We investigate the potential of current and planned hadron colliders
operating at the TeV scale in disentangling the structure of the Higgs sector
of non-minimal Supersymmetric extensions of the Standard Model with an extra
gauge singlet. We assume universality of the soft Supersymmetry breaking terms
at the GUT scale as well as a CP-even Higgs boson with mass around 115 GeV, as
suggested by LEP. We find that mixing angles between the doublet and singlet
Higgs states are always small. However, concrete prospects exist at both the
Tevatron (Run II) and the Large Hadron Collider of detecting at least one
neutral Higgs state with a dominant singlet component, in addition to those
available from a doublet Higgs sector which is similar to the one of the
Minimal Supersymmetric Standard Model.Comment: 4 pages, 2 figures, latex, contribution to the APS/DPF/DPB Summer
  Study on the `Future of Particle Physics (Snowmass 2001)', Snowmass,
  Colorado, 30 June - 21 July 200

Hugonie, C.

Moretti, S.

English

arXiv

We investigate the potential of current and planned hadron colliders operating at the TeV scale in disentangling the structure of the Higgs sector of non-minimal Supersymmetric extensions of the Standard Model with an extra gauge singlet. We assume universality of the soft Supersymmetry breaking terms at the GUT scale as well as a CP-even Higgs boson with mass around 115 GeV, as suggested by LEP. We find that mixing angles between the doublet and singlet Higgs states are always small. However, concrete prospects exist at both the Tevatron (Run II) and the Large Hadron Collider of detecting at least one neutral Higgs state with a dominant singlet component, in addition to those available from a doublet Higgs sector which is similar to the one of the Minimal Supersymmetric Standard Model.We investigate the potential of current and planned hadron colliders operating at the TeV scale in disentangling the structure of the Higgs sector of non-minimal Supersymmetric extensions of the Standard Model with an extra gauge singlet. We assume universality of the soft Supersymmetry breaking terms at the GUT scale as well as a CP-even Higgs boson with mass around 115 GeV, as suggested by LEP. We find that mixing angles between the doublet and singlet Higgs states are always small. However, concrete prospects exist at both the Tevatron (Run II) and the Large Hadron Collider of detecting at least one neutral Higgs state with a dominant singlet component, in addition to those available from a doublet Higgs sector which is similar to the one of the Minimal Supersymmetric Standard Model

