- Email: [email protected]
Z0 decay into neutralinos and the Higgs fermion mass mH
Volume 177, number 2
PHYSICS LETTERS B
11 September 1986
Z 0 DECAY INTO NEUTRALINOS AND THE HIGGS FERMION MASS m H H. KOMATSU Max Planck.lnstitut f~r Physik und Astrophysik - Werner Heisenberg-lnstitut fftr Physik, Postfaeh 401212, D-8000 Munich 40, Fed. R ep. Germany
Received 7 June 1986
The Z° decay width into neutralinos is calculated in the minimal supersymmetries SU(2) × U(1) model. In some region of the parameter space "jet(s) + missing" and "~+~- + missing" events at SPS are predicted with a ratio 5 : 1. If neutralino signals are not found at LEP and SLC, we can get a lower bound on mH independently of all other parameters.
The minimal supersymmetric version of the SU(2) × U(1) model predicts four neutral Majorana fermions (called neutralinos) which are mixed states of neutral gauginos and higgsinos ,1. Phenomenologically they are interesting because one of them is the best candi. date for the lightest superpartner which is stable due to the conservation of R-parity and should be colorless and neutral [2]. Their mass eigenvalues and mixing angles are determined by three parameters, the gauglno mass m l / 2 (or the photino mass m~), the higgsino mass m H and an angle 0 = tan -1 (o2/v "r 1), where o 1 and v 2 are vacuum expectation values of two neutral Higgs scalars. Recentlyz, s~eral authors have discussed the decays W~ ~ W± Z(7-") and Z 0 -* W+W- [3] which may explain the observed monojet events at the SPS [4]. They found that there would also be substantial "jet(s) + lepton(s) + missing P T " and "leptons + missing PT" events if these decays are kinematically allowed. Absence of such signals could lead to an experimental bound on the above parameters. However, their calculations are mainly made with 0 = 45 ° (v 1 = v2) and small ]m~ I. In thi~ paper we calculate the partial decay width F(Z 0 ~ ~i~')"" in the whole parameter space kinematically allowed, diagonalizing the neutralino mass matrix exactly, where N (N') is the (next) lightest neutralino. This is based on the idea that it is kinematically advantageous [5] and that a comparable width to ,1 For a review see e.g. ref. [1 ]. 0370-2693/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
P(Z 0 ~/a+/a - ) is expected if the higgsino components of N and N' are dominant [6]. A different bound from that obtained from charginos would be obtained. EspeciaUy a crucial bound on m H would be obtained from LEP and SLC if no neutralino signals could be found. The mass matrix of neutralinos is well known as
c~=
am~t
bm~
iM z
0 , .(1)
iM z
- m H sin 20
m H cos 20
mHcos20
rn H s i n 2 0 /
0 where
a = -~cot 0 w - -~tan 0 w,
b = ~ cot 2 0 w + s tan 20w"
(2) It is assumed here that M 1 = M 2 = M 3 = ml/2
(3)
at/a = Mx, where M1, M 2 and M 3 are gauge fermion masses of U(1), SU(2) and SU(3)c, respectively, and the renormalization group equations [7] lead to eq. (2). Although there are some different parametrizations from eq. (3) in some supergravity models [8], it is sufficient to adopt the simplest case (3) in numerical calculations. The gluino mass is then predicted as mglnino = (3~QCD/8a)m ~ --~ 5 m ~ . The mass matrix Off is diagonalized by a unitary matrix U as 201
Volume 177, number 2
PHYSICS LETTERS B
u T c ~ U = diag.(m 1 , m 2, m3, m4),
11 September 1986
(4)
where m i (i = 1 ..... 4) are positive mass eigenvalues. Then, Z - ~ i - ~ i couplings are represented by £int "" (g/4 cosOw)ZuNi'Yv(Ci/L - Ci; R)N],
f
(5) f
where a
Ci] = (U~i U3] - U*4iU4/)c°s 20 + (U3i* U 4] + U4i* U3])sin 20.
