Volume 218, number 3 PHYSICS LETTERS B 23 February 1989

PRECISION MEASUREMENTS OF W-BOSON PROPERTIES IN AN e-~, COLLIDER

Gilles COUTURE, Stephen G O D F R E Y Guelph- Waterloo Program for Graduate Work in Physics, Department of Physics, University of Guelph, Guelph, Canada N1G 2WI

and

Pat KALYNIAK Ottawa-Carleton Institute for Physics, Physics Department, Carleton University, Ottawa, Canada KIS 5B6

Received 15 November 1988

We study the possibility of making precision measurements of W-boson properties with an e-7 collider. We find that the mea- surements are comparable in sensitivity to W-pair production measurements to be made at the LEPII e+e - collider. In addition this process will be able to measure the W-photon anomalous magnetic moment, Kv, independently of the W-Z ° anomalous mag- netic moment, Xz,,. This process is potentially a goldmine of W-boson physics and we strongly encourage that serious thought be given to the possibility of building such a collider.

Although we have a very successful theory of the electroweak interactions [ 1 ], it is becoming a clich6 that it is only a low energy manifestat ion of a deeper, more fundamental theory. The problem is not that its predictions disagree with experiment but that there are many questions which the standard model does not address; for example, the number of fermion gen- erations and the large number of parameters. Given this general dissatisfaction, a widespread preoccupa- t ion of particle physicists is to discover phenomena which are inconsistent with the standard model ~. In this letter we present the results of a detailed calcu- lation of single W-boson product ion at an e-7 colli- der including the decay of the W and the relevant background processes. Our results show this reaction to be an excellent means of testing the standard model via precision measurements of the W-boson mass, width, and anomalous magnetic moment .

Because the standard model is a renormalizable field theory measurable quanti t ies can be calculated to arbitrarily high accuracy using a finite number of input parameters [3]. Comparing the theory's pre-

"t For a recent review of the standard model see ref. [2].

dictions to experiment tests the validity of the stan- dard model. Therefore, assuming that precision mea- surements of the Z ° mass and width will have already been made at the e+e - colliders SLC at SLAC or LEP at CERN, a measurement of Mw to -~_+40 MeV would, for example, put limits on the number of ad- ditional generations of quarks [4]. Similarly, preci- sion measurements of the anomalous magnetic mo- ment of the W, xv, would constrain the number of heavy fermions, Higgs bosons and supersymmetric particles. Deviat ions as large as 5% in Kv would signal new physics [ 5 ].

Recent studies and proposals have found that an e-7 collider may be feasible with current technology [6,7]. The basic idea is to fire a low energy mono- chromatic laser against the e + beam in an e+e - col- lider. The low energy photons backscatter off the e + picking up most of the e + momen tum and become high energy photons. These then collide with the e - beam. Center-of-mass energies and luminosit ies roughly comparable to the original collider are expected.

The basic process of single W production, given by the Feynman diagrams of fig. 1, have been calculated

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Volume 218, number 3 PHYSICS LETTERS B 23 February 1989

e - v e ~ ~ e

~W- W-

Fig. 1. Feynman diagrams contributing to the process e y--+W v<..

previously by Renard and Mikael ian ~2. However, an exper iment does not observe W's but rather the W decay products; hadronic jets from the quark decay mode or a single energetic lepton plus missing mo- mentum from the leptonic decay mode. Thus, we consider the three distinctive decay modes along with the background processes that give the same final state:

101 . . . . . . . . . . .

,o-I --.; . . . . "

10 -2 . . . . . . . . . . . . . . . . . . . 50 75 1 O0 125 150

,A (cev) Fig. 2. The cross section for single W production in e7 collisions as a function of the center-of-mass energy, a(e-7~W-v~) is given by the solid line, cr(e-7~vJx-,7~) is given by the dotted line, ~7(e "f~v~qq' ) is given by the dashed line, and cr(e y-,e v~v~) is given by the dash-doned line.

ey--'veW--+vegg,, ey->veqCt', ey~e -v~?~ .

We used the C A L K U L [ 9 ] me thod to obta in ana- lytic expressions for the relevant helicity ampl i tudes and integrated over the mul t id imensional phase space using s tandard Monte Carlo integrat ion techniques. The details of our calculat ion will be presented else- where [ 10 ]. We take Mzo = 92.5 GeV, Fzo = 2.5 GeV, sin20w = 0.23 and use Mw = 82 GeV and Fw = 2.7 GeV to obtain numerical values for the cross sections and the dis t r ibut ions. We also include the cut that all measurable momen ta must be at least 8 ° away from the beam.

The cross sections for the three modes are shown in fig. 2 along with the cross section for eT -veW. For ey~ve~tg, the cross section at x / s = 100 GeV is 0.17 pb. This cross section is too small to improve on ex- isting measurements o f Mw and Fw [ 11 ]. However, x v could in principle be measured to 1+0 .3 and 1 _+ 0.5 with integrated luminosi t ies of 100 pb-~ and 500 pb t respectively. This is bet ter than can be achieved at LEPI1 for comparable integrated lumi- nosities [ 12 ].

