# Presentation: 659136

## Large Rapidity gap Survival Probabilities

- G. Pancheri
- INFN Frascati National Laboratories

- ISMD, Berkeley, August 8th,  2007

## What is needed to calculate the Survival Probability for Large Rapidity Gaps

- Vector boson Vector boson   to Higgs or other VV state
- 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)                  _x0016_√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 collisions at given energy and impact parameter

- b and s need not be factorized

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## Model for hard and soft interactions

- Work with A. Achilli, A. Grau, R.M. Godbole, Y.N. Srivastava
- Eikonal mini-jet model with soft gluon resummation

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##  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 within the limits imposed by the  Froissart bound?

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## Two mechanisms

- Rise is due to increasing number of gluons which undergo “hard|” collisions, namely PQCD calculable interactions
- Saturation of Froissart bound is due to increasing acollinearity of “hard” partons because of initial state energy dependent soft gluon emission

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## Our model  is based on

-  eikonal transformation which implies multiple scattering and requires  impact parameter distributions inside scattering particles and basic scattering cross-sections
- hard component of scattering responsible for the  rise of the total cross-section
-  soft gluon emission from scattering particles which softens  the rise and gives  b-distribution

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## 1. Eikonal transformation

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## x1

- x1

- x2

- 2. Hard component of scattering responsible
- for the  rise of the total cross-section

- DGLAP
- Parton densities

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## Jet cross-sections at LO

- Using current
- DGLAP evoluted
- PDF’s :
- GRV, MRST, CTEQ

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## Hard component of scattering responsible for the rise of the total cross-section 

- 2.

- s
- Type
-  behaviour

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## 3. soft gluon emission from 

- 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 emission down to **zero momentum modes** is responsible for  the initial
- decrease in *p p* , as well as for the
-  transformation of the sharp rise due to the increase in gluon-gluon interactions
-  into a smooth behavior

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##  3. soft gluon emission from scattering particles which softens the rise and gives  b-distribution

- Soft gluon emission factor

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## What one needs to calculate A(b,s)

- Limits of _x0018__x0018_integration
-  for soft gluon factor ∫dng(k)[1-eikb]
- upper limit            **q****max****(s)**
-    lower limit k=0 but then need to model
- ∫dks(k)  down into the infrared region

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## Average

- <footer>

-  over same
-  PDF as
- for jet

- Soft gluon scale

## Our model in the infrared

- Singular but integrable
- Singularity regulated by p < 1

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## How about nsoft?

- Parametrized with a constant 0
- With ptmin dependence through A(b,s)

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## For ptmin=1.15 GeV and a chosen set of low energy parameters

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- For ptmin=1.15 GeV and a chosen set of low energy parameters

- Not
- good

- acceptable

- tot (mb)

## Comparing with data and other models

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- GRV
- MRST

## With hard pomeron models

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- Minijets+
- Soft gluons

## Survival probability

- Probability of not having an inelastic
- collision

- 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

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- Bjorken

## 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 Large Rapidity Gaps**
- Easily extended to  p and 

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## 1. eikonal transformation  implies multiple scattering

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