Test for Fractionally Charged Partons from Deep-Inelastic Bremsstrahlung in the Scaling Region

We show that measurements of deep-inelastic bremsstrahlung, $e^{\pm }+p\to e^{\pm }+\gamma +\mathrm{anything}$, in the appropriate scaling region will provide a definitive test for fractionally charged constituents in the proton, provided the parton model is valid. More precisely, measurement of the difference between the scaling inclusive bremsstrahlung cross sections of the positron and electron will allow the determination of a proton structure function $V\left(x\right)\mathrm{}$ which, unlike the deep-inelastic $e-p$ structure functions, obeys an exact sum rule based on conserved quantum numbers. In particular, we show that $\int 0^1\mathrm{dx}V\left(x\right)\mathrm{}=\frac{1}{3}Q+\frac{2}{9}B$ (=$\frac{5}{9}$ for a proton target) in the quark model, whereas $\int 0^1\mathrm{dx}V\left(x\right)\mathrm{}=Q$ in the case of integrally charged constituents. Since the result is independent of the momentum distribution of the partons, the sum rule holds for nuclear targets as well. Since $V\left(x\right)\mathrm{}$, which involves the cube of the parton charge, is related to odd-charge-conjugation exchange in the $t$ channel, Pomeranchukon, and other $C$-even contributions are not present, so that $V\left(x\right)\mathrm{}$ should have a readily integrable quasielastic peak. This, combined with the fact that there exists a simple kinematic region in which the difference is of the same order as the inclusive bremsstrahlung cross sections themselves, and the fact that there is no hadronic-decay background, should make this a feasible experiment on proton and nuclear targets.