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
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
