Anomalous Higgs boson contribution to e e bb at CERN LEP 2

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1 PHYSICAL REVIEW D VOLUME 54, NUMBER 5 1 SEPTEMBER 1996 Anomalous Higgs boson contribution to e e bb at CERN LEP 2 S. M. Lietti, S. F. Novaes, and R. Rosenfeld Instituto de Física Teórica, Universidade Estadual Paulista, Rua Pamplona 145, CEP São Paulo, Brazil Received 14 March 1996 We study the effect of anomalous H and HZ couplings, described by a general effective Lagrangian, on the process e e bb at CERN LEP 2 energies. We include the relevant irreducible standard model background to this process, and from the photon energy spectrum, we determine the reach of LEP 2 to unravel the anomalous couplings by analyzing the significance of the signal for a Higgs boson with a mass up to 150 GeV. S PACS number s : Cp, q I. INTRODUCTION The standard model SM has been tested to an unprecedented degree of accuracy of 0.1% in some of the physical observables at the CERN e e collider LEP 1, with many implications to physics beyond the SM 1. However, the Z-pole experiments are able to probe with great precision just the fermionic couplings to the vector bosons while furnishing very little information about the interaction between the gauge bosons and the Higgs sector of the SM. In principle, it is conceivable that the interactions of the Higgs boson, which is responsible for the spontaneous breaking of the electroweak symmetry and for generating fermion masses, are different from those prescribed by the SM. In this case, an effective Lagrangian formalism can be used to describe possible anomalous interactions between the Higgs boson and vector bosons. The effective Lagrangian approach is a convenient modelindependent parametrization of the low-energy effects of new physics beyond the SM that may show up at higher energies. Effective Lagrangians, employed to study processes at a typical energy scale E, can be written as a power series in 1/, where the scale is associated with the new particle masses belonging to the underlying theory. The coefficients of the different terms in the effective Lagrangian arise from integrating out the heavy degrees of freedom that are characteristic of a particular model for new physics. Invariant amplitudes, generated by such Lagrangians, will be an expansion in E/, and in practice one can only consider the first few terms of the effective Lagrangian, e.g., dimension-six operators, which are dominant for E. The anomalous H and HZ couplings have already been considered in Z and Higgs boson decays 3, ine e collisions 3,4, and at colliders 5. In this paper, we concentrate our analyses on the effect of anomalous H and HZ couplings, described by a general effective Lagrangian, on the process e e bb. This is a very interesting reaction since the SM contribution to e e H( bb ), being a one-loop process, is extremely small, and the observation of any H event at LEP 2 will be a clear signal of new physics. It may also be the only possibility of detecting a Higgs boson with mass larger than 80 GeV at LEP 2, provided that the anomalous couplings are sufficiently large. In our calculation, we include the dominant decay of the Higgs boson into a pair of bottom quarks and antiquarks in the framework of a complete tree-level calculation of the process e e bb involving both the SM and anomalous Higgs boson couplings. In this way, the irreducible SM background to the new physics is taken into account. Furthermore, we employ the photon energy spectrum to identify the existence of the anomalous Higgs boson or at least impose further bounds on its effective couplings. This paper is organized as follows. In Sec. II, we review the use of effective Lagrangians to study anomalous Higgs boson couplings, including limits on these couplings arising from precision measurements. In Sec. III, we study the process e e bb, and we present our results and trace our conclusions in Sec. IV. II. EFFECTIVE LAGRANGIANS AND THE ANOMALOUS H AND HZ COUPLINGS In order to define an effective Lagrangian, it is necessary to specify the symmetry and the particle content of the lowenergy theory. In our case, we require the effective Lagrangian to be CP conserving, invariant under SM symmetry SU L U 1 Y, and to have as fundamental fields the same ones appearing in the SM spectrum. In particular, the Higgs field will be manifest and the symmetry is realized linearly. There are 11 independent dimension-six operators 6 of which only five are relevant for our discussions. Following the notation of reference 7, we can write L eff 1 2 f BW Bˆ Ŵ f W D Ŵ D f B D Bˆ D f WW Ŵ Ŵ f BB Bˆ Bˆ, where is the Higgs field doublet, which in the unitary gauge assumes the form 0 v H / and /96/54 5 / /$ The American Physical Society

