Angular distributions in inclusive
and exclusive Drell-Yan processes
J-PARC, KEK, Tokai, Japan,January 25 2017
Oleg Teryaev
Joint Institute for Nuclear
ResearchDubna, Russia

Outline
Angular distributions of lepton pairs and densitymatrix
 Simple geometrical model of azimuthal angulardistributions
 Geometrical model and LHC dataSemi-exclusive DY and pion distribution amplitude
 Exclusive DY and GPDs

Generalizing Bloom-Gilman duality to DY processConclusions

Dilepton angular distribution
and virtual photon density matrix
Angular distribution
Positivity of the matrix (= hadronic
tensor in dilepton rest frame): OT’10+ cubic – det M0> 0
 1st line – Lam&Tung by SF methodKinematic azimuthal asymmetry
from polar one by rotation (~kT )Only polarn m
0zasymmetry with respect to m!
- azimuthal
angle appears with newGeneralized Lam-Tung relation(OT’05)
Relation between coefficients (high school
math sufficient!)

Reduced to standard LT relation fortransverse polarization ( =1) LT - contains two very different
inputs:kinematical asymmetry+transversepolarization
Positivity domain with (G)LTrelations
2“Standard” LT

Longitudinal GLT-3

1-1-2

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!

Extra probe of transverse momentum

Geometric model vs FNAL andLHC data on Z production
Interpretation of Angular Distributions of Z-boson Production at Colliders; JenChieh Peng,Wen-Chen Chang, Randall Evan McClellan, and Oleg Teryaev;
1511.09893 and PLB

Geometrical pictureNon-coplanarity – disbalance ofquark and hadron planes

CDF (1.96 TeV)
data
qq-72.5%
 qG-27.5%
 < cos 2ȹ1>=0.85±0.17
CMS (8 TeV) data
Necessity to accountfor
 qq - 41.5(1.6)%(reggeized quarks?!)
 qG - 58.5(1.6)%
 < cos 2ȹ1>=0.77
Semi-Exclusive DY (large xF) - Pion
participates through Distribution
Amplitude (Light-cone WF)

When transition to exclusivity
happen?
Pion pdf ~(1-x)a2
 HT ~ (<1/x> f/Q)
 Transition: (1-x)a ~ (<1/x> f/Q)2
 Strongly depends on pion pdf ( large xdependence) and DA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);Oganesian,Pimkov,Stefanis,OT(in progress)Pion DA(Conservative) model of Bakulev,Mikhailov, Stefanis vs (3D) fit

Angular distributions – probesof DA

UnpolarizedPolarized

Asymmetries vs E615 data

Polarization -> scanning of DA

Light-cone momenta inexclusive DY
Massive lepton pair – always requiresthat virtual photon carry both + and –light-cone momenta fractions
 Exclusive limit – limited number of finalhadrons (typically 1 or 2)
 Mechanism may be labeled by lightcone momenta of final hadrons: 0,1,2
may carry large LC moments fractions
Ways to exclusive DY:
classical“Classical”: 1 hadron in final state carrying sizable LC
momentum fraction: GPD*(π)DAMeson-nucleon DY only Version: 2 hadrons in final state carrying the same (+or -) LCM fraction and having low invariant mass
TDA*(π)DA Factorization is it the same as for DVMP? Note DVMP
problems and necessity of intrinsic TM
 Energy decrease (pion pole): small at COMPASS,
suggested for J-PARC
ExDY@J-PARC (Takahiro Sawada, Wen-ChenChang, Shunzo Kumano , Jen-Chieh Peng,
Shinya Sawada, Kazuhiro Tanaka), 1605.00364
and PRCNew ways to exclusive DY

2 hadrons in final state carrying
different (+ and -) LCM fractions andhaving large invariant mass: GPD*GPD

Also for pp
 No energy decrease: from NICA to LHC?


0,1,2 hadrons in final state carrying
small LCM fractions: transition FFs andBloom-Gilman-type duality in time-likeregion

Diagrammatics
to exclusive DY








Simplest case - pion FF(ERBL)
Change DA to GPD exclusive electroproduction
MDY~ M DVCS F pi g g*
Time from right to leftexclusive DY (DAxGPD)Berger,Diehl,Pire
Phase sign change: c.f. Sivers
for SIDIS/DY
Second DA->GPD-anothermechanism- OT’05
Longitudinal polarization
Problems with factorization analytic continuation may beused)

1s1

s2

s2

1,2

 s 2,1S

“Dispersive” factorizaton proof
Starting from (Pion)
form factor- 2 DA’s –nocuts ( x) 2F (  dx)
1 x
 1 DA -> GPD :Exclusive
mesons production:
Factorization = DR + Dsubtraction
 ( DVMP/DY) - +/M

 ( x)H ( x,  ) dx 1  x  dx x    iNext step: 2 DA’s -> 2 GPD’sDouble Diffraction
Exclusive double
diffractive DY process Analytic continuation:H ( x, 1 )H ( y,  2 )M  dxdyx  1  i  y   2 i