(6)
_(~-
f
In general, m R and m H are complex parameters, m R = Im~le i0G,
m H = IrnHle i0H,
(7)
so that c~ is a complex symmetric matrix. However, we can find that $G--¢H does not affect eq. (6). The free parameters are then Im~l, Imnl, 0 and ¢ = ¢G + OH. In the case where m~- and m H are real (i,e. ~ = 0 or zr), Ci/in eq. (6) is expressed as
Ci/2 = (fifffoiO/) (X i X~ - m2H)2 cos 2 20,
(8)
where Xi and X/are solutions of the following eigenvalue equation:
[(X-m.~)(X-bm.~)-a
2 rn.~2](X2 - m 2 )
- M2(X - m~) (X + m H sin 20) = 0,
N'
>
w ~ : i
w*-, t , t ....
(9)
and
c
Pi = m 2 c°s2 20 + (Xi + m H sin 20) 2
Fig. 1. Feynman diagrams for ~' decay into N.
+ (1/M2z)(X 2 - m2H)[1 + a2m2/(X,- rn~)2], fi = +1
for Xi >/0,
= --1
for Xi < 0.
(10)
Mass eigenvalues in eq. (4) are, of course, m i = IXil. If m H cos 20 ~ 0_there is a pure higgsino eigenstate which we call N 4, with X4 = - m H . Eq. (8), in this case, becomes
Ci2 = (ftf4/Pi) (Xi + mH)2
for i 4: 4,
B(/~' ~ N + v~) "" 24%,
(11)
and Ci/= 0 for i, j :# 4 and also C44 = 0. For complex values of m R and m H we make only numerical calculations. Before we begin with our calculations, let us consider the decay of neutralinos. If a chargino is heavier 202
than a N , N can decay into N as shown in fig. 1. Among these diagrams, fig. la is interesting for the later discussion. It gives the dominant contribution if both N and N' are almost pure higgsinos. In this case the branching ratio can be evaluated as follows:
B(I~' ~ N + q?:l) "" 63%,
(12)
where t- and b-quark contributions are neglected. Fig. 1c becomes dominant if Im R I and ImHI are sufficiently small [9]. If one of the charglnos is lighter than N , a cascade decay m~, t
Volume 177, number 2
PHYSICS LETTERS B
11 September 1986 I
N' "+ ~ / + £v (or ql El2)
50
.'ff t"
Im~l=50
I
GeV
:, - - . > /
I
. S
~
7/
-+ £'v' (or q'l (t2) + £v (or ql ?:12)+ ~
]
becomes possible, which leads "jet(s) + lepton(s) + missing" events. We are now in a position to calculate the decay width P(Z 0 -+ Ni~/)" It is convenient to see the ratio to the width F(Z 0 -+/a+/a-). We then find for i =/=]
------
/_
\
/
'
QJ
L3
"/ CD
i/
0 Irn~ 1=100 GeV
50 0 u
Rii = ['( Z0 -+ NiN/)/r(Z° -~ u+u-)
..f
..... ~'"~.
-/
I"
i~"
x
E
= ~ [(~ _ sin2 0w)2 + sin4 0W ] -1 X [ 1 - 2(m 2 +
0
rn2)/M2z+(m 2- m2)2/M47]l/2
X {ICi~l[l-(m2i
I
-50
0
+ m~.)12M2-(m 2- m~)212M4]
- 3 Re(Ci~)min~/M2z}.
mHsin
5O 20
[GeV]
Fig. 3. Same as fig. 2 on the mH sin 20 - Im H cos 201 plane with sin ¢ = 0.
(13)
In figs. 2, 3 and 4 contour lines o f the following value are shown on some planes in the parameter space: R = i
nematically allowed. As the higgsino component in N" may give a substantial contribution to eq. (13), we include it in R. For all numerical calculations we have used M z = 93 GeV and sin 2 0 w = 0.22. In fig. 5 the kinematically allowed region for the decay Z 0 ~ I~+~/- is shown at 0 = 45 ° and real m~
(14)
R includes all kinematically allowed decay modes to the different type o f neutralinos. Indeed, in some p a rameter space, the third lightest neutralino N" is ki-
200 0=60 °
>
t
aJ
L~ 100
_
E
.
