- Email: [email protected]
Fermion mass effects on Γ(Z → bb + a light Higgs) in a two-Higgs-doublet model
-_ -_ l!!iEi
a5
ELSEVIER
2 November 1995 PHYSICS
LETTERS
B
Physics Letters B 361(1995) 66-68
Fermion mass effects on I’( 2 -+ b6 + a light Higgs) in a two-Higgs-doublet model Jan Kalinowski
‘,
Maria Krawczyk
Institute of Theoretical Physics, Warsaw University, ul. Hoia 69, 00 681 Warsaw, Poland
Received 28 June 1995; revised manuscript received 24 August 1995 Editor: F?V.Landshoff
Abstract A large fermion mass effect on the Yukawa process Z --+ b6 + b&h(A) in the entire range of neutral Higgs boson masses is found. This is particularly important for light Higgs bosons, which are still not excluded experimentally in a general two-Higgs-doublet model.
The light Higgs bosons in the context of the standard model (SM) and its minimal supersymmetric extension (MSSM) have been ruled out at LEP from zero up to a value that depends on the model assumed. In the framework of the SM the dominant Higgs boson production process is the Bjorken process Z ----)HsMZ*
--f
fhff,
(1)
and the mass limit ntHSM> 65.1 GeV has been established based on the results of four collaborations collecting data at LEP [ 11. In extensions of the SM, like the MSSM or the general two-Higgs-doublet model (2HDM), the Higgs sector is much richer: there are two CP-even neutral Higgs bosons denoted by h and H (we assume that mh < mH), a CP-odd neutral-A, and a pair of charged scalars H*. The CP-even Higgs bosons can be produced via the process ( 1) , however with lower rates because they share the couplings to the Z boson, i.e., ’ Supported in part by grant 2 P302 095 05 from the Polish Committee for Scientific Research.
I(Z
-+ AZ*) =rs~(Z
-+ Hs~z*)
sin’(p-
a), (2)
r(z
-+ HZ*)
=rSM(Z
-+ &Z*)
cos2(p - a), (3)
where (Yand /3 are the mixing angles in the neutral and charged Higgs sectors, respectively, with tan p given by the ratio of the vacuum expectation values of the Higgs doublets, tan p = uz/ut . In both MSSM and 2HDM models there is another production process, namely Higgs pair production, which is complementary to (2) and (3) in the sense that T(Z -+ hA) = 0.5r(z-+ Yzqcos*(p- a)AP, (4) r(Z
-+ HA) = 0.5r(Z
+ v@) sin*@ - &)A”, (5)
where
h = (1 - fq, -
and p = 312.
0370-2693/95/$09.50 @ 1995 Elsevier Science B.V. All rights reserved XW/0370-2693(95)01102-l
KA)~
-~KJ,KA,
with Ki = F?$/m$
J. Kalinowski,M. Krawczyk/PhysicsLetters3 36111995) 66-68
Fig. 1. The Feynman diagrams for neutral Higgs boson production (h or A) via the Yukawa process.
In the MSSM the allowed domain for mh and mA is restricted theoretically and for any given mh and mA the values of sin2(p - cy) and cos2( p - a) are restricted to vary in a certain range. Since the heavier Higgs boson H cannot be produced at LEP (because mH > rnz in the MSSM), combining the negative search results from processes (2) and (4) the Delphi Collaboration [2] recently set the mass limits Mh > 44 GeV for any tan /3 and MA 2 27 GeV for tan p L 1 assuming the mass of the top quark m, = 170 GeV and degeneracy of the top-squarks with msg = 1 TeV. There is, however, no lower limit on MA when h!h 2 60 GeV. On the other hand in a general 2HDM the masses and mixing angles in the Higgs sector are unrelated and unconstrained theoretically and therefore much weaker bounds can be established. From the process (2) one can only derive an experimental upper limit, sin2(p--cu) < O.l,for Mh < 50GeV [l]. Inaddition, if one assumes the process (4) to be forbidden kinematically (i.e., MA + Mh > Mz), then either a very light h or a very light A cannot be ruled out on the basis of negative searches via processes (2) and (4). For large tanp, however, there is still another important process in the 2HDM* , namely the bremsstrahlung of the Higgs boson from the fermion line in the final state, which we will call a Yukawa process (Fig. 1.): Z -+ ff--+
f?h
or ffA.
