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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. This is guaranteed by the Kinoshita-Lee—Nauenberg theorem [15], which states that mass singularities associated with outgoing particles cancel when all final states with the same invariant mass are summed up. For \/E = 0.5 TeV one has (rx/1r)ln(s/mg) z 7%. It is, therefore, clear that any predictions for processes at the NLC that ignore initial state bremsstrahlung will vary from crude to completely inadequate. By analogy to the situation at the Z peak it is clear that in the presence of a not-too—broad Higgs resonance even a rigorous treatment to O(cx) would still fail to lead to reliable predictions. An @(02) calculation in connection with soft—photon exponentiation [16] would be in order. Unfortunately, full O(a2) results are only available for the class of processes where the electron-positron pair annihilates into a neutral gauge boson [17]. However, the pattern in which the leading logarithms arrange themselves is universal for all reactions with an e+e` initial state. Leading—order initial-state bremsstrahlung is most conveniently included by convoluting the reduced cross section with exponentiated splitting functions for the incident electron and positron beams [18]. These splitting functions characterize the probability of finding an electron (positron) with a given longitudinal—momentum fraction inside the original electron (positron) after multiple-photon emission and can be obtained by solving QCD-like evolution equations. For e+e” reactions in the continuum it is evident that initial-state bremsstrahlung should tend to reduce (enhance) a cross section which is increasing (decreasing) with increasing energy. A completely novel feature which will be faced at the NLC is the so—called beam strahlung phenomenon [19], which is an unavoidable consequence of the quest for lumi nosities which exceed current achievements by three orders of magnitude. It occurs when particles in one bunch undergo bremsstrahlung upon entering the electromagnetic field of the other bunch. These particles thus interact coherently with a sizeable part of the opposite bunch. The intensity of the emitted beamstrahlung therefore increases with the strength of the fields generated by the bunches, which in turn grows with the particle density of the bunches and hence with the luminosity per bunch crossing. Beamstrahlung effects delicately depend on the details of the machine design and operation, and a realistic estimate of their characteristics can only be obtained through Monte Carlo simulation. ln our analysis we generate beamstrahlung (and bremsstrahlung) events using the program package BEAMSPEC by Barklow [20]. For narrow-band beam designs like DLC and TESLA [21], beamstrahlung [22] affects the cross section much less than the standard initial-state photon radiation. The change of the cross section, relative to the Born cross section, is exemplified for these design studies in Fig. 4. The cleanest channel for isolating the signal from the background is provided by the OCR Output 0.2 ::;"`·· --_
`_ """ `§ ` " "" ` " \ " 0.1 ` ~ M/F-600c.v \ \ \ \ \ \
0.6
———¤¤wu•1»¤4 \
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Figure 4: Beamstrahlung corrections to the total cross section of e`*'e‘—+ ZH as a function of MH for \/E = 300, 400, and 500 GeV.
HUF/e+e‘ decay mode of the Z boson. Depending on MH, either H —> bb decays dominate for MH $ 140 GeV, or H —> WW* decays for MH 2 140 GeV. We shall assume a perfect p-vertex detector with 100% B detection efficiency, which is not far from experimental reality [24]. Z -+ ,u+;f can be tagged by allowing the invariant ,41+ p` mass to vary within |M,,+,,- — MZ] $ 6 GeV. For the cases H ——> VV" (V = W, Z), we tag the hadronic decays of the on-shell vector boson by requiring that |Mjj — My] < My / 10. While the signal events prefer the central region of the detector, as discussed later in detail, the background reactions e+e' —-> Z + X are in general strongly peaked in the forward direction due to the t-channel exchange of electrons A cut [cos 9Z| < 0.6 therefore improves the signal-to—noise ratio significantly. For the study of H -—> bb the dominant backgrounds come from e+e' —> ZZ*, Z7*, 7*7* ——> (;r+;r`)(bb), as well as e+e‘—+ tf ——> (b;.¢+u)(b;F17). The other backgrounds like e+e‘ -> Zbb, with the Z bosons radiated off the bb final state, are very small and can be safely neglected [23]. On the other hand, for H —> WW* the dominant background comes from the continuum production of e+e" —> ZWW* —> ;L+;f +X. The backgrounds for the channel H —> ZZ* are more complicated. Besides the continuum production of e"’e` —+ Z Z Z *, there are also combinatorial ambiguities in the signal process from the chain e+e` —+ ZH —> (jj)(ZZ*) —-+ (jj)(;r+;fjj), which will not contribute to the Higgs peak in the missing mass spectrum but rather broaden the continuum [see Fig. 5(c) and 6(c)]. Without loss of a large fraction of the signal events, we can assume that all the jets are very well separated, so that the QCD cross section a(e+e“—> qcjggZ) is of O(a%Va§), i.e., suppressed by a factor of dwarf compared to the signal. The main background reactions are summarized in Table 1. OCR Output The distributions with respect to the missing mass Mgewu = [(pc- + pe+) — (pp- + 12,,+)] are shown in Figs. 5(a)—(c) for the three channels defined in Table 1, assuming \/E = 500 GeV. In each channel, we consider three representative values of MH: MH = 100, 125, 150 GeV in the H —> bb case, MH = 120,150,180 GeV in the H —> WW* case, and MH = 150,200,25O GeV in the H -1 ZZ* case. In Figs. 6(a)—(c), we show the corre sponding results for \/E = 300 GeV. Signals and backgrounds have been added, the cuts specified above have been applied, and initial—state bremsstrahlung and beamstrahlung corrections have been taken into account assuming the DLC narrow—band design. For this design, the smearing due to beamstrahlung is small at \/5 : 500 GeV and almost negligible at \/E = 300 GeV. Without the energy loss connected with these initial—state radiative effects the signals would appear as a sharp peak at M,,,m;l = MH. Throughout our study we have identified jets with the partons in which they originate. In the analysis of the tf background, we have assumed mt = 150 GeV.
channel H -> bb H -> WW" H —> ZZ MH < 160 GeV MH > 110 GeV MH > 180 GeV
signal I e+e` —> (;1+;1")(bb) I e+e‘—+ (;i+;i“)(WW*) I e+e“——> (;1`*';f)(ZZ)
bkgd I e+e" —> ZZ, 27*,7*7* I e+e”—-> ZWW* e+e" —+ ZZZ e+e" —-> tf—+ bb_u+;L‘w7 Ie+e‘—> ZH —¥ (jj)(;1+;fjj)]
Table 1. Signal and main background processes to Higgs production via Higgs strahlung, e+e‘—+ HZ, for various mass ranges.
