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

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

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

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 R O N SppS LHC 14TeV

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

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

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

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.

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

Alpha-strong Parameterization: With ½<p<1 Asymptotic freedom for kT>>ΛQCD Divergent but integrable for kT 0

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

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