NLO QCD analysis of single-diffractive dijet production at the

Tevatron

Michael Klasen (LPSC Grenoble)in collaboration with G. Kramer (U Hamburg)

April 20, 2010

Phys. Rev. D 80 (2009) 074006

April 20, 2010 Michael Klasen, LPSC Grenoble 2

Publications

With G. Kramer

PLB 508 (2001) 259: p 2 jets+n

EPJC 38 (2004) 39: p 2 jets+p

PRL 93 (2004) 232002: p 2 jets+p

JPG 31 (2005) 1391: New fact. scheme

EPJC 49 (2007) 957:p 2 jets+n

MPLA 23 (2008) 1885: Review (HERA data)

PRD 80 (2009) 074006: p p 2 jets+p

_ _

Motivation

Diffractive Higgs production:Clean central events, similar to vector-boson fusion

Easier identification of h than in incl. Higgs productionRelies on understanding of pomeron flux / parton densities

Factorization breaking in single-diffractive dijets:For photoproduction established only at NLODirect vs. resolved, x-dependence of S still under discussionFor hadroproduction established already at LOThorough NLO analysis was missing since Y2K !!

April 20, 2010 Michael Klasen, LPSC Grenoble 3

Definition of the SD / ND cross sections

Hadronic cross section:

Non-diffractive PDFs:CTEQ6L1 / CTEQ6.6M

Diffractive PDFs:H1 2006 fit A, BH1 2007 fit jets (no f.b.!)MY < 1.6 GeV

1.15 larger than ZEUS LPS

April 20, 2010 Michael Klasen, LPSC Grenoble 4

Experimental cuts by CDF

PRL 84 (2000) 5043:

s = 1800 GeVRun IC (95-96), RPS

|t| < 1 GeV2

0.035 < < 0.095

R = 0.7, Rsep = 1.3R

ET 1,2 > 7 (6.5) GeV

|| < 4.2

April 20, 2010 Michael Klasen, LPSC Grenoble 5

MK and G. Kramer, PLB 366 (1996) 385

Experimental cuts by CDF

PRL 84 (2000) 5043:

s = 1800 GeVRun IC (95-96), RPS

|t| < 1 GeV2

0.035 < < 0.095

R = 0.7, Rsep = 1.3R

ET 1,2 > 7 (6.5) GeV

|| < 4.2

PRL 88 (2002)

151802:

s = 630 and 1800 GeVRun IC (95-96) UA8

|t| < 0.2 GeV2

0.035 < < 0.095

R = 0.7, Rsep = 1.3R

ET > 10 GeV

|| < 4.2

April 20, 2010 Michael Klasen, LPSC Grenoble 6

_

MK and G. Kramer, PLB 366 (1996) 385

Observables derived from JJ(th)/NJJ(exp)

Parton momentum fraction in antiproton, pomeron: directly from jets, but in convolution

Ratio of SD to ND cross sections:

Integrated over ET 1,2 and 1,2 with xp fixed

Integrate also over t and ranges, assume similar Q2 ≈ ET2

Naive estimate of non-diffractive structure function: (t-channel gluon exchange)

GRV 98 LO, <Q2> = 75 GeV2 (<ET> ≈ 8.7 GeV)

Diffractive structure function:

Weak dependence on Use <> = 0.063

April 20, 2010 Michael Klasen, LPSC Grenoble 7

__

_

Average transverse-energy distribution

Non-diffractive (ND): Single-diffractive (SD):

April 20, 2010 Michael Klasen, LPSC Grenoble 8

<ET> ≈ 8.7 GeV_

Average rapidity distribution

Non-diffractive (ND): Single-diffractive (SD):

April 20, 2010 Michael Klasen, LPSC Grenoble 9

small xp_large xp

_

Parton momentum fraction in anti-proton

Ratio SD/ND: Suppression factor:

April 20, 2010 Michael Klasen, LPSC Grenoble 10

NLO≈LO,x-dependent

Parton momentum fraction in pomeron

Diffr. structure function:

Suppression factor:

April 20, 2010 Michael Klasen, LPSC Grenoble 11

<> = 0.063GRV98LO

<Q2>=75 GeV2

weaker -dependence

Average transverse-energy distribution

Non-diffractive (ND): Single-diffractive (SD):

April 20, 2010 Michael Klasen, LPSC Grenoble 12

Average rapidity distribution

Non-diffractive (ND): Single-diffractive (SD):

April 20, 2010 Michael Klasen, LPSC Grenoble 13

Perfe

ct!

Energy dependence of ratio SD/ND

April 20, 2010 Michael Klasen, LPSC Grenoble 14

Energy dependence of suppression factor

April 20, 2010 Michael Klasen, LPSC Grenoble 15

Energy dependence of diffr. structure fct.

April 20, 2010 Michael Klasen, LPSC Grenoble 16

<> = 0.063GRV98LO

<Q2>=75 GeV2

<> = 0.063GRV98LO

<Q2>=75 GeV2

Energy dependence of suppression factor

April 20, 2010 Michael Klasen, LPSC Grenoble 17

Pomeron momentum fraction in

antiproton

Published in PRL 88Agrees with PRL 84

data:

taken at =0.1

Weak -dependence <>=0.063 not badAlso observed in (N)LO H1 pomeron flux fact.

April 20, 2010 Michael Klasen, LPSC Grenoble 18

June 7, 2006 Michael Klasen, LPSC Grenoble 19

Two-Channel Eikonal ModelDouble Pomeron exchange:

Survival probability:

Opacity / optical density: Ki = 1

Kaidalov et al., EPJC 21 (2001) 521

Fit tot, del./dt to ISR, SppS, Tevatron data

Total cross section: Determines (gIP

pp)2 = 25 mbStarting scale s0 = 1 GeV2

Large distance physics: = 0.1

Elastic amplitude: Pomeron trajectory: (t) = 1 + ’ t + Small distance physics: ’ = 0.15 GeV-2

Pomeron vertex in b-space:B = B0/2 + ’ ln (s/s0)Elastic slope: B0 = 8 GeV-2

p N* transition probability: = 0.4

Survival probability: S ≈ 0.1Small abs./size: Val., large xp, small Large abs./size: Sea, small xp, small

ConclusionLO analysis by CDF was very crude:

Cone algorithm, equal ET cuts [in PRL 84 (2000) 5043]

Proton PDFs, Q2 dependence and systematic errors cancelIntegrations over and t don´t matterStructure function ≈ t-channel gluon exchange

Still, NLO analysis confirms main conclusions:SD/ND K-factors of 1.6 (630 GeV) and 1.35 (1800 GeV)Partially compensated by exact ratios of NLO cross sectionsSuppression factor is x-dependent, in particular at small xPredicted by LO two-channel eikonal model valence/seaLess dependence on , at NLO, 630 GeV, with H1 2007 jets

April 20, 2010 Michael Klasen, LPSC Grenoble 20