In Figs. 5(a) and 6(a), the ZH ——> (;i+;t‘)(bb) signal is shown with its background added. The Mmoil distribution starts slightly below MH, rises steeply to the peak at MH, and tails off towards larger values of MMOH. For MH 5 100 GeV, the suppression of the ZZ background by ;t—vertexing is essential. For larger MH, the Higgs and Z peaks are clearly separated. Figures 5(b) and 6(b) show the Mmmu spectrum for the ZH —> (;¢+,u')lVVV"‘ signal with the continuum background added. For .MH = 120 GeV, the Higgs peak is low due to the small branching fraction of H —> WW*. Once NIH 2 140 GeV, BRIH —~> ll/l/V*) increases, however, quite fast with MH, and the Higgs peaks are very prominent in the curves for MH = 150 and 180 GeV. All these curves will eventually merge together at the high end of the M,.,c0i| spectrum because only the continuum background of e*e` —> Z IV lV* contributes there. Figures 5(c) and 6(c) exhibit essentially the same features as Figs. 5(b) and 6(b), except that the curves in these figures will not merge at high ]\I,eCO;]. This is due to the presence of the combinatorial “background" from e+e” -—> ZH —> ( j j)(;1+;i‘ j j), which will not contribute to the Higgs peak but to the continuum; in particular, the increase of the background at large il/[MOH for the 200 GeV case is due to combinatorics. In conclusion, MH can be easily determined from the Mmcou spectrum. OCR Output ‘`f¥"·¥·=•¤ ml l`·';` gr- n·;=·:·;"‘" ,,-.tb-·'·`", lE·-·"" ‘;‘:`;:.-.44 J "°“°" ...... -x0 "·'¤·T1"3"' lA ···· l ..-4 .....=I\·····—·.-{ ·--¤TI <*:\ .1 [ \ an., = { , · `· E I .._.....,.,H ... \° -. Q \ T . J I ····•,: l \ \··¤¤·· a \ . \_ |\....· | i . ‘. - E I |\,,,,,,_,·' \: é\ X \_* K .`fi ` x ! ‘· "l \····· I ¤ \ : Tx ` ' \ »` { `¤ / I', i `' \§ | ____ ";Z~~--i: ~ · D IW I- N0 I_ IE |_ IR I % lll X IM 1
lun (% Ru (U"} “»•¢ (UW)
Figure 5: Missing—mass distributions for the e+e‘——> p"’;fH signal as a function of the recoil mass in the three Higgs decay channels (a) H ——> bb for MH = 100, 125, and 150 GeV, (b) H —> WWfor(*) MH = 120,150, and 180 GeV and (c) H —> ZZfor(*) MH = 150,200, and 250 GeV. \/5 = 500 GeV and an angular cut |cos 0,,,,| < 0.6 on the p+;f pair momentum with respect to the ex axis has been used; the effects of bremsstrahlung, beamstrahlung, and beam-energy spread are taken into account.
10** .•.¤¤•·,.•,¥ 5 · uw °" I [ ,·,-,m 6 - ¤.• nv W .•'-°_ € - u W ld uq.:] |_·"•-yur; pq*¤"" 4 p,-qana¤.• L;¤··»•w1·»1 i.·¤J l.... ¢¤•n »..... (Mn L.- (um Figure 6: Same as in Fig. 5 but for (/-5 = 300 GeV. Note that there is no e+e' —> if background. At this point, we investigate the significance S/1/B of the ZH signal (S) on the ZZ background (B), assuming tagging of one b with probability eb and misidentification of one c as a b with probability E;. In the limit of perfect b tagging, eb = 1 and 6; = 0. We neglect the small probability of misidentification of light quarks as b’s. Furthermore, we make the following approximations for the branching ratios: BR(H —·> bb) >> BR(H —> cc) and BR(Z —> bb) z BR(Z —> cc). The probability that at least one of the two b’s is detected, is [1 — (1 — e;,)2]. Thus the significance achieved with at least one b tagged is a(ZH) BR(Z —> nhl-) BR(H —> bb) 1: X Pb 7 2a(ZZ) BR(Z —> n+;r) BR(Z —> bb) where L is the integrated luminosity and 1 - (1 - 6 )2 " '°° = (5) 2 . 2 [1-0-612) l+ll·(1·€2)l OCR Output The cross sections in fb for the p+;Fbb final states of ZH and ZZ origin are given in Table 2 for several values of M H at \/E = 0.5 and 0.3 TeV, where the distributions have been integrated over the recoil-mass range MH —— 5 GeV g Mwwil 3 MH + 10 GeV. Also given is the significance for a luminosity of 10 fb‘1 assuming perfect b tagging. The values for higher luminosity can be obtained by scaling up these numbers with For a realistic detector it is estimated that ez z 0.2q, [25]. Using this relation, one has Pb = 0.54, 0.72, 0.81, 0.86, 0.85 for cb = 0.2, 0.4, 0.6, 0.8, 0.9. The reduction in the significance is less than 25% as long as the single-b tagging efficiency is greater than 50%. Under such circumstances, Higgs detection in the bb mode of the Higgs strahlung process is feasible at least up to 125 GeV at a 0.5 TeV collider with 10 fb‘1 luminosity. The situation is even considerably better at x/E =: 0.3 TeV, due to the higher cross section for the signal. Taking into account also e+e'bb final states, S / x/H is scaled up by a factor of With double—b tagging, the factor Pb in Eq. (4) is replaced by Pbb = 6,2/ (eg + eQ2).1/2 Again taking ez = 0.2eb, one now has Pbb = 0.20, 0.39, 0.59, 0.78, 0.88 for the same eb values as above. The requirement of double-b tagging is considerably more costly with low b-tagging efliciency and probably unnecessary, except for confirmation. 1llH]0(ZH —> ;.t+;1`bb) I 0(ZZ —> ;.t+p"bb) S/x/E 101b-* l 1001*0-1 100 0.56 0.18 4.1 (3.2) [13.0 (10.1) 2.53 0.65 9.9 (7.7) | 31.4 (24.3) 125 0.42 0.05 5.8 (4.5) | 18.4 (14.2) 1.62 0.15 | 13.4 (10.4) [42.3 (32.7) 150 0.13 0.03 2.4 (1.8) | 7.5 (5.8) 0.37 0.10 3.7 (2.8) | 11.6 (9.0) Table 2. Cross sections of the e+e` —> ZH —> ;r+;r‘bb signal and the e+e“—+ ZZ —+ nhrbb background, integrated over the range MH - 5 GeV § Mmm,] $ MH + 10 GeV, and statistical significance, assuming perfect b tagging and, for the numbers in parentheses, Cb = 0.5 giving Pb = 0.77, for MH = 100, 125, 150 GeV and L = 10 and 100 fb`*. The upper entries refer to (/E = 0.5 TeV, the lower ones to ,/5 = 0.3 TeV. 3 WW Fusion The cross sections of Eq. (1), based on t—channel vector-boson exchanges, logarithmi cally increase with energy and eventually surpass that of Eq. (2) [26]. The Z Z—fusion mechanism has weaker couplings and hence a much smaller cross section. ln this section, we shall focus attention on the production of a heavy Higgs boson, with MH > 2MW. The dominant SM decay modes are then into four quarks via H —> VV —> qq qq (where V denotes a generic weak boson, V = W, Z ln our subsequent discussion it will be assumed that the VV pairs are measured in the corresponding four—jet final states OCR Output VV —> j1j1j3j4, with invariant masses m(j1j2) : m(j3j4) : My. At first sight, the simplest and cleanest heavy Higgs signal appears to be in the dimuon plus four—jet channel, e+e` ———> ZH —> 11+1fVV , (6) selecting invariant mass m(,u+;1") = M Z; the Higgs-boson resonance appears here as a peak in the mvy distribution, but the event rate is suppressed by the small