An Introduction To Quantum Field Theory - M. Peskin, D. Schroeder (Perseus, 1995) · Problem 17.2

Quantum Chromodynamics — M. Peskin, D. Schroeder (Perseus, 1995)

Physics — QFT · qcd-gluon-spin-test

Problem

17.2 A direct test of the spin of the gluon. In this problem, we compare the predictions of QCD with those of a model in which the interaction of quarks is mediated by a scalar boson. Let the coupling of the scalar gluon to quarks be given by δL=gSqˉq,\delta\mathcal{L} = gS\bar{q}q, and define αg=g2/4π\alpha_g = g^2/4\pi. (a) Using the technique described in parts (b) and (c) of the Final Project of Part I, compute the cross section for e+e−→qqˉSe^+e^- \to q\bar{q}S to the leading order of perturbation theory. This cross section depends on the energies of the qq, qˉ\bar{q}, and SS, which we represent as fractions x1x_1, x2x_2, x3x_3 of the electron beam energy, as in Eq. (17.18). Show that d2σdx1dx2(e+e−→qqˉS)=4πα2Qq23s⋅αg4π⋅x32(1−xq)(1−xqˉ).\frac{d^2\sigma}{dx_1 dx_2}(e^+e^- \to q\bar{q}S) = \frac{4\pi\alpha^2 Q_q^2}{3s} \cdot \frac{\alpha_g}{4\pi} \cdot \frac{x_3^2}{(1-x_q)(1-x_{\bar{q}})}. (b) In practice, it is very difficult to tell quarks from gluons experimentally, since both particles appear as jets of hadrons. Therefore, let xax_a be the largest of x1x_1, x2x_2, x3x_3, let xbx_b be the second largest, and let xcx_c be the smallest. Sum over the various possibilities to derive an expression for d2σ/dxadxbd^2\sigma/dx_a dx_b, both in QCD, using Eq. (17.18), and in the scalar gluon model. Show that these models can be distinguished by their distributions in the xa,xbx_a, x_b plane.

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