(6)
For down-type fermions f = b, T the Higgs couplings are strongly enhanced in the large tan p limit as compared to the SM coupling: in the case of the pseudoscalar the coupling is directly proportional to tan p, and for the scalar - sin cy/ cos /3. However, tan p >> *In the MSSM the process (6) is never competitive with the sum (2)+(4) for Mh I 50 GeV.
67
1 (i.e., p N 7r/2) and the experimental bound on sin2( p - LY)imply that cy is close to f7r/2 and therefore the scalar coupling can be approximated by tan /3 with good accuracy. In such a case the process (6) can produce a substantial number of Higgs bosons h or A. For example, for Mb(A) = 10 GeV and moderate values of tan p = 20 one expects about 3000 b6h (or b&A) events in IO7 Z decays. The Higgs boson then would predominantly decay to the heaviest possible ferrnion pair. Note that this is a single Higgs boson production mechanism with different topology from the Bjorken process. Such events have not been fully analysed experimentally yet, although the possible importance of the Yukawa process has been pointed out in the literature long time ago [ 3-61. The process (6) has been analysed in the literature numerically [ 4,5] for the scalar Higgs boson and analytically [6] for the pseudoscalar. The analytical treatment can however be done in the limit of vanishing fermion masses in which the formulae for h and A production are the same (after an appropriate change of the Higgs couplings and masses). In this short note we would like to point out that the proper treatment of fermion masses is quite important, not only at the edge of the available phase space when 2rnf + mh,A --+ mz but in the entire range of the Higgs boson mass. The analytical expressions in the lowest order for the differential decay distributions dI/dxi dX2 (with xi = 2Eb/Mz and x2 = 2Eb/Mz) for both Z ---f b&h and Z + b&A can be inferred from Eqs. (15) and ( 17) in Ref. [7] or for the pseudoscalar case can be found in Ref. [ 6 1. In our case both distributions scale as rni tan2 p due to the Riggs coupling N mb tan /I to the down-type fermions. In addition to the mass parameter in the coupling, the fermion mass mb enters (i) the phase space integration limits when the contribution to the total decay rate is calculated, and (ii) the matrix element. If one neglects Mb in the matrix elements the differential decay distributions for Z --+ bbh and Z + bi;A are equal, and neglecting in addition mb in (i) the integral over xt and x2 can be done in an elegant way [6]. The resulting decay widths’ as a function of the corresponding Higgs masses are shown in Figs. 2 and 3 (dotted lines). However, we find that although mb/Mz < 1 the fermion mass ntb 3r = 1 MeV corresponds to 4000 events per IO’ 2 decays.
68
J. Kalinowski, M. Krawczyk/ Physics Letters B 361 (1995) 66-68 1
,
I
I
I
I
mb= 5.0 ME wtth mb=O --~~ mb=O
o,
1
0
\
10
fan(betai=20.0
20
30
50
1
60
70
60
M_A4&a")
Fig. 2. The decay width r( 2 -+ b6A) in the 2HDM for tan /? = 20 as a function of the pseudoscalar Higgs boson mass. The solid line represents the results with full mb dependence, the dashed line that with lnb neglected only in the matrix element, and the dotted lines that with mb neglected in the matrix element and integration limits.
behaviour of the massless approximation and results in lowering the predicted decay rate by at least 15% for all MA. Comparing the dashed and solid lines in Fig. 2, we notice that once the kinematical limits are properly taken into account in (i) one can neglect rnh in the matrix element (ii). On the other hand, for Z -+ b6h (Fig. 3) keeping mb #O in (i) and (ii) leads to an enhancement of the scalar h production in Z decays in the mass region up to mh = 50 GeV (solid line). Also, contrary to the pseudoscalar case, one cannot neglect mb in the matrix element because it would lead to a wrong IR behaviour (dashed line). Similar mass effects also appear in the Yukawa process (6) with an f = 7 lepton in the final state. The results presented here have been obtained for tan /3 = 20. For other values of tan /3 the results can simply be obtained by resealing. The observed fermion mass effects are phenomenologically important as they modify significantly the predicted decay rate of the Z boson as compared to the massless approximation. They have to be taken into account when performing a detailed search for a light Higgs boson or in deriving the experimental limits on the parameters of the two-Higgs-doublet model.
