How large is the total cross section at supercollider energies?

Abstract

Although the value of the total cross section is critical for the operation and physics exploitation of supercolliders, we have until now been unable to anticipate its magnitude. Extrapolations of lowenergy data patterned after models with a varying degree of dynamical justification, and invariably a too large number of free parameters to be truly predictive, led to a wide range of predictions. We point out that a series of new measurements at the Fermilab Tevatron Collider on forward-scattering parameters dramatically narrows the range of extrapolations and we anticipate that utOt = 107 j, 4 mb at f i = 16 TeV, and utOt = 121 1 5 mb at f i = 40 TeV, using a QCD-inspired parametrization.More surprisingly, the model dependence of the extrapolations is reduced by the new data to the point that a wide range of models investigated converge on the above values. PACS number(s): 13.85.Lg; 1.38.Qk; 1.40.Gg; 12.40Pp I. I N T R O D U C T I O NThe commissioning of the Fermilab Tevatron has extended the kinematic-range over which QCD can be confronted with experiment. Recent measurements [ I , 21 of a t , t , B, and the p parameter at fi = 1800 GeV have basically completed the information we will have on forward-scattering parameters before the supercolliders are in operation. On the theoretical side there are now three main approaches to interpret this information: (i) the Regge pole model, (ii) analytic asymptotic amplitude analysis, and (iii) QCD-inspired models. Although these models can all accommodate the data, they differ .in significant aspects. Most importantly, the three models ascribe the rise of the total cross section as due to (i) a Regge power so, (ii) an asymptotic term which the d a t a now pinpoints to behave as Ins [3,4] and (iii) the dramatic increase of the number of soft partons, respectively.In actual fits the three approaches give virtually indistinguishable results in the energy region in which data are available. However, this similarity disappeares a t sufficiently high energy leading to widely varying predictions for total cross sections a t energies of the CERN Large Hadron Collider (LHC) and the Superconducting Super Collider (SSC). A study of the high energy predictions of such models is timely and important, given the critical impact of the forward-scattering parameters on tlie operation and physics exploitation of hadron colliders. Our main conclusion will be that all approaches converge on the value atot(LHC) = 107 k 41nb and at,t(SSC) = 121 f 5 mb once the new data is included.The errors are specific to an analysis performed with the models of type (iii). In the future these predictions can still be sharpened by more accurate measurements of the high energy p values. This latter statement is inodel independent, to the extent that p (at a lower energy) is connected to the higher energy behavior of utot by analyticity.What we have learned from Tevatron measurements is that even a t fi = 1.8GeV we are not witnessing the asymptotic behavior of hadron collisions, despite the fact that atOt has r...

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