A PPROXIMATION OF J ET A XIS IN R APIDITY S EPARATED D IHADRON C ORRELATIONS Josh Perry Iowa State University PHENIX Collaboration 1

M EASUREMENT AT PHENIX Collide transversely polarized protons 2 Right Left = particle yield to the left versus particle yield to the right Experiment

A SYMMETRY S OURCES Sivers Effect Initial state effect Proton spin and parton transverse momentum are correlated 3 Right Left kT

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 A SYMMETRY S OURCES 4

5 Right Left Collins Effect (coupled with Transversity) Final state effect Final state quark leaves WITHOUT asymmetry but inherits proton polarization (through transversity)

A SYMMETRY S OURCES 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 6 Right Left

M Y R ESEARCH Measure the Collins Effect independent of Sivers Find a way to ignore initial state Sivers Effect 7 Collins 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

RHIC Relativistic Heavy Ion Collider 200 GeV CMS ~60% Polarization Data I am analyzing is from Run12 (Spring of 2012) 8

PHENIX (P IONEERING H IGH E NERGY N UCLEAR I NTERACTIONS E XPERIMENT ) 9 Central arms Forward arms

PHENIX (P IONEERING H IGH E NERGY N UCLEAR I NTERACTIONS E XPERIMENT ) 10 Central arms Forward arms MPC 3.1 < | η | < 3.9 Neutral Pions Central Arms | η | < 0.35 Neutral Pions Photons Electrons Etc.

PHENIX CRAYON DRAWING 11 PHENIX Central Arm Detectors PHENIX Forward EM Calorimeter (MPC)

H ARD S CATTERING 2 -> 2 scattering at leading order Conservation of momentum Outgoing partons back-to-back in CM frame 12 G G G

H ARD S CATTERING 2 -> 2 scattering at leading order Conservation of momentum Outgoing partons back-to-back in CM frame 13 G G G Higher x

H ARD S CATTERING 2 -> 2 scattering at leading order Conservation of momentum Outgoing partons back-to-back in CM frame 14 G G G Higher x Lower x

K INEMATIC S ELECTION 15 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.

T RANSVERSITY D ISTRIBUTION How often is a quark’s spin parallel to the proton’s spin direction? 16 u-quark d-quark Spin 1/2 hep-ph/070100v3

K INEMATIC S ELECTION 17 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!

K INEMATIC S ELECTION 18 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

K INEMATIC S ELECTION 19 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…

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 20 = P_hadron/P_parton p p P_reco/P_jet Forward pionCentral jet

‘F LIP AND S WAP ’ 21 G PHENIX Central Arm Detectors PHENIX Forward EM Calorimeter (MPC) fragmention (neutral pion)/ Reconstructed (central jet)/(P_reco/P_jet) direction

‘F LIP AND S WAP ’ Perform Lorentz boost to CM frame of central jet and forward neutral pion 22 G Reconstructed (central jet)/(P_reco/P_jet) direction forward jet direction (unobserved) fragmentation (neutral pion)/

‘F LIP AND S WAP ’ Flip reconstructed central jet direction around 180 degrees 23 G forward jet proxy direction fragmentation neutral pion

‘F LIP AND S WAP ’ 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’? 24 G forward jet proxy direction forward quark proxy direction hadron quark spin  Let’s check with simulation. fragmentation neutral pion

S IMULATION 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 ( 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 25

T RANSVERSITY 26 x ToyMC consistent with published distributions; transv. opposite for down quarks. hep-ph/070100v3 ToyMC Monte Carlo

F RAGMENTATION 27 z (DSS) u-quark fragmentation z gluon fragmentation ++ -- 00 ++ K- p n p n 00 00 Particle yield Pion+ Kaon+ Proton (DSS)

28 Check implementation by reproducing Anselmino et. al. results: C OLLINS F UNCTION ToyMC Monte Carlo Phys.Rev.D75:054032,2007 Large asymmetry at high z

29 Check implementation by reproducing Anselmino et. al. results: C OLLINS F UNCTION Phys.Rev.D75:054032,2007  z Actual fragmentation function sampled is now a 2D function

‘F LIP AND S WAP ’ 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? 30 Neutral pions forward quark proxy direction hadron quark spin  Using the Anselmino group’s global fit mean values Phi

‘F LIP AND S WAP ’ 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? 31 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

P ROJECTED 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 32

F UTURE 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 33

BACKUP End 34

MPC A SYMMETRY 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 35 x_F is similar to x

RHIC The tunnel 36

37

C OMPARISON TO D ATA 38 SOLID: Collins only DASHED: Collins+Sivers Simulation Plot courtesy of John Lajoie

P ARTILE Y IELD 39 ++ -- 00 00 00 ++ K- p npn Plot courtesy of John Lajoie

C OMPARISON OF PION ASYMMETRIES 40 parton pion spin π+π+ π-π- π0π0 E704: Left-right asymmetries A N for pions: ANAN xFxF pi0 FF is taken as all favored (based on quark content) shown averaged over all quark flavors  (radians) Black – pi+ Red – pi- Blue – pi0 Plot courtesy of John Lajoie

I DEAL CASE, PROBING T RANSVERSITY *C OLLINS Throw a polarized quark, watch it fragment 41

I DEAL CASE, PROBING T RANSVERSITY *C OLLINS Throw a polarized quark, watch it fragment Put a big particle detector in front of it 42

I DEAL CASE, PROBING T RANSVERSITY *C OLLINS 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 43