Predictions of Diffractive Cross Sections in Proton-Proton Collisions

Konstantin Goulianos*

The Rockefeller University

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CONTENTS

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For details on the phenomenology of the predictions see:

DIFFRACTION 2010“Diffractive and total pp cross sections at the LHC and beyond” (KG)http://link.aip.org/link/doi/10.1063/1.3601406

This talk: an implementation of these cross sections in PYTHIA8.

INTRODUCTION The RENORM (renormalization model) soft pp cross sections previously used

in MBR (Minimum Bias Rockefeller) simulation are adapted to PYTHIA8. MBR was successful at Fermilab in fixed target and collider experiments.

RENORM predictions are based on a parton-model approach in which diffraction is derived from inclusive PDFs and color factors.

Diffractive cross sections and final states are both predicted: Cross sections vs gap width or vs forward momentum loss of proton(s):

Absolute normalization! Hadronization of dissociated proton:

A (non-perturbative) “quark string” is introduced and tuned to reproduce the MBR multiplicity and pT distributions.

dN/d, pT, and particle ID: new in this PYTHIA8 implementation (the original MBR simulation produced only ± and 0).

Unique unitarization based on a saturated “glue-ball” exchange. Total Cross section ~ln2s based on a glue-ball-like saturated-exchange.

Immune to eikonaalization-model dependences.

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STUDIES OF DIFFRACTION IN QCD

Diffractive

Colorless vacuum exchange

large-gap signature

Non-diffractive

color-exchange gaps exponentially suppressed

POMERON

Goal: probe the QCD nature of the diffractive exchange

rapidity gapIncident hadrons acquire colorand break upart

CONFINEMENT

Incident hadrons retain their quantum numbersremaining colorless

p p p p

p

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DEFINITIONS

MX

dN/d

,t

p’Rap-gap=-ln

0s

eEΣξ

iηtower-iT

all1iCAL

s

M2Xξ1- Lx

ln s

22 M

1

dM

dσ

ξ

1

dξ

dσconstant

Δηd

dσ

0t

ln Mx2

ln s

since no radiation no price paid for increasingdiffractive gap size

pp

MX

pp’

SINGLE DIFFRACTION

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DIFFRACTION AT CDF

Single Diffraction orSingle Dissociation

Double Diffraction or Double Dissociation

Double Pom. Exchange orCentral Dissociation

Single + DoubleDiffraction (SDD)

SD DD DPE /CD SDD

Elastic scattering Total cross sectionT=Im fel (t=0)

OPTICALTHEOREM

gap

JJ, b, J/W ppJJ…ee… exclusive

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Factor of ~8 (~5)suppression at √s = 1800 (540) GeV

diffractive x-section suppressed relative to Regge prediction as √s increases

see KG, PLB 358, 379 (1995)

1800

GeV

540

GeV

M,t

p

p

p’

√s=22 GeV

RENORMALIZATION

Regge

FACTORIZATION BREAKING IN SOFT DIFFRACTION

CDF

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DD at CDF

renormalized

gap probability x-section

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SDD at CDF

Excellent agreement between data and MBR (MinBiasRockefeller) MC

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CD (DPE) at CDF

Excellent agreement between data and MBR low and high masses are correctly implemented

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Two free parameters: s0 and gPPP

Obtain product gPPP•s0 from SD

Renormalized Pomeron flux

determines s0

Get unique solution for gPPP

Pomeron-proton x-section

)(sσξ)(t,fdtdξ

σdpIPIP/p

SD2

0s

)(s /20 tgPPP

Pom. flux: interpret as gap probabilityset to unity: determines gPPP and s0

KG, PLB 358 (1995) 379

So=3.7±1.5 GeV2

gPPP=0.69 mb-1/2=1.1 GeV -1

Scale s0 and triple-pom coupling

Slide #16Ddffr. 2012

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Reduce the uncertainty in s0

Cross Sections

SD single diffraction (single dissociation) DD double dissociation (double diffraction) CD central dissociation (double pomeron exchange)

tot el

SD SD DD CD

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Total, elastic, and inelastic x-sections

GeV2

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Total, elastic, and inelastic x-sections versus √s

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TOTEM vs PYTHIA8-MBR

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ALICE tot-inel vs PYTHIA8-MBR

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More on cross sections

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136

Difractive x-sections

1=0.9, 2=0.1, b1=4.6 GeV-2, b2=0.6 GeV-2, s′=s e-y, =0.17, 2(0)=0, s0=1 GeV2, 0=2.82 mb or 7.25 GeV-2

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Difractive x-sections of √s

Supress x-sections at small gaps by a factor S using the error function with yS=2 for SD and DD, and y=y1+y2 =2 for CD (DPE).

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ALICE SD and DD vs PYTHIA8-MBR

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SD and DD at 7 TeV

MBR vs PYTHIA8-4C

The differences between the PYTHIA8(4C) and MBR predictions are mainly due to the (1/M2)1+ behavior, with =1.104 in MBR vs 1,08 in PYTHIA8(4C).

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CD (DPE) x-sections at 7 TeV versus (a) y=y1+y2 and (b) y1

Both figures are MBR predictions with a y=2 cut-off in the error function. The normalization is absolute with no model uncertainty other than that due to the

determination of the parameters in the formulas as determined from data

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SUMMARY introduction The ENORM (renormalization model) soft pp cross sections previously used

in MBR (Minimum Bias Rockefeller) simulation are adapted to PYTHIA8. MBR was successful at Fermilab in fixed target and collider

experiments. RENORM predictions are based on a parton-model approach, in which

diffraction is derived from inclusive PDFs and color factors. Diffractive cross sections and final states are both predicted:

Cross sections vs gap width or vs forward-momentum loss of proton(s): Absolute normalization!

Hadronization of dissociated proton: A (non-perturbative) “quark string” is introduced and tuned to

reproduce the MBR multiplicity and pT distributions. dN/d, pT, and particle ID: new in this PYTHIA8 implementation (the original MBR simulation produced only ± and 0).

Unique unitarization based on a saturated “glue-ball” exchange. Total Cross section ~ln2s based on a glue-ball-like saturated-exchange.

Immune to eikonaalization-model dependences.

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Thank you for your attention

References in arXiv:1205.1446v2 [hep-ph]

multiplicities

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