branching fraction B(Z —+ ;1+,u") = 0.034 [27]. It is therefore attractive to investigate also the invisible Z decay to neutrinos, which has six times larger branching fraction, B(Z —> l/lj) = 0.20 [27]; this leads one to consider the channel e+e“—> 1/DVV , (7) summed over all neutrino flavors, where there is again a resonance peak in myv. The Higgs—boson signal in this channel receives contributions not only from Z H -production but also from the WW—fusion mechanism. This is both an advantage and a challenge; it further enhances the event rate and also offers the opportunity to separate and compare these contributions and hence to test the relative strengths of the H Z Z and H W+W" couplings, predicted by custodial SU(2) symmetry. The WW—fusion contribution to e+e‘ -+ 1/17W`+VV"(ZZ) is not gauge-invariant by itself however; the complete set of lowest—order Feynman diagrams for this process is contained in the generic set shown in Fig. 7. The Higgs—boson signal in channel (7) thus has a background from the non—resonant contributions of Fig. 7; it also gets backgrounds from the processes e+e` ——>€+€`W+W`(ZZ) , (8) e+e“—> F1/l/VTZ (9) when one or more charged leptons escape undetected. Processes (7) and (8) were previ ously discussed in Ref. [28]. 3.1 Weak-Boson Pair Production in the Standard Model We first consider in turn the leading contributions at tree level to the production of weak—boson pairs plus two leptons. An array of generic Feynman diagrams is shown in Fig. 7. The external fermion lines can be labelled e, 1/, or p and the external weak bosons are labeled W or Z. When the external particles are specified, standard selection rules determine the labeling of almost all the other lines. However, a virtual neutral-boson line sometimes represents both Z and 7, while the flavor of the final neutrinos is sometimes 1/6 and sometimes to be summed over 1/6,1/}), and 1/,. All the electron masses are kept finite in the formulas and in the calculations in order to regulate the mass singularities. The differential cross sections do/dm;/V for the various reactions are shown for the case lily = 200 GeV in Fig. 8; the total integrated cross sections are shown versus M H in Fig. 9. No cuts are imposed here except in the 1111VV channel, where we require m ;1,u`—(+) MZ] < 15 GeV , (10) since we are interested only in muon pairs from Z decay. Here and in subsequent figures we omit all smearing effects arising from experimental resolution in measurements of invariant masses and transverse momenta. 10 OCR Output The cross section for e+e”W+W‘ production is exceptionally large due to photon exchange processes. The Ul7W+ W` channel is particularly sensitive to Higgs—boson con tributions. The pronounced edges at MH = 2MW and MH = 2MZ in Fig. 9 indicate the onset of the resonance region for the s—channel Higgs exchange. 3.1.1 e+e‘—> l/17 W+W” The contributing Feynman diagrams are depicted in (a)—(d), (f), {h)·(o), (p), (q), (s), (t), and (v)—(y) of Fig. 7 for the "scattering” channel, where fermion lines 1 and 4 are taken to represent incoming particles, and in (a), (c), (f), (g), (h), (j), and (l)—(y) of Fig. 7 for the “annihilation” channel, where fermion lines 1 and 2 represent incoming particles. \Ve stress that both the "scattering” and “annihilation" channels of e+e" —+ 1z1?W+lV ' contribute to the Higgs-boson signal. In Fig. 8, the curve for this process includes both contributions; their interference is found to be negligible. Figure 10(a) shows separately the "scattering” and "annihilation” contributions to the da/d;6T distribution versus missing transverse momentum ;$T for MH = 200 GeV. From simple kinematics the distributions terminate at (;$T)max = (S — 4M$V) / = 224 GeV. The location of the Jacobian peak in the annihilation channel corresponds ap proximately to the maximum iT for which the intermediate Z and H bosons in e+e` —> ZH -> UHWW are both on mass shell, (;$T)p8ak = {[s — (MZ + MH)2] [S — (MZ — JWH)2] /s}/21/2 : 198 GeV. For higher ;$T, one or both bosons are off mass shell, which explains the sharp fall beyond the peak. We conclude that the scattering and annihilation contri butions can be separated by their ;6T spectra (or equivalently by their pT(VV) spectra, since = |pT(VV)| in the 1117VV final state). In Fig. 10(b), we also separate the ;$T spectrum of e+e‘ -+ 1z1`iH into the contributions from WW fusion and ZH associated production. Now the distributions terminate at (;6T)mx : (s — / = 210 GeV, but the position of the Jacobian peak in the ZH curve is unchanged. For MH = 200 GeV, a ]$T > 175 GeV cut can single out the contribution of the ZH diagram, assuming the CM energy to be 0.5 TeV. We shall see later that initial—state radiation corrections smear the CM energy and with it the $#11 dependence; nevertheless, it remains true that ZH production and VV fusion contribute in distinctively different ways and can in principle be separated by a detailed study of the HT dependence of the signal. 3.1.2 e+e‘ -—> l/DZZ The contributing Feynman diagrams are depicted in (a), (c), and (f)—(u) of Fig. 7 for the scattering channel and in (a), (b), (h)»(k), and (p)—(u) for the annihilation channel with appropriate particle labeling. This case, too, has contributions from “scattering” and "annihilation” channels, and both contain the Higgs—boson signal. However, the cross section is much smaller than that for e"'e" —> Vl7W+l/V-. The major background in this channel arises in the annihilation channel from e+e‘ -—> ZH with H —> ZZ —> Z1/17 decay [Fig. 7(b)]; it comes from the Higgs boson itself, via a different decay mode from the one we are studying, and gives the broadienhancement at large myy in Fig. 8(a). ll OCR Output (Ig) (Kg) "' 2 in,) ‘Y]* |•<¤.*v4 Fa 3v. (Vs) V1 Vs 1 (9,) (a) (bl (c) (d) (•) (f) (9) (hl (I) (i) (k) (I) (rn) (n) (o) (9) (q) (r) (s) (Q) (u) (v) (u) (x) (y) Figure 7: Generic lowest:-order Feynman diagrams for the processes e+e" —> ZIEQVIXQ. 12 OCR Output ( ) ° (bl £·0·5T•V M,.-200G•v ••:-,:p‘vv \m(pp>-M,{<¤scev D-I •g•••WW m/I /•:' `~I »a‘L//IW . r .4 ‘ '° P M ••r»·•·""' -, !“\____"(.,••-uni; \_j E ,.\,< ·u rx xI 1 \••-G \ /·¢==\ \ / ,..