The Spin-Structure of the Nucleon from pp scattering at PHENIX

The Spin-Structure of the Nucleon from pp scattering at PHENIX

Frank Ellinghaus

University of Colorado

November 2007

SLAC, Stanford, USA

Frank Ellinghaus, University of Colorado

Nucleon Structure: Early Scattering experiments

Nucleons (protons and neutrons) make up the nucleus:

10-10m 10-14m

Atomic nucleus: Geiger, Marsden, Rutherford 1909-> Scattering of -particles off a gold foil

Size of nucleon? Point-like? Structure?

Used a nucleus (Helium-4) to discover the nucleus!Improve:• Use elementary probe, interact only electromagnetically -> electron• Resolve smaller distances -> use higher energies!


Electron-Nucleon Scattering

q : Momentum transfer

Form factor is fourier transformof charge density distribution

Form factor F(q) : difference toscattering from point charge

electronscattered electron

protonrecoiling proton


With increasing resolution (“high” electron energy), there is deviation from the point charge prediction!

Structure of the nucleon in the ‘50s

What’s inside?

Electron beam at Stanford linear accelerator (Hofstadter, 1955)

R. Hofstadter and R. W. McAllisterPhys. Rev. 98, 217 (1955)

1510r m


Deep-Inelastic Scattering (DIS)Crank up the electron energy once more:

Inclusive DIS• Detect only scattered lepton• 2 degrees of freedom

– E’, xB,Q2

– xB: Fraction of the (fast moving) nucleon momentum carried by quark

– Q2=-q2

electron

photon

protonprotondebris

scattered electron

Cross section for inclusive DIS:

22

2 4 2

4( , )B

B B

d

dx dQ xF

Qx Q

F2 parametrizes the unknown

nucleon structure


The structure function F2

Q2: measure of spatial resolution; scale ~1/Q

for Q2 = 1 GeV2, 0.2 fm

Nucleon is made of point-like particles (partons)

0.25Bx

Experiments started in the late 1960s at SLAC:(Friedman, Kendall, Taylor et al.)

F2 does not depend on the resolution (Q2)

Electron beam: 7-17 GeV


The structure Function F2 : A closer look

• “Parton Model”: F2 depends on the probability of hitting a quark with momentum fraction xB

• F2 depends (weakly) on Q2?

– At higher resolution ( higher Q2) we “see” the gluons

22 ( ) ( ( ) ( ))B q B B

q

F x e q x q x

q(xB) momentum distribution of quarks in the nucleon (-> Parton Distribution Function, PDF)

PDFs fitted using F2 at Q2=4U=u+cu, D=d+sd


Parton Distribution Functions (PDFs)

• From fits to F2 measurements, unpolarized PDFs

can be inferred

– q=u,d (s,c)

( ( ) ( )) 0.5B B B Bq

dx x q x q x

PDFs fitted using F2 at Q2=4U=u+cu, D=d+sd

• The total fraction of nucleon momentum carried by quarks:

– Gluons carry the other half!

( ), ( ), ( )B B Bq x q x g x

U=u+cu, D=d+sd


What about the Spin of the Nucleon?Spin of the nucleon is 1/2 (and quark spin is ½)

Quark spins

Gluon spins

Orbital angular momenta of quarks and gluons

NO, not that easy!• It’s a composite object made out of quarks (spin ½) and gluons (spin 1)• How do their spins add up to the nucleon spin?


e-p Spins antialigned

How can we measure the nucleon spin structure?

– Electron polarization transfers to virtual photons– Compare DIS cross sections with aligned and antialigned ep spins

e-p Spins aligned~

g1 (proton) > 0-> Larger cross section for anti-aligned ep Spins -> Higher probability for aligned quark-proton Spins

212( , )B

B

dg x Q

dx dQ

• Polarize electrons and nucleons; Experiments started in mid 1970s at SLAC (E-80, E-130, V.W. Hughes, C.Y. Prescott et al.)

