8
PHYSICAL REVIEW D VOLUME 5 1, NUMBER 9 1 MAY 1995 Probing the Higgs mechanism via yy -+ W+W- A. Denner and R. Schuster Institut fur Theoretische Physik, Universitat Wurzburg, Am Hubland, 0-97074 Wurzburg, Germany S. Dittmaier Theoretische Phyaik, Universitat Bielefeld, Universitatsstrajle, 0-33501 Bielefeld, Germany (Received 21 November 1994) We investigate the sensitivity of the reaction yy + W+W- to the Higgs sector based on the complete one-loop corrections in the minimal standard model and the gauged nonlinear u model. While this sensitivity is very strong for the suppressed cross section of equally polarized photons and longitudinal W bosons, it is only marginal for the dominant mode of transverse polarizations. The corrections within the u model turn out to be UV finite in accordance with the absence of 1 n M ~ terms in the standard model with a heavy Higgs boson. PACS number(s): 11.15.Ex, 13.10.+q, 14.70.Fm, 14.80.Bn I. INTRODUCTION All present experimental results on electroweak physics confirm the conception that electromagnetic and weak interactions are unified in an SU(2) xU(1) gauge theory. However, the underlying field theory cannot be of pure Yang-Mills type since the weak gauge bosons, the W* and Z bosons, are empirically known to be massive. In the electroweak standard model (SM) this problem is solved by the well-known Higgs mechanism [I], i.e., by breaking the gauge symmetry spontaneously via a nonva- nishing vacuum expectation value of an additional com- plex scalar SU(2) doublet. Whereas three of these four scalar fields are absorbed by the longitudinal degrees of freedom of the massive gauge bosons, a physical scalar field survives, the so-called Higgs boson. Of course, the Higgs mechanism cannot be conclusively confirmed be- fore this particle is empirically detected. On the other hand, the Higgs-boson mass MH, which is a free pa- rameter of the theory, enters all theoretical predictions within the SM at least via higher orders. Since the Higgs- boson-mass dependence of low-energy observables turns out to be very mild, more precisely at most logarithmic at the one-loop level, only crude bounds on MH can be obtained from radiative corrections (RC's) to current pre- cision measurements. Experimentally, the Higgs-boson- mass is only constrained by the lower bound MH 2 60 GeV from the CERN e+e- collider LEP [2] but can well be in the TeV range. The Higgs boson can be removed from the physical particle spectrum in two different ways. On the one hand, amplitudes can be calculated within the SM for fi- nite MH, and subsequently asymptotically expanded for MH -+ m. Alternatively, the physical Higgs field can be eliminated by constraining the square of the Higgs- doublet field to be constant and equal to its (nonvanish- ing) vacuum expectation value. Then no physical Higgs particle exists from the beginning, but one is forced to introduce a nonlinear representation of the Higgs sector leading to a nonrenormalizable gauged nonlinear u model (GNLSM). The relation between the heavy-Higgs-boson limit and the GNLSM has been investigated for an SU(2) gauge theory and the SU(2)xU(1) SM in [3] and [4,5], respectively. As expected, MH acts as an effective UV cutoff. The corresponding (logarithmic) one-loop diver- gences in the GNLSM can be identified with the In MH terms in the SM only up to finite constants, which have been calculated in [5]. Although the GNLSM is mani- festly nonrenormalizable, and its observables in general violate unitarity in the high-energy limit, an investigation of the GNLSM seems reasonable since it is equivalent to the SM in the unitary gauge with the physical Higgs field omitted. Consequently, by comparing theoretical predic- tions within the GNLSM and the SM for varying MH one may get insight into the influence of the mechanism of spontaneous symmetry breaking on specific observables. The discussion of these aspects for the cross section of yy -+ W+W- represents the main issue of this paper. The process yy -+ W+W- will be one of the most important reactions at future yy colliders. In particu- lar, the measurement of the corresponding cross section yields direct information on possible anomalous yWW and yyWW couplings [6] widely independent of the cou- plings between Z and W* bosons. Moreover, a Higgs boson with a mass of several hundred GeV can be stud- ied via the resonance contribution yy -+ H* -+ W+W-, which is present owing to the yyH coupling induced at one-loop order. Since the structure of this Higgs reso- nance has already been discussed in the literature [7,8], here we mainly concentrate on the case when the center- of-mass energy is far below the Higgs-boson mass MH. We have calculated the full one-loop RC's to yy -+ W+W- including soft-photon bremsstrahlung both in the SM and GNLSM. A complete discussion of the SM RC's will be published elsewhere [9]; here we focus on the MH dependence of the SM corrections and their dif- ference to the ones within the GNLSM. Despite the non- renormalizability of the GNLSM, the corresponding one- loop RC's to yy -+ W+W- turn out to be ultraviolet finite. This fact is related to the absence of lnMH terms in the SM corrections. The limit MH -+ rn indeed exists for the SM one-loop corrections, but for longitudinal po- larized W bosons these one-loop corrected cross-sections 0556-282 1/95/5 1(9)/4738(8)/%06.00 - 51 4738 @ 1995 The American Physical Society