-\ \ , ¥` ‘’ - 5 \ \ -. ‘° .6{ •·;»i»¤ \@ \ I \_ \ 6: 6* zoo soo •oo soo zoo zoo ooo soo mw (GN) mw (G•V) Figure 8: Differential cross sections do/dmvy for the production of two leptons plus two weak bosons versus the VV invariant mass myy, where V = W or Z, for the case MH = 200 GeV. No cuts are imposed apart from the dimuon mass requirement of Eq. (10) in ;Lp.VV channels and the fake-V mass requirement of Eq. (11) in tf background cases. All contributions from both scattering and annihilation processes are included: (a) w7VV signal and background channels, (b) ;i+;FVV channels. (bl ( ) ,/{-0.5 T•V G ,/E`¤O.5 TeV ...... __....:•£ ._ ______" iv (••-•••\•lVl) ••—ppW°W` `° T l_,..x] \ \-`J?;2E.----... ••-•vF\V°vl` H \ .. ll` { `Q. Wu ••-•t¥ ”-wzz ••7••ZZ —~;-———-———————·-I-— | \ \ —\..-..-...... --..z...-..-- j \` ""’ I l`----•»•-•-••e----- 0 0.2 0.4 0.6 0.0 1.0 0 0.2 0.4 0.6 0.8 1.0 m" (T•V) mn (TeV) Figure 9: Total cross sections versus MH: (a) VDVV signal and background channels without cuts, (b) wirvv channels with |m(;i;i) — MZ| < 15 GeV. The cross section for e+e" —+ e+e“W+W' is relatively large so one fifth of it is shown. The fa.ke—V mass requirement of Eq. (11) is imposed in the ti background cases. The cross sections corresponding to four jets in the final state may be obtained by multiplication with [B (V -> jj)]2 = 0.5. 13 OCR Output 3.1.3 e‘*'e' —> e'*`e“W+W" The contributing Feynman diagrams are depicted in (a), (c), (f), (g), (i), (k), and (1) (y) of Fig. 7. Although this channel has contributions from Higgs-exchange diagrams, it is essentially a background to the Higgs signal, because it is overwhelmingly due to *y·exchange contributions. In Figs. 8(a) and 9(a) we can see that this background is potentially much bigger than the signal in the 1/17W+W" channel. But with a suitable pT(VV) cut and central—electron vetoing, we shall show that this background can be reduced to an unnoticeable level. e¢¤•t•M¤ www 5 _' % to annihilgtbn ZH progucmq é' cz m,,·2OO G•V m,,•2OO GeV (¤) •°•'—·vFW°W' (b) c°c'-•v7H -s lo 0 50 IOO |5O ZG) 250 N 0 50 IOO |5O 200 250 IT (GeV) FT (GeV) Figure 10: Differential cross sections without cuts for (a) e+e" —> wvw+w· and (b) e+e` —> w7H versus the missing transverse momentum #71, assuming M H = 200 GeV. Scattering and annihilation contributions are shown separately in (a); WW fusion and ZH production are shown separately in The contributions due to annihilation channels are summed over three neutrino flavors. 3.1.4 e+e" —> e+e'ZZ The contributing Feynman diagrams are (a), (b), (h)—(k), and (p)—(u) of Fig. 7. This channel has characteristics similar to Section 3.1.3, but the cross section is exceedingly small because of the small Zee coupling. 3.1.5 e+e" ——> e*uW*Z The contributing Feynman diagrams are (b)—(r), (t), (u), and (w)—(y) of Fig. 7. This process gives another background to the signal; the cross section depends on M H because of the Higgs—boson exchange diagram 7(b). With a pT(VV) cut and central-electron vetoing it can be greatly reduced, as explained below. Furthermore, if it became possible to distinguish accurately between W and Z from the invariant masses of their decay dijets, then this background could be removed. 14 OCR Output 3.1.6 e+e' —+ ;4+;fW+W"(ZZ) The amplitudes in these cases precisely equal the lepton annihilation amplitudes for the e+e' —> e+e‘W+W`(ZZ) cases, described in 3.1.3 and 3.1.4 above. In addition to the H ——> W+W‘(ZZ) diagrams that give the Higgs—mass peaks in the my/V distri butions, there are weak—boson scattering and Higgs strahlung diagrams that contribute backgrounds. In the ;1+,u"ZZ channel there is also a contribution from e+e‘ -—> ZH production with H —> ZZ ——+ ;i+p‘Z decays [Fig.7(b)]; this appears as a background to the Higgs signal in the m ZZ distribution, if both these Z bosons are assumed to decay hadronically. Since we have here a Z Z Z final state, the event rate in the Higgs peak (and background) could be tripled if we included all three ZZ pairings in the mzz distribution. However, this procedure would make sense only if the hadronically decaying Z bosons could be clearly distinguished from W bosons (it would be nonsensical in ;1+;i‘W+W" final states) and we do not pursue it here. 3.1.7 6+6- ··} bbW+W` ···} bbfjf2f3f4 This final state can be mistaken for l/DVV if one W boson decays leptonically lV ——> @1/, (ii) the charged lepton escapes detection while the neutrino gives large ]$T, and (iii) the final bb pair fakes a V —+ jj decay. This background can be reduced by requiring large ;$T and by vetoing central leptons, the same criteria that suppress the other backgrounds. `We note that leptonic T decays give final e or p while hadronic T decays give identifiable narrow jets; although the technical details for vetoing central taus must differ from those for vetoing central electrons and muons, we shall here treat them all the same as a first approximation. In Figs. 8(a) and 9(a), we show the potential if background in the VDVV channel, before making selective cuts, for the case m, = 150 GeV. We first calculate the cross section for fujjjj production, summing the contributions from E = e,p, T, and requiring that the fake V generated by b and b jets has invariant mass within 15 GeV of the EV or Z mass: AIM/—15GeV 15 OCR Output present analysis we do not apply this three-jet mass veto, since it would introduce a confusing multiplicity of cases to discuss; however, it remains a potentially helpful cut for future application. In Figs. 8(b) and 9(b), we show the potential tf background in the ,u;.¢VV channel, before making selective cuts, for the case m, = 150 GeV. We calculate the cross section for up j j j j production, requiring that the dimuon invariant mass satisfies the constraint Eq. (10) and that the fake V from b + b hadronic debris satisfies the constraint Eq. (11). This cross section is divided by the square of the branching fraction B (V —> jj) = 0.70 , to reduce it to an eff`ective ;4pVV cross section. Then myy denotes the invariant mass of one true W plus one fake V, as before. 