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The supersymmetric Higgs searches at LEP after radiative corrections
Volume 258, number 3,4
PHYSICS LETTERS B
11 April 1991
The supersymmetric Higgs searches at LEP after radiative corrections R. Barbieri and M. Frigeni DtparUmento dl Ftstca, Umverslta dt Ptsa, 1-56100 Ptsa, Italy and INFN, Seztone dl Ptsa, Ptsa, Italy Received 30 January 1991
Radiative corrections modify in a significant way the tree level mass of the hghtest supersymmetnc Hlggs panicle in models with Hlggs doublets only Using a simple approximate description of these corrections, their impact on the supersymmetnc Hlggs searches at LEP Is illustrated
Recent work [ 1-3 ] has shown that radiative corrections modify m a significant way the tree level mass o f the hghtest supersymmetrlc Hlggs particle. Due to the heaviness of the top quark, in models with Hlggs doublets only, the physical mass o f the hghtest Hlggs is raised relative to the tree level one in most o f the p a r a m e t e r space. Since, on the other hand, the phase space dependence is a main factor m the Hlggs searches at LEP, the effect of radiative corrections is clearly going to have a significant impact on these same searches. This effect we would like to illustrate in this paper in the simplest possible way. As is well known, in a supersymmetrlc model with two Hlggs doublets, the whole Higgs phenomenology, described at the tree level, depends on two parameters only: the ratio v2/v~ o f their v a c u u m expectation values and one of the masses o f the physical Higgses This is no longer true after taking into account the radiative corrections, which bring in the top quark mass as well as, at least in prmclple, all the other parameters related to masses and mlxings of the various s u p e r s y m m e t n c pamcles. Here we focus on the main effect which as related to the dependence of the hghtest Higgs mass on the fourth power o f the top mass m,. In this a p p r o x i m a t i o n the relevant results are obtained by expanding a r o u n d the m i n i m u m the Hlggs potential with the inclusion o f the one-loop radiative
corrections coming from top and s c a l a r - t o p loops only, V= Vtree+SV, 8V= ~ 3
[ (g2[H212+m2 )2 log(g2[H212+m 2)
_ g 2 IH214 l o g ( g 2 l H 2 1 2 ) ] ,
(1)
where gt is the top Yukawa couphng to the Higgs field //2 and m is the mass o f the top scalar partners, taken degenerate for simplicity. The overall c o m m o n scale o f the arguments of the logarithms is left unspecified, since tt can be changed by a redefinition o f the tree level parameters. In this way, the resulting mass matrix for the two neutral CP-even Hlggs scalars, m the basis of the original hypercharge mgenstates ( H b / / 2 ), IS
mzA s i n a f l + M 2 cos2fl (meA +M2)sInflcosfl~ -- (mzA + MZz)smflcosfl mE c o s e f l + M 2 sin2fl+~] -
-
(2) where mA is the physical mass o f the third neutral CPo d d scalar A, tan fl= v2/vl and the radiative correction effects are l u m p e d into the p a r a m e t e r e. The explicit expressmn for e is
3awm4t
, {,-
m2"~
e = 2 n M 2 sin2 fl iog~l ± ~2t2) ,
0370-2693/91/$ 03 50 © 1991 - Elsevier Science Publishers B V ( North-Holland )
(3)
39 5
Volume 258, number 3,4
PHYSICS LETTERS B
11 April 1991
where aw is the SU (2) fine structure constant and Mw, Mz are the mtermedmte vector boson masses. The dlagonallzatton of the matrix (2) gives the phystcal masses of the neutral scalars ~1 1 2 m ~ , = ~(mA + M z2+ e + d )
.
A= [ (m 2 + M z + e ) 2 - 4 r n ~ M ~ COS22fl E
- 4 ¢ m A s l n 2 f l - 4eM 2 cos2fl] '/2.