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PHYSICAL REVIEW D VOLUME 5 1, NUMBER 9 1 MAY 1995

Probing the Higgs mechanism via yy -+ W+W-

A. Denner and R. Schuster Institut fur Theoretische Physik, Universitat Wurzburg, Am Hubland, 0-97074 Wurzburg, Germany

S. Dittmaier Theoretische Phyaik, Universitat Bielefeld, Universitatsstrajle, 0-33501 Bielefeld, Germany

(Received 21 November 1994)

We investigate the sensitivity of the reaction yy + W+W- to the Higgs sector based on the complete one-loop corrections in the minimal standard model and the gauged nonlinear u model. While this sensitivity is very strong for the suppressed cross section of equally polarized photons and longitudinal W bosons, it is only marginal for the dominant mode of transverse polarizations. The corrections within the u model turn out to be UV finite in accordance with the absence of 1 n M ~ terms in the standard model with a heavy Higgs boson.

PACS number(s): 11.15.Ex, 13.10.+q, 14.70.Fm, 14.80.Bn

I. INTRODUCTION

All present experimental results on electroweak physics confirm the conception that electromagnetic and weak interactions are unified in an SU(2) xU(1) gauge theory. However, the underlying field theory cannot be of pure Yang-Mills type since the weak gauge bosons, the W* and Z bosons, are empirically known to be massive. In the electroweak standard model (SM) this problem is solved by the well-known Higgs mechanism [I], i.e., by breaking the gauge symmetry spontaneously via a nonva- nishing vacuum expectation value of a n additional com- plex scalar SU(2) doublet. Whereas three of these four scalar fields are absorbed by the longitudinal degrees of freedom of the massive gauge bosons, a physical scalar field survives, the so-called Higgs boson. Of course, the Higgs mechanism cannot be conclusively confirmed be- fore this particle is empirically detected. On the other hand, the Higgs-boson mass MH, which is a free pa- rameter of the theory, enters all theoretical predictions within the SM a t least via higher orders. Since the Higgs- boson-mass dependence of low-energy observables turns out to be very mild, more precisely a t most logarithmic a t the one-loop level, only crude bounds on MH can be obtained from radiative corrections (RC's) to current pre- cision measurements. Experimentally, the Higgs-boson- mass is only constrained by the lower bound MH 2 6 0 GeV from the CERN e+e- collider LEP [2] but can well be in the TeV range.

The Higgs boson can be removed from the physical particle spectrum in two different ways. On the one hand, amplitudes can be calculated within the SM for fi- nite MH, and subsequently asymptotically expanded for MH -+ m. Alternatively, the physical Higgs field can be eliminated by constraining the square of the Higgs- doublet field to be constant and equal to its (nonvanish- ing) vacuum expectation value. Then no physical Higgs particle exists from the beginning, but one is forced to introduce a nonlinear representation of the Higgs sector leading to a nonrenormalizable gauged nonlinear u model (GNLSM). The relation between the heavy-Higgs-boson

limit and the GNLSM has been investigated for a n SU(2) gauge theory and the SU(2)xU(1) SM in [3] and [4,5], respectively. As expected, MH acts as a n effective UV cutoff. The corresponding (logarithmic) one-loop diver- gences in the GNLSM can be identified with the In MH terms in the SM only up to finite constants, which have been calculated in [5]. Although the GNLSM is mani- festly nonrenormalizable, and its observables in general violate unitarity in the high-energy limit, a n investigation of the GNLSM seems reasonable since it is equivalent to the SM in the unitary gauge with the physical Higgs field omitted. Consequently, by comparing theoretical predic- tions within the GNLSM and the SM for varying MH one may get insight into the influence of the mechanism of spontaneous symmetry breaking on specific observables. The discussion of these aspects for the cross section of yy -+ W+W- represents the main issue of this paper.