3.2 Results After Kinematic Cuts At (/5 = 0.5 TeV there are seldom any events for W bosons having absolute rapidity ]y| > 1.5, and there is not much difference between rapidity cuts of 1.0 and 1.5. Furthermore, experimental acceptance will force some such cut upon us anyway, since jet measurements will be impossible close to the beam axis. In our calculations we shall therefore make the cut y(V)| < I to approximate the experimental acceptance, with no serious loss in signal. In the UDVV channel, the backgrounds from e+e”—> e+e`W+W` (mainly due to ·y— exchange processes), from e+e` —> euWZ, and from e+e‘—> tf are potentially dangerous; see Figs. 8 and 9. Our strategy to reduce the first two backgrounds is similar to that in Ref. [29]. We first suppress the contribution from the 7—exchange poles by a cut pq~(VV) > 45 GeV , (13) which effectively removes the double·7 pole contribution to e+e‘——> e+e‘W+W‘. In addition, we veto events with a visible electron. We assume that e* will be identifiable if they have high energy and are emitted in the central region (neglecting the possibility of losing electrons in jets); we therefore veto all events that contain 6* with Eze > 50 GeV and |cos(9€r)| < cos(0.15) (14) This proves to be very effective in reducing the e"”e`W+W' background, but less in suppressing the e1/WZ background. The tf background is little suppressed by the pT(VV) cut but is considerably reduced by vetoing all central leptons; for this we extend the criteria of Eq. (14) to apply to all charged leptons e, rt, and T. The results for VDVV signal and background channels are summarized in Fig. 11 for the differential cross section versus the invariant mass my/V of the weak-boson pair. The Higgs—boson signals in the ZH —> ;r;.4VV channels do not suffer from potentially large backgrounds and therefore do not need strong cuts for their extraction. However, the tf background has typically large ;$T = pq~(VV) due to the leptonic W-boson decay, unlike the signal or the other backgrounds; we therefore choose to suppress tt contributions by requiring ;$T < 40 GeV. (15) OCR Output 16 In addition to the p+;.¢` mass constraint of Eq. (10) and the fake-V mass constraint of Eq. (11), we also impose the rapidity cut of Eq. (12), approximating the likely experi mental acceptance, both on the vector bosons and on the ,u+p“ system. The total cross section and myv dependence differ little from the uncut distributions shown in Figs. 8(b) and 9(b) (apart from tt contributions), so we do not plot them again. `/;=O.5 TeV mp 200 GeV |>.,(VV)> 45 GeV Iy(V)I<1 Central lepton vetoinq for E,>5O GeV ond |cos9,| \° ..;..wz yy \\.....-.-....;.¤.,.;‘L .. w+ - •• vv w '62 ••··v7ZZ · \ _x ••··••WW ••-••ZZ a____ i ,. . . ______,_____%\/'\\\ n . \ 1 _ D 200 400 500 mw (GeV) Figure 11: Contributions to the I/DVV signals and backgrounds, with acceptance cuts but without initial-state radiative corrections, for the case MH = 200 GeV. Differential cross sections are shown for e+e" ——> 1/17(e+e',e1x)VV versus the VV invariant mass myy, where V = W, Z; here |y(V)| < 1, pT(VV) > 45 GeV, and central ef vetoing by Eei > 50 GeV and cos(0€4)| < cos(0.15) have been applied. These curves receive contributions from both scatter ing and annihilation channels. The background from e+e` —> tf production is also shown, with the fake—V mass constraint of Eq. (11) plus the corresponding pT(VV) and |y(V)| cuts and a veto on all central leptons e, ii, rr. 4 The JW = 0++ Quantum Numbers of the Higgs Boson The scalar character of the Higgs particle can be tested at e+e‘ colliders in several ways. The angular distribution of the e+e‘ -> ZH final state depends on the spin and parity of the Higgs particle. The same is true of the angular correlations in the Higgs decay to fermion and gauge boson pairs. The observation of the decay or fusion processes H Fi 77 would rule out spin :1 directly by Yang’s theorem and fixes the charge conjugation to be positive C = +. This follows also from the decay and fusion processes H `=* ZZ, as well as from the observation of the Higgs strahlung process e+e` —+ Z * —-> ZH. 17 OCR Output 4.1 Production Process Since the production of the final state e+e”—> Z * -+ ZH is mediated by a virtual Z boson [transversally polarized along the ei beam axis], the production amplitude could be a monomial in cos/ sin 0. In the SM, however, the Z ZH coupling, .C(ZZH) = (x/0-Gp)M§HZ”Z,,1/2 ~ G]HF”"F,,,,,(2 (16) is an S—wave coupling ~ E] · g2 in the laboratory frame, linear in sin0 and even under parity and charge conjugation, corresponding to the 0++ assignment of the Higgs quantum numbers. The explicit form of the angular distribution is given by d¤(ZH) 2 - 2 2 5 SID 0+8MZ/S. (17) For high energies, the Z boson is produced in a state of longitudinal polarization, : 1 - .-32 ]% 2, UL + 0T 12MZ + 52.9 (18) so that——in accordance with the equivalence theorem [9]—the production amplitude be comes equal to the amplitude M (e+e”—>°H), with ° being the neutral Goldstone boson which is absorbed to build up the longitudinal degrees of freedom of the elec troweak bosons. The angular distribution therefore approaches the spin-zero distribution asymptotically, 1 d0(Z H) 3 _ 2 -———— 0. _) Sm 19 ( ) 0 dcos0 4 Even though the nature of the Higgs phenomenon requires the Higgs field in the SM to be necessarily a scalar J=PG 0++ field, it is nevertheless interesting to confront the predictions in Eqs. (17,18) with the production e+e' —> Z* —> ZA (20) of a pseudoscalar state A(0'+) in order to underline the uniqueness of the SM prediction. The pseudoscalar case is realized in two-doublet Higgs models, in which the Z Z A couplings are induced by higher—order loop effects [30]. The effective point-like coupling, l’2 L(ZZA) : (t/§GF)M;Az#~Z,,,, (21) with n being a dimensionless factor and Z*"’ = e'“’*"’Z,,,, is a P-wave coupling, odd under parity and even under charge conjugation. It reduces to (E] >< E'2) · (51 — 52) in the laboratory frame. Since the Z spins are coupled to a vector, the angular distribution is again a binomial in sin 0, 0(Z A) 1 _ 2 ——-——— ~ l —— 9 » 22 <>OCR Output ,1.;.,.6 2 18 independent of the energy. The Z boson in the final state is purely transversally polarized, so that the cross section need not be ~ sin! 0 in this case. The total cross section is given G2 M 6 ZA = 2 F Z 2 2 V ’ ( ) T] (ae-lhve) ( ) where the momentum dependence ~ 53 is characteristically different from the ZH pro duction cross section near threshold. The angular correlations specific to the S—wave 0++ Higgs production in e+e` —> ZH can directly be confronted experimentally with the process e+e‘ -> ZZ. This process has an angular momentum structure that is distinctly different from ZH associated pro duction. Mediated by electron exchange in the t-channel, the amplitude is built-up by many partial waves, peaking in the forward/backward direction. The two distributions are compared with each other in F ig. 12. This figure demonstrates the specific character of the Higgs production process, which is not lost if experimental acceptance cuts and smearing effects are taken into account [25]. 