Looking for a 90 GeV Higgs boson in SUSY models

Volume 241, number 4

PHYSICS LETTERS B

24 May 1990

LOOKING FOR A 90 GeV HIGGS B O S O N IN SUSY M O D E L S Jan K A L I N O W S K I 1,2 Physik-Department, Technische Universitat Miinchen, D-8046 Garehing, FRG

Bohdan G R Z ~ D K O W S K I 3 and Stefan P O K O R S K I 3 Institute for Theoretical Physics, Warsaw University, Hoka 69, PL-00681 Warsaw, Poland

Received 27 January 1990

It is pointed out that in SUSY models with a hierarchy of the vacuum expectation values of the Higgs fields one of the neutral scalar Higgs bosons is approximately degenerate with the Z. Couplings of such a 90 GeV Higgs boson to quarks and gauge bosons are roughly equal to corresponding couplings of the standard-model Higgs boson with the same mass. Prospects for finding it experimentallyare briefly discussed.

1. Introduction

Although there is no established disagreement between the standard model (SM) and the experimental data [ 1 ] several i m p o r t a n t aspects of the model have not been tested. In particular the Higgs mechanism of breaking the gauge symmetry has no direct experimental evidence. In the SM the symmetry breaking is achieved by one Higgs doublet that couples to both the up- and down-sector fermions. However the SM is considered to be u n n a t u r a l [ 2 ]. Q u a n t u m corrections tend to destabilize the scale of the electroweak symmetry breaking driving it up to some high energy scale at which some hypothetical grand unification occurs. The best solution to this problem employs supersymmetry which introduces new fields (for reviews and references see, for example, ref. [ 3 ] ). Not only the gauge bosons and fermions get superpartners but the Higgs sector itself has to be enlarged. From the experimental point of view it is very interesting since it leads to new production mechaOn leave of absence from Institute for Theoretical Physics, Hoffa 69, PL-00681 Warsaw, Poland. 2 Supported by the German Bundesministerium f'dr Forschung und Technologieunder the contract 06 TM 761. 3 Supported in part by the Polish Ministry for National Education Programme CBPB 01.03. 534

nisms a n d signatures for Higgs bosons which are absent in the standard model. In the m i n i m a l SUSY model two SU (2) Higgs supermultiplets are introduced. After the breaking of gauge symmetry five physical Higgs bosons appear: two neutral scalars H~, H2, a neutral pseudoscalar H 3 and a charged pair H -+- [4]. The mass spectrum depends on two parameters, for example m3 and a mixing angle fl: m122 = ½[m~ + m 2 _+x/(m 2 + m 2 ) 2 - - 4 m ~ m ~ c o s 2 2 f l ] m2+ = m 2 +m2w.

,

(1) (2)

Here mi denotes the mass of Hi and we take H~ to be the heavier neutral scalar. The angle fl defines the mixing in the charged Higgs sector and is related to the ratio tan f l = v 2 / t ' l ,

(3)

where v~ (v2) is the v a c u u m expectation value of the Higgs that couples to the down- (up-) sector quarks. The masses of the up- and down-sector quarks are given by mu = Yuv2 ,

(4

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with Yi the corresponding Yukawa coupling matrices. The presence o f several scales vi makes the theory less predictive but offers the possibility of relating the isospin s y m m e t r y breaking to the spontaneous gauge s y m m e t r y breakdown. It has been p o i n t e d out that models with a s y m m e t r i c values v2 >> v~

(6)

would explain the large ratio o f quark masses in the up- and down-sector with Yukawa couplings approximately equal. Such a scenario is consistent with all experimental data [5 ] and can be quite naturally obt a i n e d in low energy supergravity m o d e l s [6,7]. It is interesting to note that in the limit ( 6 ) , say v 2 / v~>~5, the mass o f either H~ or H2 (or H3) is very close to mz. The presence o f a Higgs boson approximately degenerate with the Z turns out to be a general feature o f the SUSY models with the hierarchy (6). We will refer to the Higgs boson with the mass closest to mz as a 90 G e V Higgs boson ( , ~ ) . In this note we discuss properties o f the X in the m i n i m a l SUSY model ( M S M ) and in a model [8] with an a d d i t i o n a l U ( 1 ) s y m m e t r y group ( U 1 ), inspired by superstrings. Then we study prospects for its experimental observation. Preliminary, results o f our analysis have been presented in ref. [ 9 ].