The cross section for eT-~ ev~ 9~ is significantly larger than the gg , mode. The problem here is that the in- crease in the cross section comes from Z ° brems- strahlung which only obscures the W boson physics we are interested in. The signal could be improved by making a cut on the electron energy to remove the Z ° pole but this just brings us back to a s i tuat ion s imilar to the g final state.

~-' For earlier work on e7 phenomenology see ref. [ 8 ].

The qq ' decay modes will require good jet detec- t ion to be successful but is potent ial ly the most im- por tant since the W ~ q q ' branching fraction is about a factor o f six larger than the leptonic modes (where we have included the first two generations of quarks) . The cross section for M w = 8 2 GeV, F w = 2 . 7 GeV, and ~cv = 1 at xf~ = 100 GeV is about 1 pb yielding 100 events for our assumed 100 pb -~ integrated lumi- nosity. Thus, 0.1 pb devia t ions could be measured at the l a level. This corresponds to measuring Mw to about 1 GeV (500 MeV), Fw to about 400 MeV (300 MeV) , and #cv to about 0.1 (0.05) with an integrated luminosi ty of 100 p b - ~ ( 5 0 0 p b - ~ ) . The first two measurements offer little or no improvement over existing measurements but the measurement of Ky would be the first test of the 7 - W - W tr i l inear gauge coupling and might be able to detect contr ibut ions of new physics at the loop level.

Given the small cross sections we examined distri- but ions of various k inemat ic variables for more sen- sit ive measurements of W parameters . We evaluated the cross sections at , ~ = 100 GeV and assumed in- tegrated luminosi t ies of 100 p b - ~ and 500 pb i.

We start with the W mass. Dis t r ibut ions coming from the hadronic modes are the only ones with suf- ficient statistics to improve on existing measure- ments. The most useful dis t r ibut ion for de termining Mw is likely to be do'/dmqq, with the kinemat ic re- gion of interest shown in fig. 3. To obtain a crude es- t imate of the expected statistical error we per formed a X 2 fit on the dis t r ibut ion using a Bre i t -Wigner pa- rametr iza t ion with statistical uncertaint ies based on

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Volume 218, number 3 PHYSICS LETTERS B 23 February 1989

lO 0

lO_1

g 10-2

10-3

/ / '

/ / . / / ' . "/'

I J j '

70 75 80 85 90

Mqq (GeV)

Fig. 3. The differential cross section do'/d,~fqq for the process e "/-,v~q(l'. The solid line is for Mw=83 GeV, the dash-dotted line is for Mw = 82 GeV, and the dashed line is for Mw = 81 GeV.

some assumed integrated luminosi ty. Wi th this crude approach we es t imate a statist ical error in Mw of 8Mw -~ 110 MeV and 6 M w ~ 5 0 MeV at 68% confi- dence level for integrated luminosi t ies of 100 p b - and 500 p b - ~, respectively. These errors are compa- rable to those expected from e+e - ~ W + W - produc- t ion at LEPII at CERN [ 13 ]. We note that we d id not take into account hadronic je t reconstruct ion effi- ciencies and detector acceptances (o ther than the 8 ° cut on outgoing particles). Also, it is likely that a more sophis t icated analysis could improve these crude es- t imates. Despi te these inadequacies we feel that this process is promis ing enough that it deserves further considerat ion.

Turning to the measurement of Fw we again f ind it unlikely that the leptonic modes will offer significant improvemen t over other measurements . Typically, integrated luminosi t ies of 100 pb -~ and 500 p b - would result in statist ical errors of about 500 MeV and 250 MeV, respectively. Once again the hadronic modes offer bet ter statistics and hence a more precise measurement o f Fw. Using the invar iant mass distr i- but ions of qq ' jets with an integrated luminosi ty of 100 pb-~ and 500 pb-~ we est imate that Fw could be measured to approx imate ly 250 MeV and 100 MeV, respectively.