0.8 \\ (1/v) dc/dco•0 ·+•_ _• 4 1 o.c y- Q" \ \ 1 /\\ /1. X :! 0_d__ r_ "_ ¤*¤"-•ZA ,’/ 0.2 J?-soocev "`--.___f;f;`--~"` j_§?__ ul 0.0 -1.0 -0.5 0.0 0.5 1.0 cod Figure 12: Angular distributions of e+e" —+ ZH, e+e" —> ZA, and e+e" ——+ ZZ for MH = 120 GeV and \/E = 500 GeV. Since the longitudinal wave function of a vector boson grows with the energy of the particle~in contrast to the energy independent transverse wave function~tl1e Z boson in the S—wave Higgs production process (2) must asymptotically be polarized longitudinally, Fig. 13. By contrast, the Z bosons from ZA associated production or ZZ pair production 19 OCR Output 1.0 •*•` -• Z°H 0.8 Vx. / (VL + V1) 0.8 0.4 0.2 ul 0.0 200 300 500 700 1000 J? [cw] Figure 13: Cross sections for the production of longitudinal vector bosons normalized to the total cross section of e+e" —> ZH as a function of \/E for MH = 150 GeV. are transversally polarized [at high energies in the second case]. This pattern can be checked experimentally. `While the distribution of the light fermions in the Z —> ff rest frame with respect to the flight direction of the Z [see Fig. 14(a)] is given by sin? 0,. for longitudinally polarized Z bosons, it behaves as (1 ;l; cos H,.)2 for transversally polarized states, after averaging over the azimuthal angles. Including the azimuthal angles, the iinal angular correlations may be written for e+e‘—> ZH [Z -2 ff] as d¤(ZH) 2 2 * * 2 2 2 2 ss ——s s _c_+—— 1-+-c 1+0 +ss c _ 0 9. .,_, 26 29 is 2l( 0>< 0,) 0 2. 22] dC0dC0_d¢7_ 27 211eae 2vfaf 2 ———————————ss_c_——cc9_,[ Z}} v3+¤v+¤v 0 0 d’ 7 0 l (24) where Sy = sin 0, etc. As before, 0 is the Z polar angle in the laboratory frame, 9.. the fermion polar angle in the Z rest frame and ¢,, the corresponding azimuthal angle with respect to the e*Z H production plane. After integrating out the polar angles, 0 and 0., we find the familiar cos ¢* and cos 2¢,. dependence associated with P—odd and even amplitudes, respectively, ~1+a;c0s<;5,,+a2cos2qb., (25) d ZHQ5 OSl 20 OCR Output £-.[.5‘&;\ "—. A"i’• `\ Z I X, (n) *3 F`;7 ;;si%..!..&2»-E &J\ 2 HN/E (b) Figure 14: Definition of the polar and azimuthal angles in (a) e+e‘—> HZ [Z -—> ff], and (b) H —> vv><*> (f1f2)(fsf4l· with 97r” ey 2veae 2vfaf 1 1 = — al ——————t--— - — -—— . 32 72+2v§+a§v}+a§’ U2 272+2 26 ( ) The azimuthal angular dependence disappears for high energies ~ 1/cy as a result of the dominating longitudinal polarization of the Z boson. Noteagain the characteristic difference to the pseudoscalar 0"+ case e+e" —> ZA [Z —> ff], 1 1 2 E E 2 dC;i9·d;5*d ZA ; 1 + 030; —§sgsg_ —§s§sg_c2¢_ + 2 c0c9_ . (27) This time the azimuthal dependence is ’P—even and independent of the energy, in contrast to the 0++ case; after integrating out 0 and 8,,, d U ZAg 1 érl ~ 1 — T cos 2¢>,,. (28) We can thus conclude that the angular analysis of e+e` —> Z* -> ZH [Z —+ ff] allows stringent tests of the JPG = 0++ quantum numbers of the Higgs boson. This is a direct consequence of the 0++ coupling el · 62 of the Z Z H vertex in the production amplitude. 21 OCR Output 4.2 Decay Processes The zero—spin of the Higgs particle can be checked directly through the lack of any angular correlation between the initial and final state particles [25]. In the following discussion, we shall concentrate on Higgs boson decays to vector bosons V = W Z, which will provide us with signatures similar to those studied in the previous section, including the discrimina tion between 0++ and 0”+ decays. The analysis applies in a straightforward way to Higgs particles in the e+e` environment. Background problems require a more sophisticated discussion for Higgs particles produced at the LHC. Since some of the material on this method had been worked out before [31], we focus on novel points which have not been elaborated in detail so far. Above the H ——> WW and ZZ decay thresholds, the partial width into massive gauge boson pairs may be written as . I`(H —> VV) =2 6V-Mg(1— % 4a: +12x’)H, (29) where x = 5 = (/1-4x, and 5V = 2(1) for V = For large MH, the vector bosons are longitudinally polarized [see Fig. 15], I` 1 — 41* + 410 L <3¤> 2 I"L+I`T 1—4x+12a: while the L,T polarization states are democratically populated near the threshold, at at : 1/4. The H Z Z coupling el · e2 is the same S-wave coupling that we have discussed earlier. Since the longitudinal wave functions are linear in \/E, the width grows as M The electroweak radiative corrections [32] are positive and amount to a few percent above the threshold. Below the threshold for two real bosons, the Higgs particle can decay into real and virtual VV* pairs, primarily WW" pairs above MH ~ 110 GeV. The partial decay width, [V charges summed over, is given by [33] 3G2 M4 (31) 1"(H ——> VV") = —P;—l£MHR(a2)6[,,16vr 3 with 6[V = 1, 62 = 7/12 — 10 sin? 0W/9 + 40 sin4 0W/27, and 3(1—8x+20;r2) 32;-1 1-x — 2 &I`CCOS ··· + ) —§(1 ··6.7J+4.'II2)lI1.’12. The invariant mass (M,.) spectrum of the off—shell vector boson peaks close to the kinematical maximum corresponding to zero—momentum of the on- and off-shell vector bosons in the final state [see Fig. 16], dl` 3G%M{} U 6(M}302 +12M$M.?) (33) OCR Output _ (1M} 16¤¤M,, V (M3 -M3)2 +M$r$ ’ 22 1.0 H -• VV° mal- Fr / (rr. + rr) 0.0 0.4 0.2 0.0 0.5 0.7 1.0 2.0 3.0 5.0 (ul Figure 15: The width of Higgs decays to longitudinally polarized vector bosons normalized to the total width for the decays H —+ vv<*> as a function of M If / (2Mv). where B2 = [1- (MV + M,.)2/M2,] [1 — (MV — Since both V and V* pref erentially have small momenta, the transverse and longitudinal polarization states are populated with almost equal probabilities, (1rL/(1M? _ I sM3M3 — (34) dl`/dM2 M},52 +12M5M2 Neglecting the widths of the vector bosons, FV, we find after summing over all M,. values [see Fig. 15] FL + FT where R is given in Eq. (32) and 2 = -——————·———-3-16;::+20:1:2 — -——— 2 — 13 15 L(x) (43; 3x-l _1)1/2 arccos(1-0: 2x3/2) 2x ( .1*+ 2:) —§(3 —— 10.73+412) lux. (36) The angular distributions of the fermions in the 0++ decay process H —> V V* ·*(f1f2) (f:s1F4) lV I W» Zl (37) are quite similar to the rules found for the production process. Denoting polar and azimuthal angles of fl and f3 in the rest frames of the vector bosons by (01, 0) and (93, {bg), 23 OCR Output 0.0005 (xm ¤r/cu! [¤•v"1 »‘ ` ~ , , / 0.0004 0.0003 0.0002 H -• ZZ° 0.0001 - —— A -• ZZ° 0.0000 0 10 20 30 40 50 60 IL [GW] Figure 16: The distributions with respect to the invariant mass of the off—shell vector bosons in the decay processes H —> ZZ" and A —> ZZ* for MH = MA = 150 GeV. respectively, [see Fig. 14(b)] the angular distributions for the scalar case are given by dl`(H —> VV”‘) 2 2 —-——————— ~ -—————-—— d€01d€03d¢3SS+ 91 6° 2'Y1'Y:s(1 + BIB3)S 291s 203c in 1 -———-———— 1+02 1+2 +s2s2c 21%~;<1 1 M12 ll ~) ( C9) ~· 1 Ml 21110.1 2U3(l3 2 A —— 1 —————— s c + ————————-c c . 