(4)
as well as the mixing angle, which is relevant to the couplings of these Hlggs scalars (h)=.f2(
coso~ \--sin
o~
sInc~/(RR;H°
H°--v2] '
c o s 0~/
(5)
50
o .... loo
I .... lz0
I .... 14o
I .... 16o
180
Into p (GeV)
sin 2 ~ =
- ( m 2 + , ~ / 2 ) s i n 2fl
(6)
d
Fig. 1 shows the mass of the hghtest neutral scalar h m the plane (ma, tan fl) for two choices of mr and m. The quahty of the approximation leading to the elgenvalues (4) can be appreciated, in a special case, from fig 2 There we compare the range of values obtained from (4) for the hghtest Hlggs mass mh and m A = m = 1 TeV, with those obtained by mmamizang the full one-loop renormahzatlon group improved efnL The mass matrix of the two CP-even scalars m a suitable basis is also gLven m ref [ 1 ], using the same approxlmaUon as m th~s work The e~genvalues ofth~s mass matrix agree with those m eq (4) m leading logarithmic approximation for m2>> m~, although not for the fimte term
Fig 2 Comparison of the corrected Hlggs mass m. using a full one-loop renormahzatlon group improved calculanon (sohd hnes) or the approxlmanon described m the text (dashed hnes)
fectlve potential wtth all the other superpartners also at 1 TeV mass [3]. The relatively small discrepancy between the two pairs o f h m m n g curves is mainly due, for m, close to 100 GeV, to the effect of the gauge mteracnons and, for m, close to 180 GeV, to the higher order effects. The reactions of interest at LEP are Z~hg+g - .
(7a)
Z-.hA.
(7b)
Z~hy.
(7c)
and. at higher energies.
25
II
1111// " llll[lllllll///
i
20
.
lO 0
0
0
5
50
100
150
2OO
50
100
150
F~g I Contour plots of the hghtest Hlggs mass m h for (a) {mt 300 GeV) and (b) (170GeV, 1000 GeV) m l s the common mass of the top scalar partners
m)=(13OGeV,
396
(8a)
e+e - , Z H ,
(8b)
e+e--~hA.
(8c)
For Z decays, all the relevant formulae can be found, for example, in ref. [4]. The corrections to the mass mh and to the maxmg angle c~ influence the various branching ratios both in the phase space dependence and m the values of the relevant couplings. For processes (7a), (7b) one has respecnvely
15
G
e+e-~Zh,
F(Z--*hla+g- ) = sin2 (o/-- fl) , F(Z~HsMg+ g - )
(9)
with a standard model Hlggs HSM of the same mass as h, and
Volume 258, number 3,4
PHYS1CS LETTERS B
Fxgs. 3 a - 3 c and 3 e - 3 g s h o w the rates for reactions ( 7 ) with the s a m e pair o f values o f mt and m as m fig 1. U n h k e the case for processes ( 7 a ) , ( 7 b ) , the amplitude for Z - . h 7 is n o n - v a n i s h i n g only at the loop level. As a c o n s e q u e n c e , since s u p e r s y m m e t r l c part]cles can run in the loop, this rate d e p e n d s m general
f'(Z-,hA) cos2(o~-fl) F ( Z ~ g+ p - ) - 2 ( 1 - 4 sln20w + 8 sm40w) [(M~_m X
2 --,riAj ~ , 2 ~ 2 - - "A ~2~213/2 r t t t hCtt A ]
M6
(10)
,
where 0w is the w e a k m ] x m g angle. '
'
•
/
v2/v I
\
8 \
\
I
I
•
"
[
[ I -5
'/~ , ~ ....
i
i
50
I00
\ \\
V2/V1
10 .4
~ i ....
. . . .
I
.
.
~
i ....
r ( z ~ h T ) / r ( z ~ u + J * -)
,
|
J
i ....
,
I
,/,
~
,
I
I I
~~
0
. . . .
F(Z~hAl/r(Z~"+tt-)
(°)
~×10 -°
1o .....
I
r(z ~h"+"-)/r(z~tt+t~-)
\
\
11 April 1991
.
.
.
150
.
.
J~"/'l /
I
.
I
200
:,:'
i': /p
. . . .
50
i
. . . .
100
r(Z ~ h/~ +,a- )/I'(Z ~p,*/x - )
....
i
13 o'(e e - ~ Z h ) ( p b ) ]
I
,
150
,
,
,
m A (Gev)
I'(Z ~ hA)/F(Z-*,u,+/~ - )
8
\ \ a~lo -~
6
4
1 4~'x~
k
Y
10-4
8
....
I0
.--~-~
i ....
i. . . .. ... .
