jj .- lr] XU-;` pam||[||||[||[||[|||[|[IIIIIIIII]|l||I|[|[||]|| Lxsaamas. sanavn PBBGEBBS4 University of Wisconsin - Madison gtggéigéggg el Higgs Bosons: Intermediate Mass Range at e+e‘ Colliders* V. Bargerl, K. Cheungz, A. Djouadi3, B. A. Kniehl4, R. J. N. Phillips5, and P. M. Zerwas Physics Department, University of Wisconsin, Madison, WI 53706, USA Dept. of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA Lab. Phys. Nucl., Université de Montréal, Case 6128A, H3C 3J7 Montréal PQ, Canada II. Inst. f. Theor. Physik, Universiteit Hamburg, 22761 Hamburg, Germany Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, England Deutsches Elektronen-Synchrotron, DESY, 22603 Hamburg, Germany Abstract We elaborate on the production of the Standard Model Higgs particle at high energy e+e` colliders through the reactions e+e‘ -—+ ZH and e+e` —> 171/H. Partic ular emphasis is put on the intermediate mass range. In addition to the signal we discuss in detail the background processes. Angular distributions which are sensitive to the spin and parity of the Higgs particle are analyzed. 1 The Physical Basis The fundamental particles in the Standard Model (SM), gauge bosons, leptons and quarks, acquire their masses by means of the Higgs mechanism The masses are generated through the interaction with a non-zero scalar field in the ground state, inducing the spontaneous breaking of the electroweak SU(2)l >< U(1)y symmetry down to the electro magnetic U(1>EM Symmetry. To accommodate the well established electromagnetic and weak phenomena, this mechanism requires the existence of at least one weak iso-doublet scalar field. The three Goldstone bosons among the four degrees of freedom are absorbed to build up the longitudinal polarization states of the massive Wi, Z bosons. One degree of freedom is left over, corresponding to a real physical particle. The only unknown parameter in the SM Higgs sector is the mass of the Higgs particle, MH. Even though the value of MH cannot be predicted, interesting constraints can nevertheless be derived from bounds A on the energy range in which the model is taken to be valid before perturbation theory breaks down and new dynamical phenomena could emerge. lf MH is less than about 180 to 200 GeV, the SM with weakly interacting particles can be extended [2] up the GUT scale, AGUT ~ 1016 GeV. This attractive idea is very likely to play a key role in the renormalization of the electroweak mixing angle sinz Ow from the GUT symmetry value 3/8 down to the experimental value ~ 0.2 at low energies. A lower bound on MH follows in the SM from the requirement of vacuum stability for large mt. lf, for given MH, mt increases, radiative corrections drive the scalar potential to negative values [3] so that, in turn, for m, ~ 150 GeV, MH must exceed ~ 100 GeV. VVe therefore focus in this study on the important MH range M Z $ MH $ 2M Z, generically *To appear in the Proceedings of the Workshop on e+e` Collisions at 500 GeV: The Physics Potential, Munich, Annecy, Hamburg, 20 November 1992-3 April 1993, ed. by P.M. Zerwas. OCR Output 1· F v.c' H 7,6 Z"; yl W,Z W,Z e' a* (ca) (b) Figure 1: Feynman diagrams for the Higgs strahlung process, e+e‘—+ HZ, and the fusion processes, e+e' —> w7H and e+e" —> e`*`e"H. referred to as the intermediate MH range; however, we shall extend the study to higher mass values up to the kinematical limit of a given CM energy. The scale of the Higgs couplings to massive gauge bosons and quarks / leptons is set by the masses of these particles. As a result, the profile of the Higgs boson can be predicted completely for a given value of M H——the decay properties are fixed and the production mechanisms and rates can be determined. At e+e` linear colliders operating in the 300 to 500 GeV energy range [4], which we shall generically denote by Next Linear Collider (NLC), the main production processes are the WW/Z Z fusion [5] and the Higgs strahlung [6] mechanisms. The cross sections for the fusion mechanisms, e+e“—> w7(W+W') —> 1/DH, e+e` —> e+e"(ZZ) —> e+e"H, (l) rise logarithmically with energy, making these channels dominant at (/E 2 500 GeV for intermediate—mass Higgs bosons. The Higgs particles will identify themselves through a peak in the invariant mass distribution M X in e+e" —+ X +E, with E denoting the missing energy (and momentum), due to the final state neutrinos. The Higgs strahlung process, e+e"——>Z"—->Z+H, (2) is dominant for moderate values of the ratio M H / (/E, but falls off at high