38 vi + ai vg + ag 7173(1 +616:1) i 01503 $3 7173(1 1'BIB3) 91 03) ( ) For V = W, the charges are vi = ai = 1, for V = Z, they are vi = 2131 — 4e, sin! OW and ai = 2I 3;. ,8, and fyi are the velocities and cy factors of the [on / off—shell] vector bosons. As expected, the dependence on the azimuthal angle between the decay planes disappears for large MH, as a consequence of the asymptotic longitudinal V polarization. After integrating out the polar angles, we are left with dl` H VV* —L—Ll ~ 1 + a1 cos $3 + ag cos 2qb3, (39) d<6;s where 9”2 7173(1 + 6153) 2U1a1 2*130:1 al : __ 32 7f'Y§(1+ U163)2 + 2 vi + ai vii + ag, (1 = — 2 (40) OCR Output . 2 v?v;?(1 + B1p3)2 + 2 24 Both the azimuthal angular correlations and the distributions of the polar angles are sensitive to the spin-parity assignments of the Higgs particle, which affect strongly the populations of the W and Z polarization states. We shall study this point by confronting again the scalar H (0++) decay with the pseudoscalar A(0“+) decay distributions, A—>VV"—>(f1f2)(f3f.,) [V=W,Z]. (41) For the AV,,,,V”" coupling defined before, the angular distribution is given by dI`(A —> VV*) 1 1 M 2v a 2v a dC0,dC9,d¢3 1 + Cglcga — 5831 833 — T2-Sg‘Sg“C2¢°— C0‘C03 ` (42) The normalization follows from the total and differential widths, FA vv* =-iasca M6 24 M2 J 43 with CE —— IIT 17 &I`CCOS A() — (1-7)(4 -1)1/2 ··* I 33 3”`1T (1_””17-64 - 2 +§(1—9x+6x2)lnx, (44) and qr(.4 —> vw)_ _ 3G§.M3n 6, 2 M$p¢* (45) dM2 8rr3MA v(M3 —— M3)? + MEIY, where M. denotes the mass of the off-shell vector boson. The M. spectra for H —> Z *Z and A —> Z*Z are shown in Fig. 16 assuming MH = MA = 150 GeV. The mass and momentum dependence of the width are determined by the P-wave decay characteristics and the transverse polarization of the vector bosons. In the same way, the angular distributions [which are independent of the masses] reflect the transverse W and Z polarizations. For MH < 140 GeV, the dominant decay mode is in bb. A fraction of a few percent decay into T+T“. For moderate to large tgb values, these are also the main decay modes for scalar and pseudoscalar Higgs particles in the minimal supersymmetric extension of the Standard Model (MSSM). While the zero·spin can again be checked experimentally by the lack of any correlations between the final and initial state particles, it is quite difficult to verify the i parity of the states in the decay distributions. This information must be extracted from correlations between the b and b (r“ and T+) spin components in the planes transverse to the bb (7*+ T") axes, scalar/pseudoscalar : C = 1 — $6% ;l; s{_s[. The spin correlations are reflected in correlations between the f and f decay products [34]. Depolarization effects through b and b fragmentation into pseudoscalar B mesons [35] introduce systematic uncertainties into this channel which are very hard to control, so that the rare but clean T+ rr" final states are the proper instrument to study this problem. At e"'e` colliders, the parity of the Higgs bosons in the MSSM can be studied in the following way: 25 OCR Output (i) Since the scalar MSSM Higgs particles, h and H couple to vector bosons directly, the positive parity can be checked by analyzing the Z final states in e+e' —> Z * —> ZH [Z —> ff] as discussed above. This method is equivalent to the analysis of the h, H —+ VV decays. (ii) The fusion of Higgs particles by linearly polarized photon beams depends on the angle between the polarization vectors [36]. For scalar particles, the production amplitude ~ E] · E2 is non—zero only for parallel vectors, while pseudoscalar particles with amplitudes ~ E'] X Q require perpendicular polarization vectors. For typical experimental set—ups for Compton back—scattering of laser light [37], the maximum degree of linear polarization of the generated hard photon beams is less than about 30%, so that the efficiency for two polarized beams is reduced to less than 10% [38]. This method therefore requires high luminosities, and, moreover, a careful analysis of background rejection due to the enormous number of bb pairs produced in 77 collisions [39]. 5 Summary In this report, we have described the production of Higgs particles in the intermediate mass range and beyond. We have also analyzed experimental signals of their PCJ assignment. lt has been shown that the search for SM Higgs particles in the intermediate mass range is easy at e+e' colliders, since the signal sticks out of the background processes very clearly. ,u-vertexing of the b quarks will be essential for Higgs bosons in the Z-mass range. The significance of the ZH signal will only reduce by 25% when at least one b is tagged with an efficiency of 50% per b. With 50 fb"] luminosity and a b—tagging efficiency of eb = 0.5, a Higgs boson of mass 100-150 GeV could be detected with a significance S/g/H greater than 4.1 (6.3) at \/E = 500 (300) GeV. Above 110 GeV, and in particular beyond 140 GeV, the Higgs decay channels into electroweak vector—boson pairs can be exploited. As discussed previously [40], the potential for the discovery of heavy Higgs bosons may be augmented by taking the WW-fusion process into account. At \/-si = 0.5 TeV and 50 fb”1, the I/DH —> v17WW(ZZ) —> wijjjj signal and its total background have S/x/H = 6.8 (2.4) for MH = 300 (350) GeV, without the use of b tagging to identify the dominant tt background. The spin and parity assignments can, on one hand, be checked easily in Higgs decays to vector boson pairs. Angular correlations among the lepton/ quark decay products re flect their polarization states, primarily longitudinal or democratic for large or moderate Aly, respectively, if JPG = 0++, and transverse if JPG = 0`+. On the other hand, this information can also be extracted from the angular behavior of e+e‘—> ZH. The parity analysis of pseudoscalar Higgs particles, in supersymmetric extensions of the Stan dard Model for instance, requires difficult