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Large Rapidity gapSurvival Probabilities
G. PancheriINFN Frascati National Laboratories
ISMD, Berkeley, August 8th, 2007
8/8/07 ISMD07 2
What is needed to calculate theSurvival Probability for Large
Rapidity Gaps
Vector boson Vector boson to Higgs or other VVstate
Pno-inel=probability of no inelastic interactions
• Only very low-pt particle emission can take place
A(b,s)=probability to find partons
which will not undergo hard collisions
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Calculate Pno-inel
• Pno-inel= Pno-inel(b,s) √s= c.m. Energy hadrons AB parton in hadron
Hadron A
Hadron B b
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Pno-inel(b,s)
• Poisson distributed (independent)collisions
• Now sum on all possibile distributions
In Eikonal representation
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Average number of collisionsat given energy and impact
parameter
b and s need not be factorized
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Model for hard andsoft interactions
• Work with A. Achilli, A. Grau, R.M.Godbole, Y.N. Srivastava
• Eikonal mini-jet model with soft gluonresummation
8/8/07 ISMD07 7
A. Grau,
R.M.Godbole and Y.N.
Srivastava Phys. Rev.
D 72,076001(2005)
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The questions are :
• What makes the cross-section rise?
• What makes the cross-section rise withinthe limits imposed by the Froissartbound?
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Two mechanisms
• Rise is due to increasing number of gluonswhich undergo “hard|” collisions, namely PQCDcalculable interactions
• Saturation of Froissart bound is due toincreasing acollinearity of “hard” partonsbecause of initial state energy dependent softgluon emission
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Our model is based on
1. eikonal transformation which implies multiplescattering and requires impact parameterdistributions inside scattering particles and basicscattering cross-sections
2. hard component of scattering responsible for therise of the total cross-section
3. soft gluon emission from scattering particles whichsoftens the rise and gives b-distribution
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1. Eikonal transformation
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!"
!#
$
!"
!#
$ √ s √ sjet-jet
x1
x2
2. Hard component of scattering responsiblefor the rise of the total cross-section
DGLAPParton densities
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Jet cross-sections atLO
Using currentDGLAP evoluted
PDF’s :
GRV, MRST, CTEQ
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Hardcomponentofscatteringresponsiblefor the riseof the totalcross-section
2.
sεType behaviour
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!"
!#
$
!"
!#
$ √ s √ sjet-jet
x1
x2
3. soft gluon emission from
scattering particles which softens the rise and gives b-distribution
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Softening the rise
• Soft gluons change the parton collinearity• Higher energy more emission
more acollinearity
smaller x-section
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Soft gluon emission
According to our model, soft gluon emissiondown to zero momentum modes is responsible
for the initialdecrease in p p , as well as for the
transformation of the sharp rise due to theincrease in gluon-gluon interactions
into a smooth behavior
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3. soft gluon emission from
scattering particles which softensthe rise and gives b-distribution
Soft gluon emission factor
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What one needs tocalculate A(b,s)
• Limits of integration for soft gluon factor ∫dng(k)[1-eikb]
• upper limit qmax(s)
• lower limit k=0 but then need to model
∫ dk αs(k) down into the infrared region
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Our model in the infrared
• Singular but integrable
• Singularity regulated by p < 1
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Average over same PDF asfor σjet
Softgluonscale
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How about nsoft?
•Parametrized with a constant σ0
•With ptmin dependence through A(b,s)
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For ptmin=1.15 GeV and a chosen setof low energy parameters
Notgood
acceptableσ tot (mb)
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Comparing with data and other models
GRVMRST
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With hard pomeron models
Minijets+Soft gluons
8/8/07 ISMD07 26
Survival probability
Probability of not having an inelasticcollision
Can be used to calculate the survival probability of Large Rapidity Gaps for collisions at given b-value
in a colorless exchange
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Survival probability
we use the soft b-distribution
V. Khoze, J. Bjorken,…
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Comparing with other models
Bjorken
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conclusions
• We have built a model for the total cross-section which– Incorporates hard and soft gluon effects– Satisfies the limits from the Froissart bound– Can be used to study other minimum bias
effects like Survival Probability of LargeRapidity Gaps
– Easily extended to γ p and γ γ
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1. eikonaltransformationimplies multiplescattering