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!
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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?
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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 !!! ->
Frank Ellinghaus, University of Colorado
RHIC @ BNL
STARSTAR
Relativistic Heavy Ion Collider also provides longitudinally and transverselypolarized proton beams at s = 200 GeV, 62.4 GeV, (500 GeV, 2008+)
Frank Ellinghaus, University of Colorado
PHENIX Detector
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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!
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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 ->
Frank Ellinghaus, University of Colorado
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) ->
Frank Ellinghaus, University of Colorado
• 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
Frank Ellinghaus, University of Colorado
+, –, 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
Frank Ellinghaus, University of Colorado
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!
Frank Ellinghaus, University of Colorado
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:
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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!
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
• 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
Frank Ellinghaus, University of Colorado
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)
Frank Ellinghaus, University of Colorado
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.
Frank Ellinghaus, University of Colorado
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
Frank Ellinghaus, University of Colorado
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).
Frank Ellinghaus, University of Colorado
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