diffractive and total pp cross sections at lhc k. goulianos eds 2009, june 29-july 3 1 diffractive...
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EDS 2009, June 29-July 3 1Diffractive and Total pp cross sections at LHC
K. Goulianos
Diffractive and Totalpp Cross Sections at LHC
Konstantin GoulianosThe Rockefeller University
13th International Conference on Elastic & Diffractive Scattering (13th "Blois Workshop")
CERN, 29th June - 3rd July 2009
EDS 2009, June 29-July 3 2Diffractive and Total pp cross sections at LHC
K. Goulianos
Contents
References Strategy Unitarity and renormalization Cross sections @ LHC Global fit to p±p, ±p, K±p x-sections The ratio of '/Discussion
EDS 2009, June 29-July 3 3Diffractive and Total pp cross sections at LHC
K. Goulianos
References
http://physics.rockefeller.edu/dino/my.html
CDF PRD 50, 5518 (1994) el @ 1800 & 546 GeV
CDF PRD 50, 5535 (1994) D @ 1800 & 546 GeV
CDF PRD 50, 5550 (1994) T @ 1800 & 546 GeV
KG-PR Physics Reports 101, No.3 (1983) 169-219
Diffractive interactions of hadrons at high energies
KG-95 PLB 358, 379 (1995); Erratum: PLB 363, 268 (1995) Renormalization of hadronic diffraction
CMG-96 PLB 389, 176 (1996) Global fit to p±p, ± and K±p cross sectionsKG-09 arXiv:0812.4464v2 [hep-ph] 26 March 2009 Pomeron intercept and slope: the QCD connection
EDS 2009, June 29-July 3 4Diffractive and Total pp cross sections at LHC
K. Goulianos
Froissart bound (s in GeV2)
For m2 = m2 /m2 ~ 104 mb – large!
If m2 = so = (mass)2 of a large SUPERglueBALL, the bound can be
reached at a much lower s-value, sF, Determine sF and s0 from T
SD
Show that √sF < 1.8 TeV
Show that at √s = 1.8 TeV Reggeon contributions are negligible
Get cross section at the LHC as
Strategy
F
2
oFF s
sln
s
π)σ(sssσ
CDF
LHC2CDF
1800LHC14000 s
sln
πσσ
0s
s22
lnm
πσ
EDS 2009, June 29-July 3 5Diffractive and Total pp cross sections at LHC
K. Goulianos
Standard Regge Theory
Parameters: s0, s0' and g(t) set s0‘ = s0 (universal IP) g(t) g(0) ≡ gPPP see KG-PR determine s0 and gPPP – how?
(KG-95)
EDS 2009, June 29-July 3 6Diffractive and Total pp cross sections at LHC
K. Goulianos
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
EDS 2009, June 29-July 3 7Diffractive and Total pp cross sections at LHC
K. Goulianos
Renormalization
Flux integral depends on s and s0
“knee” √s-position determines s-value where flux becomes unity get so
get error in so from error in √s-knee
ss= -2 s/s = -4 (√s)/√s
Single Diffraction
2~ sSD
1dtdξξ)(t,f 02
ζ
/1ξ
IP/p
0
tmin
ssCs
1dtdξξ)(t,f0.1
ξ
IP/p
0
tmin
KG-95
)(sσξ)(t,fdtdξ
σdpIPIP/p
SD2
0s
)(s /20 tgPPP
Pomeron flux
2~ sSD
EDS 2009, June 29-July 3 8Diffractive and Total pp cross sections at LHC
K. Goulianos
The value of so - a bird’s-eye view
“knee” @ 22 ± 1 GeV s0 = 1 ± 0.2 GeV
KG-95
√s (GeV) Cool [KG] FNAL 14 20 Albrow ISR 23.3 26.9o Armitage ISR 23.3 27.4
error in knee position: ± 1 GeV
11/2 GeV1.1mb0.69(t)g PPP KG-95riple-Pomeron coupling:
EDS 2009, June 29-July 3 9Diffractive and Total pp cross sections at LHC
K. Goulianos
The value of so- limited edition
CDF
shape of renormalized SD
E396 use CDF points to fix the level of renormalized curve use E396 points to fix the level of the Regge curve both curves are somewhat high in this plot adjusting height leads to the same “knee” position
shape of Regge s
EDS 2009, June 29-July 3 10Diffractive and Total pp cross sections at LHC
K. Goulianos
The SUPERBALL cross-section
Froissart bound
Valid above “knee” at √s = 22 GeV and therefore at √s = 1.8 TeV
Use superball mass
m2 = s0 = (1±0.2) GeV2
At √s 1.8 TeV Reggeon contributions are negligible (see global fit)
mb611363324.203.80s
sln
s
πσσ
CDF
LHC2
0
CDF1800
LHC14000
s22
lnm
πσ
compatible with CGM-96 global fit result of 114 ± 5 mb (see next slides)
EDS 2009, June 29-July 3 11Diffractive and Total pp cross sections at LHC
K. Goulianos
Global fit to p±p, ±, K±p x-sectionsGlobal fit to p±p, ±, K±p x-sections
INPUT
RESULTS
CMG-96
Use standard Regge theory
negligible
EDS 2009, June 29-July 3 12Diffractive and Total pp cross sections at LHC
K. Goulianos
Born
Eikonal
T at LHC from 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) = 113 ± 6 mb
EDS 2009, June 29-July 3 13Diffractive and Total pp cross sections at LHC
K. Goulianos
Extra: the ratio of '/
1'2
exp2
sdob
ppPp00
222
03.025.0'08.0
4.012.3)2ln(4
4/1'
c
GeV
c
GeVm
2
2
2
1
2 m
Rb psdo
The key!
KG-09
EDS 2009, June 29-July 3 14Diffractive and Total pp cross sections at LHC
K. Goulianos
SUMMARY
Froissart bound
Valid above the “knee” at √s = 22 GeV in TSD vs. √s
and therefore valid at √s = 1.8 TeV of the CDF measurement
Use superball mass s0 (saturated dressed proton mass) in the Froissart- Martin formula, where s0 is determined from setting the integral of the Pomeron flux to unity at √s = 22 GeV
m2 = s0 = (1±0.2) GeV2
At √s 1.8 TeV Reggeon contributions are negligible (see global fit)
compatible with CGM-96 global fit result of 114 ± 5 mb
mb611363324.203.80s
sln
s
πσσ
CDF
LHC2
0
CDF1800
LHC14000
s22
lnm
πσ