\ <)
t i
'2
0
O0
0 m H [13eV]
100,-100
0
"j 100
m H [CieV]
Fig. 2. Contour lines for R = 1 (solid line), 0.1 (dot-dashed line), 0.01 (dot-dot-dashed line), 0.001 (dashed line), and 0 (dotted line) on the Im~l - rnH plane with sin ¢ -- 0. R is defined in eqs. (13) and (14). 203
Volume 177, number 2
S0
0 SO
my=S0 GeV, 8=~5 o .~.,~. ~'"~-~
i1''2 /
/
e=6oo
..~":;"
,.
> 0.J
L.~
IZ
0 50
PHYSICS LETTERS B
("
.oo/. . oo
"
//
.....(.. - _ _ ~ : ~ - - ~-_ .~ ~/~-
'" /
•,
1
//
/
'
//
0
,
rn.~=100 GeV, O=Z"5°
11 September 1986
7
..-""" """~"~ "'~',~..
-100
~
0
100
m H [ GeV ]
"I-
E 0 SO
I
"~
"~"
I
'-..\ i
/'.Pf
0
I
-50
t
0 m H COS~b
SO
',,I
[GeV]
Fig. 4. Same as fig. 2 on the raH cos ¢ - ImH sin ¢1 plane.
and m H . The region m~; ~< 24 GeV which has already been excluded by e+e - experiment [10] is also shown. We can see that most of the allowed region in fig. 2 with m H > 0 is covered by that in fig. 5. However, there is a region where Z 0 -+ N N ' is allowed but Z 0 ~ + ~ r - is forbidden in the space cos ¢ < 0. This can be understood in the following way: one of the charginos becomes massless if (3/8 sin 20w)m. ~ m R = M 2 sin 20,
(15)
which can be realized only if ¢ = 0. This is the reason why there are no light charginos in the region where cos ¢ < 0. Although ¢- and 0-dependence is somewhat complicated, we can find from these figures that R is larger than 1 in the region where Im~l ~ 60 GeV and - 3 0 GeV ~ m H ~ 60 GeV except for a small region with 0 ¢ 45 °. The maximum value of R is close to 4 for large Im~ I. Especially i f - 3 0 GeV ~ m H ~ - 2 0 GeV 204
Fig. 5. The kinematicaUy allowed region for Z° ~ ~'*~;- and the experimentally excluded region by rn~/< 24 GeV.
and Im~l ~ 80 GeV, for example, chargino signals are forbidden and the branching ratios of neutralino signals are given by eqs. (12). If this is the case, a part of the monojet events observed at SPS [4] may be a candidate for neutralino signals, though there are some other explanations [3,11,12]. In order to get more definite results from the ~p data, we need detailed analyses on missing PT distributions, taking into account the off-shell effects. This will be clarified at the Z 0-peak in e+e - -annihilation in the future. For small Im~[, R becomes very small, but the allowed region for neutralinos is completely different from that for charginos. This region can be searched at LEP and SLC where a large number of Z ° events are expected. Thus, a lower bound Imnl >~ 30 GeV will be obtained independently of other parameters if no neutralino signals are found in future experiments. The parameter 0 is usually predicted to be close to 45 ° in supergravity models, in which SU(2) X U(1) is broken by the top-quark Yukawa coupling with m t 50 GeV [13]. However, the analysis, in principle, depends on the parameter B which is defined in the cross term of the Higgs scalar mass Bm3/2 m H ¢~ ¢2, and B depends on the model. On the other hand, it is shown in fig. 3 that R varies rapidly at cos 20 --- 0 for some values of m H and my. Thus, it is dangerous for phenomenological analyses of neutralinos to begin with cos 20 = 0. As a summary, Z ° can decay into neutralinos if the pa-
Volume 177, number 2
PHYSICS LETTERS B
rameters are in the region shown in figs. 2 - 4 . If no neutralino signals are found in Z 0 decay, we will obtain an experimental b o u n d on the parameters, for example, I m H l ~ 30 GeV. The author would like to thank K. Tamvakis for discussions and careful reading of the manuscript.