Hugonie, Cyril

Moretti, Stefano

CERN Document Server

arXiv:hep-ph/0110241v1  17 Oct 2001RAL-TR-2001-036, CERN-TH/2001-241, IPPP/01/46Higgs Sector of Non-minimal Supersymmetric Models at Future Hadron CollidersCyril Hugonie∗Institute for Particle Physics Phenomenology, University of Durham, Durham DH1 3LE, UKStefano Moretti†CERN Theory Division, CH-1211 Geneva 23, SwitzerlandInstitute for Particle Physics Phenomenology, University of Durham, Durham DH1 3LE, UK(Dated: January 3, 2014)We investigate the potential of current and planned hadron colliders operating at the TeV scalein disentangling the structure of the Higgs sector of non-minimal Supersymmetric extensions of theStandard Model with an extra gauge singlet. We assume universality of the soft Supersymmetrybreaking terms at the GUT scale as well as a CP-even Higgs boson with mass around 115 GeV,as suggested by LEP. We find that mixing angles between the doublet and singlet Higgs statesare always small. However, concrete prospects exist at both the Tevatron (Run II) and the LargeHadron Collider of detecting at least one neutral Higgs state with a dominant singlet component,in addition to those available from a doublet Higgs sector which is similar to the one of the MinimalSupersymmetric Standard Model.I. INTRODUCTIONThe NMSSM [1, 2] (Next-to-Minimal Supersymmetric Standard Model) is defined by the addition of a gaugesinglet Superfield S to the MSSM (Minimal Supersymmetric Standard Model) and a global ZZ3 symmetry onthe renormalizable part of the Superpotential. It allows to omit the term µHuHd in the Superpotential of theMSSM (where Hu is the Higgs doublet coupled to the up-type fermions and Hd to the down-type ones) andto replace it by a Yukawa coupling (plus a singlet self coupling), hence solving the so-called ‘µ problem’ of theMSSM. Apart from the standard quark and lepton Yukawa couplings, the Superpotential of the NMSSM isW = λHuHdS +13κS3 + ... (1)and the corresponding trilinear couplings Aλ and Aκ are added to the soft Supersymmetry (SUSY) breakingterms. Once the electroweak (EW) symmetry is broken, the scalar component of S acquires a vacuum ex-pectation value (vev) s = 〈S〉, thus generating an effective µ term, µ = λs. The Superpotential (1) is scaleinvariant, and the EW scale appears only through the soft SUSY breaking terms. The possible domain wallproblem due to the spontaneous breaking of the ZZ3 symmetry at the weak scale is assumed to be solved byadding non-renormalizable interactions which break the ZZ3 symmetry without spoiling the quantum stabilitywith unwanted divergent singlet tadpoles [3]. This can be done by replacing the ZZ3 symmetry by a discreteR-symmetry, broken by the soft SUSY breaking terms [4].A similar model, called nMSSM (for new Minimal Supersymmetric Standard Model) has recently beenproposed [5], using discrete R-symmetries to forbid the singlet self-interaction in (1). In this model, n-thorder singlet tadpole graphs generate a divergent loop-suppressed term in the scalar potential, Vtadpole ∼1(16pi2)nM2SUSYMP (S+S∗) ≡ ξ3(S+S∗) (ξ ∼MSUSY). This term breaks the dangerous Peccei-Quinn symmetrypresent when κ is set to 0 in the NMSSM.The new states in both models are one additional CP-even neutral Higgs Sr (real part of the complex scalarfield S), one CP-odd neutral Higgs Si (imaginary part), as well as one additional neutralino, the ‘singlino’ S˜.These states usually mix with the corresponding MSSM states, giving three CP-even neutral ones, two CP-oddneutral Higgses and five neutralinos.In this study, we focus on the phenomenology of the neutral Higgs sector of the NMSSM and nMSSM at theTevatron (Run II,√s = 2 TeV) and the Large Hadron Collider (LHC,√s = 14 TeV). We only consider the‘direct’ production channels, namely [6] (V =W±, Z, Q = b, t and q(′) refers to any possible quark flavour):gg → Higgs (gluon− gluon fusion), qq¯(′) → V Higgs (Higgs− strahlung),qq(′) → qq(′) Higgs (V V − fusion), gg, qq¯ → QQ¯ Higgs (heavy− quark associated production). (2)Here, we neglect ‘indirect’ Higgs production via decays/bremsstrahlung off heavy SUSY particles [7].