measurements of the fermionic decay states, or polarization analyses in the case of 77 fusion. Besides the spin—parity assignments, the essential nature of the SM Higgs particle must be established by demonstrating that couplings to other fundamental particles grow with their masses. Even though we did not analyze these couplings in detail, a few remarks ought to be added to round off the discussion [12]. The Higgs couplings to massive gauge 26 OCR Output bosons can directly be determined from the measurement of the production cross sections: the H Z Z coupling in the Higgs strahlnng and in the ZZ fusion processes; the H WW coupling in the WW fusion process. For sufficiently large MH, above ~ 250 GeV, these couplings can also be determined experimentally from the decay widths H —> ZZ, WW. Higgs couplings to fermions are not easy to measure directly. For Higgs bosons in the intermediate mass range, where the decays into bb, cc, and T+T‘ are important, the decay width is so narrow that it cannot be resolved experimentally. Nevertheless, the branching ratios into T leptons and charm quarks reveal the couplings of these fermions relative to the coupling of the b quarks into which the Higgs boson decays predominantly. ln the upper part of the intermediate mass range but below the threshold for real WW decays, BR(H —> WW*) is sizeable and can be determined experimentally [41]. In this case, the absolute values of the b and eventually of the c, T couplings can be derived once the H Z Z / H WW couplings are fixed by the production cross sections. The decays H —> gg and 77, Z 7 and the fusion processes gg, 77 —> H are mediated by loop diagrams and they are proportional to the couplings of the Higgs boson to heavy particles. The number of heavy particles can be counted in these processes if their masses are generated by the Higgs mechanism and their couplings to the Higgs particles grow with the mass. [This is not the case for heavy supersymmetric particles which decouple asymptotically from the H VV vertices.] In the SM only the top quark contributes to the H gg vertex so that the H tf coupling can be measured in the gluonic decays of the Higgs particle [and, in the same way, through the cross section of gluon fusion, gg —> H, at hadron colliders]. In the case of H —> 77, Z7, additional contributions to the decay amplitudes come from ll! loops. A direct way to determine the Yukawa coupling of the intermediate—mass Higgs boson to the top quark in the range MH $ 120 GeV are provided by the Higgs strahlung process e+ e` —+ HH in high energy e+e` colliders [10] and 77 —+ tfH in photon-photon colliders [11]. For large Higgs masses above the tf threshold, the decay channel H —~> tf increases the cross section of e+e‘—+ tfZ through the reaction e+e‘—> ZH(—+ tf) [42]; without the Higgs decay, this final state is produced mainly through virtual 7 and Z bosons. We thus conclude that the essential elements of the profile of Higgs bosons in the intermediate mass range can be scanned very accurately at e+e” colliders. Our results may be summarized as follows: (i) For a heavy Higgs boson, with MH > 2Mw, the most promising signals are in the channels e+e` —+ UDH —> VDVV, where V = W,Z and V —> dijet decays are detected. Various backgrounds from other UDVV, euVV, eeVV, and tt production mechanisms can be greatly suppressed by a V—rapidity cut, a missing-transverse momentum (= pT(VV)) cut and a central—lepton veto. A detectable 1/Ujjjj signal is predicted up to masses of order MH = 300-350 GeV; see Fig. 17(b). Assuming an annual integrated luminosity of 50 fb`1, 50% instrumental efficiency, and a pes simistic beamstrahlung scenario, a mass value MH = 300 (350) GeV would imply about 30 (10) signal events per year in a narrow m(jjjj) peak, with about 50 (15) background events under this peak. (ii) Another, smaller, Higgs—boson signal appears in the channel e+e" —> ZH —> ,u+;F VV. This is not threatened by large backgrounds and requires no stringent cuts. For the same assumed luminosity and efficiency as above, a ppjjjj signal of about 27 OCR Output 5 (3) events/year above a relatively small background may be expected for M H = 250 (300) GeV; see Fig. 17(c). This signal arises entirely from the ZH diagram. The cross section for this signal is a factor of 10-40 times smaller than that in the w7VV channels. (111) A third Higgs-boson signal appears in the channel e+e‘ -1 ZH —> 6 jets. The signal here is comparable in size with the uz? j j j j signal, but the background is much larger; precise predictions would require detailed jet simulation studies. (iv) The w7H signal receives contributions both from Z H —production and from WW fusion mechanisms. These contributions can in principle be separated on the basis of their different pT(VV) dependences in the 1117VV channel, or by comparing the 1/17VV and ,u,uVV signals. If these contributions are measured separately, they will allow a direct comparison of the Z Z H and WWH coupling strengths. (V) Bremsstrahlung and beamstrahlung corrections are very important. They lower the subprocess CM energy and momentum, enhancing annihilation channels and suppressing scattering channels of Higgs-boson production, and smearing out some kinematical features like Jacobian peaks in pT(VV). Our calculations of heavy Higgs-boson signals include both initial-state bremsstrahlung effects and illustrative calculations of beamstrahlung. The net elfect in our present cases is to reduce signals and increase backgrounds. ¤ . mw offz‘:‘fwvuv |y1v•|jk\`··_“[ , 6t|__ I\/l ` -` M ` 5 ·fr1' :4.. rl 'ge-·· ••-·v¥WW i ·<¥‘ _ U-. -l ·¤'l- i;·fv: _ .__ ·_ In /V·•1ZlI- I:::: QM" / vi»n ui #•IlI\¥\•¤t|••••h•h•l ihtfbackroundlddal "`L·j—··”L:1¤a¤¤ ooo myy (G•V) my, (GN) Myy (sev) Figure 17: Differential cross sections dU/dmvv for heavy·Higgs signals and backgrounds, in cluding all acceptance cuts plus bremsstrahlung and beamstrahlung corrections for the case of DESY/Darmstadt narrow—band design: (a) w7WW and I/I-JZZ signals and backgrounds sep arately for MH : 200 GeV; (b) WWW and VDZZ channels, as well as the corresponding backgrounds from euWZ and ti are summed, for MH :200, 250, 300, and 350 GeV; (c) ,u,uWW and ;rp.ZZ channels plus the corresponding ti background are summed, for M H :200, 250, 300, and 350 GeV. Subsequent VV —+ jjjj decays may be included by multiplication with [B(V —> == 0.5. 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