Quark resonances and high E_t jets

Possible spin-3/2 quark resonances would have a significant effect on high E$_{\mbox{\rm t}}$ jet production through their contribution to the subprocess $q+{\bar q}\rightarrow g+g$. Such enhancements are compared to a, recently reported, anomaly in inclusive jet production at the CDF detector.

The possible existence of spin 1/2 quark resonances has been looked at, both theoretically [1] and experimentally [2]. In the latter two works excluded regions in the mass-coupling constant plane were obtained; these analyses were based on the absence of the direct production of such states. In this article we study the effect of a possible spin-3/2 quark resonance, q * , on the production rate of high E t jets; the exchange of such a particle in the reaction q +q → g + g will enhance high E t gluon jet production. This study is motivated by the recently observed excess of such jets in 1.8 GeV pp collisions [3].
The q − q * − g interaction Lagrangian with a minimum number of derivatives is q * ν is the Rarita-Schwinger field for a spin-3/2 particle, G νλ α is the gluon field strength tensor, M * is the resonance mass, g s is the strong coupling constant and κ parameterizes the strength of this interaction. The quark q and the corresponding q * can represent either the u or the d quark. In subsequent discussion we shall take the masses of u * , d * to be degenerate.
To order α s , the amplitude for q +q → g + g is given by the usual QCD diagrams, Fig. 1, and by the exchange of a q * , Fig. 2. For a spin-3/2 q * the amplitude due to latter will grow by one power ofŝ, the quark-antiquark center of mass energy squared, faster than the amplitude described by Fig. 1. Such growth cannot go on indefinitely as at high enoughŝ an exchange of a spin-3/2 particle will violate unitarity. However, depending on the strengths of various couplings, this increase can persist to large values ofŝ values, typically up tô s ∼ M * 2 /(α s κ 2 ); this limit is well beyond the range ofŝ needed at present.
The effect of such exchanges on E t distributions can be seen in Fig. 3, where we show the transverse energy distribution, at rapidity y = 0, for gluon jets from the parton reactions u+ u → g +g plus d+d → g +g. In all calculations presented here we used the MRSA' In Fig. 4 we plot the sum of the square of the amplitude due to the exchange of a spin-3/2 particle (Fig. 2) and the interference of this and the QCD amplitude (Fig. 1) as a percentage of the corresponding next to leading order QCD calculation [5] of the single jet inclusive cross section and compare to the experimental results of Ref. [3]; the extra contributions is averaged over the pseudorapidity range 0.1 ≤ η ≤ 0.7. We restricted the comparison to κ ≤ 1.0. For κ = 1.0, M * = 400 GeV is largest resonance mass that the data can accommodate; for smaller M * we restricted the comparison to M * ≥ 100 GeV and for the latter we obtain a good fit with κ = 0.13.
As mentioned earlier, restrictions on masses and couplings of spin-1/2 quark resonances exist [1,2]. As we are dealing with a spin-3/2 system these restrictions cannot be taken over directly; namely, restrictions on f s of Refs. [1,2] do not translate into restrictions on κ.
These analyses also assume that analogous couplings of spin-1/2 q * 's to photons and W 's are proportional to f s . The only unambiguous carry over of the spin-1/2 analysis to the spin-3/2 case is for the process of quark-gluon fusion where we find [6] σ(g + q → q * s=3/2 ) = 0.5 σ(g + q → q * s=1/2 ) and thus it is somewhat harder to produce the spin-3/2 state. Should we anyway make such a comparison, it is comforting that these are not far off; M * = 100 GeV, f s = 0.13 is in the allowed range, while for f s = 1.0 the spin-1/2 analysis would limit M * to M * > 560 GeV, again not far away from the value M * = 400 GeV used in this work.
A reanalysis of the data of Ref. [2] using spin-3/2 excited quarks is needed.
In this study we have shown that spin-3/2 quark resonances can account for the observed large high E t cross section.
I would like to thank Dr. Walter Giele for discussions and for providing me with parton structure functions.