01
We would like to thank A. Djouadi and P Zerwas for useful discussions and comments. J.K. thanks P Chappetta and the CPT Marseille for the kind hospitality at the CPT, where part of this work has been done. M.K. is grateful to W. Hollik for discussions on light Higgs bosons. We also thank our colleagues from Hoia for helpful conversations.
5 E $
1.0e-02
3: 2
ci
d
1.0e-03
1.0e-04
1.0e-05 ' 0
I
I 10
20
30
50
60
70
!\ 60
References
U_h4$e")
Fig. 3. The decay width r( 2 --) bbh) in the 2HDM for tan /? = 20 as a function of the scalar Higgs boson mass. The labeling of the lines is the same as in Fig. 2.
[ 1] A. Sopczak, CERN preprint CERN-PPE/95-46
plays an important role in the entire range of Higgs boson masses. In Figs. 2 and 3 we show the effect of retaining the fermion mass (with mb = 5 GeV) in the integration limits only and neglecting it in the matrix element (dashed lines), and keeping full mb dependence (solid lines). In the case of Z -+ b6A (Fig. 2) we see that keeping mb f 0 is very important - it cures the fake IR
[3]
[2]
[4] [5] [6] [7]
and references therein. P Abreu et al., DELPHI Collab., CERN preprint CERNPPE/94-2 18. E. Carlson, S. Glashow and U. Sarid, Nucl. Phys. B 309 (1988) 598. J. Kalinowski and S. Pokorski, Phys. Lett. B 219 (1989) 116. J. Kalinowski and H.P Nilles, Phys. Lett. B 255 ( 1991) 134. A. Djouadi, PM. &was and J. Zunft, Phys. Lett. B 259 (1991) 175. A. Djouadi, J. Kalinowski and P.M. Zerwas, Z. Phys. C 54 (1992) 255.
a5
ELSEVIER
2 November 1995 PHYSICS
LETTERS
B
Physics Letters B 361(1995) 66-68
Fermion mass effects on I’( 2 -+ b6 + a light Higgs) in a two-Higgs-doublet model Jan Kalinowski
‘,
Maria Krawczyk
Institute of Theoretical Physics, Warsaw University, ul. Hoia 69, 00 681 Warsaw, Poland
Received 28 June 1995; revised manuscript received 24 August 1995 Editor: F?V.Landshoff
Abstract A large fermion mass effect on the Yukawa process Z --+ b6 + b&h(A) in the entire range of neutral Higgs boson masses is found. This is particularly important for light Higgs bosons, which are still not excluded experimentally in a general two-Higgs-doublet model.
The light Higgs bosons in the context of the standard model (SM) and its minimal supersymmetric extension (MSSM) have been ruled out at LEP from zero up to a value that depends on the model assumed. In the framework of the SM the dominant Higgs boson production process is the Bjorken process Z ----)HsMZ*
--f
fhff,
(1)
and the mass limit ntHSM> 65.1 GeV has been established based on the results of four collaborations collecting data at LEP [ 11. In extensions of the SM, like the MSSM or the general two-Higgs-doublet model (2HDM), the Higgs sector is much richer: there are two CP-even neutral Higgs bosons denoted by h and H (we assume that mh < mH), a CP-odd neutral-A, and a pair of charged scalars H*. The CP-even Higgs bosons can be produced via the process ( 1) , however with lower rates because they share the couplings to the Z boson, i.e., ’ Supported in part by grant 2 P302 095 05 from the Polish Committee for Scientific Research.
