Z. Phys. C - Particles and Fields 29, 381-383 (1985) Partk for Physik C and 9 Springer-Verlag 1985 Test of QCD in dr1~ W-7g, the Radiation Amplitude Zero and the Magnetic Moment of the W Boson N.M. Monyonko Physics Department, University of Nairobi, Kenya J.H. Reid, M.A. Samuel, G. Tupper Physics Department, Oklahoma State University, Stillwater, OK 74078, USA Received 1 March 1985; in revised form 10 April 1985 Abstract. We have calculated the differential cross- section for the process dO--* W-?g (Jet). It is found that, although the radiation amplitude zero, which occurs for the lowest-order process dfi~ W-7, is spoiled, there remains a very large dip. Hence, both processes can be used to measure the magnetic moment of the W boson and the value of the quark charges. The presence of a dip is a test of the gauge theoretical value for the magnetic moment of the W boson g = x + 1 = 2, and the angle at which the dip occurs is a measure of the quark charges. It is well known that the process dti ~ W- 7 calculated at the tree level has an amplitude zero [1,2] in the classical null zone [3] Qi/k'ql=Qj/k'q2. In fact, the lowest-order amplitude for this process may be written in factorized form: -ieg~ ~ v To - ~.~ ~,~jj(q:)Mo(1 - v~)u,(ql) Mo=Z y~?~-7. 7~ (1) (2) with Z = (Qik'q2- Qjk'ql)/k'p, the amplitude zero factor [1]. Here ql,2 are quark momenta, p is the W- momentum, k is the photon momentum, Qi,J are quark charges and /1,2 = P -- q2,1" Since this effect is purely classical [2], it is important to consider the 0(as) quantum corrections to it. Higher- order corrections have been considered only in scalar models so far [4]. The purpose of this brief note is to consider the effect of the amplitude zero upon the related 0(as) process da~ W-yg, which would be the underlying process in the reaction p/5~W-7+jet or pp~W-?+jet. The total gluon bremsstrahlung amplitude may be exhibited in semi-factorized form as follows [5]: _ -- iegjs , v p "~aiJ Tb .... 2%/~ 137gw~g 2 "fij(q2)M(1 -- 75)ui(ql) (3) M=A+B+C+D+E (4) 1 1 1 1 B = Qik'q2 - Qjk'(ql - 9) k'p C = Qjk'ql - Qik'(q2 - #) 1 k'p 7Pr -~t ~.~.?o + ~?.(~, - ~)?~ (8) QJ - 0)7~]~7,} (9) E-Q;;p {- 7o?g?,- Yo(~2 Here g is the gluon four momentum, the amplitude A corresponds to the sum of diagrams (a) and (b) in Fig. 1, the amplitudes B and D to the sum of (c), (d) and (e), and C and E to (f), (g) and (h). The advantage of this representation is that it explicitly exhibits the dominant terms in the soft gluon limit, namely B and C. In this limit they factorize, being proportional to the lowest-order amplitude Mo, as may be seen by