Looking for Gluon Substructure at the Tevatron

The impact of nonrenormalizable gluon operators upon inclusive jet cross sections is studied. Such operators could arise in an effective strong interaction Lagrangian from gluon substructure and would induce observable cross section deviations from pure QCD at high transverse jet energies. Comparison of the theoretical predictions with recent CDF data yields a lower limit on the gluon compositeness scale Λ. We find Λ > 2.03 TeV at 95% CL. 7/93 † Work supported in part by the U.S. Dept. of Energy under DOE Grant no. DE-FG03-92ER40701 and by a DuBridge Fellowship. ‡ Work supported in part by the National Science Foundation under grant no. PHY-9218167 and the Texas National Research Laboratory Commission under grant no. RGFY93-278B The inclusive jet cross section data from the 1988-89 Fermilab Tevatron run span seven orders of magnitude and include the highest transverse jet energy measurements reported to date [1]. These data provide a stringent test of quantum chromodynamics and constrain possible new physics beyond the Standard Model. In particular, they set improved limits on hypothetical quark substructure. At energies small compared to the compositeness scale Λ, the dominant effects from quark substructure can be reproduced by four-quark operators in a low energy effective Lagrangian [2]. Although their coefficients are unknown in the absence of a detailed theory of preon dynamics, the general impact of these nonrenormalizable operators upon parton scattering may be estimated. The remarkable agreement between the experimental measurements and the predictions of QCD then places a bound on the quark compositeness scale. CDF finds a lower limit on Λ of 1.4 TeV at the 95% confidence level [1]. In this letter, we reinterpret the CDF data to probe for signals of new physics that could arise in the gluon sector. Specifically, we consider the impact upon the inclusive cross section measurements of nonrenormalizable gluonic operators which may appear in the effective strong interaction Lagrangian. Such operators could originate from a number of different sources. For example, suppose there exist new heavy colored bosons or fermions beyond those in the Standard Model. Such particles would induce nonlocal interactions among gluons through loop diagrams. The leading behavior of these graphs can readily be extracted and reexpressed via an operator product expansion in terms of local but nonrenormalizable gluon operators. Alternatively, we might speculate that gluons are bound states of some more fundamental preon constituents. Then as in the case of composite quarks, preon exchange could generate nonrenormalizable gluon interactions. In the following, we will adopt a model independent approach and not specify the underlying physics whose low energy effects are encoded in the effective Lagrangian. Instead, we simply seek to place a limit on its characteristic scale Λ. We first enumerate the lowest dimension gluon operators whose scattering effects would be easiest to observe. There exist only two independent operators of mass dimension d+ 2 in d = 4− ǫ spacetime dimensions which preserve gauge invariance along with C, P and T [3]: O1 = μg Λ2 fabcG ρ aνG ν bλG λ cρ O2 = 1 2!Λ2 DGρνDλG λν a (1)