K. Goulianos The Rockefeller University Pomeron Intercept and Slope: the QCD connection 12 th Blois...

K. GoulianosThe Rockefeller

University

Pomeron Intercept and Slope:the QCD connection

12th Blois Workshop, DESY, Hamburg, Germany 21-25 May2007

intercept

slope

12th International Conference on Elastic and Diffractive ScatteringForward Physics and QCD

Blois Workshop 2007DESY, 21-25 May 2007

Pomeron Intercept and Slope: the QCD connection K. Goulianos 2

Contents

Introduction Diffraction in QCD Pomeron intercept and slope Cross sections with/no free parameters Conclusion



The Pomeron Trajectory

Intercept=1.1

-large-

Slope=0.25

-small-

εs~



A bit of history…

Pre-1970: guess a’~1 (as for other trajectories)

~1970: ’=0.5,

=1

1995: ’=0.25,

=1.1

In this talk:The QCD connection

time

Covolan, Montagna, and GoulianosPLB 389 (1995) 176



A clue from Diffraction Dissociation

0.025t2dMdt

σd2

< 0.1

1

~1

~22 d

d

MdM

d

KG, Phys. Rep. 101, 169 (1983)

M

Why 1/M2 ?



p-p InteractionsDiffractive:

Colorless exchange withvacuum quantum numbers

Non-diffractive:Color-exchange

Incident hadrons retain their quantum numbersremaining colorless

Incident hadrons acquire colorand break apart

POMERON

rapidity gap



Diffractive Rapidity Gaps

ξ

1~

dξ

dσ

M

1~

dM

dσconstant

Δηd

dσ22

0t

p pX p

p

Particle production Rapidity gap

-ln ln MX2

ln s

X

dN/d



Another clue: Diffraction and Unitarity

Unitarity problem: Using factorization and std pomeron flux SD exceeds T at Renormalization:

Normalize Pomeron flux to unity to eliminate overlapping

gaps

)(sσξ)(t,fdtdξ

σdpIPIP/p

SD2

KG, PLB 358 (1995) 379

TeV.2s

1dtdξξ)(t,f0.1

ξ

IP/p

0

tmin

2~ sSD

εs

εs



M2-scaling

KG&JM, PRD 59 (1999) 114017

Factorization breaks down so as to ensure M2-scaling!

12

2

2 )(M

s

dM

d

renormalization

1

Independent of S over 6 orders of magnitude in M2 !



PHENOMENOLOGY

Aristotle

450 BC

earthwaterairfire

atom

Demokritos

1869

periodictable

MendeleyevPlato (427-347 B.C)

platoniclove

2007

?

candidatessuperimposed



The QCD Connection

(see E. Levin, An Introduction to Pomerons,Preprint DESY 98-120)

ses oy

oT )(y

sy ln

Emission spacing controlled by -strong

: power law rise with energy

s

’ reflects the size of the emitted cluster,

which is controlled by 1 /s and thereby is related

to

ytel etsf ),(Im

y sy ln

Forward elastic scattering amplitude

assume linear t-dependence



Gap probability MUST be normalized to unity!

Single Diffraction in QCD

yy

yt ,2 independent variables:

t

colorfactor

17.0)0(

)(

ppIP

IPIPIP tg

yo

ytp eetFC

yddt

d

222

)(

gap probability sub-energy x-section



Single diffraction (re)normalized

yo

ytpgap eetFCN

yddt

d

222

)(

s

sCdtydtyPsN s

gaptygap ln),()(

2

,1

tybsy eseCyddt

d )2()ln(2

0ln

The Pumplin bound is obeyed at all impact parameters

Grows slower than s

),( tyPgap



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

g=0.20

q=0.04

R=-0.5

fg=gluon fractionfq=quark fraction

λx

1f(x)x

18.03

125.0

8

175.0

121f

1

1f

2

Q

NN cq

cgColor factor:

12.0ww qqgg Pomeron intercept:

104.0,02.017.0

pIP

IPIPIPg

λ

/sxs~dxxf

1

1)(

CTEQ5L



Inclusive vs Diffractive DIS

CCF

Q

QQD

1212)3(

2

1

)()(

)(1),,(

2

F2 ~ x

q

KG, “Diffraction: a New Approach,” J.Phys.G26:716-720,2000 e-Print Archive:

hep-ph/0001092

P(0)-1

(q)/2

Brend Loehr@smallx-2007

12

2

2)3(2 1

),(

),,(

Q

Q

xF

xF D

Diffractive to ND ratio flat in x and Q2 for fixed



’ versus

1'2

exp2

sdob

ppPp

00

'

!14.3'

0.08) using(GeV25.0)2ln(4

4/1' 2

2

m

Constant set to o

pp

2

2

2

1

2 m

Rb psd

o



Multigap Diffraction

1y 2y1y 2y

1y 2y

(KG, hep-ph/0205141)

y



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



Diffractive Studies @ CDF

Elastic scattering Total cross section

SD DD DPE SDD=SD+DD

T=Im fel (t=0)

OPTICALTHEOREM

GAP



Central and Two-Gap CDF Results

One-gap cross sections are suppressed Two-gap/one-gap ratios are 17.0

Agreement with renormalized Regge predictions

DD SDD DPE



Gap Survival Probability

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

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

S =

Results similar to predictions by:Gotsman-Levin-MaorKaidalov-Khoze-Martin-RyskinSoft color interactions



Unexpected, notunderstood

Hadron-like

QCD factorisationnot OK

Dijets in p at HERA: the puzzle (?)slide imported from diffractive group experimental summary

of the HERA/LHC Workshop of March 14, 2007



Dijets in p at HERA: the expectation

Factor 0f ~3 suppressionexpected at W~200 GeV(just as in pp collisions) for both direct and resolved components

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



Conclusion

Use:

M2 – scaling Non-suppressed 2-gap to 1-gap ratios Renormalization

Build: QCD theory of diffraction

K. Goulianos The Rockefeller University Pomeron Intercept and Slope: the QCD connection 12 th Blois...

Documents

Transcript of K. Goulianos The Rockefeller University Pomeron Intercept and Slope: the QCD connection 12 th Blois...