Diffractive and total pp cross sections at the LHC and beyond

Konstantin GoulianosThe Rockefeller University

http://physics.rockefeller.edu/dino/myhtml/conference.html

Otranto (Lecce), ItalyHotel Baia dei Turchi September 10 - 15, 2010

DIFFRACTION 2010 International Workshop on Diffraction in High-Energy Physics

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 2 K. Goulianos

CONTENTS

Introduction

Diffractive cross sections

The total cross section

Ratio of pomeron intercept to slope

Conclusions

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 3 K. Goulianos

Diffractive pp/pp Processes

Elastic scattering Total cross section

SD DD DPE SDD=SD+DD

T=Im fel (t=0)

OPTICALTHEOREM

GAP

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 4 K. Goulianos

Basic and combined (“nested”) diffractive processes

multi-gap “nested” process

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 5 K. Goulianos

The problem: the Regge theory description violates unitarity at high s

d/dt sd grows faster than t as s increases unitarity violation at high s

(similarly for partial x-sections in impact parameter space)

the unitarity limit is already reached at √s~ 2 TeV

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 6 K. Goulianos

Standard Regge Theory

Parameters: s0, s0' and g(t) set s0‘ = s0 (universal IP) g(t) g(0) ≡ gPPP KG-1995 determine s0 and gPPP – how?

KG-1995: PLB 358, 379 (1995)

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 7 K. Goulianos

Global fit to p±p, ±, K±p x-sectionsGlobal fit to p±p, ±, K±p x-sections

INPUT

RESULTS

CMG-1996PLB 389, 176 (1996)

Regge theory eikonalized

negligible

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 8 K. Goulianos

Renormalization the key to diffraction in QCD

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 9 K. Goulianos

Diffractive gapsdefinition: gaps not exponentially suppressed

ξ

1~

dξ

dσ

M

1~

dM

dσconstant

Δηd

dσ22

0t

p pX p

Particle production Rapidity gap

-ln ln MX2

ln s

X

No ra

diat

ion

Lpξ

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 10 K. Goulianos

TSD (pp & pp) - data

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

suppressed relative to Regge for √s>22 GeV

KG, PLB 358, 379 (1995)

1800

GeV

540

GeV

M,t

p

p

p’

TSD mb

√s=22 GeV

RENORMALIZATION MODEL

CDF Run I results

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 11 K. Goulianos

M2 distribution: data

KG&JM, PRD 59 (1999) 114017

factorization breaks down to ensure M2 scaling

ε12

2ε

2 )(M

s

dM

dσ

Regge

1

Independent of s over 6 orders of magnitude in M2

M2 scaling

ddM2|t=-0.05 ~ independent of s over 6 orders of magnitude!

data

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 12 K. Goulianos

Gap probability (re)normalize to unity

Single diffraction renormalized – (1)

yy

yt ,2 independent variables:

t

colorfactor

17.0)0(

)(

ppIP

IPIPIP tg

yoyt

p eetFCyddt

d

222

)(

gap probability sub-energy x-section

EDS 2009: http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.3527v1.pdfCORFU-2001: hep-ph/0203141

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 13 K. Goulianos

Single diffraction renormalized – (2)

colorfactor

17.0)0(

)(

ppIP

IPIPIP tg

Experimentally: KG&JM, PRD 59 (114017) 1999

18.03

125.0

8

175.0

121f

1

1f

2

Q

NN cq

cgQCD:

104.0,02.017.0

pIP

IPIPIPg

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 14 K. Goulianos

Single diffraction renormalized - (3)

constsb

sssd

ln

ln~

set to unity determine so

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 15 K. Goulianos

Single diffraction renormalized – (4)

yoyt

pgap eetFCNyddt

d

222

)(

s

sCdtydtyPsN s

gaptygap ln),()(

2

,1

tybsy eseCyddt

d )2()ln(2

0ln

Pumplin bound obeyed at all impact parameters

Grows slower than s

),( tyPgap

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 16 K. Goulianos

Scale so and triple-pom coupling

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

Pomeron flux: interpret as gap probabilityset to unity: determines gPPP and s0 KG, PLB 358 (1995) 379

So=3.7±1.5 GeV2gPPP=0.69 mb-1/2=1.1 GeV -1

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 17 K. Goulianos

Multigap diffraction

1y 2y1y 2y

1y 2y

KG, hep-ph/0203141

y

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 18 K. Goulianos

Multigap cross sections

ssty ln/2~,

Same suppressionas for single gap!