I(Z
-+ AZ*) =rs~(Z
-+ Hs~z*)
sin’(p-
a), (2)
r(z
-+ HZ*)
=rSM(Z
-+ &Z*)
cos2(p - a), (3)
where (Yand /3 are the mixing angles in the neutral and charged Higgs sectors, respectively, with tan p given by the ratio of the vacuum expectation values of the Higgs doublets, tan p = uz/ut . In both MSSM and 2HDM models there is another production process, namely Higgs pair production, which is complementary to (2) and (3) in the sense that T(Z -+ hA) = 0.5r(z-+ Yzqcos*(p- a)AP, (4) r(Z
-+ HA) = 0.5r(Z
+ v@) sin*@ - &)A”, (5)
where
h = (1 - fq, -
and p = 312.
0370-2693/95/$09.50 @ 1995 Elsevier Science B.V. All rights reserved XW/0370-2693(95)01102-l
KA)~
-~KJ,KA,
with Ki = F?$/m$
J. Kalinowski,M. Krawczyk/PhysicsLetters3 36111995) 66-68
Fig. 1. The Feynman diagrams for neutral Higgs boson production (h or A) via the Yukawa process.
In the MSSM the allowed domain for mh and mA is restricted theoretically and for any given mh and mA the values of sin2(p - cy) and cos2( p - a) are restricted to vary in a certain range. Since the heavier Higgs boson H cannot be produced at LEP (because mH > rnz in the MSSM), combining the negative search results from processes (2) and (4) the Delphi Collaboration [2] recently set the mass limits Mh > 44 GeV for any tan /3 and MA 2 27 GeV for tan p L 1 assuming the mass of the top quark m, = 170 GeV and degeneracy of the top-squarks with msg = 1 TeV. There is, however, no lower limit on MA when h!h 2 60 GeV. On the other hand in a general 2HDM the masses and mixing angles in the Higgs sector are unrelated and unconstrained theoretically and therefore much weaker bounds can be established. From the process (2) one can only derive an experimental upper limit, sin2(p--cu) < O.l,for Mh < 50GeV [l]. Inaddition, if one assumes the process (4) to be forbidden kinematically (i.e., MA + Mh > Mz), then either a very light h or a very light A cannot be ruled out on the basis of negative searches via processes (2) and (4). For large tanp, however, there is still another important process in the 2HDM* , namely the bremsstrahlung of the Higgs boson from the fermion line in the final state, which we will call a Yukawa process (Fig. 1.): Z -+ ff--+
f?h
or ffA.
(6)
For down-type fermions f = b, T the Higgs couplings are strongly enhanced in the large tan p limit as compared to the SM coupling: in the case of the pseudoscalar the coupling is directly proportional to tan p, and for the scalar - sin cy/ cos /3. However, tan p >> *In the MSSM the process (6) is never competitive with the sum (2)+(4) for Mh I 50 GeV.
67
1 (i.e., p N 7r/2) and the experimental bound on sin2( p - LY)imply that cy is close to f7r/2 and therefore the scalar coupling can be approximated by tan /3 with good accuracy. In such a case the process (6) can produce a substantial number of Higgs bosons h or A. For example, for Mb(A) = 10 GeV and moderate values of tan p = 20 one expects about 3000 b6h (or b&A) events in IO7 Z decays. The Higgs boson then would predominantly decay to the heaviest possible ferrnion pair. Note that this is a single Higgs boson production mechanism with different topology from the Bjorken process. Such events have not been fully analysed experimentally yet, although the possible importance of the Yukawa process has been pointed out in the literature long time ago [ 3-61. The process (6) has been analysed in the literature numerically [ 4,5] for the scalar Higgs boson and analytically [6] for the pseudoscalar. The analytical treatment can however be done in the limit of vanishing fermion masses in which the formulae for h and A production are the same (after an appropriate change of the Higgs couplings and masses). In this short note we would like to point out that the proper treatment of fermion masses is quite important, not only at the edge of the available phase space when 2rnf + mh,A --+ mz but in the entire range of the Higgs boson mass. The analytical expressions in the lowest order for the differential decay distributions dI/dxi dX2 (with xi = 2Eb/Mz and x2 = 2Eb/Mz) for both Z ---f b&h and Z + b&A can be inferred from Eqs. (15) and ( 17) in Ref. [7] or for the pseudoscalar case can be found in Ref. [ 6 1. In our case both distributions scale as rni tan2 p due to the Riggs coupling N mb tan /I to the down-type fermions. In addition to the mass parameter in the coupling, the fermion mass mb enters (i) the phase space integration limits when the contribution to the total decay rate is calculated, and (ii) the matrix element. If one neglects Mb in the matrix elements the differential decay distributions for Z --+ bbh and Z + bi;A are equal, and neglecting in addition mb in (i) the integral over xt and x2 can be done in an elegant way [6]. The resulting decay widths’ as a function of the corresponding Higgs masses are shown in Figs. 2 and 3 (dotted lines). However, we find that although mb/Mz < 1 the fermion mass ntb 3r = 1 MeV corresponds to 4000 events per IO’ 2 decays.