The process yy -+ W+W- will be one of the most important reactions a t future yy colliders. In particu- lar, the measurement of the corresponding cross section yields direct information on possible anomalous yWW and yyWW couplings [6] widely independent of the cou- plings between Z and W* bosons. Moreover, a Higgs boson with a mass of several hundred GeV can be stud- ied via the resonance contribution yy -+ H* -+ W+W-, which is present owing to the yyH coupling induced a t one-loop order. Since the structure of this Higgs reso- nance has already been discussed in the literature [7,8], here we mainly concentrate on the case when the center- of-mass energy is far below the Higgs-boson mass MH.

We have calculated the full one-loop RC's to yy -+ W+W- including soft-photon bremsstrahlung both in the SM and GNLSM. A complete discussion of the SM RC's will be published elsewhere [9]; here we focus on the MH dependence of the SM corrections and their dif- ference to the ones within the GNLSM. Despite the non- renormalizability of the GNLSM, the corresponding one- loop RC's to yy -+ W+W- turn out to be ultraviolet finite. This fact is related to the absence of lnMH terms in the SM corrections. The limit MH -+ rn indeed exists for the SM one-loop corrections, but for longitudinal po- larized W bosons these one-loop corrected cross-sections

0556-282 1/95/5 1(9)/4738(8)/%06.00 - 51 4738 @ 1995 The American Physical Society

5 1 - PROBING THE HIGGS MECHANISM VIA y y -+ Wt W - 4739

violate unitarity for energies in the TeV range, as it is also the case in the GNLSM.

The paper is organized as follows. In Sec. 11, we discuss the MH dependence of the SM RC's and their difference to the ones within the GNLSM. The unitarity-violating effects for longitudinal W bosons are investigated in Sec. 111. Numerical results are presented in Sec. IV. Section V contains our conclusions.

11. HEAVY-HIGGS STANDARD MODEL VERSUS GAUGED NONLINEAR a MODEL

The GNLSM is related (see, e.g., [ lo]) to the SM in the unitary gauge without Higgs field by a Stueckelberg

transformation [Ill. Comparing the Lagrangians, one finds that the Feynman rules involving a t most one un- physical scalar field are identical in the GNLSM and the SM with linearly realized Higgs sector. Vertices with a t least two scalar fields are in general different. In par- ticular, the WWpp and W W X X couplings vanish in the GNLSM. By p and x we denote the charged and neutral unphysical scalar fields, respectively. For the reaction yy + W+W- a t one loop one simply has to onlit all graphs that contain internal Higgs fields, or WWpp or W W X X couplings in order to obtain the GNLSM results from the SM ones.

Obviously, the tree-level arnplitudes agree in both models yielding

The momenta k and polarization vectors E of the incoming photons are labeled by "I", "2", the ones of the outgoing W + bosons by f, respectively; they are explicitly defined in the center-of-mass (c.m.) system in [9]. The Mandelstam variables are given by

with p = dl - M&/E2 denoting the velocity of the W bosons, and 6' representing the scattering angle between photon "1" and W+.

For longitudinal W bosons the lowest-order matrix elements read, explicitly,

Here and in the following we denote the Mandelstam variables s, t , u generically by q 2 . Note that in the high-energy limit I q 2 ( >> M& the amplitudes for equal photon helicities vanish and that the other ones do not contain any t- and u-channel poles in the leading term.

