Phenomenology of Light MSSM Higgs Boson Scenario
aa r X i v : . [ h e p - ph ] N ov Phenomenology of Light MSSM Higgs Boson Scenario
Alexander Belyaev
School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, U.K.
Abstract.
We have found that in the MSSM, the possibility for the lightest CP-even Higgs boson tobe lighter than Z boson (as low as about 60 GeV) is, contrary to the usual belief, not yet excludedby LEP2 Higgs search nor any direct searches for supersymmetric particles at high energy colliders.The Light Higgs boson scenario (LHS) is realised when the ZZh coupling and the decay branchingratio Br( h/A → b ¯ b ) are simultaneously suppressed as a result of generic supersymmetric loopcorrections. Consequently, the W ± H ∓ h coupling has to be large due to the sum rule of Higgscouplings to weak gauge bosons and as we demonstrate, the associate neutral and charged Higgsboson production process, pp → H ± h ( A ), at the LHC can completely probe the LHS. PACS.
While the Standard Model (SM) of particle physicsis consistent with existing data, there is a strong be-lief in a more complete description of the underlyingphysics. Supersymmetry (SUSY), as a good candidatefor theory beyond the SM, solves principal theoreticalproblems of the SM such as hierarchy and fine tuning,as well as provides good dark matter candidate andpotentially solves the problem of baryongenesis. In theminimal supersymmetric standard model (MSSM) theHiggs sector consists of two doublet fields h d and h u togenerate masses for down- and up-type fermions, re-spectively, and to provide an anomaly-free theory. Af-ter spontaneous symmetry breaking, there remain fivephysical Higgs bosons: a pair of charged Higgs bosons H ± , two neutral CP-even scalars H (heavier) and h (lighter), and a neutral CP-odd pseudoscalar A . Higgspotential is constrained by supersymmetry such thatall the tree-level Higgs boson masses and self-couplingsare determined by only two independent unknown pa-rameters, commonly chosen to be the mass of the CP-odd pseudoscalar ( M A ) and the ratio of vacuum ex-pectation values of neutral Higgs fields, denoted astan β ≡ h h u i / h h d i .The MSSM predicts a light neutral Higgs bosonwhich is lighter than Z -boson at the tree level. How-ever, large top quark and squark (stop) loop contri-butions induce significant radiative correction to theHiggs quartic coupling, such that the lighter neutralHiggs boson mass can be as large as 130 GeV [2,3,4,5]. The negative result of Higgs boson search at LEP2via e + e − → Zh production channel imposes a lowerbound on the SM Higgs boson mass M h >
114 GeV [6], a Email: [email protected] b the study has been done in collaboration with Qing-Hong Cao, Daisuke Nomura, Kazuhiro Tobe and C.-P.Yuan [1] and excludes significant portion of MSSM parameterspace.The LEP2 collaborations have performed analysesfor the MSSM [7] using several benchmark scenariosthat were considered as typical cases for the MSSMparameter space. The two complementary processesfor MSSM Higgs boson search are e + e − → Zh/Ah [7],in which the first one occurs via
ZZh coupling g ZZh =sin( β − α )( ≡ s βα ) while the second one via ZAh cou-pling g ZAh = cos( β − α ). The obvious sum rule ( g ZZh + g ZAh = 1) puts strong constraints on the mass andcouplings of the MSSM Higgs boson h . For all stud-ied benchmark scenarios at LEP2, M h below about 90GeV is excluded [7].In this study, we propose a different region of theMSSM parameter space which has not been previouslystudied with deserved attention. We call this possi-bility light Higgs boson scenario (LHS), in which theHiggs boson h is lighter than the Z -boson and the ZZh coupling is small enough to be consistent withthe LEP2 data.To satisfy the LEP2 constraint derived from theproduction channel e + e − → Zh with M h < M Z , thecoupling g ZZh ( i.e. s βα ) has to be small. Let us de-note M as the 2 × h d , Re h u ). The mass eigenstates ( h, H ) aregiven by the diagonalization of the matrix M withthe definition: (cid:18) hH (cid:19) = (cid:18) − s α c α c α s α (cid:19) (cid:18) Re h d Re h u (cid:19) , (1)where c α ≡ cos α and s α ≡ sin α (with − π/ ≤ α ≤ π/ x ≡ M − M and y ≡ M , in termsof the components of matrix M ij . For relatively large olliders - Higgs Phenomenology Contributed Talk tan β M H + µ A M = M / M M Q
35 135 890 750 100 600 330 M h = 71, M A = 113, M H = 119Br( h/A/H → b ¯ b ) = 0 . / . / . h/A/H → τ ¯ τ ) = 0 . / . / . g ZZh = 0 . , g ZZH = g H + W − h = 0 . M ˜ χ = 100, M ˜ χ +1 = 198, M ˜ t = 126, M ˜ b = 273 ∆ρ = 6 . × − Table 1.