_ ~ , - ~
i . . . . . . . . . . .~. . . . . . . . . . ,,
. . . . .
....
, ....
r(z.hT)/r(z~u+u -)
I ....
o'(e+e- ~Zh) (pb) i
(g)
8
(h)
6
4
2 .... 0
k ,.~,
50
'
,
,
100
150
200
50
100
150
111A (Gev)
Fig 3 Contour plots for (a) F(Z--*hp+p - )/F(Z---,Ia+p-- ), (b) F ( Z - - * h A ) / F ( Z ~ p + p - ), (c) F ( Z ~ h y ) / F ( Z ~ p + I . t - ), (d) a(e+e ~hZ) at ,,/s = 190 GeV, for ( mt, rn ) = ( 130 GeV, 300 GeV) In (e)- (h) the same quantities are given for ( mr, m ) = ( 170 GeV, 1000 GeV ) 397
Volume 258, number 3,4
PHYSICS LETTERS B
on their masses, especmlly for gauglno-hlggsinos [ 5 ]. In figs. 3c and 3d we h a v e a s s u m e d t h e m to be h e a v y
enough not to contribute significantly to the rate and we h a v e used the a p p r o x i m a t i o n [ 4 ] F(Z~hy) - ~ s l n Z ( o l - f l ) 6 . 9 4 X 10 -5 F(Z-qa+~a - ) × (l _ ~'](1 MzJ\
Mz/
"
Light gauglno-hlggslnos m a y change the rate for Z - ~ h y by a factor by a factor o f 1-3 in either dlrecn o n , d e p e n d i n g u p o n the sign o f the interference o f their c o n t r i b u t i o n with the W - b o s o n loop R e a c n o n s (8), relevant to higher LEP energies, can be studied along s~milar lmes in the p a r a m e t e r space. We h a v e c o n s i d e r e d all o f t h e m at x / s = 190 G e V ( 8 a ) is the only process whose study will allow a significant e x t e n s i o n in the e x p l o r a t i o n o f the p a r a m e ter space relative to L E P I searches. R e l a t i v e to the s t a n d a r d m o d e l cross section with the SM Hlggs degenerate with h, the cross section is a(e+e
~Zh)
a ( e + e - ---~ZHsM )
= slna ( o e - , 8 ) .
(12)
We give m figs. 3d and 3h the c o n t o u r plots o f the cross section for e+e --,Zh at x / s = 190 O e V At this center o f mass energy, about 200 events should be sufficient to establish the existence o f the Hlggs o v e r the m a i n b a c k g r o u n d f r o m e+e -~ZZ, even for
398
mh--~ "/~/Z [6]. T h e d r a m a t i c d e p e n d e n c e o f the cross sectton on the top q u a r k mass ts an o b v m u s conseq u e n c e o f the phase h m l t a t i o n , in v i e w o f fig. 1. C o n versely, the m a x i m u m attainable energy will be a m a i n factor m the d e t e r m i n a t i o n o f the sensltlvtty to the search for the s u p e r s y m m e t r i c Hlggs at L E P 11. We are grateful reformation
+0.07 m~] 2
l l April 1991
to
Glgl
Rolandi
for
useful
References [1]Y Okada M Yamaguchi and T Yamagldo, Tohoku Umverslty preprlnt TU-360 (October 1990) [2] J Elhs, G Rldolfi and F Zwlrner, CERN preprlnt CERNTH 5946/90 (November 1990), H Haber and R Hempfllng, University of Santa Cruz preprlnt SCIPP-90/42 [3] R Barblerl, F Caravaghos and M Frlgenl, University of Plsa preprlnt 1FUP-TH 40/90 ( December 1990) [4] P Franzlnl and P Taxll, in Z Physics at LEP I, eds G Altarelh, R Klelss and C Verzegnassl, CERN Reporl CERN 89-08, Vol 2 (1989)p 59 [5] G Gamberlm, G F Gmdlce and G Rldolfi, Nucl Plays B 292 (1987) 237 [6] U Amaldl, talk, in Proc Cogne Meeting of the LEP Experiment Committee (September 1990), J Lefran¢ols, talk, m Proc Cogne Meeting of the LEP Experiment Committee (September 1990), D Trellle, talk, m Proc Cogne Meeting of the LEP Experlmen! Committee (September 1990)
PHYSICS LETTERS B
11 April 1991
