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Exclusive limits of DY processes QNP-2012, Ecole Polytechnique,April 19, 2012
Oleg Teryaev
JINR, Dubna
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Outline
Nucleon structure: inclusive vs exclusive (Very) simple theory for Lam-Tung relations Semi-exclusive pion-nucleon DY (COMPASS) and
pion DA Exclusive DY and GPDs BG-type duality in DY(@COMPASS&PANDA):
Sivers function and time-like formfactors
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QCD factorization mechanisms
40 years of QCD: Complicated processes without confinement theory – like pre-Darwinian biology – classification of MANY soft ingrediends (TMDs,GPDs – two faces of nucleon structure)
Various factorization mechanisms may not be completely independent (duality, matching,…)
Exclusivity for DY (TMD)pdf’s->GPDs
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Positivity for dilepton angular distribution
Angular distribution
Positivity of the matrix (= hadronic tensor in dilepton rest frame)
+ cubic – det M0> 0 1st line – Lam&Tung by SF method
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Kinematic azimuthal asymmetry from polar one by rotation (~kT )
Only polar
zasymmetry with respect to m! - azimuthal
angle appears with new
0
n m
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Matching with pQCD results (J. Collins, PRL 42,291,1979) Direct comparison: tan2 = (kT/Q)2
Off-shellness effects for colliding (anti)quarks – cancel in GI set
New ingredient – expression for Linear in kT
Saturates positivity constraint! Tests by J.-C. Peng,J.Roloff:often close to
saturation Extra probe of transverse momentum
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Generalized Lam-Tung relation (OT’05) Relation between coefficients (high
school math sufficient!)
Reduced to standard LT relation for transverse polarization ( =1)
LT - contains two very different inputs: kinematical asymmetry+transverse polarization
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Positivity domain with (G)LT relations
“Standard” LT
Longitudinal GLT
2
-2
1-1-3
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LT violation
Azimuthal asymmetries at fundamental level required
Privileged plane NLO-gluon emission BM-quark spins
Off-shell quarks (NLO,HT)
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Semi-Exclusive DY (large xF) - Pion participates through Distribution Amplitude (Light-cone WF)
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GI -> phase
Colour GI -> second diagram -> phase Unpolarized – Brandenburg, Brodsky,
Mueller(94) Longitudinally polarized –> SSA –
Brandenburg, Mueller, OT(95) Refined DA – Bakulev, Stefanis,OT(07)
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Pion DA Element of ERBL factorization Describes probability amplitude for
the (anti) quark carrying given light-cone momentum fraction
Interest recently increased due to BaBar (and expected BELLE) data for pion-photon transition formfactor-simplest exclusive process
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Pion DA
(Conservative) model of Bakulev, Mikhailov, Stefanis vs (3D) fit
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Comparison to holographic model
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Angular distributions – probes of DA
Unpolarized
Polarized
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Asymmetries vs data
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Polarization -> scanning of DA
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When transition to exclusivity happen?
Pion pdf ~(1-x)a
HT ~ (<1/x> f/Q)2 Transition: (1-x)a ~ (<1/x> f/Q)2
Strongly depends on pion pdf ( large x dependence) and DA
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From semi-to pure exclusive
Simplest case - pion FF(ERBL)
Change DA to GPD- exclusive electroproduction
Time from right to left- exclusive DY (DAxGPD)- talks of L. Szymanowski, J. Wagner
Second DA->GPD-another mechanism- OT’05 (problems with factorization -analytic continuation to be performed)
2,1
1,2 Ss s
s1
s2
1
2
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Properties of exclusive DY Polarization T->L Difference in sign between imaginary parts of
electroproduction and DY-> exclusive analog of famous Sivers function sign change
Final proton is not mandatory – small missing mass ~at rest for fixed target-possible at COMPASS
PP(NICA): TDA p->pp (to be compared with p->D)
Test of scaling Estimates for COMPASS ~ 103 events Exclusive limit with antiproton beam – relation
to time-like FF’s
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Role of subtractions (related to d term)
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SSA in DY TM integrated DY with one transverse
polarized beam – unique SSA – gluonic pole (Hammon, Schaefer, OT) – “factor 2” problem (Anikin,OT)
Related to the moment of Sivers function
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Sivers function and formfactors
Relation between Sivers function and AMM known on the level of matrix elements (Brodsky, Schmidt, Burkardt)
Phase? Duality for observables?
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DY and time-like FF’s DIS for x -> 1 relation to space-like
FF’s (Drell,Yan’70) Pdf ~(1-x)a (FF)2 ~(1/Q2)(a+1) DY(OT’08): 2 pdf’s enter BUT “duality interval” in x-space
~1/Q vs ~(1/Q)2 in DIS Same Q - dependence but –
different normalization
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BG/DYW type duality for DY SSA in exclusive limit Proton-antiproton DY – valence annihilation -
cross section is described by Dirac FF squared The same SSA due to interference of Dirac and
Pauli FF’s with a phase shift (Rekalo,Brodsky) Exclusive (large dilepton mass) limit; x -> 1 :
T(x,x)/q(x) -> Im F2/F1 (Q ~ 1 /(1-x))
Both directions – estimate of Sivers at large x and explanation of phases in FF’s
Compatible with models for Sivers ~(1-x)4-5
Possibilities; estiamate SCALE of Sivers Common fits of Sivers and FF’s?
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Conclusions
(Semi)exclusive limits of DY – interesting theoretically
Feasibility at various experiments remains to be studied
New relations to time-like FF’s