G. Baum et al, PRL 51, 1983


Results from Inclusive Polarized DIS

• Analogous to unpolarized (F2) case, g1 can be used to fit polarized PDFs:

Polarized PDFs extracted from fits to g1(proton, deuteron)

• Result: Quarks carry only about 30 % of the nucleon spin (0.3)

• Gluon contribution g not well constrained due to small range in xB,Q2 (no polarized ep collider)

( ), ( ), ( )B B Bq x q x g x

…but polarized pp Collider !!! ->


RHIC @ BNL

STARSTAR

Relativistic Heavy Ion Collider also provides longitudinally and transverselypolarized proton beams at s = 200 GeV, 62.4 GeV, (500 GeV, 2008+)


PHENIX Detector


The PHENIX Detector for Spin Physics

Central Detector:

• detection– Electromagnetic Calorimeter

•

– Drift Chamber

– Ring Imaging Cherenkov Detector

Muon Arms:• J

– Muon ID/Muon Tracker ()•

– Electromagnetic Calorimeter (MPC)

Global Detectors:• Relative Luminosity

– Beam-Beam Counter (BBC)

– Zero-Degree Calorimeter (ZDC)

• Local Polarimetry - ZDC


PHENIX longitudinally polarized pp Runs

Year s [GeV] Recorded L Pol [%] FOM (P4L)

2003 (Run-3) 200 .35 pb-1 27 1.5 nb-1

2004 (Run-4) 200 .12 pb-1 40 3.3 nb-1

2005 (Run-5) 200 3.4 pb-1 49 200 nb-1

2006 (Run-6) 200 7.5 pb-1 62* 1100 nb-1

2006 (Run-6) 62.4 .10 pb-1 48* 5.3 nb-1

* Online value!


Cross section - pQCD applicabilityRUN5 200GeV -- 0 RUN6 62.4GeV -- 0

Using a set of unpolarized PDFs and fragmentation functions the crosssection can be compared to NLO pQCD calculations => pQCD seems at work, with large scale uncertainties at 62 GeV!

PRD76:051106,2007


G via direct measurement

2 2~LL gg qg qqA a a q G aG q

Access to polarized gluon distribution function via double helicity asymmetry in inclusive polarized pp scattering:

Invariant mass spectrum of 2 photons in EMCal(M=135MeV)

Measure from DISpQCD, fragmentation fcts.

0p p X

NRN

NRN

PPA

YBLL

1

L

LR Relative Luminosity R using

beam-beam counters


G=G(x),-G(x) excluded;

GRSV: Glueck et al., PRD 63 (2001)

0 ALL at 200GeV contd.

Run 5: Phys.Rev.D76:051106,2007

consistent with zero in this model ->


Model dependence of G

g integral between

GRSV

- 0

GRSV

- std

GS-C

0<x<1 0 0.4 1

0.02<x<0.3 0 0.25 0

• Measurement averages over certain x range• Shape of G(x) cannot be extracted -> Value for first moment model dependent

• Different ranges in x can be probed in 500 GeV (2009+) running (lower x) and in running at 62 GeV (larger x, also larger scale uncertainties) ->


• At fixed xT, cross-section is 2 orders of magnitude higher at 62.4GeV than at 200GeV• Probe different x scales by using different xT

• Significant result at high xT from small data set at 62.4 GeV (0.04 pb-1) when compared to 200 GeV data set (1.8pb-1)

2 TT

px

s

Scaling variable:

0 ALL at s=62.4 GeV


+, –, 0 and the sign of G

0

0 LL LL LLG A A A

0

0 LL LL LLG A A A

Especially in the region where qg scattering is dominant,the increasing contribution of d quarks leads to: Fraction of pion production

• Charged pions begin firing the RICH at pT~4.7 GeV, which is used for particle ID

• Charged pion result from Run 5 only, using Run 6 data stat. error will decrease by ~2.5

0

d d dD D D


RUN5 200GeV –

PHENIX Run-05 Preliminary

200 GeV

• Parameterization of flavor separated FFs (comparison to 0 ALL might yield info on s) needs further data from semi-inclusive DIS. • Precision measurements from B factories very helpful too….. (precise data only at Mz -> small lever arm in s)

• No eta fragmentation functions (FFs) in the literature!• First extraction of FFs from e+e- data and this (large range in pT) pp result ( gluon FFs) performed (method/code: de Florian, Sassot, Stratmann, PRD75, 2007)

• ALL can now be compared to theory, RUN-6 result in a few days!


