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UAB-FT-434 December, 1997 hep-ph/9712491

arXiv:hep-ph/9712491v1 22 Dec 1997

SUPERSYMMETRIC QUANTUM EFFECTS ON THE HADRONIC WIDTH OF A HEAVY CHARGED HIGGS BOSON IN THE MSSM

` Joan SOLA1 Grup de F? ?sica Te`rica o and Institut de F? ?sica d’Altes Energies Universitat Aut`noma de Barcelona o 08193 Bellaterra (Barcelona), Catalonia, Spain

ABSTRACT We discuss the QCD and leading electroweak corrections to the hadronic width of the charged Higgs boson of the MSSM. In our renormalization framework, tan β is de?ned through Γ(H + → τ + ντ ). We show that a measurement of the hadronic width of H ± and/or of the branching ratio of its τ -decay mode with a modest precision of ? 20% could be su?cient to unravel the supersymmetric nature of H ± in full consistency with the low-energy data from radiative Bmeson decays.

Invited talk presented at the International Workshop on Physics Beyond the Standard Model: from Theory to Experiment , Valencia, Spain, 13-17 October, 1997. To appear in the Proceedings.

1

The discovery of a heavy top quark at the Tevatron constituted, paradoxically as it may sound, both a reassuring con?rmation of a long-standing prediction of the Standard Model (SM) of the electroweak interactions and at the same time the consolidation of an old and intriguing suspicion, namely, that the SM cannot be the last word in elementary particle physics. What are, however, the potential paradigms of new physics at our disposal?. There are a few good candidates. Notwithstanding, at present the only tenable Quantum Field Theory of the strong and the electroweak interactions beyond the SM that is able to keep pace with the SM ability to (consistently) accommodate all known high precision measurements [1] is the Minimal Supersymmetric Standard Model MSSM [2]. This fact alone, if we bare in mind the vast amount of high precision data available both from low-energy and high-energy physics, should justify (we believe) all e?orts to search for SUSY in present day particle accelerators. Moreover, the MSSM o?ers a starting point for a successful Grand Uni?ed framework [3] where a radiatively stable low-energy Higgs sector can survive. Within the SM the physics of the top quark is intimately connected with that of the Higgs sector through the Yukawa couplings. One expects that a ?rst hint of Higgs physics, if ever, should appear in concomitance with the detailed studies of top quark pheneomenology. However, if this is true in the SM, the more it should be in the MSSM where both the Higgs and the top quark sectors are virtually “doubled” with respect to the SM. As a consequence, the Yukawa coupling sector is richer in the supersymmetric model than in the standard one. This could greatly modify the phenomenology already at the level of quantum e?ects on electroweak observables. As of matter of fact in the MSSM the bottom-quark Yukawa coupling may counterbalance the smallesness of the bottom mass at the expense of a large value of tan β –the ratio v2 /v1 of the vacuum expectation values of the two Higgs doublets– the upshot being that the top-quark and bottom-quark Yukawa couplings in the superpotential g mb g mt , hb = √ , ht = √ 2 MW sin β 2 MW cos β ht < hb for tan β > mt /mb . Notice that due to the perturbative bound tan β

< ?

(1)

can be of the same order of magnitude, perhaps even showing up in “inverse” hierarchy: 60 one never reaches a situation where ht << hb . In a sense ht ? hb could be judged as a

natural relation in the MSSM. On the phenomenological side, one should not dismiss the possibility that the bottom-quark Yukawa coupling could play a momentous role in the physics of the top quark and of the Higgs bosons [4], to the extend of drastically changing standard expectations on the observables associated to them, such as decay widths and cross-sections. It is well-known [5] that the MSSM predicts the existence of two charged Higgs pseudoscalar bosons, H ± , one neutral CP-odd boson, A0 , and two neutral CP-even states, h0 2

and H 0 (Mh0 < MH 0 ). In this talk we wish to emphasize the possibility of seeing large quantum SUSY signatures in the physics of the MSSM Higgs boson decays; speci?cally, we shall concentrate on the potential supersymmetric quantum e?ects on the decays of the charged Higgs boson of the MSSM as a means to unveil its hypothetical SUSY nature. For a heavy charged Higgs boson, the main fermionic decay channel is the top quark decay mode H + → t ? whose partial width is essentially the full hadronic width of H + . b,

