Diffractive x-sections and event final states at the LHC Konstantin Goulianos The Rockefeller...

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Diffractive x-sectionsand event final states at the LHC

Konstantin GoulianosThe Rockefeller University

http://physics.rockefeller.edu/

Diffraction Day7 May 2010 CERN

D-day 7 May 2010 CERN Diffractive x-sections and event final states at the LHC 2 K. Goulianos

Describe a phenomenology based on pre-LHC results and use it to: make predictions for LHC suggest measurements to confirm / modify parameters suggest scheme to be implemented in MC simulations propose method to measure luminosity

Current MC generators: unreliable for extrapolations to LHC MC tuning based on multi-parameter tuning of ill-defined

event topologies Solution: use nested x-sections

Contents define diffractive x-section event topologies

nested diffractive gaps describe in terms of proton pdf’’s and QCD color factors normalize to guarantee unitarity renormalization model

OUTLINE


REMARKS

MC generators inadequate:

e.g. PYTHIA and PHOJET predictions of diffractive processes disagree with each other and with data. Diffractive factorization at HERA? Breakdown observed in, e.g.

Vector mesons: vs. W, b-slopes of t-distributionsDijets: ET

jet dependence, resolved vs. direct components, . ..

RENORM model: describes both p(pbar)-p and p

Luminosity measurement: requires a known x-section

suggest SD – well defined and slowly varying


Diffractive pp(pp) processes @ CDF

Single Diffractiondissociation (SD)

Double Diffractiondissociation (DD)

Double PomeronExchange (DPE)

Central Diffraction

Single + DoubleDiffraction (SDD)

SD SD SD SDD

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

OPTICALTHEOREM

gap

nested gap

Use nesting until no diffractive gap fits in √s'


Definitions

s

Mξ-1

2

L x

22 M

1

dM

dσ

ξ

1

dξ

dσconstant

Δηd

dσ

0t

dN/d

M

pp’

p’rap-gap

=-ln0

p

M,t

p

p

p’ Lpξ

ln M2

ln s

particles

M2 scaling: no price paid for increasingdiffractive gap size


M2 scaling

KG&JM, PRD 59 (1999) 114017

factorization breaks down to ensure M2 scaling - why?

12

2

2 )(M

s

dM

d

Regge

1

Independent of s over 6 orders of magnitude in M2 !

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

data


TSD (pp & pp)

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

suppressed relative to Regge

KG, PLB 358, 379 (1995)

1800

GeV

540

GeV

M,t

p

p

p’

TSD mb

√s=22 GeV


Gap probability MUST be normalized to unity!

Single Diffraction

yy

yt ,2 independent variables:

t

colorfactor

17.0)0(

)(

ppIP

IPIPIP tg

yoyt

p eetFCyddt

d

222

)(

gap probability sub-energy x-section


Single diffraction (re)normalized

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


Unitarity and Renormalization

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 gap probabilitySet to unity – determines gPPP and s0

KG, PLB 358 (1995) 379


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)


Multi-gap Diffraction

1y 2y1y 2y

1y 2y

(KG, hep-ph/0205141)

y


Multi-gap 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


Rapidity Gaps in Fireworks


Gap survival probability

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

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

S =


Diffractive Structure Function

CDF

H1

momentum fraction of parton in “Pomeron” – note quotes

Using preliminary pdf’s from

same suppressionas in soft diffraction – why?

Xdijetppp

Breakdown of QCD factorization


Diffractive dijets @ Tevatron

),/(1

),,( 22

21 QQ xFxF D

pjet

reorganizep

jet


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


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


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


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 !!!


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


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


SD and ratio of '


The total x-section

√sF=22 GeV

SUPERBALL MODEL


Strategy and Conclusion

T from SUPERBALL model optical theorem Im fel(t=0) dispersion relations Re fel(t=0) differential SD from RENORM use nested pp multiplicities forpomeron-proton collisions at √s‘ For a phenomenological approach see: K. Goulianos, Phys. Lett. B 193 (1987) 151 pp

T

optical theoremIm fel(t=0)

dispersion relationsRe fel(t=0)

STRATEGY

CONCUSIONmore to come…

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Diffractive x-sections and event final states at the LHC Konstantin Goulianos The Rockefeller...

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