douglas fields university of new mexico. direct vs. indirect measurement width of room tape measure...
TRANSCRIPT
Douglas Fields
University of New Mexico
Experimental Evidence for Partonic Orbital Angular
Momentum at RHIC
2Douglas Fields PacSPIN2011, Cairns, QLD, Australia
Direct vs. Indirect MeasurementWidth of room
Tape measureSpin ½ of proton
Stern-Gerlach experiment ΔΣ
DIS ΔG
DIS Q2 dependence, RHICBut, definition is unclear
Lg, Lq, Lg+q
Can one simply say L = ½ - ΔΣ - ΔG? No!Other methods…
Temperature of roomTape measure?
“Experimental Evidence”
6/21/2011
3Douglas Fields PacSPIN2011, Cairns, QLD, Australia
“Directly” measured quantity
Theory basis for implying indirect measurement
Limits on indirect measurement from experimental and theoretical uncertainties
6/21/2011
Template for Indirect Measurements
4Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
RHIC Spin
BRAHMS & PP2PP (p)
STAR (p)
PHENIX (p)
AGS
LINACBOOSTER
Pol. Proton Source500 mA, 300 ms
%uptoPol
GeVs
70
50050
Spin Rotators
Partial Siberian Snake
Siberian Snakes
200 MeV Polarimeter AGS Internal PolarimeterRf Dipoles
RHIC pC PolarimetersAbsolute Polarimeter (H jet)
2 1011 Pol. Protons / Bunche = 20 p mm mrad
5Douglas Fields PacSPIN2011, Cairns, QLD, Australia
Spin transport in Snake Magnets
Burkardt & Schnell Phys. Rev. D 74, 013002 (2006)Toy model for u-quarks in the valence region yields:
I.e., very weak (but nonzero) constraint on contributions of nonzero orbital angular momentum states to each quark flavor.
But the sum over flavors is not necessarily nonzero!
6/21/2011
Anomalous Magnetic Moment
5
1
91
5 Lx q x
6Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Single Spin Asymmetries (SSAs)
left
right
1 left rightN
left right
N NA
P N N
Fixed target pion SSAs (E704)
QCD prediction -> zero
7Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Early theoretical connection to OAM
There is a long history of trying to explain SSA’s with orbital motion. C.Boros, et al., PRL 70
p1751 (1993).Interaction with orbiting
valence quarks.
8Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
More Modern Approach
Sivers Effect
Collins Effect
Sivers Function (angular momentum)
Transversity
(structure)
Collins Function (Fragmentation)
1 1 1
1 ...left right
N T
left right
N NA f D δq H
P N N
9Douglas Fields PacSPIN2011, Cairns, QLD, Australia
• Nice conceptual picture from D. Sivers (talk given at UNM/RBRC Workshop on Parton Orbital Angular Momentum).
• Summary:– Sivers effect
requires orbital motion.
– Is process dependent.
6/21/2011
How can you get a net kT?
10Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Relation to GPDs• Leads to Asymmetric
parton densities.• Which leads to
preferential left-right interaction depending upon direction of OAM relative to spin direction.
• Which leads to left-right scattering depending upon the initial/final state interactions.
11Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Effect requires OAM
• So what do we see at RHIC?
14Douglas Fields PacSPIN2011, Cairns, QLD, Australia
xF scaling
Larger asymmetries at larger xF
Valence quark effects?
6/21/2011
Combined π0 forward
15Douglas Fields PacSPIN2011, Cairns, QLD, Australia
Charged mesons in muon arms.
6/21/2011
Charged meson SSAs (PHENIX forward)
17Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Combined charged meson SSAs (forward)
18Douglas Fields PacSPIN2011, Cairns, QLD, Australia
Seen as a limit on Gluon Sivers
6/21/2011
Charged/neutral meson SSAs (PHENIX central)
19Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Sivers functionsHave extracted Siver’s
functions for DIS.Can extend to include
RHIC data?What does it mean for
OAM?
20Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
p+p and p+C CNI Asymmetry
Prelim
inar
yRer5=0, Imr5=0no hadron spin-flip
p+p CNI (jet) p+C CNI
21Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Some (rather old) theoretical connection…
22Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Forward Neutron SSA~ 1800cm
10cm±3 mradDx magnetblue beam yellow beam
24Douglas Fields PacSPIN2011, Cairns, QLD, Australia
OPE fails to predict both the cross section and the asymmetry.
Also possible relation to OAM?
6/21/2011
Model prediction
B.Z. Kopeliovich et al.arXiv: 0807:1449
25Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Jet SSAs (STAR)
Boer & Vogelsang, PRD 69 (2004) 094025
jet
jet
AN pbeam (kT ST)
pbeam into page
Idea: directly measure kT by observing momentum imbalance of a pair of jets produced in p+p collision and attempt to measure if kT is correlated with incoming proton spin
Douglas Fields PacSPIN2011, Cairns, QLD, Australia
276/21/2011
What is the origin of jet kT?
Intrinsic (Confinement) kT 200 MeV/c
Breaks collinear factorization
Soft QCD radiation.
An example - J/ production.
Extra gluon kick
pTJ/ =1.80.230.16 GeV/c
Phys. Rev. Lett. 92, 051802, (2004).
28Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Origin of Jet kT
Di-hadron pT
kT
Net transverse momentum of a di-hadron pair in a factorization ansatz
• I = initial – fermi motion of the confined partons, initial-state gluon radiation… • S = soft – one or several soft gluons emitted• H = hard – final-state radiation (three-jet)…
Another Possibility:Spin-correlated transverse momentum – partonic
orbital angular momentumCan examine the helicity dependence of each term:
2
2
2
0?
0
0?
T initial
T soft
T hard
k
k
k
29Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Peripheral Collisions
Larger
Jet 1
Jet 2 w/<kT>=0
Jet 2
Integrate over b, leftwith some residual kT
2Tk
Net pT kick
Central Collisions
Smaller 2TkJet 2
Jet 1
Jet 2 w/<kT>=0
Like helicities: Beam momenta
Partonic orbital angular momentum leads to rotation of partons correlated with the proton spin vector
This leads to different pT imbalances (pT-kicks) of jet pairs in semiclassical models
Can be measured by measuring helicity dependence of <kT
2>
For details on jets see: Phys. Rev. D 74, 072002 (2006)
kT Asymmetry
30Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Partonic orbital angular momentum leads to rotation of partons correlated with the proton spin vector
This leads to different pT imbalances (pT-kicks) of jet pairs in semiclassical models
Can be measured by measuring helicity dependence of <kT
2>
Integrate over b, leftwith different residual kT
Net pT kick
Central Collisions
Larger 2TkJet 2
Jet 1
Jet 2 w/<kT>=0
2Tk
Peripheral Collisions
Smaller Jet 1
Jet 2 w/<kT>=0
Jet 2
Unlike helicities: Beam momenta
For details see: Phys. Rev. D 74, 072002 (2006)
kT Asymmetry
31Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Integrating over Impact Parameter
Drell-Yan pair production in polarized p+p collisions.(Meng Ta-Chung et al. Phys. Rev. D 1989)
kPR
kTR
kPR
Like Helicity
Un-like Helicity
kTR),(),()( 222 bpbpbp ttt
TPTRPRTRPRTPt kkkkbp cos);,,(22
2
Averaging over D(b):
Integrating over impact parameter b:
TRPRR
Rt
kkk
kp
22 9.1
32Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Measuring jet kT – di-hadron correlationIntra-jet pairs angular width : near jT
Inter-jet pairs angular width : far jT j Typ Tt
p Ta
p Ta^
p Tt^• Zero kT
33Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Measuring jet kT – di-hadron correlation
• Non-Zero kT
kT
Intra-jet pairs angular width : near jT
Inter-jet pairs angular width : far jT j Typ Tt
p Tap Ta^
p Tt^
k Ty
34Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Jet Kinematics
Tt
Ttt p
pz
ˆ
j Typ Tt
p Tap Ta^
p Tt^
k Ty
p Ttp out
For details, see PRD 74, 072002 (2006)
35Douglas Fields PacSPIN2011, Cairns, QLD, Australia
6/21/2011
Measuring jet kT – di-hadron correlationo- h± azimuthal correlation
Trigger on a particle, e.g. o, with transverse momentum pTt. Measure azimuthal angular distribution w.r.t. the azimuth of associated (charged) particle with transverse momentum pTa. The strong same and away side peaks in p-p collisions indicate di-jet origin from hard scattering partons.