2 54 ANOMALOUS HIGGS BOSON CONTRIBUTION TO Bˆ i g 2 B, Ŵ i g 2 a a W, a with B and W being the field strength tensors of the respective U 1 and SU gauge fields. This Lagrangian gives rise to the following anomalous H and HZ couplings, in the unitary gauge 3 : H,HZ g H HA A 1 g HZ A Z H L eff g HZ HA Z, 3 where A(Z) A(Z) A(Z) and the coupling constants g H and g HZ are related to the coefficients of the operators appearing in Eqs. through g HZ g H gm W 2 gm W 2 1 g HZ s2 f BB f WW f BW, 2 gm W s f W f B 2, 4 2c s 2s2 f BB 2c 2 f WW c 2 s 2 f BW, 2c with g being the electroweak coupling constant and s(c) sin(cos) W. The coefficients f B and f W can be related to triple vector boson anomalous couplings and are bounded, for instance, by the direct measurement of WW vertex at hadron colliders. However, more stringent bounds on the coefficients of the effective Lagrangian 1 come from the precision measurements of the electroweak parameters obtained at LEP 1 7. Typically one has that f W,B,WW,BB / 2 can be as large as 100 TeV 2, whereas f BW / 2 should be at most 1 TeV 2. III. ANOMALOUS COUPLINGS AND HIGGS BOSON CONTRIBUTION TO e e bb An interesting option to test the couplings described by Eq. 3 at LEP 2 is via the reaction e e H, with the subsequent decay of the Higgs boson into a bb pair. In the SM, at the tree level, there are eight Feynman diagrams that contribute to the process e e bb see Figs. 1 a 1 d. A SM Higgs boson contribution to this process appears only at the one-loop level and is extremely small. For instance, the total cross setion for the process e e H, 8 at s 175 GeV, varies from 0.2 fb to 0.02 fb, for a Higgs boson mass in the range 70 M H 150 GeV. Therefore, with the expected LEP 2 luminosity, no such events should be seen. Even in the minimal supersymmetric standard model, one cannot expect an enhancement larger than a factor of 3 with respect to the SM result 9. In this way, we neglect this loop contribution in our calculation. The bulk of the SM cross section comes from the Z boson contribution to the diagrams of Figs. 1 a 1 b when the Z boson is on mass shell and the process is effectively a twobody one. This implies that the majority of the photons emitted are monochromatic, with energy given by E Z (s M Z 2 )/(2 s). FIG. 1. Feynman diagrams for e e bb in the standard model at a tree level a, b, c, d and the anomalous Higgs boson contribution e. When we take into account the anomalous Higgs boson couplings described above, two additional diagrams should be considered see Fig. 1 e. Their contributions are dominated by the on-mass-shell H production, with H bb. Therefore, we can anticipate the existence of a a secondary peak in the photon energy spectrum, generated at an energy E H s M 2 H, 5 2 s which would be a very clear signal for the Higgs boson. In order to evaluate the total cross section and kinematical distributions for the process e e bb, we have used the package MADGRAPH 10 coupled to DHELAS, the doubleprecision version of HELAS 11, for generating the tree-level SM amplitudes. We have written the relevant subroutines for the Higgs anomalous couplings, and included in the MADGRAPH-generated file two additional anomalous amplitudes. In this way, all interference effects between the SM and the anomalous amplitudes were taken into account. We checked for electromagnetic gauge invariance of the whole invariant amplitude and incorporated a three-body phase space code based on 12. Since the Higgs boson resonance is very narrow, (H bb ) 5 MeV, for M H 100 GeV, we make sure to use appropriate variables to take care of the Higgs events close to the resonance peak. Finally, we used VEGAS 13 to perform the phase space integration.

3 3268 S. M. LIETTI, S. F. NOVAES, AND R. ROSENFELD 54 FIG. 2. Photon energy distribution (d /de ) of the process e e bb, for the standard model contribution dashed histogram. We also show the Higgs boson peaks solid histogram for different values of its mass, and g H 10 3 GeV 1. In our analyses we have assumed a center-of-mass energy of s 175 GeV for the LEP 2 collider, with a luminosity of 0.5 fb 1. Our results were obtained using the following energy and angular cuts: E 20 GeV, cos e e 0.87, cos b b The photon energy cut 6 is intended to reject the background from an unresolved pair of photons from 0 decays and assures, in principle, a sensitivity to M H up to 150 GeV. The cuts in cos e (e ) and cos b(b ) were introduced to reduce initial and final state radiation, respectively. IV. RESULTS AND CONCLUSIONS Our purpose is to determine the range of anomalous H and HZ couplings that could be probed at LEP 2 by searching for a signal of the Higgs boson in the process e e bb. We assume that the Higgs couplings to fermions are the standard ones, which make the B(H bb ) dominant in the range 70 M H 150 GeV, for f i / 2 TeV 2 3. Figure 2 shows our typical results for the photon energy distribution presented as a 1 GeV bin histogram. We have taken g H 10 3 GeV 1, g HZ 0, and varied the Higgs boson mass between 70 and 120 GeV. We should point out that the general behavior of the energy distribution remains the same when we consider other couplings, g HZ different from zero. We can identify the Z-boson peak around E 64 GeV and also the various secondary peaks due to the Higgs boson at the energies given by Eq. 5. We can notice that the smaller the Higgs boson mass, the larger is its effect on the E distribution. Its detectability should rely on a careful analyses of the tail in the case where M H M Z ) of the SM contribution to the photon energy spectrum in the process e e bb. In Fig. 3, for the sake of comparison between the signal (H) and background (Z) behavior, we present separately the FIG. 3. Normalized angular distribution (1/ )d /dcos i, for i e, b, be, and bb. The solid dotted lines represent the anomalous standard model contributions, for g H 10 3 GeV 1. normalized angular distribution for SM and anomalous contributions for g H 10 3 GeV 1 and M H 110 GeV. We consider the angles between the electron beam and the final particles ( e and be ) and also the ones between the final particles ( b and bb ). We can see that the signal has a very small contribution at e /2, due to the scalar nature of the Higgs boson, whereas the events from the background yield some events from transversal Z s in the central region. The bb angular distribution shows that the produced quarks have a minimum angle between themselves, which depends on the mass and energy of the parent particle, i.e., bb min Z(H) 2arcsin(M Z(H) /E Z(H) ). This variable could be used to further increase the signal to background ratio. For instance, for M H M Z, the cut bb min H is able to get rid of most of the bb events coming from the Z. In fact, at the Z peak, the number of events is reduced by a factor of 3 when this cut is implemented for a Higgs boson of 110 GeV. On the other hand, for M H M Z, a cut bb min Z plays the same role. We should point out that there is no difference among the distributions coming from the three anomalous couplings 4. Therefore, it will be very difficult to make a distinction among these couplings based only on these kinematical distributions 4. FIG. 4. Significance of anomalous events as a function of the coupling constants g H and g HZ and different Higgs boson masses: 70 GeV dot-dashed line, 90GeV dashed line, 110 GeV solid line, and 130 GeV dotted line.