Finally, we consider the measurement of icy. While Mw and Fw can be measured with s imilar precis ion elsewhere, in par t icular at LEPII, the process e - 7 ~ W v ~ offers a unique means of s tudying ~c v in- dependent of Xzo. In fact the s i tuat ion is even bet ter since the cross sections and dis t r ibut ions are quite sensit ive to ~cv. Wi th integrated luminosi t ies of 100 and 500 p b - ~ the process with the smallest cross sec- tion, ey - ,v~gg , , will be able to measure ~cy to about

30% and 10%, respectively, which offers significant improvemen t over what can be achieved at LEPII with comparable luminosi t ies [12]. The si tuat ion is s imilar for eT--,e veV~. Looking at the dis t r ibut ions, say da/dPr~ where PT~ is the transverse m o m e n t u m of the charged lepton, shown in fig. 4, and integrating over part of the kinemat ical ly allowed region to elim- inate the effects of the Z ° pole ~cv could be measured to about 30% and 10% with integrated luminosi t ies of 100 pb -~ and 500 pb - j . For the measurement of ~cv in hadronic modes we show in fig. 5 the effects of varying xv on the angular d is t r ibut ion of the W. As- suming that the W-boson momen tum can be recon- s tructed from jets, measurements of ~ can be made to 10% and 5% for integrated luminosi t ies of 100 and 500 p b - ~, respectively. Measurements at this level of precision will start to probe the loop contr ibut ions to x 7 .

We conclude that an e7 coll ider offers a unique

10 o

© r.~ 10-1

n o_

10-2 0

F-- £3-

~2~ 10-3

b q3

10 -4 10 20 30 40 50

PTe (GeV)

Fig. 4. The differential cross section da/dPz~ for the process ey~e-veP~ for several values of ~cx. The solid line is for xy=0.5, the dash-dotted line is for ~cy= 1.0, and the dashed line is for ~:y= 1.5.

101

Q. ~-~ 10 0

o . .~ 10 - I

b X2

1 0 - 2 -1 .o -0.5 0,o 0.5 1.o

cos 0 Fig. 5. The W boson angular distribution as reconstructed from the hadronic decay modes. The line labelling is as in fig. 4.

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Volume 218, number 3 PHYSICS LETTERS B 23 February 1989

means o f mak ing precise m e a s u r e m e n t s o f W-boson

parameters and test ing the s tandard model . The cross

sect ions are c o m p a r a b l e in m a g n i t u d e o f W + W -

p r o d u c t i o n cross sect ions at e+e - col l iders once W-

decay branching fract ions are taken into account . The

crucial ques t ion in all this is ob ta in ing a d e q u a t e lu-

minos i ty . It is our hope tha t i f no th ing else this le t ter

will have s t imu la t ed the in teres t o f o thers enough to

explore the feasibi l i ty o f such an expe r imen t .

T h e au thors grateful ly acknowledge J i m D a v i s and

his group for the use o f the i r g-Vax. S.G. is mos t

grateful to L.B. H o p s o n for helpful conversa t ions .

Th is work was funded by the Na tu ra l Sc ience and

Engineer ing Research Counc i l o f C a n a d a th rough

grants # U O 5 3 0 and # U O 5 7 3 .

References

[ 1 ] S.L Glashow, Nucl. Phys. 22 ( 1961 ) 579; S. Weinberg, Phys. Rev. Lett. 19 (1967 ) 1264; A. Salam, Proc. 8th Nobel Syrup., ed. N. Svartholm (Wiley, New York, 1968 ).

[2] J. Rosner, Proc. 1987 Theoretical Advanced Study Institute (St. John's College, Santa Fe, NM) (World Scientific, Singapore, 1988 ).

[3]See e.g.S. Sakakibara, Proc. Workshop on Radiative corrections in SU (2) L X U ( 1 ), eds. B.W. Lynn and J.F. Wheater (World Scientific, Singapore, 1983 ); Phys. Rev. D 24 (1981) 1149; F. Dydak et al., Proc. ECFA Workshop on LEP 200, eds. A. Bohm and W. Hoogland, CERN report CERN 87-08 ( 1987 ), unpublished.

[4] W.J. Marciano and A. Sirlin, Phys. Rev. D 29 (1984) 945, and references therein.

[5] See e.g.G. Couture, J.N. Ng, J.L Hewett and T.G. Rizzo, Iowa State University report IS-J 2831-Rev (1988), unpublished, and references therein.

[6] C. Akerlof, University of Michigan report UM HE 81-59 ( 1981 ), unpublished.

[ 7 ] I.F. Ginzburg et al., Sov. J. Nucl. Phys. 38 (1984) 222. [8] K.O. Mikaelian, Phys. Rev. D 17 (1978) 750:

F.M. Renard, Z. Phys. C 14 (1982) 209. [9] R. Kleiss and W.J. Stirling, Nucl. Phys. B 262 (1985) 235,

and references therein. [10] G. Couture, S. Godfrey and P. Kalyniak, University of

Guelph report GIPP 88-5 ( 1988 ), unpublished. [11] T. Mfiller, CERN report CERN-EP/88-48 (1988),

unpublished. [ 12] A. Blondel et al., Proc. ECFA Workshop on LEP 200, eds.

A. Bohm and W. Hoogland, CERN report CERN 87-08 (1987) p. 120, unpublished.

[ 13 ] J. Bijnens et al., Proc. ECFA Workshop on LEP 200, eds. A. Bohm and W. Hoogland. CERN report CERN 87-08 ( 1987 ) p. 49, unpublished.

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