double helicity dependence of jet properties
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Double Helicity Dependence of Jet Properties
Douglas FieldsUniversity of New Mexico
Douglas Fields - BNL Nuclear Physics Seminar 2
But First…
11/17/2009
Second in series:http://panda.unm.edu/Fields/PartonOrbital.html
Douglas Fields - BNL Nuclear Physics Seminar 3
Workshop Wish List• Model calculation to estimate effects of TMD-moments evolution• Identify observables to isolate off-diagonal elements of q-g correlators• Bridge BFKL and Collins-Soper evolution equations• Model calculation to check transverse spin sum rule• Explain soft factor in TMD factorization (connections to low-x physics?)• Does integration of TMDs give back integrated PDFs?• Is there any definition of OAM for which TMD provide constraints?• Manifestly gauge-invariant definition of JM OAM decomposition• Gluon polarization on the lattice• What are the physical meanings to magnitude and sign of each TMD?• (transverse-spin) Drell-Yan measurements (with various hadron combinations)• Can we trust DSS? -> COMPASS data on fragmentation (multiplicities)• TMD fragmentation functions from e+e-• Polarize anti-protons• DDVCS
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Douglas Fields - BNL Nuclear Physics Seminar 4
What is (L or L)?
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In Defense of Semi-classical Arguments
• 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.
• I would like to just follow this conceptual picture to see where it may lead.
Douglas Fields - BNL Nuclear Physics Seminar
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Sivers Effect
No Sivers Effectwithout interactionwith absorber.
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Spatial asymmetries
P.H. Hägler, et. al.
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Leads to more formal approach…
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Meng Paper
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Douglas Fields - BNL Nuclear Physics Seminar
“Experiment B”Drell-Yan pair production in polarized p+p collisions.(Meng Ta-Chung et al. Phys. Rev. D 1989)
kTRkPR
kTR
kPR
Like Helicity
Un-like Helicity
),(),()( 222 bpbpbp ttt
TPTRPRTRPRTPt kkkkbp cos);,,(222
Averaging over D(b):
Integrating over impact parameter b:
TRPRR
Rt
kkk
kp
22 9.1
1511/17/2009
Mechanism for .
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2 0T initialk
Central Collisions
Smaller
Peripheral Collisions
Larger
Integrate over b, leftwith some residual kT
Measure jetPeripheral Collisions
Larger
2Tk
2Tk
2Tk
Same Helicity
Mechanism for .
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2 0T initialk
Peripheral Collisions
Smaller
Central Collisions
Larger
Integrate over b, leftwith some differentresidual kT
2Tk
2Tk
Opposite Helicity
Douglas Fields - BNL Nuclear Physics Seminar
1811/17/2009
From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989)
For a particular impact parameter, b, the average transverse momentum
Where, is the product of the Jacobian and the density profile of partons, and D(b) is the overlap region.
Total transverse momentum squared of partons
kTRkPR
Douglas Fields - BNL Nuclear Physics Seminar
1911/17/2009
From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989)
The constant terms in pt cancel and we have
We can now helicity separate:b
We can then average over the impact parameter
kTRkPR
kTR
kPR
Like Helicity
Un-like Helicity
Douglas Fields - BNL Nuclear Physics Seminar
2011/17/2009
From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989)
This paper makes the following assumptions:1) Uniform spherical density F(b,θP,θT)2) kPR~kTR~kR (no dependence on b, θP, θT.)
Then,
Evaluated numerically
Douglas Fields - BNL Nuclear Physics Seminar 2111/17/2009
Our Model
• Use different transverse density distributions to get pt kick from coherent spin-dependent motion:
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Our Model Results
• Basically independent of transverse density distribution.
• Ranges from 0.3 to 0.6 times the initial momentum.
• Very crude – would like suggestions to improve.
11/17/2009Douglas Fields - BNL Nuclear Physics
Seminar23
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/cPhys. Rev. Lett. 92, 051802, (2004).
Origin of Jet kT
Another Possibility:• Spin-correlated transverse momentum – partonic orbital angular
momentum• Can examine the helicity dependence of each term:
Di-hadron pT
kT
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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)…
2
2
2
0?
0
0?
T initial
T soft
T hard
k
k
k
• Zero kT
Measuring jet kT – di-hadron correlation
Intra-jet pairs angular width : near jT
Inter-jet pairs angular width : far jT
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j Typ Tt
p Ta
p Ta^
p Tt^
• Zero kT
Measuring jet kT – di-hadron correlation
• Non-Zero kT
kT
Intra-jet pairs angular width : near jT
Inter-jet pairs angular width : far jT
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j Typ Tt
p Tap Ta^
p Tt^
k Ty
For details, see PRD 74, 072002 (2006)
Jet Kinematics
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j Typ Tt
p Tap Ta^
p Tt^
k Ty
p Ttp out
Tt
Ttt p
pzˆ
Measuring jet kT – di-hadron correlationo- h± azimuthal correlation
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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.
PHENIX Detector
•Central Arms:||<0.35, =2900
Charged particle ID and tracking; photon ID. EM Calorimetry.Muon Arm:1.2<||<2.4Muon ID and tracking.
•Global DetectorsCollision triggerCollision vertex characterizationRelative luminosityLocal Polarimetry
•Philosophy:– High resolution at the cost of acceptance– High rate capable DAQ– Excellent trigger capability for rare events
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π° Identificaton
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π° → γ+γ
The pions are selected within Mπ◦ ±2.0σπ◦
Photon trigger:EMCal cluster energy > 1.4 GeV
The mass, Mπ◦, and the width, σπ◦ , are determined by fitting the di-photon mass spectrum with gaus+pol3.
Correlation Function
• Blue – real (raw Δφ)• Red – background (mixed events)
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Fit Function
• Blue – real (raw Δφ)• Red – Fit from above
equation
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2
22
22
2/3
2/
2/3
2/21
2sinexp
/22
cos
)0(1
out
Ta
outTaout
Taaway
awayo
mixreal
pp
ppErfp
pd
dN
ddN
CGausCCddN
NddN
Need <zt> and xh
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<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)
^
kT results for unpolarized case
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Preliminary Results• Take the difference Like – Unlike helicities• Normalized by beam polarizations• <j2
T > asymmetry (-3 ± 8(stat) ± 5(syst) MeV out of ~630 MeV unpolarized)• <k2
T > asymmetry also small (-37 ± 88(stat) ± 14(syst) MeV out of ~2.8 GeV unpolarized).
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• 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.
• Since PYTHIA studies show that the final state studied here is dominated by gg scattering (~50%),
• We can interpret this as a 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).
Interpretation
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Douglas Fields - BNL Nuclear Physics Seminar 37
Relating to Meng…
11/17/2009
Summary
• 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!
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