Direct Photons at s=200 GeV

Run-5

At the end of the day all these (and the DIS, SIDIS) asymmetry data need to go into a “global” QCD fit in order to extract G!

q

g q-> small unc. from FFs-> better access to sign of G (q times G)

Theoretically clean “Golden Channel” is luminosity hungry…

Dominated by qg Compton:


Summary longitudinal Spin Structure

gq LLG 2

1

2

1

G

Quarks carry only about 30% (EMC 1988, ….) of the nucleon spin

Indirect measurements via fits to inclusive DIS data (small lever arm in x, ) and direct measurements by HERMES, COMPASS, SMC (small -> large scale uncertainties), and by PHENIX, STAR:Gluon contribution small in measured range

Contributions unknown: Only known quantitative way via “measurements” (DVCS etc.) of GPDs (Ji, 97) by H1, ZEUS, HERMES, JLabQualitative: Sivers Function

)( ,, gqgq JL

2Q2Q


longitudinally polarizedlongitudinally polarizedquarks and nucleonsquarks and nucleons

q(x): helicity differenceq(x): helicity difference

q1h

q1g q

1f

unpolarised quarksunpolarised quarksand nucleonsand nucleons

q(x): spin averagedq(x): spin averaged

transversely polarizedtransversely polarizedquarks and nucleonsquarks and nucleons

q(x): q(x): helicity fliphelicity flip

Transversity and friends

Transversity: The 3rd Twist-2 structure function…fundamental!

Friends: • Collins fragmentation function-> spin-dependent fragmentation of the transversely polarized quarks, teams up with transversity• Sivers distribution function -> transverse momentum distribution of unpolarized quarks in transversely polarized nucleon• ……

Sizeable asymmetries seen in ep (HERMES) and e+e- (Belle) and especially in pp!


Single Transverse Spin Asymmetries in pp

Left RightN

Left Right

d dA

d d

Large Single Spin Asymmetries in pp scattering at large xF at FERMILAB E704 sustain to = 200 GeV at STAR (Sivers?, Collins?, higher twist, ….)

AN at xF ~ 0 (and small pT) is consistent with zero

s=19.4 GeV, pT=0.5-2.0 GeV/c

s

s=200 GeV


• AN consistent with zero at mid-rapidity and small pT (see E704). • Mid-rapidity data at small pT sensitive to gluons, constrains magnitude of gluon Sivers function (Anselmino et al., PRD 74, 2006)• What happens if qq sets in (valence quarks) at high pT?

process contribution to 0, =0, s=200 GeV

PLB 603,173 (2004)p+p0+X at s=200 GeV/c2

PRL 95, 202001 (2005)

AN : h+/h-

AN of mid-rapidity 0 and h at s=200 GeV


The Muon Piston Calorimeter (MPC)

array of ≈ 220 PbWO4 crystals

PreAmp

APD Holder

PbWO4 Crystal

Large xF region for 0 can now be explored at PHENIX with recently installedforward calorimeters (Muon Piston calorimeter, MPC)


First result…

MPC (south) commissioned during 200 GeV transverse running in RUN 6 (early 2006)MPC ready in time for a few days of transverse data taking at 62.4 GeV

s=19.4 GeV, pT=0.5-2.0 GeV/cs=62.4 GeV

Very promising result from only a few days (!) of data taking. North MPC installed recently.


AN of J/ at s=200 GeV

• No theoretical predictions for J/ production yet • Asymmetry sensitive to sivers function in open charm production (Anselmino et al., PRD 70 2004)• What can measurements in J/ production tell us? How problematic is it that the production mechanism is not well known? Need help from theory…..

Quark Sivers = MaxGluon Sivers = 0

Quark Sivers = 0Gluon Sivers = Max


Future: Flavor separation of q and q

W a b a bL

a b a b

u(x )d(x ) d(x )u(x )A

u(x )d(x ) d(x )u(x )

W production:W production:

• Projections for RHIC assume that ∫Ldt ~980pb-1 can be delivered at √s=500 GeV between 2009 and 2012-> 300 pb-1 recorded. • Smearing for muons not taken into account.

Requires high luminosity at 500 GeV and a muon trigger upgrade (under construction).


Summary• Using longitudinally polarized pp scattering PHENIX adds a

dataset especially sensitive to the polarized gluon PDF for a global QCD fit to “all” DIS, SIDIS and pp data

• Measurements of transverse single spin asymmetries at forward and mid-rapidity serve as a valuable data set in the investigation of the transverse spin puzzle

• Future efforts are focused on the measurement of W at 500GeV (2009+) in order to investigate the flavor separated polarized quark PDFs

Documents

The Spin-Structure of the Nucleon from pp scattering at PHENIX