Diffractive and total pp cross sections at the LHC and beyond Konstantin Goulianos The Rockefeller University http://physics.rockefeller.edu/dino/myhtml/conference.html Otranto (Lecce), Italy Hotel Baia dei Turchi September 10 - 15, 2010 DIFFRACTION 2010 International Workshop on Diffraction in High-Energy Physics
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Diffractive and total pp cross sections at the LHC and beyond
Diffractive and total pp cross sections at the LHC and beyond. Konstantin Goulianos The Rockefeller University http://physics.rockefeller.edu/dino/myhtml/conference.html. DIFFRACTION 2010 International Workshop on Diffraction in High-Energy Physics. - PowerPoint PPT Presentation
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Diffractive and total pp cross sections at the LHC and beyond
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