diffractive, elastic, and total pp cross sections at the lhc
DESCRIPTION
Diffractive, Elastic, and Total pp Cross Sections at the LHC. Konstantin Goulianos The Rockefeller University. Contents. References Single diffraction Renormalization triple-Pomeron coupling ratio of a ' /e Total cross section the SUPERBALL cross section - PowerPoint PPT PresentationTRANSCRIPT
Diffractive, Elastic, and Totalpp Cross Sections at the LHC
Konstantin GoulianosThe Rockefeller University
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 2
Contents
References Single diffraction Renormalization triple-Pomeron coupling ratio of ' Total cross section the SUPERBALL cross section cross section from a global fit The elastic cross section Discussion
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 3
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
KG-95 PLB 358, 379 (1995) Renormalization
Erratum: PLB 363, 268 (1995)
CMG-96 PLB 389, 176 (1996) Global fit to p±p, ±, K±p
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 4
Single diffraction
Two free parameters: so and gPPP Obtain product gPPP•so
from SD
Renormalized Pomeron flux determines so
Get unique solution for gPPP
KG-95
Pomeron-proton x-section
)(sσξ)(t,fdtdξ
σd1/
SD2
PppP
os
)(s /2o tgPPP
Pomeron flux
p2
p1
P
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 5
Standard Regge theory
Parameters: so, so' and g(t) set so‘ = so (universal) P g(t) g(0) ≡ gPPP see KG-PR determine so and gPPP – how?
KG-95
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 6
The triple-Pomeron coupling in QCD
Experimentally: KG&JM, PRD 59 (114017) 1999
02.017.0 Pp
PPPg
yoyt
pgap eetFCNyddt
d
222
)(
),( tyPgap soT
18.03
125.0
8
175.0
121f
1
1f
2
Q
NN cq
cgColor factor:
gluon fraction
quark fraction
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 7
Renormalization
Flux integral depends on s and s0
“knee” √s-position determines the ssb value where flux becomes unity get so
ss= -2 s/s = -4 (√s)/√s
get error in so from error in √s-knee
Tsd renormalized
2~ sSD
1dtdξξ)(t,f 02
ζ
/1ξ
/
0
tmin
ssCs
pP
2~ sSD
KG-95
)(sσξ)(t,fdξdt
σd1 /
SD2
PppP
0s
)(s /20 tgPPP
Pomeron flux
ssb=22 GeV
p1
p2
1dtdξξ)(t,f0.1
ξ
/
0
tmin
pP
P
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 8
yoyt
pgap eetFCNyddt
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
Renormalization and Pumplin bound
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 9
Tsd (s∞) and ratio of '/
1'2
exp2
sdob
ppPp
00
)!14.3
'0.08) using(GeV25.0
)2ln(4
4/1' 2
2
m
2
2
2
1
2 m
Rb psdo
arXiv:0812.4464v1[hep-ph] submitted to PLB
Constant set to o
pp
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 10
The value of so - a bird’s-eye view
“knee” @ 22 ± 1 GeV so = 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
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 11
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
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 12
Froissart-Martin bound: (s in GeV2)
For m2 = m2 / m2 ~ 104 mb – very large!
But if m2 = so = (mass)2 of a large SUPERglueBALL, a ln2s behavior
ala Froissart-Martin an be reached at a much lower s-value, ssb,
Determine ssb and so from T
SD
Show that √ssb < 1.8 TeV
Show that at √s = 1.8 TeV Reggeon contributions are negligible
Get cross section at the LHC from
The total cross section
sb
2
osbsb s
sln
s
π)σ(sssσ
s22
lnm
πσ
F
CDF2
F
LHC2CDF
1800LHC
s
sln
s
sln
πσσ
0s
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 13
The SUPERBALL T
Froissart-Martin bound
Valid above “knee” at √s = 22 GeV and therefore at √s = 1.8 TeV
Use superball mass
m2 = so = (1±0.2) GeV2
At √s 1.8 TeV Reggeon contributions are negligible (CMG-96))
s22
lnm
πσ
compatible with CGM-96 global fit result of 114 ± 5 mb (see next 2 slides)
mb611963924.203.80s
sln
s
sln
s
πσσ
F
CDF2
F
LHC2
0
CDF1800
LHC14000
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 14
Global fit to p±p, ±, K±p x-sections
INPUT
RESULTS
CMG-96
Use standard Regge theory
negligible
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 15
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
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 16
The elastic cross section Optical theorem: obtain imaginary part of the amplitude from T
Dispersion relations: obtain real part of the amplitude from T
Add Coulomb amplitude
Get differential elastic cross section and -value
T
optical theoremIm fel(t=0)
dispersion relationsRe fel(t=0)
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 17
DISCUSSION
LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 18
thank you