1. Effects of soft gluon emission on total pp / pp cross-section at LHC energies
Andrea Achilli
Università degli Studi di Perugia & INFN Perugia
XIII Spring School "B. Touschek" 2008

2. Outline Froissart-Martin bound QCD mini-jet Eikonal mini-jet model
Soft gluon emission effects
Results

3. Froissart-Martin Bound
Respected by strong interaction (consequence of confinement C ~ 1/m2π )
Perturbative QCD is insufficient to represent σtot
QCD mini-jet violates FM bound as a consequence of the infinite range of QCD
Implementation of FM bound needs the introduction of non perturbative effects which restore the finite range of the interaction

4. Data on total cross-section
Agreement with FM bound
Saturation of the bound?
( ln2(s) or slower? )
LHC measurement uncertainty ~ 1mb (TOTEM estimate)
Discrimination between different asymptotic behaviors
[P.D.G. Collaboration, W. M. Yao et al., J. Phys. G33 (2006) ]
proton-antiproton
proton-proton
Cosmic Ray T E V A R O N
SppS
LHC
14TeV

5. Mini-jet QCD
The rise of the total cross section is due to production of jets from high energy partonic collisions. These are typical hard processes (pTmin ~ 1-2 GeV)
f(x,pT2) :Parton Density Functions (GRV, MRST, CTEQ) at LO
As the parton flux increases with energy, integrated jet cross-sections increase rapidly with energy

6. σjet ~ Asymptotic behavior of σjet for different PDF: CTEQ: ∆~0.3
GRV98: ∆~0.4
GRV: ∆~0.4

7. Eikonal mini-jet model
A formalism necessary to incorporate unitarity in mini-jet cross-section.
It requires as input the spatial distribution of matter inside colliding hadrons
High energies Reχ(b,s) ~ 0
Average number of partonic collision
[A. Corsetti, R. M. Godbole and G. Pancheri, Phys. Lett. B 435 (1998) 441]
Responsible only for the low energy behavior

8. Soft Gluon resummation
Soft gluon emissions from colliding particles softens the rise and gives a b-distribution A(b)
it breaks collinearity of the scattering partons
more energy more emissions more acollinearity
A(b) A(b,s)
it subtracts energy from the partonic hard processes taming the excessive rise of σjet.

9. Overlap function Based on a Bloch-Nordsiek inspired formalism
[P. Chiappetta and M. Greco Nucl. Phys. B 199 (1982)77]

10. Alpha-strong Parameterization: With ½<p<1
Asymptotic freedom for kT>>ΛQCD
Divergent but integrable for kT

11. Results
Varying its parameters the model gives a range of values for σtot at high energies which could be compared with other phenomenological results
GeV
σtot(14 TeV) ~ 100 mb
Our results are well fitted by a parameterization of the kind:
a0 ~ 20 mb
a1 ~ 125 mb ( p - p )
~ 65 mb ( p - p )
b = -0.5
a2 ~ 1.6 mb
a3 ~ 0.14 mb
Agreement with FM bound

12. Summary
The model depends on a set of parameters fixed by phenomenological considerations (pTmin, p, etc..)
Through soft gluon emissions finite range of hadronic interaction is achieved
Froissart-Martin bound is satisfied by the model
Predictions comparable with other phenomenological models
Possible extension to other processes