The supersymmetric Higgs searches at LEP after radiative corrections R. Barbieri and M. Frigeni DtparUmento dl Ftstca, Umverslta dt Ptsa, 1-56100 Ptsa, Italy and INFN, Seztone dl Ptsa, Ptsa, Italy Received 30 January 1991
Radiative corrections modify in a significant way the tree level mass of the hghtest supersymmetnc Hlggs panicle in models with Hlggs doublets only Using a simple approximate description of these corrections, their impact on the supersymmetnc Hlggs searches at LEP Is illustrated
Recent work [ 1-3 ] has shown that radiative corrections modify m a significant way the tree level mass o f the hghtest supersymmetrlc Hlggs particle. Due to the heaviness of the top quark, in models with Hlggs doublets only, the physical mass o f the hghtest Hlggs is raised relative to the tree level one in most o f the p a r a m e t e r space. Since, on the other hand, the phase space dependence is a main factor m the Hlggs searches at LEP, the effect of radiative corrections is clearly going to have a significant impact on these same searches. This effect we would like to illustrate in this paper in the simplest possible way. As is well known, in a supersymmetrlc model with two Hlggs doublets, the whole Higgs phenomenology, described at the tree level, depends on two parameters only: the ratio v2/v~ o f their v a c u u m expectation values and one of the masses o f the physical Higgses This is no longer true after taking into account the radiative corrections, which bring in the top quark mass as well as, at least in prmclple, all the other parameters related to masses and mlxings of the various s u p e r s y m m e t n c pamcles. Here we focus on the main effect which as related to the dependence of the hghtest Higgs mass on the fourth power o f the top mass m,. In this a p p r o x i m a t i o n the relevant results are obtained by expanding a r o u n d the m i n i m u m the Hlggs potential with the inclusion o f the one-loop radiative
corrections coming from top and s c a l a r - t o p loops only, V= Vtree+SV, 8V= ~ 3
[ (g2[H212+m2 )2 log(g2[H212+m 2)
_ g 2 IH214 l o g ( g 2 l H 2 1 2 ) ] ,
(1)
where gt is the top Yukawa couphng to the Higgs field //2 and m is the mass o f the top scalar partners, taken degenerate for simplicity. The overall c o m m o n scale o f the arguments of the logarithms is left unspecified, since tt can be changed by a redefinition o f the tree level parameters. In this way, the resulting mass matrix for the two neutral CP-even Hlggs scalars, m the basis of the original hypercharge mgenstates ( H b / / 2 ), IS
mzA s i n a f l + M 2 cos2fl (meA +M2)sInflcosfl~ -- (mzA + MZz)smflcosfl mE c o s e f l + M 2 sin2fl+~] -
-
(2) where mA is the physical mass o f the third neutral CPo d d scalar A, tan fl= v2/vl and the radiative correction effects are l u m p e d into the p a r a m e t e r e. The explicit expressmn for e is
3awm4t
, {,-
m2"~
e = 2 n M 2 sin2 fl iog~l ± ~2t2) ,
0370-2693/91/$ 03 50 © 1991 - Elsevier Science Publishers B V ( North-Holland )
(3)
39 5
Volume 258, number 3,4
PHYSICS LETTERS B
11 April 1991
where aw is the SU (2) fine structure constant and Mw, Mz are the mtermedmte vector boson masses. The dlagonallzatton of the matrix (2) gives the phystcal masses of the neutral scalars ~1 1 2 m ~ , = ~(mA + M z2+ e + d )
.
A= [ (m 2 + M z + e ) 2 - 4 r n ~ M ~ COS22fl E
- 4 ¢ m A s l n 2 f l - 4eM 2 cos2fl] '/2.
