Measurement and QCD Analysis of Jet Cross Sections in Deep-Inelastic Positron-Proton Collisions at sqrt(s) of 300 GeV

According to our current knowledge the proton is not an elementary particle. It consists of electrically charged constituents, the quarks, and electrically neutral constituents, the gluons. The quarks and gluons are bound in the proton through the strong interaction which is described by the theory of Quantum-Chromodynamics (QCD). The strength of the strong interaction is given by a parameter, the strong coupling constant: alpha_s.

The strong interaction confines the quarks and gluons in the proton, but it does not play a role on macroscopic scales in everyday's life. In particle collisions at high energy, however, effects due to the strong interaction can become directly visible in events in which large numbers of particles are radiated in small angular regions. These collimated sprays of particles are called jets.
Studies of the production rates of multi-jet events therefore allow to investigate properties of the strong interaction and to test the theoretical predictions of QCD.

While QCD does predict the properties of the interactions between quarks and gluons it does neither predict the coupling strength alpha_s nor the distributions of the quarks and gluons inside the proton, the quark and gluon density functions.
Both alpha_s and the quark and gluon density functions can be determined from comparisons of the QCD predictions to experimental measurements. In this analysis the H1 collaboration has carried out a determination of the strong coupling constant alpha_s and the gluon density in the proton from inclusive jet and dijet cross sections measured in deep-inelastic positron-proton collisions.

The deep-inelastic scattering (DIS) of a positron off a proton proceeds via the exchange of a photon. Since the photon couples only directly to the charged constituents of the proton, the positron inclusive DIS cross section is directly sensitive only to the quark content of the proton. In most DIS events the final state therefore consists of a single quark which is scattered under a large angle with respect to the proton remnant. Due to the properties of the strong interaction the scattered quark evolves to a jet of particles which can then be measured in a detector.
The gluon content of the proton contributes to the DIS cross section only through processes in which a gluon splits into a quark-antiquark pair from which one couples to the photon. Since the gluon splitting proceeds through the strong interaction this process also involves the strong coupling constant alpha_s. A specific feature of these processes is the presence of the second quark in the final state. Experimentally these processes can therefore be tagged by selecting DIS events in which the final state contains two jets of particles.

The H1 collaboration has measured inclusive jet and dijet cross sections in DIS over a large range of momentum transfers Q² between 5 and 15000 GeV² and transverse jet energies E_T in the Breit frame between 7 and 60 GeV. The results are presented multi-differentially as a function of various variables that describe the dynamics of the underlying hard scattering process. The predictions of QCD which are using the current world knowledge on the strong coupling constant alpha_s and the quark and gluon density functions of the proton give a good description of the data. The large kinematic region and the variety of measured distributions allow for the first time to demonstrate unequivocally the success of QCD in describing jet production in DIS.

QCD fits are performed in which alpha_s and the gluon and quark densities in the proton are determined. Using the world knowledge on the quark and gluon density functions, the strong coupling constant is determined as a function of the transverse jet energy E_T (figure 1). The observed decrease of alpha_s towards higher E_T is consistent with the theoretical prediction by the "renormalization group equation", indicated by the lines in figure 1. A combined fit to all data gives a result which, when extrapolated to the mass of the Z boson, is alpha_s(M_Z) = 0.1186 +- 0.0059.

Using, alternatively, the world knowledge on alpha_s, the gluon density in the proton is determined (together with the quark densities) in the range of proton momentum fractions 0.01 < x < 0.1 carried by the gluons. The gluon density is seen to increase strongly towards smaller values of x (figure 2). This result in good agreement with results obtained in other analyses using different observables.

In addition an analysis of the data in which both alpha_s and the gluon density are determined simultaneously is presented. This is the first simultaneous determination from observables with direct sensitivity to both. The results (figure 3) are displayed as a correlation plot between alpha_s(M_Z) and the gluon density at four different values of the proton momentum fraction x=0.01, 0.02, 0.04, 0.1. The error ellipses indicate the strong anti-correlation between alpha_s and the gluon density in the proton which is a clear demonstration that the jet cross section is essentially depending on their product.

Last Update October 8, 2000, M. Wobisch