References [1] H.E. Haber and G.L. Kane, Phys. Rep. 117 (1985) 75. [2] H. Goldberg, Phys. Rev. Lett. 50 (1983) 1419; J. Ellis, J.S. Hagelin, D.V. Nanopoulos, K.A. Olive and M. Srednicki, Nucl. Phys. B 238 (1984) 453. [3] V. Barger, R.W. Robinett, W.Y. Keung and R.J.N. Phillips, Phys. Lett. B 131 (1983) 372; H. Baer and X. Tata, Phys. Lett. B 155 (1985) 278; H. Baer, K. Hagiwara and X. Tata, preprint ANL-HEPPR-86-07, DESY-86-015, OITS-318. [4 ] C. Rubia, Proc. Intern. Symp. on Lepton and photon interactions at high energy (Kyoto, 1985).
11 September 1986
[5] J. Ellis, J.-M. Fr6re, J.S. Hagelin, G.L. Kane and S.T. Peteov, Phys. Lett. B 132 (1983) 436. [6] P. Fayet, Phys. Lett. B 133 (1983) 363. [7] K. Inoue, A. Kakuto, H. Komatsu and S. Takeshita, Prog. Theor. Phys. 68 (1982) 927; 71 (1984) 413. [8] J. Ellis, K. Enqvist, D.V. Nanopoulos and K. Tamvakis, Phys. Lett. B 155 (1985) 381; M. Quir6s, G.L. Kane and H.E. Haber, preprint UM TH 85 -8. [9] H. Komatsu and J. Kubo, Phys. Lett. B 157 (1985) 90; Nucl. Phys. B 263 (1986) 265. [10] S. Komamiya, Proc. Intern. Symp. on Lepton and photon interactions at high energies (Kyoto, 1985). [11 ] E. Reya and D.P. Roy, Phys. Lett. B 141 (1984) 442; Phys. Rev. D 32 (1985) 645; R.M. Barnett, H.E. Haber and G.L. Kane, Phys. Rev. Lett. 54 (1985) 1983. [12] S.D. Ellis, R. Kleiss and W.J. Stifling, Phys. Lett. B 158 (1983) 341. [13] J. Ellis, H.S. Hagelin, D.V. Nanopoulos and K. Tamvakis, Phys. Lett. B 125 (1983) 275; C. Kounnas, A.B. Lahanas, D.V. Nanopoulos and M. Quir6s, Phys. Lett. B 132 (1983) 95.
205
PHYSICS LETTERS B
11 September 1986
Z 0 DECAY INTO NEUTRALINOS AND THE HIGGS FERMION MASS m H H. KOMATSU Max Planck.lnstitut f~r Physik und Astrophysik - Werner Heisenberg-lnstitut fftr Physik, Postfaeh 401212, D-8000 Munich 40, Fed. R ep. Germany
Received 7 June 1986
The Z° decay width into neutralinos is calculated in the minimal supersymmetries SU(2) × U(1) model. In some region of the parameter space "jet(s) + missing" and "~+~- + missing" events at SPS are predicted with a ratio 5 : 1. If neutralino signals are not found at LEP and SLC, we can get a lower bound on mH independently of all other parameters.
The minimal supersymmetric version of the SU(2) × U(1) model predicts four neutral Majorana fermions (called neutralinos) which are mixed states of neutral gauginos and higgsinos ,1. Phenomenologically they are interesting because one of them is the best candi. date for the lightest superpartner which is stable due to the conservation of R-parity and should be colorless and neutral [2]. Their mass eigenvalues and mixing angles are determined by three parameters, the gauglno mass m l / 2 (or the photino mass m~), the higgsino mass m H and an angle 0 = tan -1 (o2/v "r 1), where o 1 and v 2 are vacuum expectation values of two neutral Higgs scalars. Recentlyz, s~eral authors have discussed the decays W~ ~ W± Z(7-") and Z 0 -* W+W- [3] which may explain the observed monojet events at the SPS [4]. They found that there would also be substantial "jet(s) + lepton(s) + missing P T " and "leptons + missing PT" events if these decays are kinematically allowed. Absence of such signals could lead to an experimental bound on the above parameters. However, their calculations are mainly made with 0 = 45 ° (v 1 = v2) and small ]m~ I. In thi~ paper we calculate the partial decay width F(Z 0 ~ ~i~')"" in the whole parameter space kinematically allowed, diagonalizing the neutralino mass matrix exactly, where N (N') is the (next) lightest neutralino. This is based on the idea that it is kinematically advantageous [5] and that a comparable width to ,1 For a review see e.g. ref. [1 ]. 0370-2693/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