2. Minimal SUSY model Let us start with the m i n i m a l SUSY model. The mass spectrum (2) as a function o f m 3 is illustrated in fig. l a for several values o f tan ft. The set o f curves above (below) the line m u = m z is for H~ (H2). We see that for tan fl> 5 one o f the scalar Higgs bosons is a p p r o x i m a t e l y degenerate with the Z, i.e. ,#=HI =H2

form3 m z .

(7)

F o r m3 ~ mz all the Higgs bosons are degenerate with the Z. The scalar Higgs boson couplings in the M S M to quarks and gauge bosons are m o d i f i e d with respect to the analogous couplings in the SM by the factors shown in table 1, where c~ is the mixing angle in the scalar neutral Higgs sector and is related to m 3 and fl as follows: Table 1 Higgs boson HI

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(8)

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In fig. lb we plot the angle a as a function of m 3 for several choices of tan ft. Note that for large tan fl the angle a very quickly approaches the extreme values O~-, -- ½X for m3 < m z , --.0

for m3 > m z .

(9)

Therefore if m 3 < mz ( m 3 > mz) then the modifying factors listed in table 1 for Hi (Ha) are ~ 1. In other words the 90 GeV Higgs boson ~ couplings (no matter whether it is actually the H~ or H2) to quarks and W and Z boson pairs are approximately (within a factor 2) equal to the corresponding couplings of the SM Higgs boson.

3. U1 model

In the U 1 model [ 8 ] one introduces an additional SU (2) singlet Higgs lq that couples to Higgs doublets IZI~and IZI2via a term of the form

w=2fl,f121q

(lO)

in the superpotential (the caret denotes a superfield). After the gauge symmetry breaking four neutral physical Higgs bosons appear: three scalars denoted H~, H2 and H4 and a pseudoscalar denoted H3. The scalar Higgs potential is completely fixed in terms of the vacuum expectation values v,, v2 and n of neutral scalar components of IZI, ICI2and 1'74,respectively, and two additional parameters: 2 defined above and 2A which specifies the strength of the soft-supersymmetry breaking scalar potential. The VEVs are fixed in terms of the W and the additional neutral Z' gauge boson masses as follows: v21 + v 2 = v = 2 m 2 w / g 2 ,

24 May 1990

and we have taken gl = g ' = g t a n 0w. Here g and g' are the usual SU(2) and U( 1 ) gauge couplings and g~ is the coupling associated with the additional U(1 ) group. Taking t a n f l = v : / v t , m z , , m3 and 2 as independent we can eliminate Ld and compute numerically the mass spectrum of physical Higgs bosons. The requirement that all Higgs bosons have positive mass squared for m 3~ 2 TeV and tan fl>~2 restricts 2 ~<0.4 (2 is positive by definition [ 8] ). We will present the results for 2 = 0.01. In choosing this value for 2 we are biased by the small value o f / t ~ O ( 2 0 GeV) found in ref. [6] which in the U1 model translates t o / ~ 2 n . In fig. 2 the results for rnt, rn2 and m4 with rnz, =600 GeV and 2=0.01 as functions of m 3 are presented. The set of curves below mu = mz is for H2, between rnz and mz, it is for HI and above mz, it is for H4 (in this case all curves almost overlap each other). In the region m3 < mz, the results are almost insensitive to the actual value of mz, provided m z , > 2 0 0 GeV. Similarly the 2-dependence is very weak; only for 2 > 0.1 and tan fl~< 5 the results for m2 are modified. Notice that the Higgs mass spectrum in the U1 model is similar to the one in the MSM assuming the hierarchy (6). In particular we see again the presence of Y{, i.e. that one of the scalar Higgs bosons, HI or H2, is almost degenerate with the Z. The couplings of H~ and H2 to quarks and W and

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Z bosons in the U1 model are again modified [8] with respect to analogous couplings in the MSM due to the mixing of neutral scalar components of I2I~and I212with lq and the Z - Z ' mixing. However, these additional modification factors are l + O ( v / n ) and consequently ~ 1. Therefore, the main conclusion is that in supersymmetric models with the hierarchy (6) we know not only the mass of one of the Higgs particles (m,~ ~ mz) but also its couplings to quarks and gauge bosons.