36Douglas Fields PacSPIN2011, Cairns, QLD, Australia
Both jT and kT consistent with zero.
We now have higher statistics data which we will soon analyze.
6/21/2011
PHENIX Results
37Douglas Fields PacSPIN2011, Cairns, QLD, Australia
The first term can be related in the “Meng conjecture” to partonic transverse momentum:
where cij give the initial state weights and Wij give the impact parameter weighting.
6/21/2011
Interpretation
39Douglas Fields PacSPIN2011, Cairns, QLD, Australia
Since PYTHIA studies show that the final state studied here is dominated by gg scattering (~50%),
We can interpret this as a (rather weak) constraint on the gluon orbital angular momentum.
Consistent with previous (Sivers) measurements, and complimentary, since one naïvely needs no initial or final state interactions (although Sivers measures orbital in transversely polarized proton).
6/21/2011
Interpretation
40Douglas Fields PacSPIN2011, Cairns, QLD, Australia
We have an analysis tool – di-hadron azimuthal correlations - that allows us to measure kT.
We are studying this in helicity-sorted collisions to see if there is a spin-dependent, coherent component of kT.
In our kinematic range, we find jT RMS = -3 ± 8(stat) ± 5(syst) MeV, and kT RMS = -37 ± 88 ± 14(syst) MeV.
While this is consistent with other measurements related to gluon OAM, the connection to parton OAM needs theoretical guidance!
6/21/2011
kT Asymmetry Summary
41Douglas Fields PacSPIN2011, Cairns, QLD, Australia
Drell Yan:
Plans to look at intermediate mass range.Is that
sufficient?
6/21/2011
Future
ϒ-states
J/Ψ
Drell Yan
Ψ’
charm
bottom
42Douglas Fields PacSPIN2011, Cairns, QLD, Australia
For the non-zero DIS result, Q2=1GeV.
6/21/2011
Drell Yan
0.1 0.2 0.3 x
Siv
ers
Am
plit
ude
0
HERMES Sivers Results
Markus DiefenthalerDIS WorkshopMűnchen, April 2007
43Douglas Fields PacSPIN2011, Cairns, QLD, Australia
There are many direct measurements that have been/will be made at RHIC that have a connection to Partonic Orbital Angular Momentum.
Theoretical work is needed to relate these measurements to OAM on a more quantitative footing.
6/21/2011
Summary
Fit Function
• Blue – real (raw Δφ)• Red – Fit from above
equation
11/11/2009 45 Douglas Fields - OAM'09
2
22
22
2/3
2/
2/3
2/
21
2
sinexp
/22
cos
)0(1
out
Ta
outTaout
Taaway
awayo
mixreal
p
p
ppErfp
p
d
dN
d
dNCGausCC
d
dN
Nd
dN
Need <zt> and xh
11/11/2009 46 Douglas Fields - OAM'09
<k2T> asymmetry results are
not sensitive to this xh and <zt> values – only needed to set the scale.
^
xh and <zt> are determined through a combined analysis of the π° inclusive cross section and using jet fragmentation function measured in e+e- collisions. Ref. PRD 74, 072002 (2006)
^