(4)
as well as the mixing angle, which is relevant to the couplings of these Hlggs scalars (h)=.f2(
coso~ \--sin
o~
sInc~/(RR;H°
H°--v2] '
c o s 0~/
(5)
50
o .... loo
I .... lz0
I .... 14o
I .... 16o
180
Into p (GeV)
sin 2 ~ =
- ( m 2 + , ~ / 2 ) s i n 2fl
(6)
d
Fig. 1 shows the mass of the hghtest neutral scalar h m the plane (ma, tan fl) for two choices of mr and m. The quahty of the approximation leading to the elgenvalues (4) can be appreciated, in a special case, from fig 2 There we compare the range of values obtained from (4) for the hghtest Hlggs mass mh and m A = m = 1 TeV, with those obtained by mmamizang the full one-loop renormahzatlon group improved efnL The mass matrix of the two CP-even scalars m a suitable basis is also gLven m ref [ 1 ], using the same approxlmaUon as m th~s work The e~genvalues ofth~s mass matrix agree with those m eq (4) m leading logarithmic approximation for m2>> m~, although not for the fimte term
Fig 2 Comparison of the corrected Hlggs mass m. using a full one-loop renormahzatlon group improved calculanon (sohd hnes) or the approxlmanon described m the text (dashed hnes)
fectlve potential wtth all the other superpartners also at 1 TeV mass [3]. The relatively small discrepancy between the two pairs o f h m m n g curves is mainly due, for m, close to 100 GeV, to the effect of the gauge mteracnons and, for m, close to 180 GeV, to the higher order effects. The reactions of interest at LEP are Z~hg+g - .
(7a)
Z-.hA.
(7b)
Z~hy.
(7c)
and. at higher energies.
25
II
1111// " llll[lllllll///
i
20
.
lO 0
0
0
5
50
100
150
2OO
50
100
150
F~g I Contour plots of the hghtest Hlggs mass m h for (a) {mt 300 GeV) and (b) (170GeV, 1000 GeV) m l s the common mass of the top scalar partners
m)=(13OGeV,
396
(8a)
e+e - , Z H ,
(8b)
e+e--~hA.
(8c)
For Z decays, all the relevant formulae can be found, for example, in ref. [4]. The corrections to the mass mh and to the maxmg angle c~ influence the various branching ratios both in the phase space dependence and m the values of the relevant couplings. For processes (7a), (7b) one has respecnvely
15
G
e+e-~Zh,
F(Z--*hla+g- ) = sin2 (o/-- fl) , F(Z~HsMg+ g - )
(9)
with a standard model Hlggs HSM of the same mass as h, and
Volume 258, number 3,4
PHYS1CS LETTERS B
Fxgs. 3 a - 3 c and 3 e - 3 g s h o w the rates for reactions ( 7 ) with the s a m e pair o f values o f mt and m as m fig 1. U n h k e the case for processes ( 7 a ) , ( 7 b ) , the amplitude for Z - . h 7 is n o n - v a n i s h i n g only at the loop level. As a c o n s e q u e n c e , since s u p e r s y m m e t r l c part]cles can run in the loop, this rate d e p e n d s m general
f'(Z-,hA) cos2(o~-fl) F ( Z ~ g+ p - ) - 2 ( 1 - 4 sln20w + 8 sm40w) [(M~_m X
2 --,riAj ~ , 2 ~ 2 - - "A ~2~213/2 r t t t hCtt A ]
M6
(10)
,
where 0w is the w e a k m ] x m g angle. '
'
•
/
v2/v I
\
8 \
\
I
I
•
"
[
[ I -5
'/~ , ~ ....
i
i
50
I00
\ \\
V2/V1
10 .4
~ i ....
. . . .
I
.
.
~
i ....
r ( z ~ h T ) / r ( z ~ u + J * -)
,
|
J
i ....
,
I
,/,
~
,
I
I I
~~
0
. . . .
F(Z~hAl/r(Z~"+tt-)
(°)
~×10 -°
1o .....
I
r(z ~h"+"-)/r(z~tt+t~-)
\
\
11 April 1991
.
.
.
150
.
.
J~"/'l /
I
.
I
200
:,:'
i': /p
. . . .
50
i
. . . .
100
r(Z ~ h/~ +,a- )/I'(Z ~p,*/x - )
....
i
13 o'(e e - ~ Z h ) ( p b ) ]
I
,
150
,
,
,
m A (Gev)
I'(Z ~ hA)/F(Z-*,u,+/~ - )
8
\ \ a~lo -~
6
4
1 4~'x~
k
Y
10-4
8
....
I0
.--~-~
i ....
i. . . .. ... .
_ ~ , - ~
i . . . . . . . . . . .~. . . . . . . . . . ,,
. . . . .