4. Looking for the Jq~ We now turn to the prospects of finding the ,~ experimentally. For the expected production rates the loop induced Higgs couplings are of interest as well. In particular the Higgs-gluon-gluon coupling is important since the dominant production mechanism in pp collisions proceeds via the gluon-gluon fusion. Apart from the quark loop there is an additional contribution coming from the squark loop with threepoint and four-point gluon-squark interactions. In fig. 3 we present the results for the H i - g - g couplings normalized to the SM coupling. It demonstrates that in both models the coupling ~ g g is approximately the same as in the standard model. Since the couplings of the ,~" are similar to the SM

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24 May 1990

strength the production rates are also similar. A fair number of the ,~ should be expected at the LEP II and the SSC. Numerous studies have shown [ 10 ] that it will be very difficult to find the SM Higgs boson if its mass happens to be almost degenerate with the Z due to a large SM background. Because we are discussing the .;#, there are new supersymmetric panicles which can couple to the 90 GeV Higgs boson and, if kinematically allowed, can be important for the phenomenology. Current experimental limits [ 11 ] suggest that squarks and sleptons are too heavy for the ,~ decay and recent results of the ALEPH Collaboration exclude pure winos and pure higgsinos below 45 GeV [ 12 ]. Therefore only neutralinos (~o) may still be light enough. These particles are the neutral mass eigenstates of the gauge and Higgs fermion system. For illustration we will discuss the MSM model. The results for the U 1 model are qualitatively similar. To compute the corresponding branching ratios we have to specify other parameters that appear in the soft-supersymmetry breaking lagrangian: the universal gaugino (M) and higgsino (#) masses. Inspired by the renormalization-group analysis of ref. [ 6 ] we have taken M = 1 TeV and - 60
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the 90 GeV Higgs boson, so we present in fig. 4 the b r a n c h i n g ratios for H2 (for completeness we also show the b r a n c h i n g ratio into the lightest charginos). We see that the branching ratios into the neutralinos 2°)~° and 2°2 ° can be quite large ( ~ 10%). H o w e v e r to explore these channels experimentally will be extremely difficult. In a d d i t i o n these channels will be available for the Z decay as well which will complicate the problem. Let us go back to the SM decay channels. W i t h the top quark too heavy ~1 for the ~ decay there is still ~ The CDF Collaboration finds a limit mt >_-77 GeV [ 11 ]. 538

some hope to see it in e + e - ~ Z + ~ " with , * ~ b l ~ [13,14]. The m a i n background comes from e + e - ~ Z + Z with Z - , bb (the b a c k g r o u n d from W W and Q C D can be e l i m i n a t e d by a p r o p e r choice o f e x p e r i m e n t a l cuts). At v / ] = 200 GeV we have [ 141 a(Z.*)=0.5pb,

a(ZZ)=2.2pb.

(13)

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e(vgZ) =0.7 pb.

(14)

N o w with the branching ratio B R ( , * - - , b D ) ~ 1 and B R ( Z - , b b ) ~ 0 . 1 5 and assuming an integrated lu-

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PHYSICS LETTERS B

m i n o s i t y of 500 p b - 1 we get the following n u m b e r s of the vvbl~ events: 45 for the signal Z , g a n d 58 for the Z Z background. Taking mbb within a 10 GeV bin a r o u n d the mz ( m z ! 5 G e V ) will reduce the n u m b e r o f background events to 37. Thus, one expects 37 such events (no ~ ) or 82 events (with ~'¢). To d i m i n i s h systematic errors one can also look for the electron and m u o n pairs (i.e. vge+e - and vgit+la - ) in the 10 GeV bin. Then we expect zero events for the signal and 18 events for the background. Therefore for the ratio R = n u m b e r o f ( v?e + e - , v'~p + i t - ) events n u m b e r o f (vgb'o) events

( 15 )

we have R=~ ~8 --82

no ,* , with,g

(16)

In pp collisions the process p p ~ W + H with H ~ b 6 seems to be the most p r o m i s i n g [ 15 ] as a way to see an i n t e r m e d i a t e mass Higgs boson. A recent analysis o f this process shows [ 16] that due to the W Z b a c k g r o u n d the mass region mz +_ 5 GeV will be very difficult to explore unless extremely good accuracy for the b-quark energy and the rob6 can be achieved. Therefore we can try to play the same game as we d i d for the e + e - process. We consider triggering on W+--,vit +. F o r pp collisions at the SSC, , , / s = 40 TeV, we have [ 16 ] (in parenthesis for the L H C at x/s = 16 TeV) a ( v g + b 6 ) , ~ 0 . 2 5 (0.15) pb

from W ~ ,

~ 0 . 2 5 (0.15) pb

from W Z ,

~ 0 . 2 0 (0.12) pb

from W G ,

( 17 )

for rnb6 within a 10 GeV bin a r o u n d mz. N o w if we count the e+e - and I t + i t - pairs in the same bin then only the W Z subprocess will contribute with the cross section o f 0.15 pb (0.07 p b ) . Therefore for the ratio o f the e+e - a n d i t + g - pairs over bb we expect (at the SSC and L H C ) R~

no,~,

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(18)

