Higgs Boson Decays in the Minimal Supersymmetric Standard Model with Radiative Higgs Sector CP Violation
ABSTRACT We re-evaluate the decays of the Higgs bosons in the minimal supersymmetric standard model (MSSM) where the tree-level CP invariance of the Higgs potential is explicitly broken by the loop effects of the third-generation squarks with CP-violating soft-breaking Yukawa interactions. This study is based on the mass matrix of the neutral Higgs bosons that is valid for arbitrary values of all the relevant MSSM parameters. It extends the previous work considerably by including neutral Higgs-boson decays into virtual gauge bosons and those into top-squark pairs, by implementing squark-loop contributions to the two-gluon decay channel, and by incorporating the decays of the charged Higgs boson. The constraints from the electron electric dipole moment on the CP phases are also discussed. We find that the branching fractions of both the neutral and charged Higgs-boson decays and their total decay widths depend strongly on the CP phases of the top (and bottom) squark sectors through the loop-induced neutral Higgs boson mixing as well as the direct couplings of the neutral Higgs bosons to top squark pairs. Comment: 17 pages, 5 eps figures. Comments on the color and electric-charge breaking minima and references added. To appear in the Phys. Rev. D
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arXiv:hep-ph/0103294v2 17 May 2001
February 1, 2008
Higgs Boson Decays in the Minimal Supersymmetric Standard
Model with Radiative Higgs Sector CP Violation
S.Y. Choi1, Kaoru Hagiwara2and Jae Sik Lee2
1Department of Physics, Chonbuk National University, Chonju 561–756, Korea
2Theory Group, KEK, Tsukuba, Ibaraki 305–0801, Japan
We re–evaluate the decays of the Higgs bosons in the minimal supersymmetric
standard model (MSSM) where the tree-level CP invariance of the Higgs po-
tential is explicitly broken by the loop effects of the third–generation squarks
with CP–violating soft–breaking Yukawa interactions. This study is based on
the mass matrix of the neutral Higgs bosons that is valid for arbitrary values
of all the relevant MSSM parameters. It extends the previous work consider-
ably by including neutral Higgs–boson decays into virtual gauge bosons and
those into top–squark pairs, by implementing squark–loop contributions to
the two–gluon decay channel, and by incorporating the decays of the charged
Higgs boson. The constraints from the electron electric dipole moment on the
CP phases are also discussed. We find that the branching fractions of both the
neutral and charged Higgs–boson decays and their total decay widths depend
strongly on the CP phases of the top (and bottom) squark sectors through
the loop–induced neutral Higgs boson mixing as well as the direct couplings
of the neutral Higgs bosons to top squark pairs.
PACS number(s): 14.80.Cp, 11.30.Er, 12.60.Jv
Typeset using REVTEX
The soft CP violating Yukawa interactions in the minimal supersymmetric standard
model (MSSM) cause the CP–even and CP–odd neutral Higgs bosons to mix via loop cor-
rections [1–5]. Although the mixing is a radiative effect, the induced CP violation in the
MSSM Higgs sector can be large enough to affect the Higgs phenomenology significantly at
present and future colliders [1,3,5–11].
In the light of the possible large CP–violating mixing, we have studied in Ref.  all
the dominant two–body decay branching fractions of the three neutral Higgs bosons based
on the mass matrix derived by Pilaftsis and Wagner . The mass matrix, however, is
not applicable for large squark mass splitting. In the present work, we re–evaluate all the
two–body decay modes of the neutral Higgs bosons with the newly–calculated mass matrix
 which is valid for any values of the soft–breaking parameters. Furthermore, we extend
the work significantly by including the Higgs–boson decay modes containing virtual gauge
bosons and those into squark pairs and, also by taking into account the squark–loop contri-
butions to the gluon–gluon decay modes. In addition, we study the dominant decay modes
of the charged Higgs boson in the presence of the non–trivial CP–violating mixing.
This paper is organized as follows. In Sec. II we give a brief review of the calculation 
of the loop–induced CP–violating mass matrix of the three neutral Higgs bosons. We also
consider the constraints by the electron electric dipole moment (EDM) on the space of the
relevant supersymmetric parameters. In Sec. III we discuss the effects of the CP phases on
the neutral Higgs boson decays. The effects of the CP phases on the charged Higgs boson
decays are discussed in Sec. IV. Finally, we summarize our findings in Sec. V.
