Diapositiva 1

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Effects of soft gluon emission on total pp / pp
cross-section at LHC energies
Andrea Achilli andrea.achilli_at_fisica.unipg.it Univ
ersità degli Studi di Perugia INFN Perugia
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Outline

• Froissart-Martin bound
• QCD mini-jet
• Eikonal mini-jet model
• Soft gluon emission effects
• Results

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Froissart-Martin Bound
Respected by strong interaction (consequence of
confinement C 1/m2p )
Perturbative QCD is insufficient to represent
stot 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
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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) 1-1232
proton-antiproton proton-proton
Cosmic Ray
T E V A T R O N
SppS
LHC 14TeV
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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
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sjet
Asymptotic behavior of sjet for different PDF
CTEQ ?0.3 GRV98 ?0.4 GRV
?0.4 CTEQ ?0.3
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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 Re?(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
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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 sjet.

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

• With ½ltplt1
• Asymptotic freedom for kTgtgt?QCD
• Divergent but integrable for kT 0

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Results
Varying its parameters the model gives a range of
values for stot at high energies which could be
compared with other phenomenological results
GeV
stot(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
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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

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qmax(s)
Maximum transverse momentum of a single gluon
emitted in a hard collision allowed by kinematics
P. Chiappetta and M. Greco Nucl. Phys. B 199
(1982)77
Averaged over all partonic processes and parton
densities (the same used for sjet)
zmin 4(pTmin)2 / (sx1x2)
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PDF GRV98 MRST GRV
PDF GRV98 MRST GRV