P(Z 0 ~/a+/a - ) is expected if the higgsino components of N and N' are dominant [6]. A different bound from that obtained from charginos would be obtained. EspeciaUy a crucial bound on m H would be obtained from LEP and SLC if no neutralino signals could be found. The mass matrix of neutralinos is well known as
c~=
am~t
bm~
iM z
0 , .(1)
iM z
- m H sin 20
m H cos 20
mHcos20
rn H s i n 2 0 /
0 where
a = -~cot 0 w - -~tan 0 w,
b = ~ cot 2 0 w + s tan 20w"
(2) It is assumed here that M 1 = M 2 = M 3 = ml/2
(3)
at/a = Mx, where M1, M 2 and M 3 are gauge fermion masses of U(1), SU(2) and SU(3)c, respectively, and the renormalization group equations [7] lead to eq. (2). Although there are some different parametrizations from eq. (3) in some supergravity models [8], it is sufficient to adopt the simplest case (3) in numerical calculations. The gluino mass is then predicted as mglnino = (3~QCD/8a)m ~ --~ 5 m ~ . The mass matrix Off is diagonalized by a unitary matrix U as 201
Volume 177, number 2
PHYSICS LETTERS B
u T c ~ U = diag.(m 1 , m 2, m3, m4),
11 September 1986
(4)
where m i (i = 1 ..... 4) are positive mass eigenvalues. Then, Z - ~ i - ~ i couplings are represented by £int "" (g/4 cosOw)ZuNi'Yv(Ci/L - Ci; R)N],
f
(5) f
where a
Ci] = (U~i U3] - U*4iU4/)c°s 20 + (U3i* U 4] + U4i* U3])sin 20.
(6)
_(~-
f
In general, m R and m H are complex parameters, m R = Im~le i0G,
m H = IrnHle i0H,
(7)
so that c~ is a complex symmetric matrix. However, we can find that $G--¢H does not affect eq. (6). The free parameters are then Im~l, Imnl, 0 and ¢ = ¢G + OH. In the case where m~- and m H are real (i,e. ~ = 0 or zr), Ci/in eq. (6) is expressed as
Ci/2 = (fifffoiO/) (X i X~ - m2H)2 cos 2 20,
(8)
where Xi and X/are solutions of the following eigenvalue equation:
[(X-m.~)(X-bm.~)-a
2 rn.~2](X2 - m 2 )
- M2(X - m~) (X + m H sin 20) = 0,
N'
>
w ~ : i
w*-, t , t ....
(9)
and
c
Pi = m 2 c°s2 20 + (Xi + m H sin 20) 2
Fig. 1. Feynman diagrams for ~' decay into N.
+ (1/M2z)(X 2 - m2H)[1 + a2m2/(X,- rn~)2], fi = +1
for Xi >/0,
= --1
for Xi < 0.
(10)
Mass eigenvalues in eq. (4) are, of course, m i = IXil. If m H cos 20 ~ 0_there is a pure higgsino eigenstate which we call N 4, with X4 = - m H . Eq. (8), in this case, becomes
Ci2 = (ftf4/Pi) (Xi + mH)2
for i 4: 4,
B(/~' ~ N + v~) "" 24%,
(11)
and Ci/= 0 for i, j :# 4 and also C44 = 0. For complex values of m R and m H we make only numerical calculations. Before we begin with our calculations, let us consider the decay of neutralinos. If a chargino is heavier 202
than a N , N can decay into N as shown in fig. 1. Among these diagrams, fig. la is interesting for the later discussion. It gives the dominant contribution if both N and N' are almost pure higgsinos. In this case the branching ratio can be evaluated as follows:
B(I~' ~ N + q?:l) "" 63%,
(12)
where t- and b-quark contributions are neglected. Fig. 1c becomes dominant if Im R I and ImHI are sufficiently small [9]. If one of the charglnos is lighter than N , a cascade decay m~, t
Volume 177, number 2
PHYSICS LETTERS B
11 September 1986 I
N' "+ ~ / + £v (or ql El2)
50
.'ff t"
Im~l=50
I
GeV
:, - - . > /
I
. S
~
7/
-+ £'v' (or q'l (t2) + £v (or ql ?:12)+ ~
]
becomes possible, which leads "jet(s) + lepton(s) + missing" events. We are now in a position to calculate the decay width P(Z 0 -+ Ni~/)" It is convenient to see the ratio to the width F(Z 0 -+/a+/a-). We then find for i =/=]
------
/_
\
/
'
QJ
L3
"/ CD
i/
0 Irn~ 1=100 GeV
50 0 u
Rii = ['( Z0 -+ NiN/)/r(Z° -~ u+u-)
..f
..... ~'"~.
