Single spin asymmetries in hard scattering processes
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Transcript of Single spin asymmetries in hard scattering processes
Single spin asymmetries in hard scattering processes
Vrije Universiteit Amsterdam
Fetze Pijlman
•D. Boer•C.J. Bomhof•P.J. Mulders
in collaboration with
Partonic structure of hadrons9 / 14 May 2005, Trento
2Contents
• Factorization and universality
• Wilson lines in transverse momentum dependent parton distribution functions
• Experimental input
• Interpretation of the Sivers effect
3Factorized approach
• Cross-sections are usually expressed as:
• Questions: Which observables allow for a factorized description? Are the parton distributions universal?
• Recent claims on transverse momentum dependent factorization:(DY / SIDIS / e+ e- ) Factorization & universality
Ji, Ma, Yuan (2004) yes
Bomhof, Mulders, Pijlman (2004)
unclear due to gauge link
Pijlman (2004) looks problematic for some processes
Collins, Metz (2004) yes
Ji, Ma, Yuan (2005) probably yes
4Diagrammatic approach
• A field-theory-based approach to hard scattering processes in which hadrons are observed in initial and final state
• Extension of the parton model
• Valid in perturbation theory
• The diagrammatic approach does not make any assumption on factorization or universality
5Diagrammatic approach in semi-inclusive DIS
• Resummation of a class of interactions leads to a gauge link in parton distributions
• fragmentation functions also contain a gauge link (via minus infinity)
semi-inclusive DIS at leading order in M/Q
+ + + + ... =
Efremov Radyushkin, Theor.Math.Phys. 44 (1981) 774, Belitsky Ji, Yuan, Nucl.Phys.B656 (2003) 165, Boer, Mulders, F.P., Nucl.Phys. B667 (2003) 201
6Leading order cross-section of SIDIS
• The other interactions are believed to be suppressed; they need to be worked out and verified.
• At this order the cross-section appears to be factorized:
7The gauge link in Drell-Yan
Resumming the same class of interactions leads alsoto gauge links in the distribution functions
The result can also be written in a factorized form, but it contains different functions. What about universality??
8Universality relations
Transverse momentum dependent distribution functions• T-even/T-odd:• Matrix element T-odd:
Transverse momentum dependent fragmentation functions
• in semi-inclusive DIS via (-) infinity• in electron-positron annihilation via (+) infinity• there is no relation between the two (unless some higher
symmetry)
• problem for extracting transversity via Collins effect
Boer, Mulders, F.P., Nucl.Phys. B667 (2003) 201 Metz, Phys.Lett.B549 (2002) 139
9Higher order in SIDIS
Bomhof, Mulders, F.P., Phys.Lett.B596 (2004) 277
10Higher order in Drell-Yan
What is happening here?
Bomhof, Mulders, F.P., Phys.Lett.B596 (2004) 277
11Evolution of parton distributions
Semi-inclusive DIS
Real:
Virtual:
Drell-Yan
Real:
Virtual:
Is the evolution of (transverse momentum dependent) distribution functions is process-dependent?
not a peculiarity of QCD
also appears in QED
12Factorization
• For general tree-level diagrams the gauge link can be calculated with a straight-forward algorithm. The gauge link turns out to be diagram-dependent
• At first order the gauge link is not modified by virtual corrections
• Gauge links in distribution functions get modified under gluon radiation if there are two incoming hadrons (such as pp scattering)
• Gauge links in fragmentation functions get modified if there is an incoming hadron (like semi-inclusive DIS, but not in electron-positron annihilation)
F.P., hep-ph/0409332 & hep-ph/0411307
13How to tackle the problems experimentally?
• Measure the Sivers function , and Boer-Mulders function ( if zero ): no effect from gauge link, factorization & universality if nonzero: factorization & universality needs to be studied
• Compare T-odd distribution functions in different processes, is there a sign change or more?
• Compare transverse momentum dependent fragmentation functions
T-even and T-odd
• Measure in jet-production in electron-proton scattering
14 in jet-production
• Gauge link in the correlator introduces an extra vector, violating
the Lorentz invariance relations
• This extra vector leads at twist 3 to new functions for transversely polarized hadrons and unpolarized hadrons,
• Beam-spin asymmetry for the jet
Goeke, Metz, Pobylitsa, Polyakov, Phys.Lett.B567:27,2003Bacchetta, Mulders, F.P., Phys.Lett.B595:309 (2004)
Metz, Schlegel, Eur.Phys.J.A. 22:489 (2004)Goeke, Metz, Schlegel, hep-ph0504130
15Interpretation of the Sivers effect
Aharanov-Bohm effect
• L-R asymmetry• magnetic fields only
nonzero in solenoid, vector fields provide the effect
• topological effect (1, 2, etc)
The first QCD analogue of the Aharanov-Bohm effect?
Sivers effect
• L-R asymmetry• gluon-magnetic field only
nonzero in hadron, vector fields provide the effect
• topological effect (1, 5/4,etc)
16Summary
• Transverse momentum dependent distribution and fragmentation functions contain rich information on the structure of the nucleon and theoretical progress is being made
• Access to non-perturbative physics with interesting interpretations
• Gauge links are essential for understanding SSA’s (such as SIDIS, Drell-Yan, and also p+p -> + X)
• In general gauge loops can appear in processes and will probably be an essential ingredient in considerations on factorization
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