PHYSICAL REVIEW D VOLUME 26, NUMBER 9

Rapid Communications

1 NOVEMBER 1982

The Rapid Communications section is intended for the accelerated publication of important new results. Manuscripts submitted ro this section are given prioriy in handling in the editorial ofhe and in production. A Rapid Communication may be no longer than 3% printed pages and must be accompanied by an abstract. Page proofs are sent to authors, but, because of rhe rapid publication schedule, publication is not delayed for receipt of corrections unless requested by the author.

Amplitude zeros in pjicollisions and the quark magnetic moment

Morten L. Laursen, Mark A. Samuel, and Achin Sen Department of Physics, Oklahoma State UniversiQ, Stillwater, Oklahoma 74078

(Received 26 July 1982)

The effect of the quarks having an anomalous magnetic moment on the zeros (dips) in the angular distribution for the process dii + W-y (pj? + W-yX) is studied. It is found that for small values of the quark anomaly [ a = ( g -2)/21 the distributions are practically unaffected and as a Increases, the dips gradually disappear. This study might provide us with a way of obtaining an upper bound for the anomalous magnetic moment of the Wbosons.

The weak intermediate vector bosons W' and Zo are expected to be produced within a year or so. The next step would be the measurement of some of the weak-boson properties. The study of the differential cross section of p p 4 W ' ~ X has been shown to pro- vide a sensitive test of the anomalous magnetic mo- ment of the Wboson. It has been found' that the basic quark cross section d u ( d i i - W-y)/d cos8 has a zero at cos8 = -f, provided the quarks and the W bosons have no anomalous magnetic moments. More examples of such zeros have been found2 in connection with other processes, and recently Brod- sky and Brown3 and ,Samuel4 have shown the ex- istence of such zeros in a wide variety of processes, provided some basic constraints are satisfied.

The zeros occur in the various qq -+ W-y cross sections and hence d v ( p p 4 W-yX)/dcosO exhibits

1 a very prominent dip at cosO,, = -7 if neither the W boson nor the quarks have an anomalous magnetic moment. The effect of a nonzero anomalous mag- netic moment of W- on this dip has been investigat- ed in detail' and it offers a way of measuring the W magnetic moment. In this Communication, we shall study the effect of a quark anomalous magnetic mo- ment on the angular distributions for both dii -+ W-y and pj i4 W-yX, assuming that the magnetic mo- ment of the W boson has its gauge value p w = e/Mw. We shall study the effect as a function of the quark anomaly defined as a = ( g - 2112. For simplicity, we have chosen a, = ad. We have used the standard coupling of the W boson with the other particles. The point is that if, in an actual experi- ment, a deviation from the results predicted by the

standard model (with no quark or W-boson anomaly) is observed, it would be of interest to know how much of this deviation could be attributed to the quark anomaly and thus place an upper bound on the W-boson anomalous magnetic moment. Of related interest, anomalous magnetic moments provide very tight constraints on possible composite models of quarks and leptons.'

The differential cross section for the process di i+ W-y has been calculated and can be expressed as

where

8 is the angle between the W- and the d i n the dE ( W-y) c.m. frame.

The function F(yl,yz,a) can be expressed in terms of yl , y2, a, the mass ratio R = ( M ~ l m 12, and the combination Z = Q l - $ J y 2 / ( ~ 1 fy2) (in our case,

1 Ql = -7 for d, Q2 = -.j- for ii, and Q Q1 + Q2 = -1 ) in the following form:

26 2535 01982 The American Physical Society

2536 RAPID COMMUNICATIONS 26

The terms proportional to Z exhibit a zero at the point Q1/Q2=y2/y1, i.e., at cosO=-1/(3p) --i in

I our case as p = 1. Notice that if p < 7 (nonrelativis- tic limit) the zero moves out of the physical regions4 For zero quark anomaly, Eq. (2) agrees with the results obtained by Nilles6 We also notice that in the limit a -0 the result is proportional to Z2 and hence the zero persists for nonzero quark masses2 (provid-