The MSSM parameters (at the weak scale) of anLHS sample point. The dimension of mass parameters isin unit of GeV. M i ( i = 1 , . . . , M Q and A are gauginomasses, the universal soft-breaking sfermion mass and uni-versal trilinear A-term for the third-generation at the weakscale, respectively. M ˜ χ +1 , M ˜ t and M ˜ b are pole masses forthe lightest chargino, stop and sbottom, respectively. tan β (as preferred by the LHS) and y/x ≃
0, we find s βα ≃ ( | x | + x ) / √ | x | which vanishes for x <
0. Therefore,conditions y/x ≃ x < s βα . The light Higgs boson h mainly consists of h d ,and the neutral Higgs boson masses are approximatelygiven by M h ≃ M and M H ≃ M . This feature isdifferent from the usual scenarios in which M h ≃ M and M H ≃ M . As it is well-known, M (i.e. h u -component) receives large positive logarithmic correc-tion from top and stop contributions. This correction,which helps to significantly increase the mass of h inthe usual scenarios, increases the mass of H in theLHS and changes the sign of x value from positive (attree level) to negative when M A ∼ M Z . The condition y/x ∼ M =2 M ), the supersymmetric Higgs mass µ -parameter( µ ), the universal soft-breaking sfermion mass ( M Q ),and the trilinear A-term ( A ) for the third-generationat the weak scale are all at (or below) TeV scale. Forour numerical analysis, we use CPsuperH program [8]and assume CP is conserved. For the LHS sample pointspecified in Table I, x > y/x ≃ − . s βα ≃ . M ≃ (71 . , M ≃ (119 . , and M ≃ − (19 . , hence, x < y/x ≃ . s βα ( ≃ . M h ≃ p M ∼ M Z when M A ∼ M Z . This feature is qualitatively very differ-ent from the commonly discussed MSSM scenarios inwhich M h receives large radiative corrections. More-over, the mass of the heavier CP-even Higgs boson H must receive large radiative corrections to exceedabout 114 GeV in order to agree with LEP2 data, sincethe ZZH coupling is close to the SM value.To find the allowed parameter space for the LHSwith µ >
0, we scan the following set of MSSM pa-rameters: tan β [1 . , M H + / TeV) [0 . , . A / TeV)[ − , M / TeV) [0 . , M / TeV) [0 . , M Q / TeV) [0 . ,
1] and ( µ/ TeV) [0 , M Q ] , within the range denotedin brackets. Since a too large µ -parameter induces notonly the color breaking vacuum in the general direc-tion of the scalar potential but also the fine-tuningin the Higgs mass parameter, we require µ to be lessthan 3 M Q in our analysis [9,10]. Then, we check theLHS parameter space against the full set of the ex-perimental and theoretical constraints. They are: (1)LEP2 Zh/ZH and
Ah/AH constraints, cf. Tables 14and 17 of Ref. [7]; (2) Chargino ( M ˜ χ +1 ), stop ( M ˜ t ),sbottom ( M ˜ b ) and gluino ( M ) mass limits: M ˜ χ +1 >
103 GeV [11], M ˜ t >
96 GeV [11], M ˜ b >
220 GeVfor M ˜ χ <
90 GeV and M ˜ b − M ˜ χ > M ˜ χ is the lightest neutralino mass) [12] or M ˜ b > M >
270 GeVfor M ˜ b <
220 GeV and M − M ˜ b > M >
240 GeV for all other regions [14]; (3) elec-troweak constraint: one-loop stop contributions to ρ -parameter | ∆ρ stop | < × − [15]; (4) color breakingconstraint: A < M Q + M h u + µ ) where M h u isthe soft-breaking mass for Higgs h u [9,10]. Fig. 1.