The calculation of the one-loop amplitude for yy + W+W- is simplified considerably by use of a nonlinear gauge- fixing condition for the W-boson field, suggested in [12], rendering the ypW coiipli~ig zero [9]. Using this gauge-fixing condition in the GNLSM as well, we have evaluated the difference of the one-loop matrix elements for yy -i W t W - in the SM and the GNLSM:

where S M always denotes one-loop contributions to the amplitude. In the limit of very large Higgs-boson mass, M& >> I q 2 1 , M& our result simplifies to

a ' 6MHI = ( ~ ( € 1 . E ; ) ( ~ 2 . E*) + 2(&1 . € 2 ) (k1 . E ; ) (k2 . ~ t )

M x + m ~ s & ( M & - t)

-(el . E ; ) (kl . E : ) (k- . €2) + ( ~ 1 . E ? ) (k1 . E ; ) (k- . ~ 2 )

-(&z . E + ) ( ~ z . ~ ; ) ( k + . e l ) + (€2 . €;)(k2 . ~ f _ ) ( k + . E ~ ) ) + ("1" f _ ~ LL21), t + ?L) , ( 5 )

A. DENNER, R. SCHUSTER, AND S. DITTMAIER

FIG. 1. Feynman diagrams for yy + p'p- in the GNLSM relevant for the leading high-energy behavior.

whereas the exact analytical form of 6MH for arbitrary Higgs-boson mass is not very illuminating. In this con- text, we mention that we have derived ( 5 ) also using the effective Lagrangian for the difference of the SM limit MH -+ m and the GNLSM given in [4,5].'

The logarithmic one-loop UV diveGgences occurring in the nonrenormalizable GNLSM are directly related to the lnMH terms in the SM with a heavy Higgs boson; i.e., MH can be regarded as an effective UV cutoff in this limit. This fact has already been pointed out in [4] and shown by explicit calculation in [5]. Thus, the ab- sence of lnMH terms in SMsM and the UV finiteness of 6MGNLSM have the same root; however, the difference

6 M H is nonvanishing even for MH -+ m. Of course, all results derived in nonrenormalizable models are not free from ambiguities or assumptions that fix these ambigui- ties so that such results have to be interpreted carefully. But the finiteness of 6MGNLSM shows that the prediction for yy -+ W+W- within the GNLSM is independent of any cutoff A whatever regularization procedure may be used. Note that such a A will play a role as "scale of new physics" if the GNLSM is embedded into a more complete field theory such as the SM (where A - MH) or even beyond. Moreover, the difference 6 M H indicates to which extent the SM prediction might be modified by effects of new physics concerning the Higgs sector.

111. PRODUCTION OF LONGITUDINAL W BOSONS IN THE HIGH-ENERGY LIMIT

Observables involving longitudinally polarized massive gauge bosons are most sensitive to deviations from the Yang- Mills interactions and the mechanism of spontaneous symmetry breaking of the underlying gauge theory for energies far above the scale of the gauge-boson masses. This is due to the well-known "gauge cancellations" which guarantee that the enhancement factor E / M of the longitudinal polarization vector (of a vector boson with energy E and mass M ) is canceled between the individual contributions to the S-matrix elements. The eauivalence theorem IET'I I131

L I L 3

states that in the SM the leading contribution to amplitudes involving external longitudinally polarized gauge bosons can be simply obtained by the replacement of this vector field by the corresponding unphysical scalar field, if all energy scales qf are far above all masses mi, l q f l >> mf. Moreover, the E T can be generalized to the heavy-Higgs-boson SM, Iqfl, M& >> m:, and the GNLSM [14,15].

Applying the ET to yy -+ W z WL within the heavy-Higgs-boson SM and the GNLSM, all one-loop RC's of the order M&/M&, q2/M& (q2 = S, t , u) can be obtained from Feynman diagrams of yy -+ p + p involving only scalar inner pa~ticles, as can be deduced by power counting [15]. In the heavy-Higgs-boson SM these diagrams are shown and calculated in [7] for equal photon helicities. The result for yy + W ~ W L with general photon helicities is given by

for s , -t, -u, M i >> M$ , (7)

'More precisely, some missing counterterms involving all had to be supplemented in the Feynman rules of [4], and the finite parts of the contributing ai could be taken from [ 5 ] .

