Baryogenesis from top squark transport

6 Pages·0.13 MB·English

by  Mayumi Aoki

Baryogenesis from top squark transport
Mayumi Aokia
8 Graduate School of Humanities and Sciences
9
Ochanomizu University
9
Otsuka 2-1-1, Bunkyo-ku, Tokyo 112, Japan
1
E-mail: [email protected]

n
a NoriyukiOshimo
J
Institute for Cosmic Ray Research

4 University of Tokyo
1
Midori-cho 3-2-1, Tanashi, Tokyo 188, Japan

E-mail: [email protected]
1
v
Baryon asymmetry of the universe is generated in the supersymmetric standard
6
model (SSM) through the charge transport mechanism mediated by top squarks.
9
NecessaryCP violationoriginatesfromacomplexphasecontainedinmass-squared
2
matrices of squarks and sleptons. This complex phase also gives contributions
1
to the electric dipole moments (EDMs) of the neutron and the electron. The
0
amountofinducedbaryonasymmetryisconsistentwithitsobservedvaluewithin
8
reasonable ranges of SSM parameters. The EDMs are predicted to be slightly
9 smallerthantheirexperimentalupperlimits.
/
h
p
- Baryon asymmetry of the universe may be produced at the electroweak
p phase transition 1, since all the necessary conditions for baryogenesis seem
e
to be satisfied within the framework of electroweak theories. However, CP
h
: violation in the standard model (SM) arising from the Kobayashi-Maskawa
v
phase is not large enough to produce a sufficient amount of asymmetry. An
i
X extension of the SM is necessary to describe baryogenesis.
r In this note we discuss baryogenesis at the electroweak phase transition,
a
assuming the supersymmetric standard model (SSM) based on N = 1 super-
gravity coupled to grand unified theories. This model, which is one of the
most plausible extensions of the SM, has new sources of CP violation needed
2
forbaryogenesis. Itisshown thatasufficientlylargeamountofbaryonasym-
metry is producedthroughthe chargetransportmechanism3 mediatedby top
squarks. A complex phase in the mass-squared matrix of top squarks is the
origin of CP violation. This CP-violating phase also contributes to the elec-
tric dipole moments (EDMs) of the neutron and the electron. The EDMs are
predicted to have fairly large values around their experimental upper limits.
The SSM has severalcomplex parameters in addition to the Yukawa cou-
aResearchFellowoftheJapanSocietyforthePromotionofScience.
1
pling constants for quarks and leptons. By redefining the phases of particle
fields, without loss of generality,we can take as the physical complex parame-
ters a Higgsino mass parameter m for the bilinear term of Higgs superfields
H
in the superpotential and several dimensionless coupling constants A for the
f
trilinear terms of scalar fields which break supersymmetry softly. We express
these parameters as m =|m |exp(iθ) and A =A=|A|exp(iα). Since A
H H f f
are considered to have the same value of order unity at the grand unification
scale, their differences at the electroweak scale are small and thus can be ne-
glected. Thephaseθiscontainedinthecharginoandneutralinomassmatrices
and the squark and slepton mass-squared matrices. The phase α is contained
only in the latter.
The new sources of CP violation in the SSM give contributions to the
EDMs of the neutron and the electron at the one-loop level through diagrams
in which charginos, neutralinos or gluinos propagate together with squarks
or sleptons. If the CP-violating phase θ is of order unity, these EDMs receive
contributionsdominantlyfromthecharginodiagrams. Fromexperimentalcon-
straints on the EDMs, the masses of squarks and sleptons are predicted to be
largerthan1TeV4. Inthiscase,topsquarksareoutofthermalequilibriumat
the electroweak phase transition, and thus cannot mediate the charge trans-
portmechanism. Weassumethatthephaseθissufficientlysmallerthanunity,
making the charginocontributions to the EDMs negligible. Then, sizable new
CP-violating phenomena can only be induced by the phase α. The neutron
andelectronEDMsreceivedominantcontributionsrespectivelyfromthegluino
andneutralinodiagrams,leadingtorelaxedconstraintsonthemassesofR-odd
