Fermi National Accelerator Laboratory


FERMILAB-Conf-99/192-T





B Decays as a Probe of Spontaneous CP-Violation in SUSY Models



Oleg Lebedev

For the CDF Collaboration

Virginia Tech
Blacksburg, Virginia 24061-0435



Fermi National Accelerator Laboratory
P.O. Box 500, Batavia, Illinois 60510





July 1999




Presented at SUSY'99,

Fermilab, Batavia, Illinois, June 14-19, 1999





Operated by Universities Research Association Inc. under Contract No. DE-AC02-76CH03000 with the United States Department of Energy


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p-Conf-99-192-T



B Decays as a Probe of Spontaneous CP-Violation
in SUSY Models


Oleg Lebedev

Physics Department, Virginia Tech
Blacksburg, VA 24061-0435



Talk given at SUSY'99 (Fermilab, IL) and
PHENO'99 (Madison, WI)



Abstract: We consider phenomenological implications of susy models with
spontaneously broken CP-symmetry. In particular, we analyze CP-asymmetries in B
decays and find that the predictions of these models are vastly different from those of the
SM. These features are common to NMSSM-like models with an arbitrary number of
sterile superfields and the MSSM with broken R-parity.




1.Introduction
One of the most fundamental from complex phases in the Higgs
problems of particle physics is VEV's [1]. In supersymmetric
understanding the origin of CP- models, this approach allows to
violation. In the Standard Model significantly reduce the number of
all CP-violating effects are free parameters and to aviod
described via Cabibbo-Kobayashi- excessive CP-violation inherent in
Maskawa mechanism. In this low energy supersymmetry [2]. In
approach, CP-violation originates this work we discuss the CP
from the quark mixing. However, phenomenology of these models
in more general models, the origin which is quite different from what
of CP-violation can be quite one expects in the Standard Model
different. For example, in multi and, thus, allows to distinguish
Higgs Doublet Models, CP- between the two approaches.
symmetry can be broken To begin with, we consider the
spontaneously, that is to say, all NMSSM which has been shown to
CP-violating effects come entirely be the simplest acceptable susy



1


model allowing for spontaneous extracted from the following
CP-violation [3]. The Higgs decays [4]:
neutral components develop the
following VEV's: B \ KS a sin2E (1)
B S+ S- a sin2D
<H1>= v1 , <H2>= v2eiU, BS U KS a sin2J
<N>= nei[ .
If the BL-BH lifetime difference
These complex phases enter the and the tree-penguin interference
left-right squark and gaugino- effects can be neglected, the rate of
higgsino mixings, as well as the the B decays into a final CP-
quark masses. By a universal eigenstate is described by a simple
phase redefinition of the right- formula:
handed quarks and squarks, the
quark masses as well as the gauge *(Bfi) e-*t (1 - sin2Di
interaction vertices can be made sin 'mt) (2)
real. Thus the effect of the
complex VEV's shows up only in Here Di are the angles of the
the Higgs (higgsino) sector and the unitarity triangle. In the SM this
left-right squark mixing.1 This can relation is not exact since the
lead to observable CP-violating interference between the tree and
effects in the quark sector through penguin contributions can be
loop effects involving super- significant. One has to invoke
particles. It has been shown [2] isospin and SU(3) relations among
that with a favorable choice of the different processes to separate
parameters the model can predict these contributions and to
correct values of H and H'. In this determine the angles of the
work, we analyze the implications unitarity triangle more precisely.
of the model for B physics. However, in susy models with
spontaneous CP-violation, relation
(2) is much more precise. This
2. CP-violation in B decays happens due to the fact that the
One of the peculiar predictions of CP-violating contribution comes
the Standard Model is the from the superpenguin diagram
existence of the unitarity triangle. (Fig.1) which is strongly
Information about the angles of suppressed by heavy propagators
this triangle can, for example, be and loop factors. As a result, the
interference between the tree and
1 In general, the left-right squark mixing cannot superpenguin contributions is
be redefined to be real by a universal phase negligible. It is important to note
transformation due to the presence of A-terms.



2


~ ~
W ~ ~
b H Q b W H q




q q
q ~
W b


Fig.1.Dominant CP-violating contri- ~ ~
bution to B decays. b W q
H

that, in our model, the angles of
the unitarity triangle do not have a
process independent meaning. In ~ ~
fact, they are defined by Eq.(2). q H W b
The angles of the unitarity triangle
can be expressed in terms of the
complex phases entering the Fig.2. Dominant CP-violating contri-
mixing and decay diagrams: butions to the mixing (the cross on the
scalar propagator denotes the L-R stop
mixing).
sin2Di = sin(2ID + IM) (3)