5 1 - PROBING THE HIGGS MECHANISM VIA y y - W + W - 4741

where (6) is in agreement with [7].' The graphs which are relevant in the GNLSM are shown in Fig. 1. Note that the corresporlding cpcpcpcp coupling in the GNLSM i~rlplicitly contains enhancement factors of the type q2/M&,. The final result reads

Using (6) and (7) we can compare the q2/M& terms of the GNLSM with the corresponding SM limit MH -+ m, given by

for jq21 >> M& . ( 9 )

Consequently, even the unitarity-violating s/M&, terms are different in the SM with MH -+ m and the GNLSM. Of course, these terms are absent in the high-energy limit of the SM if MH is kept finite, i.e., l q 2 / >> M i >> M&. In this case ( 6 ) and (7) reduce to

for l q 2 / >> M& >> M& , (10)

for /q2/ >> M& >> M$ . ( 1 1 )

The way these various leading corrections influence the complete one-loop RC's can be seen in the numerical dis- cussion of the next section.

IV. NUMERICAL RESULTS

For the numerical evaluations we use the parameters of [2]. In particular, the W-boson mass is kept fixed to Mw = 80.22 GeV. All integrated cross sections are ob- tained from the angular range 10' < 0 < 170'. The polarizations of the external particles are indicated by four labels, the first two corresponding to the photons and the last two to the W bosons. The label U stands for unpolarized, + for right handed, - for left handed, T for transverse and L for longitudinal. Since we are in- terested only in the MH dependence of the SM RC's and their difference to the ones within the GNLSM we omit all

he difference in the global sign is due to deviating phase conventions for the polarization vectors.

l n ( A E / E ) terms, which represent the cutoff-dependent corrections originating from soft-bremsstrahlung photons of energy E, < AE. As already mentioned, a more com- plete discussion of the SM RC's to yy -+ W + W - will be published elsewhere [91.

In order to set the scale, we first show in Fig. 2 the lowest-order integrated cross sections for various polar- izations. At high energies, the unpolarized cross section as^&^ is dominated by transverse W bosons and all po- larized cross sections involving two transverse W bosorls are of the same order. The cross sections involving longi- tudinal W bosons are smaller owing to the suppression of the t- and u-channel poles [see (3)] . While the cross sec- tions for opposite photon polarizations and mixed trans- verse and longitudinal W-boson polarizations o z ~ $ ~ and

are suppressed by a n additional factor l / s , the corresponding ones for equal photon helicities vanish a t lowest order. Finally, the cross section for equal photon helicities and purely longitudinal W bosons aP&, the most interesting one for the study of the Higgs sector, behaves like l /s3 a t high energies and is suppressed with respect to the unpolarized cross section by more than 4 orders of magnitude already a t E,,,,,, = 1 TeV.

Owing to the strong suppression of the lowest-order cross section and the presence of unitarity-violating ef- fects in the O ( a ) corrections, the cross section U*+LL is dominated by the O ( a ) corrections a t high energies. Consequently, we have calculated the corrected cross sec- tion for this polarization by squaring the complete ma- trix element so that the large relative corrections of or- der O ( a 2 s 2 / ~ & ) are treated properly. Squaring also the nonleading one-loop RC's changes the result only a t the order of the neglected two-loop corrections. In order to get an IR-finite result we have also squared the real soft- bremsstrahlung correction, which is proportional to the lowest-order cross section and thus very small. For all other polarized cross sections we include only the strict O ( a ) corrections, i.e., the interference of the corrections with the lowest-order amplitude but not the square of the O ( a ) corrections. The unpolarized cross sections are obtained by summing the polarized ones calculated as described above.

The strong enhancement of CT+*LL arising from the higher-order corrections is demonstrated in Fig. 3. For large Higgs-boson masses it amounts to more than 2 or- ders of magnitude a t 2 TeV. For high energies the cross sectiorl depends very strongly on the Higgs-boson mass. While for MH >> s the behavior of the cross section is governed by (9), for MH << s it is given by (10). The two regions are separated by the Higgs resonance. The cross section for MH = m grows with s and eventually vio- lates unitarity. I t deviates from the one of the GNLSM by a factor of roughly & a t high energies in accordance with (8) and (9). Figure 3 qualitatively agrees with the one shown in [7] where only the enhanced terms of order O(aM&/h f&) and O(as /M&,) for yy + W L W F were calculated. The strong sensitivity of W + + L L to the Higgs sector will probably be very hard to exploit in the pres- ence of the enormous background of transverse W-boson production.