II. CP VIOLATION IN THE MSSM HIGGS SECTOR
The loop–corrected mass matrix of the neutral Higgs bosons in the MSSM can be calcu-
lated from the effective potential [12,13]
12|(φ1a2+ φ2a1)sin(ξ + θ12) +ˆ g2
2) − |m2
12|(φ1φ2− a1a2)cos(ξ + θ12)
with D = φ2
the neutral components of the two Higgs doublets:
1, ˆ g2= (g2+ g′2)/4, and φiand ai(i = 1,2) are the real fields of
√2(φ1+ ia1) ,H0
√2(φ2+ ia2) .(2)
The parameters g and g′are the SU(2)Land U(1)Y gauge couplings, respectively, and Q
denotes the renormalization scale. All the tree–level parameters of the effective potential (1)
such as m2
The potential (1) is then almost independent of Q up to two–loop–order corrections. The
12|eiθ12, are the running parameters evaluated at the scale Q.
super–trace is to be taken over all the bosons and fermions that couple to the Higgs fields.
The matrix M in Eq. (1) is the field–dependent mass matrix of all modes that couple
to the Higgs bosons. The dominant contributions in the MSSM come from third generation
quarks and squarks because of their large Yukawa couplings. The field–dependent masses
of the third generation quarks are given by
where hband htare the bottom and top Yukawa couplings, respectively. The corresponding
squark mass matrices read:
? Q, m2
symmetric Higgsino mass parameter.
? Q+ m2
? Q+ m2
? Dare the real soft SUSY–breaking squark-mass parameters, Aband
? U+ m2
? D+ m2
? Uand m2
Atare the complex soft SUSY–breaking trilinear parameters, and µ is the complex super-
The mass matrix of the Higgs bosons (at vanishing external momenta) is then given by
the second derivatives of the potential, evaluated at its minimum point
(φ1, φ2, a1, a2) = (?φ1?, ?φ2?, ?a1?, ?a2?) = (v cosβ, vsinβ, 0, 0),
where v = (√2GF)−1/2≃ 246 GeV. The massless state G0= a1cosβ−a2sinβ is the would–
be–Goldstone mode to be absorbed by the Z boson. We are thus left with a mass–squared
and symmetric, i.e. it has 6 independent entries. The diagonal entry for the pseudoscalar
component a reads:
where mAis the loop–corrected pseudoscalar mass in the CP invariant theories. The CP–
violating entries of the mass matrix, which mix a with φ1and φ2, are given by
Hfor three physical states, a(= a1sinβ+a2cosβ), φ1and φ2. This matrix is real
Xtcotβ − 2|ht|2Rt
− ˆ g2cotβ logm2
ˆ g2− 2|hb|2?
ˆ g2− 2|ht|2?
Xbtanβ − 2|hb|2Rb
− ˆ g2tanβ logm2
where g(x,y) = 2 − [(x + y)/(x − y)]log(x/y). The size of these CP–violating entries is
determined by the re–phasing invariant quantities
which measure the amount of CP violation in the top and bottom squark–mass matrices.
In the CP–conserving limit, both ∆˜tand ∆˜bvanish, leading to |m2
definition of the mass–squared m2
well as the other CP–preserving entries of the mass matrix squared M2
Ref. . The real and symmetric matrix M2
Our convention for the three mass eigenvalues is mH1≤ mH2≤ mH3.
12| sin(ξ + θ12) = 0. The
Aand the dimensionless quantities Xt,b, Rt,band R′
H, can be found in
Hcan now be diagonalized with an orthogonal
The loop–corrected neutral–Higgs–boson sector depends on various parameters from the
other sectors of the MSSM; mA, tanβ, µ, At, Ab, the renormalization scale Q, and the real
soft–breaking masses, m˜Q, m˜U, and m˜D, as well as on the complex gluino–mass parameter
M? gthrough one–loop corrections to the top and bottom quark masses . Noting that
combinations Atµeiξand Abµeiξ, see Eq. (9), we take for our numerical analysis the following
set of parameters:
the size of the radiative Higgs sector CP violation is determined by the rephasing invariant
|At| = |Ab| = 1 TeV,
M? Q,? U,? D= |M? g| = 0.5 TeV,
under the constraint;
|µ| = 2 TeV,
ξ + Arg(µ) = Arg(M? g) = 0,(11)
Φ ≡ Arg(Atµeiξ) = Arg(Abµeiξ). (12)
We vary the common phase Φ as well as mAand tanβ in the following numerical studies.