energies ac cording to the scaling law ~ s“1. Since this process is fully constrained, missing-mass techniques can be applied which allow to search for the Higgs particle without any restric tions on the decay modes. [Higgs events in the ZZ fusion process, e+e”—> e+e`(Z Z) —> e+e‘H, can also be reconstructed completely, yet the production rate is smaller by an order of magnitude; see Fig. 2.] Once the Higgs boson is found, it will be very important to explore its properties. This is possible by exploiting the Higgs strahlung process (2) The zero-spin is reflected in the angular distribution This distribution must approach the sin? 0 law asymptoti cally since, according to the equivalence theorem [9], massive gauge bosons act at high OCR Output °°°F-LL e im. .·.--2.1 me ss"~` ` ¢ s-· 9 V H irs! 199 [T FS \, -··· E -300 sev Gssoocev \_ as FS `\` ~¤ i \_ | \ Q MH(GcVl 50 100 150 200 250 300 350 Figure 2: Production cross sections for Higgs strahlung and fusion in the SM. energies like the Goldstone bosons, which are absorbed to build up the longitudinal de grees of freedom. The parity can also be studied by analyzing angular correlations. Of tantamount importance is the measurement of the Higgs couplings to gauge bosons and matter particles. The strength of the couplings to Z and EV bosons is reflected in the magnitude of the production cross section. The relative strength of the couplings to fermions is ac cessible through the decay branching ratios. The absolute magnitude is difficult to mea sure directly. The direct measurement is possible in the small mass window where the Higgs decays to bb and WW* compete with each other; otherwise Higgs strahlung off top quarks [10, 11] provides an opportunity to measure the ttH coupling in a limited range of intermediate MH values. All these couplings grow with the masses of the source par ticles, a direct consequence of the very nature of the mass generation through the Higgs mechanism. The measurement of these couplings is therefore an important experimental task in the electroweak sector. 2 Higgs strahlung The cross section for the Higgs strahlung process (2) can be written in a compact form [12], _ G%Mé 2 2 H2 +12M%/S ¤(ZH)—·§€·E—(Ue+¤€)U » (3) Tg where ve : -1 + 4sin2 GW and ae = -1 are the Z charges of the electron, and 52 = [1 - (MH + MZ)2/s] [1 - (MH - MZ)2/s] is the usual two—particle phase—space factor, pro portional to the momentum squared of the particles in the final state. The cross section, which peaks near MH z (\/E- MH) /y/2, is shown in Fig. 3(a) for \/E = 300, 400, and 500 GeV as a function of MH, and in Fig. 3(b) for three representative values of MH as a function of With 0 ~ 200 fb, a rate of ~ 4,000 Higgs particles in the intermediate mass range is produced at an energy \/5 = 300 GeV and for an integrated luminosity of f£dt = 20 fb`1 within one year of running. Asymptotically, a(ZH) scales as s` OCR Output v(•°•` ·• H) [fb] — % (l) - - — Born approx. ;E - 4000•v \` 1/ •1•ct:·0v••k corr. _ _ _ ` ml- ` é N \ E.; ¤ 150GOv »¤;E¤BE.?~=~.\° \·,\, \ `K F - ¤¤¤<=•vl·\ ~ _ ` \ ` X ` §` ` \ \¤ 10 00 100 150 ¤0¤ 250 $00 $50 Ks [°•V] ll" 0(•°•" -• ZH) [fb] (b) null ·—— Born approx. [A 1/ •l•0tr0rw••k car!. • \ mol- l J s\ I" \ m,¤150G•V fx. `§ 1: 11, - 1NG•V W 2: I. ¤ 160G•V 8: II - 1.BOG•V 10 200 400 000 1100 1000 V? [6•V1 Figure 3: Total cross sections for the Higgs strahlung process: (a.) as a function of M H for \/E = 300, 400 and 500 GeV and (b) as a. function of \/E for MH = 120, 150 and 180 GeV. While the dashed curves represent the cross sections in the Born approximation, the solid curves include the one—loop electroweak corrections assuming mt = 150 GeV. OCR Output It is well known that cross sections measured in high—energy e+e" collisions are greatly affected by QED radiative corrections. (However, we can as a first approximation neglect weak corrections, which are known to vary between -7% and +6% for the e+e` —+ ZH cross section at (/-§ = 0.5 TeV [13].) In general, the main effect is due to bremsstrahlung from the initial state, which lowers the effective CM energy available in the main process and leads to a typical smearing of the distributions in the subprocess CM energy The size of the effect can be easily estimated by considering the large leading logarithms. In C’)(cx") they are of the form (cr/7r)" ln"(s/mg) (n = 1, 2, . .), which follows from Sudakov’s theorem [14]. In an inclusive experiment there are no similar logarithms due to final—state particles.