Predictions for proton-proton interaction cross-sections at LHC
aa r X i v : . [ h e p - ph ] S e p Predictions for proton-proton interaction cross-sections at LHC
A.B. Kaidalov , M.G. Poghosyan Institute of Theoretical and Experimental Physics, 117526 Moscow, Russia Universit`a di Torino and INFN, 10125 Torino, Italy
Abstract
This is a short communication with a summary of results obtained with a model based on Gribov’sreggeon calculus, which was proposed and applied to processes of soft diffraction at high energies. Wepresent a brief description of the model and its predictions for various LHC energies.
Regge theory [1] is the main method for describing high-energy soft processes. The asymptotic behaviorof the cross-sections of elastic scattering and multiple productions of hadrons is determined by the propertiesof the Pomeron, the right-most pole singularity of the elastic amplitude in the complex-momentum plane( j -plane). The experimentally observed increase of the total cross-section with increasing energy makesit necessary to consider the Pomeron with intercept α P = 1 + ∆ > σ tot ∼ s ∆ ). The inclusion of onlythe Pomeron pole contribution in the elastic scattering amplitude leads to violation of the unitarity. Thisdifficulty is removed by taking into account the contribution of branch points of the amplitude in the j -plane, which corresponds to the multi-Reggeon exchange in the t -channel. A Regge-pole exchange can beinterpreted as a single scattering while branch points correspond to multiple scatterings on the constituentsof hadrons.The contribution of the branch points involved in the exchange of several Reggeons associated with ρ, f, ω, etc. decreases very quickly with increasing collision energy and the contribution of such branch points canbe neglected with respect to the branch points due to the exchange of one of them and any number ofPomerons. In the eikonal approximation, where the interaction between Pomerons is neglected, the elasticscattering amplitude can be parametrized by the sum of diagrams shown in Fig. 1.In these graphs, the wavy lines labeled with R correspond to Pomeron and Reggeon exchanges, whereas R + R P + R … P P
Figure 1: Single Regge-pole and multi-Pomeron exchange diagrams. The inclusion of the multi-Pomeronexchange (eikonalisation) suppresses the fast growth of the total cross-section which is expected fromPomeron pole exchange, and restores unitarity.the wavy lines labeled with P correspond only to Pomeron exchange. The account of the multi-Pomeronexchange restores unitarity of the scattering amplitude, which leads to a behavior of the total cross-section1or s >> m N : σ tot ∼ ln s , which satisfies the Froissart bound.For the analysis of pp and p ¯ p total and elastic cross-section data we saturate the matrix elements bythe contribution of f - and ω - Reggeons. Thus, we assume M = M P + M f − M ω for pp collisions and M = M P + M f + M ω for p ¯ p ones. The values of parameters found from a fit to data can be found in [2].The fit result is compared with data in Fig. 2.The processes of single- and double- diffraction dissociation are closely related to small angle elastic GeVs m b s totalelasticpppp -t GeV G e V (cid:215) / d t m b e l s d = G e V s ) · ( = G e V s ) · ( = G e V s ) · ( = T e V s Kwak et al.CDFE710
Figure 2: Comparison of the fit result with data on pp and p ¯ p total and elastic cross-section [3].scattering in which each of the incoming hadrons may become a system, which will then decay into anumber of stable final state particles. In high energy physics, diffraction is usually defined as any processinvolving Pomeron exchange. Experimentally, there is no possibility to distinguish processes that are causedby Pomeron exchange from those that are caused by Reggeon (e.g. f -trajectory) exchange. Therefore,we define diffraction dissociation as the exchange of both Pomeron and Reggeon. In [2] it is proposed todescribe data on soft diffraction dissociation in pp and p ¯ p interactions by taking into account all possiblenon-enhanced absorptive corrections to triple-Regge vertices and loop diagrams (see Fig. 3). The valuesof triple-Reggeon coupling constants were found from fit to data on double differential single-diffractivecross-section versus diffracted mass and transferred momentum. The predictions for integrated single- anddouble- diffractive cross-sections are compared with data in Fig. 4Predictions of the model on total, elastic, single- and double- diffractive cross-sections and on the elasticscattering slope ( B = − [ d (ln σ el ) /dt ] t =0 ) at various LHC energies are presented in Table 1. The uncertaintyof the predictions are expected to be 3% for total and elastic cross-sections and 10% for single- and double-2igure 3: Eikonalised triple-Reggeon and loop diagrams used for describing the single-diffraction dissoci-ation process in hadronic collisions. The solid lines correspond to Pomeron and Reggeon exchanges andthe dotted lines correspond to any number Pomeron exchange. GeVs m b S D s / s < . M / s < . M / s < . M / s < . M GeVs m b DD s > 3 hD Figure 4: Integrated single- (right) and double- (left) diffractive cross-section as a function of √ s . Theintegrations are done in accordance with corresponding measurement as they are indicated in the plots.Data are taken from [4].diffraction ones. Table 1: Predictions for LHC. √ s TeV σ tot mb σ el mb B GeV − σ SD ( M < . s ) mb σ DD (∆ η >
3) mb0.9 66.8 14.6 15.4 9.3 5.72.76 81.8 19.6 17.3 11.2 5.97 96.4 24.8 19 12.9 6.110 102 27 19.8 13.6 6.214 108 29.5 20.5 14.3 6.4
Acknowledgments
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