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Correlations in J / pair production as SPS versus DPS discriminators
Sergey Baranov
P.N.Leb edev Institute of Physics, Moscow, Russia

A.M.Snigirev and N.P. Zotov
SINP, Lomonosov Moscow State University, Russia

W. SchЁfer and A. Szczurek a
Institute of Nuclear Physics PAN, Cracow, Poland PLAN 1 2 3 4 . . . . OF THE TALK

Motivation Transverse momentum and azimuthal correlations Rapidity correlations Conclusions


Sergey Baranov,

QFTHEP'2013, St.Petersburg, Russia

MOTIVATION
Disentangling the single- and double-parton scattering

Encouraged by the recent LHCb measurent
R. Aaij et al. (LHCb Collab.,) Phys.Lett.B 707, 52 (2012)

The two mechanisms have comparable cross sections
A.V.Berezhnoy, A.K.Likho ded, A.V.Luchinsky, A.A.Novoselov, Phys. Rev. D 84, 094023 (2011) C.-H.Kom, A.Kulesza, W.J.Stirling, Phys. Rev. Lett. 107, 082002 (2011) S.P.Baranov, A.M.Snigirev, N.P.Zotov, Phys.Lett.B 705, 116 (2011)

DPS can b e discriminated from SPS if the kinematics is different we need a detailed understanding of the production prop erties with all of the p ossible contributions carefully taken into account
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Sergey Baranov,

QFTHEP'2013, St.Petersburg, Russia

THEORETICAL FRAMEWORK
Subpro cesses taken into consideration on the SPS side:
4 Leading-Order direct production O(s )

g + g J / + J /

6 Onium-onium (pseudodiffractive) scattering O(s ) (can mimic the DPS kinematics) one-gluon exchange g + g J / + J / + g + g two-gluon exchange g + g J / + J /

on the DPS side: Inclisuve direct J / production Inclisuve direct c production g + g J / + g g + g c +

Straightforward calculations, all done in the kt -factorization approach
S.P.Baranov,A.M.Snigirev,N.P.Zotov,A.Szczurek,W.SchЁfer (Phys. Rev. D 87, 034035 (2013)) a

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Sergey Baranov,

QFTHEP'2013, St.Petersburg, Russia

Examples of Feynman diagrams for SPS contributions

Direct gluon-gluon fusion (Leading-Order)

Onium-onium scattering: one-gluon exchange two-gluon exchange

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Sergey Baranov,

QFTHEP'2013, St.Petersburg, Russia

Double Parton interactions Two indep endent interactions A and B at a time: ^ ^ 1 2 AB DPS = ij (x1 , x1 ; b1 , b2 ; Q2 , Q )ik (x1 , x2 , Q2 ) ^A 2 i,j,k,l 2 2 вkl (x2 , x2 ; b1 -b, b2 -b; Q2 , Q )j l (x1 , x2 , Q ) ^B
вdx1 dx2 dx1 dx2 d2 b1 d2 b2 d2 b

with bi b eing the impact parameters and Q2 the probing scales
N. Paver, D. Treleani, Nuovo Cimento A 70, 215 (1982)

Further assumptions: Decoupling of longitudinal and transversal variables ij (x, x ; b1 , b2 ; Q2 , Q ) = Dij (x, x ; Q2 , Q )f (b1 )f (b2 ) Factorization of parton distributions Di j ( x, x ; Q 2 , Q ) = Fi ( x, Q 2 ) Fj ( x , Q ) Result in
AB DPS 2 2 A B S PS S PS eff 2 2

=

1 2



with



eff

= 14.5 mb

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Sergey Baranov,

QFTHEP'2013, St.Petersburg, Russia

NUMERICAL RESULTS
Transverse momentum correlations: fraction of the cross section after imp osing cuts pt (J / ) > p
t,min

Dashed = cuts on only one J / in the SPS production mode (equivalent to cuts on b oth J / 's if they were fully back-to-back) Dotted = square of dashed line (idealistic indep endent mode) Dash-dotted = cuts on b oth J / 's in the true DPS production mo de Solid line = cuts on b oth J / 's in the true SPS production mode

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Sergey Baranov,

QFTHEP'2013, St.Petersburg, Russia
t,min

Azimuthal angle correlations in SPS, effect of cuts pt (J / ) > p

DPS is always flat in SPS is very similar to DPS at pt,min < 4 Gev. At hihger pt the SPS production b ecomes correlated, but the cross section falls dramatically. Difficult to detect exp erimentally

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Sergey Baranov,

QFTHEP'2013, St.Petersburg, Russia

J / - J / rapidity difference

Dotted line = direct LO gluon-gluon fusion (SPS mo de) Dash-dotted = Double Parton Scattering Dashed line = one-gluon exchange (multiplied by 1000) Solid line = two-gluon exchange (multiplied by 25)

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Sergey Baranov,

QFTHEP'2013, St.Petersburg, Russia

Reasons for pseudo-diffractive processes to b e small ­ Two extra p owers of s ­ Larger average invariant mass M ( ) ­ Color: Direct g + g J / + J /
2 2 |tr{T a T c T c T b }|2 = |[(Nc - 1)/(4Nc )] ab |2 = [ 3 ab ]2 = 32/9

compared to Pseudodiffractive one- and two-gluon exchange [
1 ace 1 bde 2 d 4d ] 4 2 2 (Nc -1)(Nc -4)2 0 = = 216 290 0.1 2 5 256 Nc

­ Sp ecific prop erties of the one-gluon exchange amplitude (vanishes when any of the gluons b ecomes soft)

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Sergey Baranov,

QFTHEP'2013, St.Petersburg, Russia

CONCLUSIONS
A careful insp ection of all p ossible contributions shows that: ­ Total SPS and DPS rates are comparable in size ­ Transverse momentum and azimuthal correlations: SPS and DPS look similar at pt (J / ) < 4 GeV, they b ecome different at larger pt (J / ) but the cross sections fall dramatically ­ Rapidity difference y = y (1 ) - y (2 ): a very good discriminator; SPS is concenrated within |y | < 2, DPS spreads far b eyond |y | >> 2 ­ No contamination from onium-onium scattering

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