UCD-96-6 University of California - Davis MADPH-96-930 University of Wisconsin - Madison IUHET-328 January 1996 + − Higgs Boson Physics in the s-channel at � � Colliders a b c c V. Barger , M.S. Berger , J.F. Gunion , T. Han , a Physics Department, University of Wisconsin, Madison, WI 53706, USA b Physics Department, Indiana University, Bloomington, IN 47405, USA c Physics Department, University of California, Davis, CA 95616, USA Abstract Techniques and strategies for discovering and measuring the properties of + − Higgs bosons via s-channel production at a � � collider, and the associated requirements for the machine and detector, are discussed in detail. The unique feature of s-channel production is that, with good energy resolution, the mass, total width and partial widths of a Higgs boson can be directly measured with remarkable accuracy in most cases. For the expected machine parameters and < luminosity the Standard Model (SM) Higgs boson hSM, with mass � 2mW, 0 the light h of the minimal supersymmetric Standard Model (MSSM), and the 0 0 heavier MSSM Higgs bosons (the CP-odd A and the CP-even H ) can all be studied in the s-channel, with the heavier states accessible up to the maximal p s over a large fraction of the MSSM parameter space. In addition, it may 0 0 be possible to discover the A and H by running the collider at full energy and observing excess events in the bremsstrahlung tail at lower energy. The integrated luminosity, beam resolution and machine/detector features required 0 to distinguish between the hSM and h are delineated. Contents 1 Introduction 1 1.1 Higgs bosons in the SM and the MSSM : : : : : : : : : : : : : : : : : 1 + − 1.2 s-channel Higgs boson physics at � � colliders : : : : : : : : : : : : 9 2 A SM-like Higgs boson 16 2.1 Discovery and study without s-channel production : : : : : : : : : : : 16 2.2 s-channel production of a SM-like h : : : : : : : : : : : : : : : : : : : 19 p 2.2.1 Choosing the right s : : : : : : : : : : : : : : : : : : : : : : 20 2.2.2 Detecting a SM-like h in the s-channel : : : : : : : : : : : : : 21 tot 2.3 Precision measurements: mh and Γh : : : : : : : : : : : : : : : : : : 27 + − 2.4 Precision measurements: Γ(h ! � � ) � BF(h ! X) : : : : : : : : 34 0 2.5 h or hSM? : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 34 tot 2.5.1 Interpreting a measurement of Γh : : : : : : : : : : : : : : : 36 2.5.2 Interpreting a measurement of Γ(h ! ��) � BF(h ! bb) : : : 39 2.5.3 Combining measurements : : : : : : : : : : : : : : : : : : : : 40 ? ? 2.5.4 The WW and ZZ channels : : : : : : : : : : : : : : : : : : 42 3 Non-SM-like Higgs bosons in the MSSM 42 p 3.1 MSSM Higgs bosons in the s-channel: s = mh : : : : : : : : : : : : 43 3.1.1 Resolution compared to Higgs widths : : : : : : : : : : : : : : 45 3.1.2 Overlapping Higgs resonances : : : : : : : : : : : : : : : : : : 48 0 0 0 3.1.3 Observability for h ; H and A : : : : : : : : : : : : : : : : : 48 p 0 0 3.1.4 Detecting the H and A by scanning in s : : : : : : : : : : 54 3.1.5 Non-bb �nal state modes for heavy Higgs detection : : : : : : 55 3.2 MSSM Higgs boson detection using the bremsstrahlung tail spectrum 58 3.2.1 Mass peaks : : : : : : : : : : : : : : : : : : : : : : : : : : : : 59 3.2.2 Signi�cance of signals : : : : : : : : : : : : : : : : : : : : : : : 60 3.2.3 Strategy: scan vs. maximum energy : : : : : : : : : : : : : : : 63 0 0 3.3 Detailed studies of the H and A : : : : : : : : : : : : : : : : : : : : 63 3.4 Determining a Higgs boson’s CP properties : : : : : : : : : : : : : : : 65 4 Summary and Conclusion 66 4.1 SM-like Higgs boson : : : : : : : : : : : : : : : : : : : : : : : : : : : 66 i 4.2 Non-SM-like Higgs bosons : : : : : : : : : : : : : : : : : : : : : : : : 67 4.3 Summary of machine and detector requirements : : : : : : : : : : : : 69 Appendices 72 A E�ects of bremsstrahlung 72 + − (?) (?) B The � � ! h ! WW ;ZZ modes 78 tot C Three-point determination of mh SM and ΓhSM 80 ii 1 Introduction Despite the extraordinary success of the Standard Model (SM) in describing par- ticle physics up to the highest energy available today, the mechanism responsible for electroweak symmetry-breaking (EWSB) has yet to be determined. In particular, the Higgs bosons predicted in the