For the other polarizations, the relative corrections

4742

uBorn (pb)

A. DENNER, R. SCHUSTER, AND S. DITTMAIER

FIG. 2. Lowest-order inte- grated cross section for various polarizations (10' < 0 < 170").

-

GNLSM \ %

- \

- M H =700 GeV --- \ \ \ '7

M H = 1500 GeV - - - - \\,

M H = O O . . . . . . . \

I I I I I I I I I \

FIG. 3. Integrated cross sec- tion for equal photon helici- ties and purely longitudinal W bosons.

FIG. 4. Corrections to the integrated cross section for un- (equal photon helicities and purely longitudinal W bosons (left) or mixed transverse and longitudinal W bosons (right).

PROBING THE HIGGS MECHANISM VIA y y + W + W -

I I I I I I I I I

M ~ = 7 0 0 G e V --- - MH = 1500 GeV - - - - -

- -

-

-

-

- I I I I I I I I I

M H = 1500 GeV - - - -

1

GNLSM - - - MH = 700 GeV --- - M H = 1500 GeV - - - - I

........ M H = w Born - - ..................................................

_ .- _____-- - - - - . - - -_ .__ . J + t' r;' r j __-----__ -. . . ii

'\ ! 1:

,' '..__._..' I I I 1 - I I I

L

MH = 700 GeV ---

I

FIG. 5. Corrections to the integrated cross section for un- polarized W bosons and equally polarized photons (left) or un- polarized photons (right).

FIG. 6. Differential cross section for purely longitudinal W bosons and equal photon he- licities (left) or unequal photon helicities (right). E ,.,.,. = 2 TeV.

FIG. 7. Differential cross section for unequal photon helicities and mixed transverse and longitudinal W bosons (left) or unpolarized W bosons and photons (right). E ,.,... = 2 TeV.

A. DENNER, R. SCHUSTER, AND S. DITTMAIER

TABLE I. Variation of various polarized cross sections with the Higgs-boson mass in the range 60 GeV < Mx < co including the difference to the GNLSM in percent of the cross section for MH + cc at E,.m.,. = 2 TeV.

I-T,L + - I L T + T L ) + I U U U U T T UUUU

0 = 9 0 " 13 15 (15) 2.6 0.9 3.4 Integrated over 1 0 " < 0 < 170 10 2 (9) 0.1 0.1 0.1

6 = a/aB,,, - 1 to the integrated cross section are illus- trated in Figs. 4 and 5 . Note that in all those cross sec- tions no unitarity-violating terms appear for MH = co in the SM or in the GNLSM and that for finite but not very small MH no Higgs resonance is visible. More precisely, the Higgs resonance is only present for equally polarized photons but suppressed for transverse W bosons. While for the polarizations involving longitudinal W bosons a dependence on the Higgs-bosons mass of nearly 10% shows up (Fig. 4), such a dependence is not visible for purely transverse W bosons and all cross sections includ- ing these polarizations (Fig. 5).

The background of transverse W bosons can be re- duced by more stringent angular cuts. This can most eas- ily be seen by considering the differential cross sections plotted in Figs. 6 and 7 for E ,.,.,. = 2 TeV. While the angular distribution for longitudinal W bosons is rather flat, the one for transverse W bosons (and thus also for unpolarized ones) is strongly peaked in the forward and backward directions owing to the t- and u-channel poles at high energies. But even a t 90' scattering angle, U++LL

is still smaller than a*+uu by a t least a factor of 50. While U**LL shows a very strong dependence on MH and related to that also a sizable difference between the SM and the GNLSM, the variation of all other polarized cross sections with M H , which is in general maximal at 90 ", is comparably small. In particular, for unpolarized W bosons it is so small, that in Fig. 7 the SM curves for the various values of MH coincide with the one of the GNLSM and that only the lowest-order cross section can be distinguished. Note furthermore that for O*?(LT+TL)

the curves for MH = 700 GeV and the GNLSM in Fig. 7, and for U * ~ L L the curves for MH = co and the GNLSM in Fig. 6 can hardly be separated.