particles4. A recentanalysisshows5 that evenif the phaseαis oforderunity,
squarks and sleptons are allowed to have masses of order 100 GeV under the
conditions mH ∼ 100 GeV and m˜2 > 500 GeV, m˜2 being the SU(2) gaugino
mass.
For the charge transport mechanism to work, the electroweak phase tran-
sition has to be strongly first order. Accordingly, the Higgs potential is con-
strained,leadingtoanupperlimitforthemassofaHiggsboson. Althoughthis
limit in the SM is not compatible with experimental results, that in the SSM
has not yet been ruled out. Furthermore, if a top squark is light, quantum
corrections make it easy for the Higgs potential to yield a phase transition
of strongly first order. We thus assume an electroweak phase transition of
strongly first order in the following discussions.
At the electroweakphase transition, bubbles of the brokenphase nucleate
inthe SU(2)× U(1)symmetric phase. Neglectinggenerationmixings,the left-
handed top squark t˜ and the right-handed top squark t˜ are in mass eigen-
L R
states in the symmetric phase, where the vacuum expectation values (vevs)
2
v1 and v2 of Higgs bosons vanish. In the broken phase and the bubble wall,
they are mixed to form mass eigenstates, owing to non-vanishing vevs. At
the bubble wall, t˜ coming from the symmetric phase can be reflected to be-
L
come t˜R, and vice verse. The mass eigenstates of top squarks t˜1 and t˜2 in the
broken phase can be transmitted to the symmetric phase and become t˜ or
L
t˜ . Intheseprocesses,the complexphaseαinthe masssquared-matrixoftop
R
squarksinducesCP violation,causingdifferencesinreflectionandtransmission
rates between CP conjugate processes. Although other squarks and sleptons
alsohaveCP-violatingratesforthe transitions,the resultantasymmetriesare
neglected because of the small Yukawa coupling constants of corresponding
quarks and leptons.
The transition rates at the wall are obtained by solving Klein-Gordon
equations. For the profile of the bubble wall, we assume a hyperbolic-tangent
dependenceofpv12+v22 onthespacecoordinate,changingfrom0tothevalue
ofthebrokenphase. Theratiov2/v1mustalsovaryinthewallforCP violation
to occur. We assume that it changes linearly by ∆(v2/v1)∼1−10. The wall
width δ has been estimated in the SM as δ ∼ 10/T 6, where T stands
W W
for the temperature of the electroweak phase transition. This width generally
becomes thinner if the phase transition is strongly first order.
TheinducedCP asymmetriesofthereflectionandtransmissionratescause
a net flux of hypercharge emitted from the bubble wall into the symmetric
phase. In the symmetric phase, the chemicalpotential µ of the baryonnum-
B
ber is related to the hypercharge density ρ through equilibrium conditions.
Y
Taking the densities for the total baryon number, baryonnumber of the third
generation,andleptonnumbertoapproximatelyvanish,weobtaintherelation
µ = −2ρ /9T2. A net hypercharge density in front of the wall makes µ
B Y B
non-vanishing, which favors a non-vanishing value of the baryon number.
The baryon number changes through an electroweak anomaly. This rate
is notsmall in the symmetric phase,contraryto its negligible smallness in the
brokenphase. Assuming detailed balance for the transitions among the states
of different baryon numbers, the rate equation of the baryon number density
ρ is given by dρ /dt = −(Γ/T)µ , Γ = 3κ(α T)4, where Γ denotes the
B B B W
rate for the transition and κ is estimated as 0.1−17. Solving this equation,
the ratio of the baryon number density to the entropy density s is given by
ρB/s = 15κα4WFYτT/π2g∗vWT2, where g∗ represents the relativistic degree
of freedom for the particles in thermal equilibrium, τ is the time which the
T
carriers of the hypercharge flux spend in the symmetric phase before being
capturedbythewall,v isthevelocityofthewall,andF isthehypercharge
W Y
flux emitted from the wall.
We now calculate the baryon asymmetry for θ ≪1 and α∼1. The mass
3
parameters for squarks and sleptons are taken to be of order 100 GeV. The