If one could separate the b a c k g r o u n d from the gluon, W G , then we would get 3 and 3 , respectively. An ad-

24 May 1990

ditional advantage of this analysis for pp collisions is that the ratio R is insensitive to uncertainties from the proton structure function.

5. Summary We have shown that in supersymmetric models with the hierarchy o f the vacuum expectation values ( 6 ) one o f the neutral scalar Higgs bosons becomes nearly degenerate with the Z boson, The couplings o f the ,~ to the SM fermions and bosons are approximately equal to the corresponding SM Higgs boson couplings. Thus the production rates, signatures and, in particular, experimental difficulties in observing the ,~ will be similar to the ones for the 90 GeV SM Higgs boson. The m a i n difficulty in a direct search for the ,~ stems from the Z decay. We propose to measure the n u m b e r o f lepton and b-quark pairs as a way to observe it indirectly. It is i m p o r t a n t to stress that finding a Higgs boson with mass ~ rnz and the SM couplings will not necessarily imply the confirmation o f the standard model. F u r t h e r analysis will be needed to see whether it is the HsM or the ~ o f the SUSY models.

References [ 1] G.S. Abrams et al., Phys. Rev. Len. 63 (1989) 2173; L3 Collab., 13.Adeva et al., Phys. Len. B 231 (1989) 509; ALEPH Collab., D. Decamp et al., Phys. Lett. B 231 ( 1989 ) 519; OPAL Collab., M.Z. Akrawy et al., Phys. Len. B 231 (1989) 530; DELPHI Collab., P. Aarnio et al., Phys. Len. B 231 (1989) 539. [2 ] M. Veltman, Acta Phys. Pol. B 8 (1977) 475. [3] H.P. Nilles, Phys. Rep. 110 (1984) 1; H.E. Haber and G.L. Kane, Phys. Rep. 117 (1985) 75; A.B. Lahanas and D.V. Nanopoulos, Phys. Rep. 145 (1987) I. [4] J.F. Gunion and H.E. Haber, Nucl. Phys. B 272 (1986) 1; B278 (1986) 449. [5] P. Krawczyk and S. Pokorski, Phys. Rev. Lett. 60 (1988) 182. [6] M. Olechowski and S. Pokorski, Phys. Len, B 214 (1988) 393. [7] G.F. Giudice and G. Ridolfi, Z. Phys. C 41 (1988) 447; G, Gamberini, G. Ridolfi and F, Zwirner, preprint UCB/ PTH/89/14. 539

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[8] J.F. Gunion, L. Roszkowski and H.E. Haber, Phys. Rev. D 38 (1988) 105. [9] B. Grzodkowski, J. Kalinowski and S. Pokorski, preprint RAL-89-077. [ 10] J. Ellis and R. Peccei, eds., Physics at LEP, CERN report CERN 86-02; A. B6hm and W. Hoogland, eds., ECFA Workshop on LEP 200, CERN report CERN 87-08, ECFA 87/108 ( 1987); R. Donaldson and J. Marx, eds., Snowmass Workshop on the Design and utilization of the Superconducting Super Collider.

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[ 1 l ] F. Abe et al., Phys. Rev. Lett. 42 (1990) 142; S. Geer, report Fermilab-Conf-89/207-E. [ 12 ] D. Descamp, CERN preprint CERN-EP/89-158. [ 13 ] J.F. Gunion, P. Kalyniak, M. Soldate and P. Galison, Phys. Rev. D 34 (1986) 101. [ 14] S.L. Wu et al., ECFA Workshop on LEP 200, eds. A. B6hm and W. Hoogland, CERN Report CERN 87-08, ECFA 87/ 108 (1987). [ 15 ] P. Agrawal and S.D. Ellis, Phys. Lett. B 229 (1989) 145. [ 16] J. Kalinowski, preprint TUM-T31-4/89.