DIFFERS from direct
calculation – NOfactorization in physicalregion
H ( x, 1 ) H ( y, 2 )M   dxdy
( x  1 )( y  2 )  i

1s1



s

2

s2

1,2

 s 2,1S

Intrinsic TM for various
exclusive DY mechanisms
Collinear GPDs – typically too large
contribution to DVMP
 Intrinsic TM for meson WF (GK model) Neglected in GPD – more hope for“factorization” (product of ComptonFFs) in GPD*GPDKinematical regions
(Nucleon GPD)x(pion Compton FF) –very forward region(Nucleon GPD)x(pion Compton GPD) –all xF
How to select? – interference with EM(Nucleon FF)x(pion FF)

Interference effects
Interference with pure EM (FFxFF)
production of (C-even) lepton paircontains only real IR safe part of theamplitude and gives rise to charge
asymmetry (work in progress)
 Both for pion-nucleon and pp
 The way to extract GPDxGPD in centralregion from inclusive DYInterference of EM, GPD and TDA(for pion-nucleon DY) mechanisms(2 diagrams)(16 diagrams)

(8 diagrams)

Interference with EMmechanismCharge asymmetry (muon-antimuoninterchange) vs cm muon angle

(Anti)muon Lab frame
asymmetryExclusive large x limitConsider the dilepton carrying the mostof collision energy; small number ofhadrons in the central region;
correspond to large x of pdf’s
DIS – Bloom Gilman duality, Drell-YanWest relations

Is there any analog for DY?

Exclusive limit : DIS and spacelike (transitional and elastic) FFs


Small invariant mass

May be related to unitarity, analyticityand DR (OT’05)
 Relation between x ->1 and large Q2
 pdf ~ (FF)2
Exclusive limit of DY and timelike FFs (OT’12)(Proton-antiproton) DY at small s - Q2(pdf)2~ (Dirac) (FF)2Other beams – baryon number conservation – time-liketransition FFs
Tests similar to tests of BG@JLab?!

Comparing space-like andtime-like FFs“Duality intervals” - from mass to LC x-space
 DIS:~ pion mass
related scale Deviation offrom 1



DY:



Deviation offrom 1

DR: FFs from duality intervals


DIS:

DY:
 Proton-antiproton DY –same parton
distributionsP

Pion: a=1 supported !?

SL vs TLSame Q-dependenceNormalization –defined by distribution scale(~5) and duality intervals



Asymptotically coincide – scales close toQCDSR pion duality interval (rather than pionmass) similar (equal?!) for DIS and DY)!?

Sivers function andformfactors
Relation between Sivers function andAMM known on the level of matrix
elements (Brodsky, Schmidt, Burkardt)
 Phase (lensing function)?
 Duality for observables?
BG/DYW type duality for DY
SSA in exclusive limit
Proton-antiproton DY – valence annihilation –analyticity - cross section is described by
Dirac FF squared The SSA (analyticity?!) similar to twist 3 onedue to interference of Dirac and Pauli FF’s
with a phase shift (Rekalo,Brodsky)
 Exclusive large energy limit; x -> 1 :T(x,x)/q(x) -> Im F2/F1(Q2~M2(1-x))
 Both directions – estimate of Sivers at large xand explanation of phases in FF’sCONCLUSIONS/OUTLOOK
Angular asymmetries are related to virtual photon
density matrix and are the sensitive test of dynamics
 Geometric model – applicable for LHC/FNAL
 Semi-explusive DY – sensitive to pion DA
 Exclusive DY – GPD’s
 Interference and QCD induced charge asymmetry forlepton pairs production at LHC/COMPASS/J-PARC
 Generalization of BG/DYW for time-like (transition)
FF’s – natural physical interpretation of Sivers
function
NICA (Nuclotron based Ion Colider fAcility)– the flagship project in HEPof Joint Institute for Nuclear Research (JINR)(slides by A. Sorin)
Main targets of “NICA Complex”:- study of hot and dense baryonic matter- investigation of nucleon spin structure,polarization phenomena- development of accelerator facility for HEP @ JINR providing
intensive beams of relativistic ions from p to Au

polarized protons and deuterons
with energy up to√SNN = 11 GeV (Au79+ , L ~ 1032 cm-2 c-1)
√S =27 GeV (p, L ~ 1032 cm-2 c-1)
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Joint Institute for Nuclear Research, Dubna
nica.jinr.ru

NICAVolgariver

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NICA ComplexBaryonic Matter at Nuclotron (BM@N)
SPD (Spin Physics Detector)

MultiPurpose Detector(MPD)

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All basic parts of the NICA complex
are at the stages of fabrication or TDR approval.
The major milestones for the commissioning:

accelerator complex
start-up configuration
the design configuration– 2019– 2023

BM@NMPDSPD

the I stage
the II stage– 2017– 2019the I stage
upgraded (IT + end-cups)– 2019– 2023project is under preparation
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