Moreover, the NEDM bound
As we have argued above, the constraints the phases quite
decay phase ID is vanishingly severely. As a result, large CP-
small. The mixing phase IM can be violation cannot be accommodated
considerably larger since both the within such models.
SM and susy contribute at one From Eq.(3) one can determine
loop level. In our model, there is a typical values of the angles of the
number of large CP-conserving unitarity triangle. Since I
contributions to 'B=2 operator M does
not exceed 0.1 as required by the
such as the SM box, charged Higgs NEDM, the resulting triangle is
box, and the gluino and chargino either flat or very squashed and
superboxes. All of these non-closing [6]. To be more
contributions interfere construc- quantitative, one can compare the
tively. On the other hand, all but prediction for the angle E with its
the chargino CP-violating contri- SM value. In order for the CKM
butions (Fig.2) are suppressed by approach to be consistent, sin2E
powers of mb / mW [5]. In order to has to be greater than 0.4 (the CP
have a sizeable CP-violation in this asymmetry observed by CDF
model, the existence of relatively Collab. in B decays seems to agree
light susy particles is required.


3


with this prediction). It is parameters of the model, i.e. tanE,
interesting to see how large CP- chargino mass, GIM cancellation
parameter, etc. [5].



sin
z = ,
0 =
.
0 ,
5 tan = ,
1 m =
~ 100 GeV
W


1


d d 0.8
L R
B K S
0.6



g
~ 0.4



0.2
NEDM
m
0 q
~

100 225 350 475 600 Ge V





Fig.4. Regions of the parameter space
allowed by sin2E0.4 and the NEDM.

d L dR
In fact, the same considerations are
~ ~ valid for a more general situation 
W H when one includes more than one
sterile superfield. Even though
Fig.3. The NEDM diagrams allowing to
constrain the phases entering the left- there are many more phases in the
right squark and gaugino-higgsino scalar VEV's, these phases enter
mixings. the NEDM and neutral meson
mixing diagrams in the same
violating phase is required in our combination.
model to reproduce this result and Thus, if the SM prediction for
whether it is compatible with the sin2E gets confirmed, a whole
NEDM bound. An illustrative plot class of susy models with
showing parameter space regions spontaneous CP-violation will be
allowed by sin2E0.4 and the ruled out.
NEDM is given in Fig.4. Another "next-to-minimal" mo-
Apparently, the NEDM and del admitting spontaneous CPV is
sin2E0.4 cannot be accom- the MSSM with broken R-parity.
modated at the same time. It can In general, the sneutrinos can
also be shown that the gap develop complex VEV's and, in
between the upper and lower this case, one effectively deals
bounds does not decrease with a 5 Higgs Doublet Model.
considerably as one varies Besides that, the FCNC are



4


couplings.2 Then, in order to
c produce CP-violation, one would
~ have to make left-right sparticle
d s
R mixing insertions on the
b propagators. Due to the chiral
structure of the R-breaking
interactions, at least two such
c
insertions are required on each
propagator. As a result, CP-
s
violating diagrams get suppressed
c by the fermion mass squared and
e~L can be neglected as compared to
b
their CP-conserving counterparts.
This means that large CP-violation
c
in the B sector (sin2E0.4) cannot
be produced and the model suffers
from the same shortcoming as the
b b ones described previously.
~L To summarize, the SM and susy
models with spontaneous CP-
violation lead to vastly different
d d phenomenology in the B sector.
The latter will be ruled out3 if the
SM prediction, sin2E0.4, is
Fig.5. R-breaking contributions to experimentally confirmed.
B \ KS decay and B-B mixing.

The author is grateful to the
Fermilab Theory Group where part
generated at the tree level. The of this work was done.
diagrams relevant to our
considerations are given in Fig.5.
They are required not to exceed
their SM counterparts. Since we
are interested in CP-violation in
the down type quark sector, we
may neglect the effect of complex 2 Via the O'LQD interactions, the sneutrino
sneutrino VEV's due to the strict VEV's may produce non-universal phases in the
down type quark mass matrix. The effect,
constraints on the absolute values however, is small as explained above.
of the latter (~250 keV) [7] and O' 3 We do not consider the possibility of accidental
cancellations among contributions to the NEDM.
The conclusions would not hold if such cancel-
lations occurred.



5


References


[1] T.D. Lee, Phys. Rev. D 8 (1973) 1226.


[2] A. Pomarol, Phys. Rev. D 47 (1993) 273.


[3] A.T. Davies, C. D. Froggatt, A. Usai, in: Proc. of the Inter. Europhys.
Conf. On HEP, Jerusalem (1997); .


[4] I.I. Bigi, F. Gabbiani, Nucl. Phys. B 352 (1991) 309.


[5] O. Lebedev, .


[6] O. Lebedev, Phys. Lett. B 452 (1999) 294; .


[7] V. Bednyakov, A. Faessler, S. Kovalenko, Phys. Lett. B 442 (1998) 203;
.





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