I ed, of course, that p > -j-). The symmetry corre-

I

sponding to the interchange of particles 1 and 2,

F (y l ,y~ ,a ) = F(yz,yl, -a with 91 -92 ,

is also manifestly exhibited. We now study the effect of having R >> 1, since

this is the actual situation. For small a values such that Ra2 << 1, the term proportional to Za dom- inates, and hence, the effect of the zero (in the form of a prominent dip) is observed. For sizable values

COS 9

FIG. 1. The differential cross section for dii - W-y. 8 is the angle between the W- and the din the c.m. frame. -& = 200 GeV and Mw = 77.4 GeV.

FIG. 2. The differential cross section for pp4 W-yX with a photon energy cut E , > 30 GeV. O,,,, is the angle between the W- and the proton beam in the W-y c.m. frame. -& 540 GeV and Mw = 77.4 GeV.

26 RAPID COMMUNICATIONS 2537

of a ( R a 2 -- 1 ) this should disappear and for large a values, i.e., R a 2 >> 1, the leading term is proportion- al to a2.

Figure 1 shows the differential cross section for dfi- W-y as a function of cos0. We have taken the values 6 = 200 GeV, Mw = 77.4 GeV, and mu = md =0.3 GeV. As expected, one finds the zero at cos0 = -f for a =O. For values a 5 lo4 the distri- bution is almost indistinguishable from the a = O case. For a 2 there appears a significant change in the distribution and this increases as a increases. Beyond a = even a dip is hardly noticeable and the whole curve moves up higher. For a 2 the R a 2 term dominates the cross section, as expected.

Figure 2 shows the differential cross section for pj? 4 W-y X as a function of cosO,,, where O,,, is the angle between the W- and the proton beam in the W-y c.m. frame. We have chosen the c.m. energy to be 6 - 540 GeV, Mw = 77.4 GeV, and md = mu = m, =0.3 GeV. We also have introduced a cut in the photon energy E, > 30 GeV. The effect of put- ting the strange-quark mass equal to the u (and d - )

quark mass has been estimated to introduce an error of less than 10%. Looking at Fig. 2, we again ob-

1 serve very sharp dips (at cosO,,,, = - T ) for small a values. For larger values of a, the dip disappears, as expected. The parton-model formulas for the pji cross section in terms of the p and pdistribution functions are given in Ref. 1.

We have not shown the pp -+ W-yX differential cross section-but here, even for small a, the dips at the places cosO,, = ++ tend to be washed out. One can, however, overcome this by proper binning of events. A detailed discussion of this will be pub- lished elsewhere.

It is a pleasure to thank Sheldon Glashow for very interesting discussions and encouragement in this research project. We are also happy to acknowledge valuable discussions with Karnig Mikaelian, Bob Brown, Stan Brodsky, Kimball Milton, and Gary Tupper. This work was supported by the U.S. Department of Energy under Contract No. EY-76-S- 05-5074.

'K. 0. Mikaelian, M. A. Samuel, and D. Sahdev, Phys. Rev. Lett. 43, 746 (1979).

2T. R. Grose and K. 0. Mikaelian, Phys. Rev. D 23, 123 (1981).

)S. J. Brodsky and R. W. Brown, Report No. Fermilab-Pub- 82135-THY, 1982 (unpublished).

4M. A. Samuel, Oklahoma State University Research Note 133, 1982 (unpublished).

SG. L. Shaw, D. Silverman, and R. Slansky, Phys. Lett.

m, 57 (1980); S. J. Brodsky and S. D. Drell, Phys. Rev. D 22, 2236 (1980); M. Bander, T. W. Chiu, G. L. Shaw, and D. Silverman, Phys. Rev. Lett. 47, 549 (1981). For a recent calculation of the effect of quark or 7 form factors at large q2 in e+e- annihilation (as distinct from the static moments considered in this paper), see D. Silverman and G. L. Shaw, University of California, Irvine, Report No. 82-1 1, 1982 (unpublished).

6H. P. Nilles, Phys. Rev. Lett. 45, 319 (1980).