In fact, the other two standard fermionic decay modes are H + → c s and H + → τ + ντ . ? decay is negligibly small, whereas that of the latter is subdominant but not negligible (see later on). The bare interaction Lagrangian describing the H + t ? b-vertex in the MSSM reads as follows [5]: g Vtb ? H + t [mt cot β PL + mb tan β PR ] b + h.c. , LHtb = √ 2MW

However, for any charged Higgs mass MH and tan β > 2, the branching ratio of the former

(2)

where PL,R = 1/2(1 ? γ5 ) are the chiral projector operators and Vtb is the CKM matrix element – henceforth we set Vtb = 1. The corresponding counterterm Lagrangian follows right away after re-expressing everything in terms of renormalized parameters and ?elds in the standard electroweak on-shell scheme [6]. It takes on the form: δLHtb = √ with δCL = δCR 1 b 1 t δmt δv 1 ? + δZH + + δZL + δZR ? δ tan β + δZHW tan β , mt v 2 2 2 δmb δv 1 1 t 1 b = ? + δZH + + δZL + δZR + δ tan β ? δZHW cot β . mb v 2 2 2 (4) Here δv is the counterterm for v =

2 2 v1 + v2 =

g ? H + t [δCL mt cot β PL + δCR mb tan β PR ] b + h.c. , 2 MW

(3)

√

2 MW /g; δZH and δZHW stand respec-

The remaining are standard wave-function and mass renormalization counterterms for the fermion external lines [6]. We remark the counterterm δ tan β, which is ?xed here by the renormalization condieither in the α or in the GF schemes 2 . From this it follows that [8] 1 δ tan β = tan β 2

2

tively for the charged Higgs and mixed H ? W wave-function renormalization factors.

tion that the parameter tan β is inputed from the tree-level expression for Γ(H + → τ + ντ )

2 δg 2 δMW ? 2 2 MW g

1 ? δZH + cot β δZHW + ?τ , 2

(5)

One could also de?ne tan β through the τ -decay of the CP-odd Higgs boson, A0 → τ + τ ? , and then compute quantum corrections to Γ(H + → τ + ντ ) [7]. Conversely, in the framework of the present paper we could compute one-loop e?ects on the partial width of A0 → τ + τ ? .

3

H

+

? a

t

? gr

t

H

_

+

? a

t

0 ψα

t

bb

0 ψα ? b

?

b t t

H

_

+

bb

ψi+

_ ?

_

b t ba

?

H

+

ψi+

b

0 ψα

_

b

Figure 1: SUSY-QCD and SUSY-EW one-loop vertices for H + → t ? b. and so the various one-loop diagrams for H + → t ? can be parametrized in terms of two b form factors FL , FR and the remaining counterterms: iΛ = √ where ΛL = FL + ? ΛR δmt 1 b 1 t + δZL + δZR ? ?τ mt 2 2 ig [mt cot β (1 + ΛL ) PL + mb tan β (1 + ΛR ) PR ] , 2 MW (6)

δv 2 + δZH + + (tan β ? cot β) δZHW , v2 1 b δmb 1 t + δZL + δZR + ?τ . = FR + mb 2 2

(7)

In these equations, ?τ involves the complete set of MSSM one-loop e?ects on the τ -lepton decay width of H ± . The basic free parameters of our analysis, in the electroweak sector, are contained in the stop and sbottom mass matrices: M2 = ? t

2 M? = b 2 2 t mt MLR Mt2 + m2 + cos 2β( 1 ? 3 s2 ) MZ ?L W t 2 2 2 t mt MLR Mt2 + m2 + 3 cos 2β s2 MZ ?R W t 1 2 b 2 mb MLR M? + m2 + cos 2β(? 2 + 1 s2 ) MZ b 3 W bL b 2 2 mb MLR M? + m2 ? 1 cos 2β s2 MZ b W 3 b

R

(8)

(9)

with

t MLR = At ? ? cot β , b MLR = Ab ? ? tan β ,

(10)

? being the SUSY Higgs mass parameter in the superpotential. The At,b are the trilinear soft SUSY-breaking parameters and the MqL,R are soft SUSY-breaking masses. By ? SU(2)L -gauge invariance we must have MtL = M?L , whereas MtR , M?R are in general ? ? b b independent parameters. We denote by mt1 and m?1 the lightest stop and sbottom mass ? b eigenvalues. In the strong supersymmetric gaugino sector, the basic parameter is the gluino mass, mg . ? 4

H

+

t

0 0

t

H , h , A_, G

0 0

b

b

H

+

H

+

t b

H

_

+

G

+

t b

_

H,h

0 0

b

H ,h ,A

0 0

0

b

H,h H

+

0 0

t t

H

_

+

H ,h ,A

0 0

0

t t

_

H

+

b

G

+

b

Figure 2: One-loop vertices from the Higgs sector of the MSSM for H + → t ? b.