Finally we give in Table I some numbers for the vari- ation of the SM corrections with MH in percent of the cross section for MH + co. While the deviation between the SM and the GNLSM in general is covered by this range it is given separately for ( T + ~ (LT+TL) in parenthe- ses. The numbers confirm that the cross sections involv- ing two transverse W bosons depend hardly on the Higgs sector apart from the region close to 90" where the cross sections are small.

V. CONCLUSIONS

We have calculated the one-loop radiative corrections to yy -+ W+W- in the SM and the GNLSM. Despite the nonrenormalizability of the GNLSM the latter turn out to be UV finite. The same holds for the limit MH -+ co of the SM corrections since the (logarithmic) one-loop divergences of the GNLSM and the In MH terms in the SM are directly related. However, the complete one-loop results differ by finite terms.

The unitarity-violating effects, which are also differ- ent in the SM and the GNLSM, appear only for equal helicities of the incoming photons and purely longitudi- nal W bosons. The corresponding cross section depends strongly on the Higgs-boson mass and changes notice- ably when going from the SM to the GNLSM. On the other hand, it is strongly suppressed with respect to the one for purely transverse W bosons. The cross section for transverse W-boson production and also the one for unpolarized W-boson production hardly depend on MH and on the realization of the Higgs sector.

In [a] it was demonstrated that a SM Higgs boson of mass MH - 200 GeV can be seen in yy --t W+W- as a resonance dip in the cross section. Here we added the results for Higgs-boson masses of several hundred GeV up to the TeV range. Heavy-Higgs-boson effects will only be significant if longitudinally polarized W bosons can be isolated which seems to be extremely difficult owing to the huge background of transversely polarized ones. On the other hand, producing transverse W bosons via yy + W+W- turns out to be practically independent of the mechanism of spontaneous symmetry breaking so that these channels are well suited for the investigation of other features such as anomalous y W W couplings.

ACKNOWLEDGMENTS

The authors would like to thank C. Grosse-Knetter and H. Spiesberger for useful discussions. R.S. was sup- ported by the Deutsche Forschungsgemeinschaft. S.D. was supported by the Bundesministerium fib Forschung und Technologie, Bonn, Germany.

[I] P. W. Higgs, Phys. Lett. 12, 132 (1964); Phys. Rev. Lett. 50, 1173 (1994). 13, 508 (1964); Phys. Rev. 145, 1156 (1966); T. W. B . [3] T. Appelquist and C. Bernard, Phys. Rev. D 22, 200 Kibble, ibid. 155, 1554 (1967). (1980).

[2] Particle Data Group, L. Montanet et al., Phys. Rev. D [4] C. Longhitano, Nucl. Phys. B188, 118 (1981).

51 - PROBING THE HIGGS MECHANISM VIA yy - W + W - 4745

151 M. J. Herrero and E. R. Morales, Nucl. Phys. B418, 431 (1994); B437, 319 (1995).

[6] G. Bdlanger and F. Boudjema, Phys. Lett. B 288, 210 (1992), and references therein.

[7] E. E. Boos and G. V. Jikia, Phys. Lett. B 275, 164 (1992).

[8] D. A. Morris, T . N. Truong, and D. Zappali, Phys. Lett. B 323, 421 (1994).

[9] A. Denner, S. Dittmaier, and R. Schuster, Report No. BI-TP 95/04 (unpublished).

[lo] S. Dittmaier, C. Grosse-Knetter, and D. Schildknecht, Z. Phys. C (to be published).

[ll] E. C. G. Stueckelberg, Helv. Phys. Acta 11, 299 (1938); 30, 209 (1956).

[12] M. B. Gavela, G . Girardi, C. Malleville, and P. Sorba, Nucl. Phys. B193, 257 (1981).

[13] M. S. Chanowitz and M. K. Gaillard, Nucl. Phys. B261, 379 (1985); G. J. Gounaris, R. Kogerler, and H. Neufeld, Phys. Rev. D 34, 3257 (1986); H. Veltman, ibid. 41, 2294 (1990).

[14] A. Dobado and J. R. PelEiez, Phys. Lett. B 329, 469 (1994).

[15] C . Grosse-Knetter, Z. Phys. C (to be published).