∗C.Hugonie@durham.ac.uk†Stefano.Moretti@cern.ch2II. PARAMETER SPACE OF THE MODELSIn order to study the Higgs spectrum of both models, we have numerically scanned their free parameterspaces using a similar program as described in Refs. [2, 5]. First, we constrained the soft terms of both modelsby requiring universality at the GUT scale. The independent parameters of the models are then: a universalgaugino mass M1/2, a universal mass for the scalars m0, a universal trilinear coupling A0, the Yukawa couplingλ and the the singlet self-coupling κ (NMSSM) or the tadpole coefficient ξ (nMSSM). The (well-known) valueof the Z-boson mass fixes one of these parameters with respect to the others, so that we end up with four freeparameters at the GUT scale, i.e., as many as in the MSSM with universal soft terms. In principle, one couldchoose the same set of free parameters as in the MSSM, i.e., M1/2, m0, A0 and tanβ(≡ huhd ), with s, λ, and κ(ξ) being determined by the three minimisation equations. However, this appears to be not easily feasible, as λ(κ) also influences the running of the renormalization group equations (RGEs) for the soft parameters betweenthe GUT and the weak scale. Therefore, we took the following input parameters: m0/M1/2, A0/M1/2, λ andκ (ξ/M1/2). We then integrated numerically the RGEs between the GUT and the weak scale and minimisedthe two-loop effective potential. This gives tanβ and s and the overall scale M1/2 is fixed by MZ . Finally, weimposed the current experimental bounds on (s)particle masses and couplings, especially the LEP limits on theHiggs mass vs. its coupling to gauge bosons, see [8]. Furthermore, we assumed the existence of one neutralCP-even Higgs boson with mass 115 GeV and sufficient coupling to gauge bosons, as suggested by LEP [9].III. RESULTSThe main result of this numerical analysis, as already pointed out in Refs. [2, 5], is that the additionalcouplings appearing in (1) are always small: λ(κ) < 10−2 (NMSSM) and λ < 0.2 (nMSSM). (Higher valueswould lead to unphysical minima of the scalar potential.) The mixing angles of the additional singlet states(described in Sect. I) to the non-singlet sector, being proportional to these couplings, are always small and thesinglet sector of the universal NMSSM/nMSSM is quasi decoupled. (In the non-universal scenario, the outcomemay be quite different: see Ref. [10]). Hence, the neutral Higgs sector consists of a quasi pure (qp) CP-evenHiggs singlet state, Sr, a qp CP-odd singlet, Si, and the doublet sector is basically MSSM-like, apart from smallperturbations of order ∼ λ2, so that results known for the Higgs sector of the MSSM are also valid in our case.Fixing the mass of the lightest visible (non-singlet) CP-even Higgs at 115 GeV puts further constraints onthe parameter space of both models: we find that tanβ is always larger than 4, the CP-odd doublet Higgs massMA is larger than 160 GeV and MSUSY is larger than 350 GeV. In this limit, the CP-even doublet states areqp interaction eigenstates. The Higgs state with mass 115 GeV is a qp Hu, and the qp Hd is heavy (with masslarger than 300 GeV). On the other hand, the masses of the singlet Higgs states, Sr and Si, can vary from afew GeV to 1 TeV.For each of the five neutral Higgs bosons, we have computed the total number of events obtained by summingthe rates of all production processes in (2), assuming 15 fb−1 for Tevatron (Run II) and 300 fb−1 for the LHC,as integrated luminosities. We have plotted these rates versus the mass of the given Higgs states in Figs. 1–2.If, as threshold of detectability of a signal, we assume 100 events, the conclusions are similar in both models.First, at Tevatron the non-singlet CP-even Higgs with mass 115 GeV, the qp Hu, is of course always visible,but the other non-singlet CP-even state, the qp Hd, is not, as it is too heavy. The non-singlet CP-odd state,the qp A, will be visible if it is light enough (MA < 300−400 GeV for a total number of events NA > 100). Thesinglet CP-even state, the qp Sr, will also be visible up to masses of ∼ 300 GeV if λ >∼ 10−3 (so that this stateis not too decoupled), particularly when it is quasi mass degenerate with the qp Hu state (notice the peaks atMSr ∼ 115 GeV). On the other hand, the singlet CP-odd state, the qp Si, will remain invisible at Tevatron. Torender this manifest, we have plotted in Fig. 1 the total number of events produced at Tevatron with Sr in thefinal state, NSr (two left plots) in green (light) when the corresponding A state is also visible (NA > 100) andin red (dark) when it is not (NA < 100). Similarly, we did for A (two right plots), with green (light) when thecorresponding Sr is visible (NSr > 100) and red (dark) when it is not (NSr < 100). The upper plots correspondto the NMSSM and the lower ones to the nMSSM. From these plots it is easy to see in which cases one, two orthree Higgs states will be visible (with more than 100 produced events) at Tevatron.At LHC, on the other hand, due to the large center of mass energy available, all three non-singlet states, Hu,Hd and A, will be visible. In the singlet sector, the Sr should be visible if its mass is<∼ 600 GeV and λ is nottoo small. In the NMSSM, this covers most of the parameter space. Moreover, the CP-odd singlet, Si shouldbe visible for an appreciable part of the parameter space, at least for the NMSSM. These results are shown inFig. 