SUSY Decays of Higgs Particles

Home , Neutralino

CERN PPE/96-34

DESY 95{212

IFT{96{05

KA{TP{08{96

SUSY Decays of Higgs Particles

1;2 3 4y 1

A. Djouadi , P. Janot , J. Kalinowski and P.M. Zerwas

Deutsches Elektronen{Synchrotron DESY, D{22603 Hamburg/FRG.

Inst. Theor. Physik, Univ. Karlsruhe, D{76128 Karlsruhe/FRG.

PPE Division, CERN, CH{1211, Geneva 23/Switzerland.

Institute of Theoretical Physics, Warsaw University, PL{00681 Warsaw/Poland.

Abstract

Among the p ossible decay mo des of Higgs particles into sup ersymmetric states,

neutralino and chargino decays play a prominentr^ole. The exp erimental op-

p ortunities of observing such decay mo des at LEP2 and at future e e linear

colliders are analyzed within the frame of the Minimal Sup ersymmetric exten-

sion of the Standard Mo del. For heavy Higgs particles, the chargino/neutralino

decay mo des can b e very imp ortant, while only a small window is op en for the

lightest CP{even Higgs particle. If charginos/neutralinos are found at LEP2,

such decay mo des can b e searched for in a small area of the parameter space,

and invisible decays may reduce the exclusion limits of the lightest CP-even

Higgs particle slightly; if charginos/neutralino s are not found at LEP2 in direct

searches, the Higgs search will not b e a ected by the SUSY particle sector.

Supp orted by Deutsche Forschungsgemeinschaft DFG (Bonn).

Supp orted in part by Committee for Scienti c Research and by the EC under contract CHRX-CT92- 0004.

1. New light will b e shed on the Higgs sector of sup ersymmetric theories in the forthcom-

ing LEP2 exp eriments [1]. In fact, if the parameter tan in the Minimal Sup ersymmetric

Standard Mo del (MSSM) is realized within the range b etween 1 and 3 as suggested

by uni cation of b{ Yukawa couplings [2], prosp ects of discovering at least the lightest

CP{even neutral Higgs b oson h at LEP2 are very go o d. At future e e linear colliders,

the entire parameter space can b e explored. The lightest Higgs b oson h can b e discovered

with certainty, and the Higgs b osons H; A and H are accessible in ma jor parts of the

parameter space.

Most theoretical predictions of Higgs decay prop erties have fo cussed in the past on

nal states built up by the electroweak gauge b osons, standard quarks/leptons and cascade

decays [3]. While decays to squarks and sleptons are exp ected to b e less imp ortant and

are in general forbidden kinematically for fairly light Higgs b osons, decays to neutralinos

and charginos

0 0 +

h; H ; A ! and ;

i j i j

H ! ; (1)

i j

[i; j = 1{4 for neutral, and i; j =1;2 for charged states], in particular to the light

states, could play a p otentially imp ortantr^ole [4, 5]. The nal states would have

interesting top ologi es. If R{parity is conserved and is the lightest sup ersymmetric

0 0 0

stable particle (LSP), the nal states are invisible. In the other mo des, and

1 1 i

decay cascades [5, 6 ] would come with large missing energies in the events. For instance,

0 0 0 0

the decays h; A ! could lead to nal states f f , with the two LSPs escaping

1 2 1 1

undetected.

These novel decay mo des can only b e relevant if the standard decay mo des are not

overwhelming. Prime interest is therefore restricted to low to mo derate tan values since

b and decays are otherwise dominant. It turns out aposteriori that when decay

channels are op en, the branching ratios can b e close to 100%, op ening opp ortunities for

the exp erimental analysis of the fundamental parameters in sup ersymmetric theories.

In this note, p ossible decays of Higgs particles are analyzed in the parameter range

of LEP2 and future e e linear colliders which should eventually run with energies up to 2

TeV, sweeping the entire MSSM Higgs sp ectrum up to masses of order 1 TeV [7]. These

0 0

unconventional Higgs decays, in particular the invisible nal states, could change

1 1

the exp erimental analyses for discovering MSSM Higgs particles at the LHC rather

dramatically, making the search of these particles much more dicult. This problem is

much less severe at e e colliders so that the MSSM Higgs parameter space can still b e

covered completely [8]. It would only b e more dicult to detect the CP{o dd A particle

for small tan where it is pro duced only in asso ciation with the light CP{even particle

h, leading to invisible events altogether if b oth particles decayinto LSP nal states.