-/
I"
i~"
x
E
= ~ [(~ _ sin2 0w)2 + sin4 0W ] -1 X [ 1 - 2(m 2 +
0
rn2)/M2z+(m 2- m2)2/M47]l/2
X {ICi~l[l-(m2i
I
-50
0
+ m~.)12M2-(m 2- m~)212M4]
- 3 Re(Ci~)min~/M2z}.
mHsin
5O 20
[GeV]
Fig. 3. Same as fig. 2 on the mH sin 20 - Im H cos 201 plane with sin ¢ = 0.
(13)
In figs. 2, 3 and 4 contour lines o f the following value are shown on some planes in the parameter space: R = i
nematically allowed. As the higgsino component in N" may give a substantial contribution to eq. (13), we include it in R. For all numerical calculations we have used M z = 93 GeV and sin 2 0 w = 0.22. In fig. 5 the kinematically allowed region for the decay Z 0 ~ I~+~/- is shown at 0 = 45 ° and real m~
(14)
R includes all kinematically allowed decay modes to the different type o f neutralinos. Indeed, in some p a rameter space, the third lightest neutralino N" is ki-
200 0=60 °
>
t
aJ
L~ 100
_
E
.
\ <)
t i
'2
0
O0
0 m H [13eV]
100,-100
0
"j 100
m H [CieV]
Fig. 2. Contour lines for R = 1 (solid line), 0.1 (dot-dashed line), 0.01 (dot-dot-dashed line), 0.001 (dashed line), and 0 (dotted line) on the Im~l - rnH plane with sin ¢ -- 0. R is defined in eqs. (13) and (14). 203
Volume 177, number 2
S0
0 SO
my=S0 GeV, 8=~5 o .~.,~. ~'"~-~
i1''2 /
/
e=6oo
..~":;"
,.
> 0.J
L.~
IZ
0 50
PHYSICS LETTERS B
("
.oo/. . oo
"
//
.....(.. - _ _ ~ : ~ - - ~-_ .~ ~/~-
'" /
•,
1
//
/
'
//
0
,
rn.~=100 GeV, O=Z"5°
11 September 1986
7
..-""" """~"~ "'~',~..
-100
~
0
100
m H [ GeV ]
"I-
E 0 SO
I
"~
"~"
I
'-..\ i
/'.Pf
0
I
-50
t
0 m H COS~b
SO
',,I
[GeV]
Fig. 4. Same as fig. 2 on the raH cos ¢ - ImH sin ¢1 plane.
and m H . The region m~; ~< 24 GeV which has already been excluded by e+e - experiment [10] is also shown. We can see that most of the allowed region in fig. 2 with m H > 0 is covered by that in fig. 5. However, there is a region where Z 0 -+ N N ' is allowed but Z 0 ~ + ~ r - is forbidden in the space cos ¢ < 0. This can be understood in the following way: one of the charginos becomes massless if (3/8 sin 20w)m. ~ m R = M 2 sin 20,
(15)
which can be realized only if ¢ = 0. This is the reason why there are no light charginos in the region where cos ¢ < 0. Although ¢- and 0-dependence is somewhat complicated, we can find from these figures that R is larger than 1 in the region where Im~l ~ 60 GeV and - 3 0 GeV ~ m H ~ 60 GeV except for a small region with 0 ¢ 45 °. The maximum value of R is close to 4 for large Im~ I. Especially i f - 3 0 GeV ~ m H ~ - 2 0 GeV 204
Fig. 5. The kinematicaUy allowed region for Z° ~ ~'*~;- and the experimentally excluded region by rn~/< 24 GeV.