68
J. Kalinowski, M. Krawczyk/ Physics Letters B 361 (1995) 66-68 1
,
I
I
I
I
mb= 5.0 ME wtth mb=O --~~ mb=O
o,
1
0
\
10
fan(betai=20.0
20
30
50
1
60
70
60
M_A4&a")
Fig. 2. The decay width r( 2 -+ b6A) in the 2HDM for tan /? = 20 as a function of the pseudoscalar Higgs boson mass. The solid line represents the results with full mb dependence, the dashed line that with lnb neglected only in the matrix element, and the dotted lines that with mb neglected in the matrix element and integration limits.
behaviour of the massless approximation and results in lowering the predicted decay rate by at least 15% for all MA. Comparing the dashed and solid lines in Fig. 2, we notice that once the kinematical limits are properly taken into account in (i) one can neglect rnh in the matrix element (ii). On the other hand, for Z -+ b6h (Fig. 3) keeping mb #O in (i) and (ii) leads to an enhancement of the scalar h production in Z decays in the mass region up to mh = 50 GeV (solid line). Also, contrary to the pseudoscalar case, one cannot neglect mb in the matrix element because it would lead to a wrong IR behaviour (dashed line). Similar mass effects also appear in the Yukawa process (6) with an f = 7 lepton in the final state. The results presented here have been obtained for tan /3 = 20. For other values of tan /3 the results can simply be obtained by resealing. The observed fermion mass effects are phenomenologically important as they modify significantly the predicted decay rate of the Z boson as compared to the massless approximation. They have to be taken into account when performing a detailed search for a light Higgs boson or in deriving the experimental limits on the parameters of the two-Higgs-doublet model.
01
We would like to thank A. Djouadi and P Zerwas for useful discussions and comments. J.K. thanks P Chappetta and the CPT Marseille for the kind hospitality at the CPT, where part of this work has been done. M.K. is grateful to W. Hollik for discussions on light Higgs bosons. We also thank our colleagues from Hoia for helpful conversations.
5 E $
1.0e-02
3: 2
ci
d
1.0e-03
1.0e-04
1.0e-05 ' 0
I
I 10
20
30
50
60
70
!\ 60
References
U_h4$e")
Fig. 3. The decay width r( 2 --) bbh) in the 2HDM for tan /? = 20 as a function of the scalar Higgs boson mass. The labeling of the lines is the same as in Fig. 2.
[ 1] A. Sopczak, CERN preprint CERN-PPE/95-46
plays an important role in the entire range of Higgs boson masses. In Figs. 2 and 3 we show the effect of retaining the fermion mass (with mb = 5 GeV) in the integration limits only and neglecting it in the matrix element (dashed lines), and keeping full mb dependence (solid lines). In the case of Z -+ b6A (Fig. 2) we see that keeping mb f 0 is very important - it cures the fake IR
[3]
[2]
[4] [5] [6] [7]
and references therein. P Abreu et al., DELPHI Collab., CERN preprint CERNPPE/94-2 18. E. Carlson, S. Glashow and U. Sarid, Nucl. Phys. B 309 (1988) 598. J. Kalinowski and S. Pokorski, Phys. Lett. B 219 (1989) 116. J. Kalinowski and H.P Nilles, Phys. Lett. B 255 ( 1991) 134. A. Djouadi, PM. &was and J. Zunft, Phys. Lett. B 259 (1991) 175. A. Djouadi, J. Kalinowski and P.M. Zerwas, Z. Phys. C 54 (1992) 255.