0 0

However, since the branching ratios for is always less than unity [esp ecially when

1 1

other decays are kinematically p ossible], such a problem can b e solved by increasing

the integrated luminosity. 2

In the subsequent analysis, the fact is taken into account that neither charginos nor

neutralinos have b een found at LEP1.5 [9].

2. Besides the conventional parameters of the MSSM Higgs sector, the masses and

couplings to the Higgs particles are determined by the Higgs{higgsi no mass parameter

and the SU(2) gaugino mass parameter M .

The general chargino mass matrix [10],

" #

M 2M sin

2 W

M = ; (2)

2M cos

is diagonalized bytwo matrices U and V , leading to the masses

1;2

2 2 2

m = M + +2M

2 W

1;2

h i

2 2 2 2 2 2 2 2

(M ) +4M cos 2 +4M (M + +2M sin 2 ) : (3)

2 W W 2

When one of the two parameters or M is large, one of the charginos corresp onds to

a pure gaugino state while the other corresp onds to a pure higgsino state; in these cases

the masses approach the asymptotic values:

jjM and M M : m M ;m jj;

Z 2 Z 2

1 2

jjM and M M : m jj ;m M: (4)

Z 2 Z 2

1 2

The four-dimensional neutralino mass matrix dep ends on the same two mass param-

1 5

tan M ' M [10] is used. In the bino{wino{ eters if the SUGRA relation M =

W 2 2 1

3 2

0 0

~ ~ ~ ~

higgsino basis (iB; iW ; H ; H ) the matrix has the form

1 2

2 3

M 0 M sin cos M sin sin

1 Z W Z W

6 7

0 M M cos cos M cos sin

6 7

2 Z W Z W

M = : (5)

6 7

4 M sin cos M cos cos 0 5

Z W Z W

M sin sin M cos sin 0

Z W Z W

It can b e diagonali zed analytically [11] by a single matrix Z ; as the nal results for the

masses are rather involved, they should not b e recorded here. Again, for large values of

one of the parameters or M ,two neutralinos are pure gaugino states while the two

others are pure higgsino states, and the masses are given in these limits by

0 0 0 0

jj M and M M : m M ;m M ;m m jj;

Z 2 Z 1 2

1 2 3 4

0 0 0 0

jj M and M M : m m jj ; m M ;m M: (6)

Z 2 Z 1 2

1 2 3 4

Atypical set of the neutralino/chargino masses [the lightest of which could b e observed

at LEP2] is shown as a function of in Fig.1a for M = 150 GeV and tan =1:6.

+ 0 0

The non{observation of chargino and neutralino pro duction e e ! and at

1 1

2 1 3

+ 0 0

LEP1.5 [9] roughly translates to lower limits on 2m and m + m of 135 GeV, so that

2 1

< <

the range 40 GeV 140 GeV is ruled out for M = 150 GeV and tan =1:6. [For

= 0 and also for mo derate values, the lightest neutralino and chargino states could

have b een massless|these values are of course already ruled out by the negative search

of chargino states at LEP1.]

3. The decay widths of the Higgs b osons (H )= (H ; h; A; H )into neutralino and

chargino pairs are given by [4]

" !

2 1=2

G M M

F H

2 2 k

(H ! )= (F + F ) 1

k i j

ij k jik

2 2

1+ M M

2 2

H H

k k

m m

i j

4 F F ; (7)

k i j ij k jik

where = +1, = 1 and = 0 unless the nal state consists of two identical

1;2;4 3 ij

(Ma jorana) neutralinos in which case =1; =1 is the sign of the neutralino mass

ii i

2 2 2 2 2 2 2 4

eigenvalue [ = 1 for charginos]; =(1m =M m =M ) 4m m =M is the

H H H

i j i j

k k k

usual two{b o dy phase space function.

In the case of neutral Higgs b oson decays, the co ecients F are related to the

ij k

elements of the matrices U; V for charginos and Z for neutralinos,

H ! : F = [e V U d V U ] ;

k ij k k i1 j 2 k i2 j 1

i j

0 0

H ! : F = (Z tan Z )(e Z + d Z )+i$j; (8)

k ij k j 2 W j 1 k i3 k i4

i j

with the co ecients e and d given by

k k

e =d = cos = sin ; e =d = sin = cos ; e =d = sin = cos : (9)

1 1 2 2 3 3

The partial widths of the neutral Higgs particles for decays to the lightest neutralino or

chargino states can b e written in a particularly simple form,

" #

G M

(H ! )= M 1 ; (10)

k 1 1 H

2 2

with p = 3 for h; H and p = 1 for A, corresp onding to P{ and S{wave nal states as

required by the CP= quantum numb ers of the Higgs b osons.