?

bL

b m b MLR ?

?

bR bR bL

? R

t

t m t MLR ?

? L

t

bL

? g

? H2

? H1

bR

(a)

(b)

Figure 3: Leading SUSY-QCD (a) and SUSY-EW (b) contributions to δmb /mb in the ? electroweak-eigenstate basis. The Hi (i = 1, 2) are the charged higgsinos. The one-loop vertices contributing to the above on-shell form factors in the MSSM are displayed in Figs. 1 and 2. Speci?cally, in Fig. 1 we show the SUSY-QCD contributions from gluinos gr (r = 1, ..., 8) and bottom- and top-squarks ?a , tb (a, b = 1, 2). Also shown ? b ? are the leading supersymmetric electroweak e?ects (SUSY-EW) driven by the Yukawa couplings (1); the latter e?ects consist of the genuine (R-odd) SUSY contributions from chargino-neutralinos Ψ+ , Ψ0 (i = 1, 2; α = 1, .., 4) and bottom- and top-squarks. On the i α other hand in Fig. 2 we detail the various Higgs and Goldstone boson graphs – which we compute in the Feynman gauge. As we said, the three-point functions in Figs. 1 and 2 are renormalized Green functions, so that appropriate counterterms for all the fermionic and Higgs wave-function external lines are already included. In particular, in Fig. 3 we single out the (?nite) leading parts of the bottom quark supersymmetric self-energy loops. They feed the form factor ΛR in

5

eq.(7) through the bottom mass counterterm and are numerically very relevant: δmb mb 2αs (mt ) mg ? tan β I(m?1 , m?2 , mg ) ? ? b b 3π h2 t ? tan β At I(mt1 , mt2 , ?) , ? ? ? 16π 2 ? ?

1 3 m2 m2 ln m2 + m2 m2 ln m2 + m2 m2 ln m2 2 1 2 2 3 1 3 2 3 1

(11)

m2

where I(m1 , m2 , m3 ) =

m2

m2

For the numerical analysis we wish to single out the Tevatron accessible window for the

1

(m2 ? m2 ) (m2 ? m2 ) (m2 ? m2 ) 1 2 2 3 1 3

.

(12)

0.5 0.4

tanβ = 30 M =175 GeV m~ = 150 GeV t1 m~ = 400 GeV g mu = mν = 1 TeV ~ ?

BR(H →τ ντ)

+

+

0.3

0.2 A = ?200 GeV ? = 200 GeV mb = 300 GeV ~

1

0.1

QCD

A = 600 GeV ? = ?200 GeV 0.05 200

m~ = 500 GeV b

1

300

400

500

600

MH (GeV)

Figure 4: The branching ratio of H + → τ + ντ as a function of the charged Higgs mass for ?xed values of the other parameters; A is a common value for the trilinear couplings. The central curve includes the standard QCD e?ects only. charged Higgs mass mt

< ?

MH

< ?

300 GeV .

(13)

This window is especially signi?cant in that the CLEO measurements [9] of BR(b → s γ) forbid most of this domain within the context of a generic two-Higgs-doublet model with the b → s γ-allowed region. At this point it may be wise to make the following (2HDM). In contrast, within the MSSM the mass interval (13) is perfectly consistent [10] remark. Although the inclusion of the NLO e?ects on the charged Higgs corrected ampli-

tude may considerably shift [11] the range (13) up to higher values of MH , within the strict 6

2HDM, the NLO corrections on the SUSY amplitudes have not been computed, and so as in the LO case they could also contribute to compensate the Higgs counterpart. We recall