Our choice of relatively large magnitudes of |Atµ| = |Abµ| enhances CP–violation effects in
the MSSM Higgs sector1.
1Our choice of the set of parameters satisfies the necessary condition to avoid a color and electric–
charge breaking (CCB) minimum in the direction |?Q| = |?U| = |H0
to those of M? Q,? U,? Dcould give rise to a dangerous CCB minima in the potential which could be
presence of the non–trivial CP–violating mixing among the neutral Higgs bosons deserves further
2| : |At|2≤ 3(M2
But, according to the more general study , our relatively large values of |At,b| and |µ| compared
deeper than the electro–weak vacuum. Therefore, a detailed study of the CCB minima in the
Before studying the CP–violation effects on the neutral and charged Higgs–boson decays,
it is worthwhile to examine the present experimental constraints on the above parameter
values (11). The charginos, neutralinos, and squarks of the first two generations are suffi-
ciently heavy for the parameter set (11). The lightest squark is the lighter top squark˜t1, the
mass of which can be as low as 200 GeV for tanβ = 4 and Φ = 0o. The CP–violating phase
could weaken the LEP lower limit on the lightest Higgs boson mass significantly [17,18]. In
our analysis we show our results when the lightest Higgs–boson mass is above 70 GeV.
The one–loop effective couplings of the CP–odd components of the Higgs boson to the
gauge bosons give rise to the electron and neutron EDM’s  at two–loop level. The effects
could be significant for large tanβ at large |At|,|Ab| and |µ| so that some region of our
parameter space is already excluded by the present 2σ upper bounds on the electron and
neutron EDM’s : |de| < 0.5×10−26ecm and |dn| < 1.12×10−25ecm, respectively . The
dark–shaded region in Fig. 1 is excluded by the electron EDM constraint in the (Φ, mA)
plane for tanβ = 4 and 10. The unshaded regions give mH1< 70 GeV. The EDM con-
straints are avoided only :n the lightly shaded region. The excluded region becomes larger
for larger tanβ. Even for tanβ = 4 as shown in Fig. 1, some parameter space with small
mAand large CP–violating phase can be excluded by the EDM constraint.
It should be noted, however, that the strong two–loop EDM constraints due to the
one–loop effective couplings of the CP–odd components of the Higgs bosons to the gauge
bosons may not be valid if there appears cancellation among different EDM contributions.
Such cancellations may occur between one– and two–loop contributions, or among two–loop
contributions themselves [18,21]. In fact, the excluded regions of Fig. 1 disappear if such
cancellation takes place at 50 % (20 %) level for tanβ = 4 (tanβ = 10). In this paper, we
show our results for the whole parameter space (11).
III. NEUTRAL HIGGS BOSON DECAYS
In this section we discuss the phenomenological consequences of the CP–violating Higgs–
boson mixing on the total decay widths and decay branching fractions of the neutral Higgs
bosons. We choose tanβ = 4 throughout this section, which leads larger CP–violating ef-
fects than the tanβ = 10 case .
The most important decay channels of the Higgs bosons are two–body decays into the
heaviest fermions and bosons because the Higgs couplings are proportional to the particle
masses. We refer to Ref.  for explicit forms of the two–body decay widths of each Higgs
boson and the relevant interaction Lagrangians.
The Higgs boson decays into virtual gauge bosons V(∗)V(∗)are also important for the
Higgs bosons of the intermediate mass region, 110 GeV<
of the importance of these 3–body and 4–body decay modes, we extend the previous work
 to include the Higgs–boson decays into virtual gauge boson pairs and those into a lighter
Higgs boson and a virtual Z boson. The partial decay width of Hi→ V(∗)V(∗)is given by
∼150 GeV [22–24]. Because