4 54 ANOMALOUS HIGGS BOSON CONTRIBUTION TO (1) TABLE I. Values of the anomalous couplings g H, g HZ number of signal and background events. and g HZ corresponding to a significance of 5, and the ratio of the total M H GeV g H GeV 1 (1) ) g HZ GeV 1 ) g HZ GeV 1 ) Signal background / / / / / / / / /0.97 In order to estimate the reach of LEP 2 to disentangle the anomalous Higgs boson couplings, we have evaluated the significance (S signal/ background) of the signal based on the Higgs boson peaks in the E distribution, assuming a Poisson distribution for both signal and background. We have scanned the parameter space for the three anomalous couplings, keeping only one nonzero coupling in each run, for different values of the Higgs boson mass. We took the coupling constants g H and g HZ in the range GeV 1, 14 and we assumed a b-tagging efficiency of 68% 15. In Fig. 4 we present the significance for each of these couplings, assuming four different values of the Higgs boson mass M H 70, 90, 110, and 130 GeV. We should notice that for M H 90 GeV the significance is reduced due to the presence of the Z boson peak. In Table I, we show the values of the coupling constants g H and g HZ that correspond to a 5 effect in the 1 GeV bin of the E distribution around the Higgs boson peaks, for different Higgs boson masses. We also present the total number of signal and background events in these bins. For M H 90 GeV, a large numbers of events is needed due to the Z boson peak. Since the signal increases with the square of the anomalous couplings, for some values of the coupling constants, we could expect to have a reliable signal for the anomalous Higgs boson in less than 1 year of a LEP 2 run. In this study, we have not taken into account initial state radiation, which would result in an energy degradation of the original e e beams, and we have not included a realistic simulation of the electromagnetic energy resolution. It is important to notice that an increase in the b-tagging efficiency and a good resolution of the electromagnetic calorimeter can help to select the bb events, increasing the signal to background ratio and improving the resolution of the Higgs boson peak in the photon energy distribution. In order to compare the values of the Higgs couplings that can be explored by LEP 2 see Table I with the present and expected bounds on the anomalous vector boson couplings, let us assume that all the coefficients of the dimension-six operators are equal, i.e., f W,B,WW,BB,BW f. In this scenario 16, we can relate the Higgs boson couplings with triple vector boson anomalous coupling in a simple way, since 1 (M 2 W / 2 (1) ) f. In this case, g HZ 0, and g HZ g H gs2 2M W, gsc 1 s2 /c 2 2M. W Then, we obtain g H g HZ 10 3 GeV 1. The best present direct constraint on was obtained by the Collider Detector at Fermilab CDF Collaboration 17 from the process pp WW,WZ l jj: , at a 95% C.L. At LEP 2, the angular distribution of final state fermions coming from the W W pairs can improve the present bound on to , at a 95% C.L. 16, for s 176 GeV. We should point out that these bounds are more stringent than the constraints coming from loop contributions to high-precision data. Therefore, in this scenario 7,16, the LEP 2 sensitivity to is of the same order of magnitude as its capability to prove the coupling g H, for a light Higgs boson, through the reaction e e bb see Fig. 4. In conclusion, we have shown that the study of the process e e bb can be a very important tool in the search of these interactions, and we suggested some suitable angular cuts to improve the signal to background ratio. We found that anomalous couplings g H, g HZ 10 2 GeV 1 are necessary for identifying an anomalous Higgs boson of 150 GeV, but, for a lighter Higgs boson, couplings as small as GeV 1 should be sufficient to assure a 5 effect. Therefore, searching for an anomalous Higgs boson at LEP 2 provides a complementary way to scrutinize effective interactions that give rise to both Higgs and vector boson anomalous couplings. ACKNOWLEDGMENTS We would like to thank O. J. P. Éboli for useful discussions. This work was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico CNPq and by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior CAPES.

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