< that for light charginos and stops (? 100 GeV ) the CLEO data [9] on b → s γ allow [12]

supersymmetric charged Higgs bosons to exist in the kinematical window enabling the top quark decay t → H + b [13], which is crossed to the one under consideration. In the following we present some of the results of the numerical analysis [10]. It was

already shown [14] that SUSY-QCD e?ects decrease signi?cantly with increasing sbottom important. Here we wish to concentrate on a region of the MSSM parameter space where the only relevant charged Higgs boson decays are H + → t ? and H + → τ + ντ . An b masses. Even so, for m?1 of a few hundred GeV (e.g. 100 ? 200 GeV ) they remain b

scenario like this is possible if the squarks are su?ciently heavy that the direct SUSY ?? Higgs decays into top and sbottom squarks, namely H + → ti ?j [15], are not possible. b Moreover, the H + → W + h0 decay which is sizeable enough at low tan β it becomes H + → χ+ χ0 , are not tan β-enhanced and remain negligible. In practice we may e?ectively i α extremely depleted [14] at high tan β. Finally, the decays into charginos and neutralinos, set up the desired scenario if we assume that the sbottoms are rather heavy (i.e. typically m?1 ≥ 300 GeV ). It is known [10] that this assumption is compatible with the MSSM b analysis of b → s γ at large tan β. Therefore, we expect that the SUSY-QCD e?ects will squark corrections could be compensated by the SUSY-EW contributions triggered by the Yukawa couplings. mass interval (13) and that it never decreases below 5 ? 10% in the whole mass range up In Fig. 4 we con?rm that BR(H + → τ + ντ ) at high tan β is quite large in the Higgs

be somewhat depressed, but now the question is whether this withdrawal of the gluino-

to about 1 T eV . Hence this process can safely be used to input tan β from experiment

in Figs. 5a-5d. The corrections are de?ned in terms of the quantity δ= Γ(H + → t ? ? Γ0 (H + → t ? b) b) , + → t? Γ0 (H b)

and in this way we are ready to study the evolution of the quantum corrections to the original decay H + → t ? as a function of the most signi?cant parameters. These are shown b

(14)

which traces the size of the e?ect with respect to the tree-level width. The MSSM correction (14) includes the full QCD yield (both from gluons [16] and gluinos [14]) at O(αs ) plus all the leading MSSM electroweak e?ects [10] driven by the Yukawa couplings (1). In order to assess the impact of the electroweak e?ects, we demonstrate that a typical set of inputs can be chosen such that the SUSY-QCD and SUSY-EW outputs are of comparable size. In Figs. 5a and 5b we display δ, eq.(14), as a function respectively of region). Remarkably, in spite of the fact that all sparticle masses are beyond the scope of 7 ? < 0 and tan β for ?xed values of the other parameters (within the b → s γ allowed

0.4

0.5

(a)

0.3

(b)

0.4

? = ?200 GeV

0.3

0.2

0.2

0.1

δ

0.0

MH = 250 GeV m~ = 500 GeV b

1

δ

δSUSY EW δSUSY QCD δQCD δMSSM

δHiggs

0.1

A = 600 GeV

?0.1

0.0

?0.1

?0.2

?0.2

?0.3 ?300

?275

?250

?225

? (GeV)

?200

?175

?150

?125

?0.3

0

10

20

30

40

50

tanβ

0.6

0.3

0.5

(c)

0.2

(d)

0.4

0.3

0.1

δ

0.2

δ

0.0

0.1

0.0

?0.1

?0.1 ?0.2 ?0.2

?0.3 200

300

400

1

500

600

700

800

?0.3

80

100

120

140

1

160

180

200

220

mb (GeV) ~

mt~ (GeV)

Figure 5: (a) The SUSY-EW, SUSY-QCD, standard QCD and full MSSM contributions, eq.(14), as a function of ?; (b) As in (a), but as a function of tan β. Also shown in (b) is the Higgs contribution, δHiggs ; (c) As in (a), but as a function of m?1 ; (d) As a function b of mt1 . Remaining inputs as in Fig. 4. ?

8

LEP 200 the corrections are fairly large. We have individually plot the SUSY-EW, SUSYQCD, standard QCD and total MSSM e?ects. The Higgs-Goldstone boson corrections are isolated only in Fig. 5b just to make clear that they add up non-trivially to a very tiny value in the whole large tan β range, and that only in the small corner tan β < 1 they can be signi?cant. We point out that for general (non-SUSY) 2HDM’s, the Higgs sector may give a more relevant contribution, whose origin stems not only from the top quark Yukawas [17], but also from the bottom quark sector [18]. In Figs. 5c-5d we render the various corrections (14) as a function of the relevant squark masses. For m?1 < 200 GeV we observe (Cf. Fig. 5c) that the SUSY-EW contribution is b non-negligible (δSU SY ?EW ? +20%) but the SUSY-QCD loops induced by squarks and gluinos are by far the leading SUSY e?ects (δSU SY ?QCD > 50%) – the standard QCD correction staying invariable over ?20% and the standard EW correction (not shown)