2122

2-1i1

2

51

5

)( yyo

ytp

ii

eetFCdV

dii

Gap probability Sub-energy cross section(for regions with particles)

1y 2y1y 2y

1y 2y

1t 21 yyy 5 independent variables2t color

factor

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 19 K. Goulianos

Gap survival probability

0.23GeV)(1800S gapgap/01gapgap/12

0.29GeV)(630S gapgap/01gapgap/12

S =

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 20 K. Goulianos

The total x-section

√sF=22 GeV

SUPERBALL MODEL

98 ± 8 mb at 7 TeV109 ±12 mb at 14 TeV

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 21 K. Goulianos

Born

Eikonal

T at LHC from CMG global fit

@ LHC √s=14 TeV: 122 ± 5 mb Born, 114 ± 5 mb eikonal error estimated from the error in given in CMG-96

caveat: so=1 GeV2 was used in global fit!

Compare with SUPERBALL (14 TeV) = 109 ± 6 mb

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 22 K. Goulianos

SD and ratio of '

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 23 K. Goulianos

Monte Carlo Strategy for the LHC

T from SUPERBALL model optical theorem Im fel(t=0) dispersion relations Re fel(t=0) differential SD from RENORM use nested pp final states forpp collisions at the IP p sub-energy √s‘

Strategy similar to that employed in the MBR (Minimum Bias Rockefeller) MC used in CDF based on multiplicities from: K. Goulianos, Phys. Lett. B 193 (1987) 151 pp“A new statistical description of hardonic and e+e− multiplicity distributions “

T

optical theoremIm fel(t=0)

dispersion relationsRe fel(t=0)

MONTE CARLO STRATEGY

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 24 K. Goulianos

Dijets in p at HERA from RENORM

Factor of ~3 suppressionexpected at W~200 GeV(just as in pp collisions)

for both direct and resolved components

K. Goulianos, POS (DIFF2006) 055 (p. 8)

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 25 K. Goulianos

SUMMARY

Froissart bound Valid above the “knee” at √s = 22 GeV in T

SD vs. √sand therefore valid at √s = 1.8 TeV of the CDF measurement

Use superball scale s0 (saturated exchange) in the Froissart formula, where s0= 3.7±1.5 GeV2as determined from setting the integral of the Pomeron flux to unity at the “kneee” of s√s = 22 GeV

m2 = s0 = (3.7±1.5 GeV2

At √s 1.8 TeV Reggeon contributions are negligible (see global fit)

compatible with CGM-96 global fit result of 114 ± 5 mb

t= (98 ± 8) mb at 7 TeV – wait and see!

sm 2)2 ln/(σ

mb12109122924.203.80s

sln

s

sln

s

πσσ

F

CDF2

F

LHC2

0

CDF1800

LHC14000

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 26 K. Goulianos

BACKUP

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 27 K. Goulianos

Diffractive dijets @ Tevatron

),/(1

),,( 22

21 QQ xFxF D

pjet

reorganize

pjet

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 28 K. Goulianos

FDJJ(,Q2) @ Tevatron

2

sβ

ξ

dξN

ε

ε

2sβ

1

β

xξ1

ξ 211

renorm

minmin

min

)2(

)(1

12

2R

2RENORM

xQs

xSDND

4.02.0 xg

)()(renorm

22

2

2

2 )(12

)/(

)(1N),,( 21221 Q

Q

Q

QQ

C

sx

CF D

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 29 K. Goulianos

SD/ND dijet ratio vs. xBj@ CDF

(x)F

(x)FR(x) ND

jj

SDjj

0.035 < < 0.095

Flat dependencefor < 0.5

CDF Run I

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 30 K. Goulianos

Diffractive DIS @ HERA

),(1

),,( 221

2)3(2 QQ xFxF D

eQ2*

p

jet

reorganize

J. Collins: factorization holds (but under what conditions?)

e*

tp

IP

Pomeron exchange Color reorganization

Results favor color reorganization

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 31 K. Goulianos

Vector meson production(Pierre Marage, HERA-LHC 2008)

left - why different vs. W slopes? more room for particles right - why smaller b-slope in *p? same reason

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 32 K. Goulianos

Dijets in p at HERA - 2008

DIS 2008 talk by W. Slomiński,

ZEUS

20-50 % apparent rise when ETjet 510 GeV

due to suppression at low ETjet !!!

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 33 K. Goulianos

Unexpected, notunderstood

QCD factorisationnot OK

Dijets in p at HERA – 2007

Hadron-like

eQ2*

p

jet

reorganize

Direct vs. resolved

the reorganization diagram predicts:

suppression at low Z|Pjets, since larger is available for particles

same suppression for direct and resolved processes

DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 34 K. Goulianos

The end