Post on 13-Dec-2015
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 3
The Pomeron Trajectory
Intercept=1.1
-large-
Slope=0.25
-small-
εs~
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 4
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 5
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 ?
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 6
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 7
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 8
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 9
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 !
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 10
PHENOMENOLOGY
Aristotle
450 BC
earthwaterairfire
atom
Demokritos
1869
periodictable
MendeleyevPlato (427-347 B.C)
platoniclove
2007
?
candidatessuperimposed
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 11
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 12
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 13
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 14
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 15
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 16
’ 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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 17
Multigap Diffraction
1y 2y1y 2y
1y 2y
(KG, hep-ph/0205141)
y
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 18
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 19
Diffractive Studies @ CDF
Elastic scattering Total cross section
SD DD DPE SDD=SD+DD
T=Im fel (t=0)
OPTICALTHEOREM
GAP
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 20
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 21
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 22
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
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 23
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)
Blois Workshop 2007DESY, 21-25 May 2007
Pomeron Intercept and Slope: the QCD connection K. Goulianos 24
Conclusion
Use:
M2 – scaling Non-suppressed 2-gap to 1-gap ratios Renormalization
Build: QCD theory of diffraction