2, with the same lay out and colour coding as for Fig. 1, but this time for Sr and Si at LHC.Finally, it should be noted that the discovery areas of multiple Higgs boson states identified in Figs. 1–2 areindeed associated to the same regions of parameter space. However, a first glance at the total number of CP-odd3Total number of Sr events, NSr0.0010.010.11101001000100001000001e+060 100 200 300 400 500 600Total number of A events, NA0.0010.010.11101001000100001000001e+06100 200 300 400 500 600 700 800 900 10001e-101e-081e-060.00010.011100100001e+060 100 200 300 400 500 600 700 800 900 10001e-050.00010.0010.010.1110100100010000100000100 200 300 400 500 600 700 800 900 1000MSr (GeV) MA (GeV)FIG. 1: Total number of events produced through processes (2) at the Tevatron (Run II) after 15 fb−1 in the NMSSM(upper plots) and nMSSM (lower plots) for the CP-even singlet Sr (left plots) and the CP-odd non-singlet A (right plots)as a function of the produced Higgs mass. (For an explanation of the colour coding, see the text).non-singlet A produced at Tevatron in both models (Fig. 1, right-hand plots) might indicate that nearly allthe parameter space of the models is already covered by the CP-even singlet Sr search at Tevatron, as all theplotted points are in green (light). This is however not the case, as one can check from the left-hand plots (NSrvs. MSr at Tevatron), where a lot of points are still under the 100 events threshold. The fact that one seesonly green (light) points on the right-hand plots is due to the very high density of points plotted, green (light)points being plotted after red (dark) ones. Hence, there are red (dark) areas, uncovered by the Sr searches,behind green (light), covered, ones. This remark applies also for associated Sr, Si searches at LHC (Fig. 2).IV. CONCLUSIONS AND FINAL REMARKSThe conclusions of this preliminary study are that, although the singlet sector of non-minimal models tendsto decouple from the rest of the spectrum in the universal case, quasi pure singlet states could still be found atfuture hadron colliders. One has to remember that a very light CP-even Higgs state is not excluded by LEPsearches if its coupling to gauge bosons is small enough. Such a Higgs state should be looked for at Tevatron(Run II) where up to three neutral Higgses could be found in our models (the CP-even non-singlet Hu withmass 115 GeV, and the CP-odd non-singlet A and CP-even singlet Sr if their mass is small enough). On theother hand, the large center of mass energy of LHC will allow us to see at least the three non-singlet Higgses(Hu, Hd and A) and its huge luminosity will trace the CP-even singlet state up to masses of<∼ 600 GeV and, insome cases, the CP-odd one, making the whole neutral Higgs spectrum visible.The caveat of our analysis is that we have not performed a full Higgs decay analysis in the NMSSM/nMSSM.One may question whether the additional Higgs states would actually be visible. For example, they wouldcertainly couple to singlinos – S˜ is always the Lightest Supersymmetric Particles (LSP) in our context – hencedecay into the latter and thus remain undetected. This should however not be the case. In fact, the couplingof the singlet states to ordinary matter are generally stronger in comparison (of order λ, whereas those to twosinglinos are ∼ λ3). So that, in the end, the main decay channels of singlet Higgs states should be those intodetectable fermions and gauge bosons.4Total number of Sr events, NSr1101001000100001000001e+061e+071e+080 100 200 300 400 500 600Total number of Si events, NSi0.0010.010.11101001000100001000000 200 400 600 800 10000.0010.010.11101001000100001000001e+060 100 200 300 400 500 600 700 800 900 10000.00010.0010.010.11101001000100000 100 200 300 400 500 600 700 800 900 1000MSr (GeV) MSi (GeV)FIG. 2: As Fig. 1 for the CP-even singlet Sr (left plots) and the CP-odd singlet Si (right plots), at LHC after 300 fb−1.AcknowledgmentsC.H. would like to thank the late theory group of the Rutherford Appleton Laboratory and the TheoreticalPhysics Department of Oxford, where this work was achieved, for their kind hospitality. We are both gratefulto the UK-PPARC for financial support.[1] H.P. Nilles, M. Srednicki and D. Wyler, Phys. Lett. B 120, (1983) 346;J.M. Frere, D.R.T. Jones and S. Raby, Nucl. Phys. 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Higgs Sector of Non-minimal Supersymmetric Models at Future Hadron Colliders

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