet direction

around 180 degrees

G

forward jet proxy direction

fragmentation neutral pion

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q

‘FLIP AND SWAP’ Flip reconstructed central jet direction

around 180 degrees Measure the hadron’s direction relative

to the forward jet (proxy) direction (and projected spin axis)

Asymmetry seen in fragmentation? Too much smearing due to ‘Flip and

Swap’?G

forward jet proxy direction

forward quark proxy direction

hadronquark spin

f

Let’s check with simulation.

fragmentation neutral pion

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SIMULATION No simulation existed to do what we needed

proton-proton collisions Transversity to give final state quarks a polarization Collins fragmentation

ToyMC Monte Carlo (simulation) Created at Iowa State University

Now available publically as TPPMC (http://code.google.com/p/tppmc/)

PYTHIA simulation package Performs hard scattering

Using Anselmino et al. global fits from HERMES and COMPASS fixed target data Initial state transversity weighting

Gives final state quarks polarization Independent fragmentation model

Applies Collins Effect to fragmentation Sivers final state event weighting is also available

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TRANSVERSITY

x

ToyMC consistent with published distributions; transv. opposite for down quarks.

hep-

ph/0

7010

0v3

ToyM

C M

onte

Car

lo

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FRAGMENTATION

z

(DSS)

u-quark fragmentation

z

gluon fragmentation

p+ p- p0

K+K- p np nK0 K0

Particle yield

Pion+Kaon+Proton(DSS)

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• Check implementation by reproducing Anselmino et. al. results:

COLLINS FUNCTION

ToyM

C M

onte

Car

lo

Phys

.Rev

.D75

:054

032,

2007

Large asymmetry at high z

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• Check implementation by reproducing Anselmino et. al. results:

COLLINS FUNCTION

Phys

.Rev

.D75

:054

032,

2007

fz

Actual fragmentation function sampled is now a 2D function

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‘FLIP AND SWAP’ SIMULATION RESULTS Use the ToyMC Monte Carlo Perform the ‘Flip and Swap’ procedure Collins effect seen? Sin(phi) distribution of

fragmentation hadrons about quark direction?

Neutral pionsforward quark proxy direction

hadronquark spin

f

Using the Anselmino group’s global fit mean values

Phi

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‘FLIP AND SWAP’ SIMULATION RESULTS Use the ToyMC Monte Carlo Perform the ‘Flip and Swap’ procedure Collins effect seen? Sin(phi) distribution of

fragmentation hadrons about quark direction?

Neutral pions

Using the Anselmino group’s global fit mean values

Phi

Large smearing Jet axis reconstruction ‘Flip and Swap’

Large asymmetry at high z

The asymmtery is large enough to be seen through the smearing

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PROJECTED RESOLUTION Simulation parameters

Statistical yield based on Run8 ‘proof of principle’ data analysis

Error bars are statistical errors for 33 pb^-1 (Run12+13) Taking into account PHENIX uptime, z vertex cut, etc.

Solid and dashed lines: 100% and 25% Collins contributions

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FUTURE Run 12 data currently being analyzed Central arm + forward MPC triggered events

Sampled: 17.6 pb-1

Collected: 215 million 58% polarization More statistics than projected

Lower central arm trigger threshold between Run8 and Run12 The ‘Flip and Swap’ method is viable

Collins can be measured at PHENIX The MPC-EX detector is being built at PHENIX to

enhance the MPC Allows measurement of direct photons for direct access to

Sivers A ‘full picture’ of Collins and Sivers in pp collisions is in our

future

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BACKUP End

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MPC ASYMMETRY Run8 (2008) transverse spin MPC data Instead of a fancy A*sin(phi) this compares

left and right halves Effectively A*sin(phi) with only two phi bins

x_F is similar to x

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RHIC The tunnel

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COMPARISON TO DATA

SOLID: Collins onlyDASHED: Collins+Sivers

Simulation

Simulation

Plot courtesy of John Lajoie

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PARTILE YIELD

p+ p- p0

K0 K0 K+ K- p np n

Plot courtesy of John Lajoie

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COMPARISON OF PION ASYMMETRIESparton

pionspin

π+

π-

π0

E704: Left-right asymmetries AN for pions:

AN

xF

• pi0 FF is taken as all favored (based on quark content)• shown averaged over all quark flavors

f (radians)

Black – pi+Red – pi-Blue – pi0

Plot courtesy of John Lajoie

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IDEAL CASE, PROBING TRANSVERSITY*COLLINS Throw a polarized quark,

watch it fragment

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IDEAL CASE, PROBING TRANSVERSITY*COLLINS Throw a polarized quark,

watch it fragment Put a big particle detector in

front of it

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IDEAL CASE, PROBING TRANSVERSITY*COLLINS Throw a polarized quark,

watch it fragment Put a big particle detector in

front of it … but of course we need a

quark from a proton At high x Polarized quark No gluons