....
, ....
r(z.hT)/r(z~u+u -)
I ....
o'(e+e- ~Zh) (pb) i
(g)
8
(h)
6
4
2 .... 0
k ,.~,
50
'
,
,
100
150
200
50
100
150
111A (Gev)
Fig 3 Contour plots for (a) F(Z--*hp+p - )/F(Z---,Ia+p-- ), (b) F ( Z - - * h A ) / F ( Z ~ p + p - ), (c) F ( Z ~ h y ) / F ( Z ~ p + I . t - ), (d) a(e+e ~hZ) at ,,/s = 190 GeV, for ( mt, rn ) = ( 130 GeV, 300 GeV) In (e)- (h) the same quantities are given for ( mr, m ) = ( 170 GeV, 1000 GeV ) 397
Volume 258, number 3,4
PHYSICS LETTERS B
on their masses, especmlly for gauglno-hlggsinos [ 5 ]. In figs. 3c and 3d we h a v e a s s u m e d t h e m to be h e a v y
enough not to contribute significantly to the rate and we h a v e used the a p p r o x i m a t i o n [ 4 ] F(Z~hy) - ~ s l n Z ( o l - f l ) 6 . 9 4 X 10 -5 F(Z-qa+~a - ) × (l _ ~'](1 MzJ\
Mz/
"
Light gauglno-hlggslnos m a y change the rate for Z - ~ h y by a factor by a factor o f 1-3 in either dlrecn o n , d e p e n d i n g u p o n the sign o f the interference o f their c o n t r i b u t i o n with the W - b o s o n loop R e a c n o n s (8), relevant to higher LEP energies, can be studied along s~milar lmes in the p a r a m e t e r space. We h a v e c o n s i d e r e d all o f t h e m at x / s = 190 G e V ( 8 a ) is the only process whose study will allow a significant e x t e n s i o n in the e x p l o r a t i o n o f the p a r a m e ter space relative to L E P I searches. R e l a t i v e to the s t a n d a r d m o d e l cross section with the SM Hlggs degenerate with h, the cross section is a(e+e
~Zh)
a ( e + e - ---~ZHsM )
= slna ( o e - , 8 ) .
(12)
We give m figs. 3d and 3h the c o n t o u r plots o f the cross section for e+e --,Zh at x / s = 190 O e V At this center o f mass energy, about 200 events should be sufficient to establish the existence o f the Hlggs o v e r the m a i n b a c k g r o u n d f r o m e+e -~ZZ, even for
398
mh--~ "/~/Z [6]. T h e d r a m a t i c d e p e n d e n c e o f the cross sectton on the top q u a r k mass ts an o b v m u s conseq u e n c e o f the phase h m l t a t i o n , in v i e w o f fig. 1. C o n versely, the m a x i m u m attainable energy will be a m a i n factor m the d e t e r m i n a t i o n o f the sensltlvtty to the search for the s u p e r s y m m e t r i c Hlggs at L E P 11. We are grateful reformation
+0.07 m~] 2
l l April 1991
to
Glgl
Rolandi
for
useful
References [1]Y Okada M Yamaguchi and T Yamagldo, Tohoku Umverslty preprlnt TU-360 (October 1990) [2] J Elhs, G Rldolfi and F Zwlrner, CERN preprlnt CERNTH 5946/90 (November 1990), H Haber and R Hempfllng, University of Santa Cruz preprlnt SCIPP-90/42 [3] R Barblerl, F Caravaghos and M Frlgenl, University of Plsa preprlnt 1FUP-TH 40/90 ( December 1990) [4] P Franzlnl and P Taxll, in Z Physics at LEP I, eds G Altarelh, R Klelss and C Verzegnassl, CERN Reporl CERN 89-08, Vol 2 (1989)p 59 [5] G Gamberlm, G F Gmdlce and G Rldolfi, Nucl Plays B 292 (1987) 237 [6] U Amaldl, talk, in Proc Cogne Meeting of the LEP Experiment Committee (September 1990), J Lefran¢ols, talk, m Proc Cogne Meeting of the LEP Experiment Committee (September 1990), D Trellle, talk, m Proc Cogne Meeting of the LEP Experlmen! Committee (September 1990)