minimal Standard Model and the theoretically attrac- tive Supersymmetric (SUSY) Grand Uni�ed Theory (GUT) extensions thereof have yet to be observed. If EWSB does indeed derive from non-zero vacuum expectation values for elementary scalar Higgs �elds, then one of the primary goals of constructing future colliders must be to completely delineate the associated Higgs boson sector. In particular, it will be crucial to discover all of the physical Higgs bosons and determine their masses, widths and couplings. The remainder of the introduction is divided into two subsections. In the �rst, we briefly review crucial properties of the Standard Model and MSSM Higgs bosons. In + − the second, we outline basic features and parameters of the proposed � � colliders, and give a �rst description of how they relate to our ability to discover and study the + − SM and MSSM Higgs bosons in s-channel � � collisions. 1.1 Higgs bosons in the SM and the MSSM The EWSB mechanism in the Standard Model is phenomenologically characterized by a single Higgs boson (hSM) in the physical particle spectrum. The mass of the hSM is undetermined by the theory, but its couplings to fermions and vector bosons are completely determined, being given by gmf=(2mW), gmW and gmZ= cos �W for a fermion f, the W and the Z, respectively. Although the SM Higgs sector is very simple, it leads to problems associated with naturalness and mass hierarchies which suggest that the SM is simply an e�ective low-energy theory. Recent summaries of the phenomenology of the SM Higgs sector can be found in Refs. [1,2]. The most attractive extensions of the SM that solve the naturalness and hierarchy problems are those based on supersymmetry. The Higgs sector of a supersymmetric model must contain at least two Higgs doublet �elds in order to give masses to both up and down quarks and to be free of anomalies. If it contains two, and only two, Higgs doublet �elds, then the strong and electroweak coupling constants all unify reasonably 16 well at a GUT scale of order 10 GeV. Thus, the minimal supersymmetric Standard Model, de�ned as having exactly two Higgs doublets, is especially attractive. The 1 resulting spectrum of physical Higgs �elds includes three neutral Higgs bosons, the 0 0 0 CP-even h and H and the CP-odd A . At tree-level the entire Higgs sector is completely determined by choosing values for the parameters tan � = v2=v1 (where v2 and v1 are the vacuum expectation values of the neutral members of the Higgs doublets responsible for up-type and down-type fermion masses, respectively) and 0 mA0 (the mass of the CP-odd A ). For a summary, see Refs. [1,2]. In the MSSM there is a theoretical upper bound on the mass of the lightest 0 state h [3,4] which is approached at large mA0 and large tan �. After including two-loop/RGE-improved radiative corrections [5,6] the bound depends upon the top e quark (t) and top squark (t) masses and upon parameters associated with squark < mixing. Assuming mt = 175 GeV and m et � 1 TeV, the maximal mass is max m h0 � 113 to 130 GeV ; (1) depending upon the amount of squark mixing. The 113 GeV value is obtained in 0 the absence of squark mixing. Figure 1 illustrates the mass of the h versus the parameter tan � for mA0 = 100, 200 and 1000 GeV. Mass contours for the MSSM Higgs bosons are illustrated in Fig. 2 in the conventional mA0; tan � parameter plane. Both these �gures include two-loop/RGE-improved radiative corrections to the Higgs masses computed for mt = 175 GeV, m et = 1 TeV and neglecting squark mixing. The Higgs sector of the MSSM can be extended to include extra singlet �elds without a�ecting any of its attractive features. A general supersymmetric model bound of < mh0 � 130 � 150 GeV (2) applies for such non-minimal extensions of the MSSM, assuming a perturbative renor- malization group (RGE) evolved grand uni�ed theory (GUT) framework. The couplings of the MSSM Higgs bosons to fermions and vector bosons are generally proportional to the couplings of the SM Higgs boson, with the constant of proportionality being determined by the angle � (from tan �) and the mixing angle � between the neutral Higgs states (� is determined by mA0, tan �, mt, m et, and the amount of stop mixing). Those couplings of interest in this report are [7] + − + − 0 � � ; bb tt ZZ;W W ZA 0 h − sin�= cos � cos �= sin � sin(� − �) cos(� − �) (3) 0 H cos �= cos � sin�= sin � cos(� − �) − sin(� − �) 0 A −iγ5 tan� −iγ5= tan � 0 0 2 Figure 1: mh0 versus tan� for mA0 = 100, 200 and 1000 GeV. Two- loop/RGE-improved radiative corrections are included, see Refs. [5,6], tak- ing mt = 175 GeV, m et = 1 TeV and neglecting squark mixing. 