being negligible. In contrast, for larger and larger m?1 > 300 GeV , say m?1 = 400 or b b 500 GeV , and ?xed stop mass at a moderate value mt1 = 150 GeV , the SUSY-EW output ? is longly sustained whereas the SUSY-QCD one steadily goes down. However, the total SUSY pay-o? adds up to about +40% and the net MSSM yield still reaches a level around +20%, i.e. in this case being of equal value but opposite in sign to the conventional QCD result. A qualitatively distinct and quantitatively sizeable quantum signature like that could not be missed!. pinned down indirectly from the renormalization e?ect on the branching ratio of the τ branching ratio of the τ -lepton decay mode of H + (central curve in that ?gure) as a ?ducial From another point of view, the virtual SUSY e?ects on Γ(H + → t ? could also be b)

mode H + → τ + ντ . Indeed, returning to Fig. 4 and taking the standard QCD-corrected quantity, we see that BR(H + → τ + ντ ) undergoes an e?ective MSSM renormalization of order ±(40 ? 50)%. The sign of this correction is given by the sign of ?. In practice this could be a good alternative method to experimentally tag this e?ect, for the observable at e.g. the Tevatron and the LHC. BR(H + → τ + ντ ) should be directly measurable from the cross-section for τ -production In summary, the SUSY contributions to the hadronic width Γ(H + → t ? could be b)

quite large, namely of the order of several ten percent. These results have been obtained within the domain of experimental compatibility of the MSSM with b → s γ. In general the leading supersymmetric contribution stems from the SUSY-QCD sector. However, we have produced an scenario where the SUSY-EW could be equally important. The upshot is that the whole range of charged Higgs masses up to about 1 T eV could be probed and,

Alternatively, one could look for indirect SUSY quantum e?ects on the branching ratio

within the present renormalization framework, its potential supersymmetric nature be unravelled through a measurement of Γ(H + → t ? with a modest precision of ? 20%. b)

9

of H + → τ + ντ by measuring this observable to within a similar degree of precision. At the end of the day we have found that the physics of the combined decays H + → t ? and b quantum e?ects that would strongly hint at the SUSY nature of the charged Higgs.

H + → τ + ντ could be the ideal environment where to target our search for large non-SM

Acknowledgements: This work has been partially supported by CICYT under project No. AEN93-0474. I am grateful to Toni Coarasa, David Garcia, Jaume Guasch and R.A. Jim?nez for a fruitful collaboration. I am also indebted to Toni for helping me e to prepare the plots for the writing up of my talk.

References

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[9] M.S. Alam et al. (CLEO Collab.) Phys. Rev. Lett. 74 (1995) 2885. [10] J. A. Coarasa, D. Garcia, J. Guasch, R.A. Jim?nez, J. Sol`, preprint UAB-FT-433 e a [hep-ph/9711472]. [11] M. Ciucini, G. Degrassi, P. Gambino, G.F. Giudice, CERN-TH/97-279 [hepph/9710335]. [12] S. Bertolini, F. Borzumati, A. Masiero, G. Ridol?, Nucl. Phys. B 353 (1991) 591; R. Barbieri, G.F. Giudice, Phys. Lett. B 309 (1993) 86; R. Garisto, J.N. Ng, Phys. Lett. B 315 (1993) 372; M. A. Diaz, Phys. Lett. B 322 (1994) 207; F. Borzumati, Z. Phys. C 63 (1994) 291; S. Bertolini, F. Vissani, Z. Phys. C 67 (1995) 513; M. Carena, C.E.M. Wagner, Nucl. Phys. B 452 (1995) 45; R. Rattazzi, U. Sarid, Phys. Rev. D 53 (1996) 1553. [13] J. Guasch, J. Sol`, Phys. Lett. B 416 (1997) 353. a [14] R.A. Jim?nez, J. Sol`, Phys. Lett. B 389 (1996) 53; A. Bartl, H. Eberl, K. Hidaka, e a T. Kon, W. Majerotto, Y. Yamada, Phys. Lett. B 378 (1996) 167. [15] A. Bartl, K. Hidaka, Y. Kizukuri, T. Kon, W. Majerotto, (1993) 360. [16] C.S. Li, R.J. Oakes, Phys. Rev. D 43 (1991) 855. [17] J.M. Yang, C.S. Li, B.Q. Hu, Phys. Rev. D 47 (1993) 2872. [18] J.A. Coarasa, J. Guasch, J. Sol`, preprint UAB-FT, in preparation. a Phys. Lett. B 315

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