For the light scalar and the pseudoscalar Higgs decays to the lightest neutralinos,

0 0

h=A ! , the co ecients are given by

1 1

= (Z tan Z ) (sin Z + cos Z ) ;

h 12 W 11 13 14

= (Z tan Z )(sin Z + cos Z ) : (11)

A 12 W 11 13 14 4

For the decays to the lightest charginos, h=A ! , the co ecients are of the form

1 1

= (sin V U cos V U ) ;

h 11 12 12 11

= ( sin V U + cos V U ) : (12)

A 11 12 12 11

It follows from Eq.(11) that the Higgs b osons couple to mixtures of gaugino and higgsino

comp onents of the lightest neutralino, corresp onding to the matrix elements Z ;Z and

11 12

Z ;Z resp ectively. If the were either a pure gaugino or a pure higgsino state, the

13 14

0 0 0 0

h and A couplings would vanish. The matrix elements are displayed for the same

1 1 1 1

set of parameters as for the neutralino/chargino masses in Fig.1b. It is obvious from the

gure that decays to LSPs play a less prominentr^ole for <0 than for >0 since for

negative , the state tends to b e either gaugino{ or higgsino{li ke. In this case, only

in a small window around M do the couplings reach the level of a few p ercent, as

is shown in Fig.1c. [For the values tan =1:6 and M = 100 GeV that were chosen for

illustration, the couplings and are approximately equal.]

h A

For the charged Higgs b oson, the decay widths into neutralino/chargino pairs [4] are

given by Eq.(7), with

" #

F = cos Z V + (Z + tan Z ) V ;

ij 4 j 4 i1 j 2 W j 1 i2

" #

F = sin Z U (Z + tan Z ) U : (13)

ji4 j 3 i1 j 2 W j 1 i2

4. Examples of branching ratios are shown in Fig.2a for Higgs b oson masses M and M

h A

typically accessible at LEP2. The partial decay widths to R{even particles are treated

0 0

according to the current knowledge [3]. Whenever the decay is kinematically allowed,

1 1

the branching ratio is close to 100% for p ositive values. For <0 the branching ratio

never exceeds the 20% level. As p ointed out previously, the branching ratios b ecome

smaller for increasing tan , except when h reaches its maximal mass value: the hbb

coupling is no longer enhanced in this case. These M values are not accessible at LEP2,

but they would b e accessible at future colliders.

The branching ratios for the sum into all p ossible neutralino and chargino states

are shown in Fig.2b for (H ; A; H ) particles which can b e pro duced at high{energy e e

colliders. Mixing [12] in the Higgs sector has b een treated prop erly for 6=0, A = 6M

t S

[so-called \maximal mixing"] and A = 0, with M =1 TeV. These branching ratios are

b S

always large except in three cases: (i)For H in the mass range b etween 140 and 200 GeV,

esp ecially if >0, due to the large value of BR(H ! hh); (ii)For small A masses and

negative values as discussed ab ove; and (iii)For H just ab ove the tb threshold if not

all the decaychannels into heavy states are op en. [A similar pattern holds for the other 5

values of and M discussed ab ove.]

Even ab ove the thresholds of decaychannels including top quarks, the branching ratios

for the decays into charginos and neutralinos are sizeable. For very large Higgs b oson

masses, they reach a common value of 40% for tan =1:6. In fact, as a consequence

of the unitarity of the U; V and Z matrices, the total widths of the three Higgs b oson

decays to charginos and neutralinos do not dep end on M , or tan in the asymptotic

regime M m ,

3G M 1

W 2

(H ! )= M 1+ ; (14) tan

k i j H W

4 2

i;j

giving rise to the branching ratio

2 2

M 1+ tan

; (15) BR(H ! )=

k i j

2 2 2

M + m cot + m tan 1+ tan

i;j

Only the leading tt, bb mo des for neutral and the tb mo des for the charged Higgs b osons

need b e included in the total widths. This branching ratio is shown in Fig.2c as a function

of tan . It is always large, even for extreme values of tan 1 or 50, where it still is at

the 20% level.