Projected planes of scanned parameter space in-dicating the LHS region in accord with experimental data.(See detail explanation in the text.)
Our result is shown in Fig. 1 where blue (darker)and green (lighter) color indicates allowed parameterspace with M h < M Z and M h > M Z , respectively.Fig. 1a ( M H + - M h plane) shows that LHS scenariois realized for low values of charged Higgs boson mass:120 GeV < M H + <
150 GeV, indicating the non- lexander Belyaev Light MSSM Higgs Boson Scenario and its Test at Hadron Colliders decoupling regime. Much lighter charged Higgses areexcluded mainly by the LEP2 Higgs search via the Ah production channel. The scenario requires intermediate-to-large values of the A-term and µ -parameter, | A | >
400 GeV and µ ∼ > g ZZh small, as indicated in Fig. 1d. On the other hand,a larger positive value of the product M µ tan β givesrise to larger negative correction to the bottom Yukawacoupling y hbb . This large negative correction to y hbb is non-universal with respect to the τ Yukawa coupling y hττ and leads to a suppression in Br( h/A → b ¯ b ) [16]large enough to avoid LEP2 constraint from the Ah channel with low M h values. In the LHS parameterspace, Br( h/A → b ¯ b ) can be suppressed down to about50% (cf. Fig. 1e), and consequently Br( h/A → τ ¯ τ )is enhanced up to about 50%, so that Ah channel isnot observed: b ¯ bb ¯ b decay mode is largely suppressed,while b ¯ bτ ¯ τ or τ ¯ τ τ ¯ τ signatures are not enhanced enoughto exclude 60 GeV . M h < M Z . Fig. 1e presents theBr( h → b ¯ b )– M h correlations. It is interesting to notethat the relatively large µ -parameter simultaneouslysuppress both s βα and Br( h/A → b ¯ b ) to be consistentwith the LEP2 data. We also note that a lighter Higgsboson is preferred for a larger tan β value, cf. Fig. 1f.It is worth mentioning that although the heavier Higgsboson ( H ) couplings to vector bosons are SM-like,its couplings to down-type fermions are further sup-pressed as compared to those of h and A (cf. Table 1).Moreover, M A ranges from 90 to 120 GeV, which canbe well approximated by M A = q M H + − M W .Since in the LHS, g ZZh (= s βα ) is suppressed, H + W − h coupling is inevitably enhanced due to the sum rulesin Higgs boson couplings to weak gauge bosons, i.e., g ZZh + g H + W − h = 1 = g H + W − A . In this case the q ¯ q ′ → H ± h ( A ) production via W boson exchange could besizable with the production cross section ∼
10 fb at theTevatron and ∼
100 fb at the LHC for M h/A ∼ Fig. 2.
Rates for p ¯ p, pp → H + h ( A ) → τ + νb ¯ b → π + ¯ ννb ¯ b signature at the Tevatron and the LHC. section of the p ¯ p, pp → H + h ( A ) → τ + νb ¯ b → π + ¯ ννb ¯ b signature at the Tevatron and the LHC in the M H ± - M h plane. For simplicity, we have combined the H + h and H + A production rates. (We note that the treelevel production rate of H + A pair in the MSSM isindependent of tan β .)As clearly shown in Fig. 2, the LHC can be sensitiveto the entire LHS parameter space, assuming that theabove signal event signature can be measured at the1 fb level [18]. The potential of the Tevatron to observethe H + A/H + h production processes deserves specialinvestigation and will be reported elsewhere [19]. Wealso note that when s βα is small, the tree level bottomand τ Yukawa couplings are enhanced by a factor of( − sin α/ cos β ) ≃ tan β , compared with the SM values.Therefore, the LHS, which is realized in intermediate-to-high tan β region, can be potentially probed evenat the Tevatron via several tan β -enhanced processes,such as p ¯ p → h ( A ) (produced via gluon-gluon fusionprocess) with h/A → τ ¯ τ , p ¯ p → b ¯ bh ( A ), as well as p ¯ p → t ¯ t with t → H + b . At present luminosity, thoseprocesses are sensitive only to very large values oftan β & −
50, while at 10 fb − , tan β &
30 couldbe probed [20,21]. At the LHC, a smaller tan β value( &
10) of the LHS can be tested via the tan β -enhancedprocesses, such as pp → ( h, H, A ) → τ ¯ τ [22]. Further-more, given the expected large number ( ∼ ) of topquark pairs produced at the LHC, the LHS can man-ifest itself in the copious t → H + b decays as long as M H + is not too large (below about 140 GeV) [23]. Conclusions:
We have shown that in the MSSM thepossibility for the CP-even Higgs boson h to be lighterthan Z -boson (as low as about 60 GeV) is, contrary tothe usual belief, not yet excluded by the existing di-rect search experiments. The characteristic of the lightHiggs boson scenario (LHS) is that the ZZh couplingand the decay branching ratio Br( h/A → b ¯ b ) are simul-taneously suppressed as a result of SUSY loop correc-tions. We would also note that the region of MSSMparameter space considered for explaining the non-conclusive LEP2 excess of the ∼
98 GeV ’Higgs-like’events [6], as studied in the literature (see, e.g., [24,25]), is a subset of the more generic LHS parameterspace that we have found in this paper. Our resultwould be useful for clarifying the parameter space re-sponsible for this excess.The implications of the LHS to the usual LHC(and Tevatron) search strategies for the lighter CP-even Higgs boson ( h ) can be summarized as follows.In view of its production mechanisms, both the vectorboson fusion process and the associated productionof h with vector boson are largely suppressed, whilethe associated production of h and H + is enhancedby the large W - h - H + coupling. In view of its decaychannels, the decay branching ratio of h into b ¯ b modeis reduced and the τ + τ − mode is enhanced. Also, ascompared to the SM rates, the gg → h → γγ rate isreduced by a couple of orders of magnitudes and the gg → h → τ + τ − rate is enhanced by about an orderof magnitude for h around 60 GeV. Since the mass of olliders - Higgs Phenomenology Contributed Talk the heavier CP-even Higgs boson is below 130 GeV inthe LHS, there is no resonance enhanced hh pair pro-duction from gg fusion process. The only large Higgspair production rate at the LHC is via pp → H ± h ( A )whose production cross sections are sizable (above afew hundreds fb) and insensitive to the value of tan β .(The tree level AH ± rate is independent of tan β .)Hence, if this production channel is not observed atthe LHC, it would undoubtedly exclude the LHS. Onthe other hand, if this production channel is detected,a large production rate of the heavier Higgs boson H via vector boson fusion process is expected in the LHS.Finally, we note that in the LHS, B physics pro-cesses at B -factories, Tevatron and LHC, such as b → sγ , B − → τ − ¯ ν , B d,s → µ + µ − and B s − ¯ B s oscillationmeasurements, could be largely modified due to thesizable contributions from light (neutral and charged)Higgs bosons. Since the predictions on those processescould strongly depend on the flavor structure of theSUSY breaking parameters, we do not impose any con-straints from flavor physics to further restrict the al-lowed MSSM parameter space of the LHS presented inthis work. A detailed study of the constraints from fla-vor physics, under a specific assumption of the flavorstructure, is interesting and deserves a separate study. Fig. 3.
The allowed LHS parameter space (green area) af-ter application constraints from B-physics (black and grayareas) combined with LEP2constraints (red, dark red andyellow areas).
Our preliminary study [19] shows that even for thecommonly discussed minimal-flavor-violation (MFV)scenario in which flavor violation is solely generatedby SM Cabibbo-Kobayashi-Maskawa (CKM) matrix,the LHS can be consistent with all the present B -physics data though its parameter space is largely re-duced. In Fig. 3 we present the allowed LHS parame-ter space indicated by green area after application B-physics constraints (black and gray areas) combinedwith LEP2 constraints (red, dark red and yellow ar-eas). The blue color indicates the allowed parameterspace for m h > M Z . All other colors indicate the ex-cluded regions. One can see that m h is required to belarger than about 80 GeV while tan β is bounded tobe less than about 20, mainly due to the B d,s → µ + µ − constraint represented by black area. Hence, it is ex-pected that the MSSM LHS would require a non-MFVflavor sector, should h boson be much lighter than Z boson. Its detail will be published in a forthcomingpaper [19]. Acknowledgments:
A. B. thanks SUSY 2007 organizers for warm hos-pitality.
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