and Im~l ~ 80 GeV, for example, chargino signals are forbidden and the branching ratios of neutralino signals are given by eqs. (12). If this is the case, a part of the monojet events observed at SPS [4] may be a candidate for neutralino signals, though there are some other explanations [3,11,12]. In order to get more definite results from the ~p data, we need detailed analyses on missing PT distributions, taking into account the off-shell effects. This will be clarified at the Z 0-peak in e+e - -annihilation in the future. For small Im~[, R becomes very small, but the allowed region for neutralinos is completely different from that for charginos. This region can be searched at LEP and SLC where a large number of Z ° events are expected. Thus, a lower bound Imnl >~ 30 GeV will be obtained independently of other parameters if no neutralino signals are found in future experiments. The parameter 0 is usually predicted to be close to 45 ° in supergravity models, in which SU(2) X U(1) is broken by the top-quark Yukawa coupling with m t 50 GeV [13]. However, the analysis, in principle, depends on the parameter B which is defined in the cross term of the Higgs scalar mass Bm3/2 m H ¢~ ¢2, and B depends on the model. On the other hand, it is shown in fig. 3 that R varies rapidly at cos 20 --- 0 for some values of m H and my. Thus, it is dangerous for phenomenological analyses of neutralinos to begin with cos 20 = 0. As a summary, Z ° can decay into neutralinos if the pa-
Volume 177, number 2
PHYSICS LETTERS B
rameters are in the region shown in figs. 2 - 4 . If no neutralino signals are found in Z 0 decay, we will obtain an experimental b o u n d on the parameters, for example, I m H l ~ 30 GeV. The author would like to thank K. Tamvakis for discussions and careful reading of the manuscript.
References [1] H.E. Haber and G.L. Kane, Phys. Rep. 117 (1985) 75. [2] H. Goldberg, Phys. Rev. Lett. 50 (1983) 1419; J. Ellis, J.S. Hagelin, D.V. Nanopoulos, K.A. Olive and M. Srednicki, Nucl. Phys. B 238 (1984) 453. [3] V. Barger, R.W. Robinett, W.Y. Keung and R.J.N. Phillips, Phys. Lett. B 131 (1983) 372; H. Baer and X. Tata, Phys. Lett. B 155 (1985) 278; H. Baer, K. Hagiwara and X. Tata, preprint ANL-HEPPR-86-07, DESY-86-015, OITS-318. [4 ] C. Rubia, Proc. Intern. Symp. on Lepton and photon interactions at high energy (Kyoto, 1985).
11 September 1986
[5] J. Ellis, J.-M. Fr6re, J.S. Hagelin, G.L. Kane and S.T. Peteov, Phys. Lett. B 132 (1983) 436. [6] P. Fayet, Phys. Lett. B 133 (1983) 363. [7] K. Inoue, A. Kakuto, H. Komatsu and S. Takeshita, Prog. Theor. Phys. 68 (1982) 927; 71 (1984) 413. [8] J. Ellis, K. Enqvist, D.V. Nanopoulos and K. Tamvakis, Phys. Lett. B 155 (1985) 381; M. Quir6s, G.L. Kane and H.E. Haber, preprint UM TH 85 -8. [9] H. Komatsu and J. Kubo, Phys. Lett. B 157 (1985) 90; Nucl. Phys. B 263 (1986) 265. [10] S. Komamiya, Proc. Intern. Symp. on Lepton and photon interactions at high energies (Kyoto, 1985). [11 ] E. Reya and D.P. Roy, Phys. Lett. B 141 (1984) 442; Phys. Rev. D 32 (1985) 645; R.M. Barnett, H.E. Haber and G.L. Kane, Phys. Rev. Lett. 54 (1985) 1983. [12] S.D. Ellis, R. Kleiss and W.J. Stifling, Phys. Lett. B 158 (1983) 341. [13] J. Ellis, H.S. Hagelin, D.V. Nanopoulos and K. Tamvakis, Phys. Lett. B 125 (1983) 275; C. Kounnas, A.B. Lahanas, D.V. Nanopoulos and M. Quir6s, Phys. Lett. B 132 (1983) 95.
205