5. To discuss the impact of invisible decays on the search of Higgs particles at LEP2, two

cases must b e distinguished.

(i) The region in the [; M ] parameter space in which CP-even h Higgs b oson decays

0 0

into the lightest neutralino can b e observed at LEP2, is illustrated in Fig. 3a for the

1 1

mass M = 90 GeV. The same mixing pattern as b efore has b een considered: 6=0,A =

h t

6M and A = 0, with M =1TeV. To nd the region which is exp erimentally accessible

S b S

0 0

by the search for invisible decays of the Higgs b oson, the pro duct R = BR(h ! )

inv

1 1

sin ( ) has to exceed 0.45 [13] under the LEP2 luminosity conditions. The small

parameter range in which the invisible Higgs decays could b e detected is shown in Fig. 3a

together with the corresp onding [; M ] range which can b e investigated by direct chargino

+ 0 0

and neutralino searches at LEP2, e e ! and .For the latter, a minimum

i j

total cross-section of 100 fb [14 ], relevant for a total integrated luminosity of 150 pb

that should b e delivered eachyear to the four LEP exp eriments, was required for large

mass splitting b etween the lightest neutralino and the charginos and other neutralinos,

and the unavoidable loss of eciency for small mass di erences was parameterized in a

realistic manner [15].

It can immediately b e seen from this example that the region in which the light Higgs

0 0

b oson h could b e detected in the decay mo de is small if the LEP1.5 results are taken

1 1

into account, and it is emb edded completely in the area covered by direct neutralino and

chargino searches. Since this holds true for any Higgs b oson mass at all centre-of-mass

energies of LEP2, the [; M ] area cannot b e extended through the Higgs b oson search.

(ii) The exclusion limits of the lightest CP{even Higgs b oson h are a ected byinvisible

decay mo des. This is shown at tan =1:6 for a few examples of the parameters and 6

M in Fig. 3b. It is well-known that LEP2 covers the entire h mass range for tan 2if

hdecays only into SM particles [13 ]. However, it is apparent from the examples in Fig. 3b

that for and M values in a small strip, adjacent to the upp er right b oundary of the

crossed range in Fig. 3a, the exclusion limit is signi cantly smaller than the theoretical

upp er Higgs mass limit. For these values of and M , b oth R and R =BR(h !

2 inv vis

bb)sin ( ) drop b elow the lower limits, given in Figs.31 and 32 of Ref.[13], for which

Higgs events could b e detected in either of the twochannels. Thus, in a small area of the

SUSY parameter space Higgs b osons could escap e undetected under the LEP2 running

conditions even for low tan . 7

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[15] L. Du ot and M. Schmitt, private communication. 8

Fig. 1: (a) Chargino [dashed lines] and neutralino [solid lines] masses as a function of

; (b) the mixing matrix elements Z of the lightest neutralino as a function of ; (c) the

couplings and of the h; A Higgs bosons to as a function of . M is xedto150

h A 2

GeV and tan =1:6. 9

Fig. 2a: Branching ratios of the decays of the h and A bosons into the lightest neutralino

0 0

pair as a function of the Higgs masses for a set of and M values; tan =1:6.

1 1 10

Fig. 2b/c: Branching ratios of the decays of the heavy A [solid], H [dashed] and H

[dot{dashed] Higgs bosons into the sum of neutralino and chargino pairs as a function

of the Higgs mass [for a set of =M values and tan xed to 1.6] in (b1) and (b2).

The inclusive decay branching ratio as a function of tan in the asymptotic region

[M M M =1 TeV m ] in (c).

A H

H 11

Fig. 3a: In the [; M ] parameter space, ranges covered at LEP2, with a centre-of-mass

of 192 GeV and an integrated luminosity of 150 pb deliveredtoeach of the four ex-

periments, by the direct chargino and neutralino searches, and by the search for invisible

0 0

Higgs decays h ! for M =90 GeV and tan =1:6, (maximal mixing conditions).

1 1

The dash{dotted lines represent the boundary of [; M ] values after the LEP1.5 results

are taken into account. 12

Fig. 3b: Exclusion limits on the mass of the lightest CP{even Higgs boson h for a set

of [; M ] values and tan =1:6. The ful l lines refer to the search based on the invisible

0 0

decay channel, the dashed lines to bb decays of h. The invisible decays are dominant

1 1

whenever this channel is open, the fast fal l{o corresponds to the kinematical boundary. 13