3 times the Standard-Model factor of gmf=(2mW) in the case of fermions (where mf is the relevant fermion mass), or gmW; gmZ= cos �W in the case of the W;Z, and � 0 g(pA − ph) =2 cos �W in the case of ZA , where pA(ph) is the outgoing momentum of 0 0 0 A (h ;H ). 20 20 15 15 10 10 5 5 0 200 400 0 200 400 20 20 15 15 10 10 5 5 0 200 400 0 200 400 0 0 Figure 2: Contours for the h and H masses in (m A0; tan�) parameter space. Results include two-loop/RGE-improved radiative corrections com- puted for mt = 175 GeV, with m et = 1 TeV (upper plots) and met = 500 GeV (lower plots), neglecting squark mixing. > An important illustrative limit is mA0 � 2mZ, since this is typical of SUSY GUT models [8]. In this limit, � � � − �=2, mA0 � mH0, mh0 approaches its upper limit for the given value of tan �, and the coupling factors of the Higgs bosons are 4 approximately + − + − 0 � � ; bb tt ZZ;W W ZA 0 h 1 1 1 0 (4) 0 H tan � −1= tan � 0 −1 0 A −iγ5 tan� −iγ5= tan � 0 0 times the Standard-Model factors as given below Eq. (3). Thus at large mA0 it is the 0 0 0 h which is SM-like, while the H , A have similar fermion couplings and small, zero 0 0 (respectively) tree-level WW;ZZ couplings. Note that the H and A couplings to + − � � and bb are enhanced in the (preferred) tan� > 1 portion of parameter space. < 0 0 0 For mA0 � mZ, the roles of the h and H are reversed: in this mass range the H 0 becomes roughly SM-like, while the h has couplings (up to a possible overall sign) 0 roughly like those given for H in Eq. (4). (See Refs. [2,9,1] for details; Ref. [1] gives the corrections that imply that the simple rules are only roughly correct after includ- 0 0 0 0 ing radiative corrections.) It is also useful to recall [7,9] that the ZA H (ZA h ) coupling is maximal (� 0) at large mA0, while at small mA0 the reverse is true. The following discussions emphasize the case of large mA0. The Higgs boson widths are crucial parameters for the searches and studies. In p particular, we shall see that the width compared to the resolution in s of the machine is a crucial issue. Widths for the Standard Model Higgs hSM and the three neutral 0 0 0 Higgs bosons h , H , A of the MSSM are illustrated in Fig. 3; for the MSSM Higgs bosons, results at tan� = 2 and 20 are shown. As a function of tan�, the total 0 width of h is plotted in Fig. 4 for mh0 = 100, 110 and 120 GeV. We note that for 0 masses below � 130 GeV, both the hSM and a SM-like h have very small widths (in the few MeV range); we will discover that these widths are often smaller than p + − the expected resolution in s. At high tan� and large mA0 � mH0, the � � , + − 0 0 � � and bb couplings of the H and A are greatly enhanced (being proportional to p tot tot tan �). Consequently, Γ 0 and Γ 0 are generally large compared to the expected s H A resolution. + − (?) Figure 5 illustrates the hSM branching fractions for the � � , bb, WW and (?) < ZZ decay modes. For an hSM with mh SM � 130 GeV, the bb branching fraction is of order 0.8{0.9, implying that this will be the most useful discovery channel. Once (?) (?) > the WW and ZZ modes turn on (mh SM � 2mW), the hSM becomes broad and the + − branching fraction BF(hSM ! � � ), which governs s-channel production, declines 5 Figure 3: Total width versus mass of the SM and MSSM Higgs bosons for mt = 175 GeV. In the case of the MSSM, we have plotted results for tan� = 2 and 20, taking m = 1 TeV and including two-loop radiative corrections et following Refs. [5,6] neglecting squark mixing; SUSY decay channels are assumed to be absent. 6 tot Figure 4: Γ h0 versus tan� for mh0 = 80, 100, 110 and 113 GeV, assuming mt = 175 GeV. Two-loop/RGE-improved radiative corrections to Higgs masses, mixing angles and self-couplings have been included, taking m = et 1 TeV and neglecting squark mixing. SUSY decay channels are assumed to be absent. 7