Higgsinomassparameter|m |issmallerthanoraroundthesemassparameters
H
to have a neutralino lighter than the squarks and sleptons, as required on
cosmological grounds. For definiteness, we take g∗ = 214.75, where all the
particles excluding the gluinos are taken into account. The time τ may be
T
approximated by the mean free time of the carriers of the hypercharge flux.
A rough estimate gives τ ∼ 10/T for quarks8, which is considered to be
T
applicable to squarks. The wall velocity is estimated as v = 0.1−16. The
W
temperature T is of order 100 GeV.
−11
The obtainedratioofbaryonnumberto entropyisρ /s=(1−5)×10
B
forκ∼1,whichiscompatiblewiththeobservedvalue. Thesignofρ depends
B
on the phase α and on whether the ratio v2/v1 increases or decreases in the
wall. If the phase α becomes of order 0.1, it is difficult to produce a sufficient
degree of asymmetry. The value of κ should also be of order unity.
The CP-violatingphase α induces the EDMs ofthe neutron andthe elec-
tron,respectively,throughthegluinoandtheneutralinodiagrams. Thegluino
mass is determined by the SU(2) gaugino mass m˜2. The neutralino masses
are determined by m˜2, mH, and the ratio v2/v1. The masses of the squarks
and sleptons of the first generation are roughly the same as those of the third
generation. Among these parameters on which the EDMs depend, the SU(2)
gaugino mass m˜2 is not directly related to the baryon asymmetry. In the pa-
rameterrangeswherethe baryonasymmetrycanbe explained, the magnitude
−25 −26
of the neutron EDM is 10 − 10 ecm for m˜2 = 500−1000 GeV. This
is consistent with the experimental constraint, though not much smaller than
the experimental upper limit. For m˜2 < 500 GeV, the EDM becomes larger
than this limit. The electronEDM is predictedto be 10−26−10−27ecmin the
samerangesofparameters,whichisalsoslightlysmallerthanits experimental
upper limit.
IntheSSMthechargetransportmechanismforbaryogenesiscouldalsobe
mediatedbycharginosorneutralinos. Forθ ∼1,althoughsquarksandsleptons
havetoberatherheavy,thecharginosandneutralinoscanhavemassesoforder
100 GeV. A sufficiently large amount of baryon number is actually produced
by the charginos9. In this case, the neutron and electron EDMs are predicted
to be 10−25 −10−26ecm and 10−26 −10−27ecm, respectively, for the squark
and slepton masses of 1−10 TeV.
In summary, we have studied the possibility of baryogenesis in the SSM.
The baryonasymmetrycanbe producedsufficiently throughthechargetrans-
portmechanismmediatedbytopsquarkswithmassesoforder100GeV,ifone
CP-violatingphaseαisnotsuppressedwhile anotherphaseθ keptsmall. The
EDMs of the neutron and the electron are predicted to have magnitudes not
4
so small compared to their present experimental upper limits.
Acknowledgments
We thank J.W.F. Valle and the staff of the organizing committee for their
kind hospitality. The work of M.A. is supported in part by the Grant-in-Aid
for Scientific Research from the Ministry of Education, Science and Culture
of Japan. This work is supported in part by the Grant-in-Aid for Scientific
Research (No. 08044089, No. 08640357, No. 09246211) from the Ministry of
Education, Science and Culture, Japan.
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ICRR-Report-406-97-29
OCHA-PP-112
(cid:3)
Baryogenesis from top squark transport
y
Mayumi Aoki
Graduate School of Humanities and Sciences
Ochanomizu University
Otsuka 2-1-1, Bunkyo-ku, Tokyo 112, Japan
E-mail: [email protected]
Noriyuki Oshimo
Institute for Cosmic Ray Research
University of Tokyo
Midori-cho 3-2-1, Tanashi, Tokyo 188, Japan
E-mail: [email protected]
Abstract
Baryon asymmetry of the universe is generated in the supersymmetric standard
model (SSM) through the charge transport mechanism mediated by top squarks.
Necessary CP violation originates from a complex phase contained in mass-squared
matrices of squarks and sleptons. This complex phase also givescontributions to the
electric dipole moments (EDMs) of the neutron and the electron. The amount of
induced baryon asymmetry is consistent with its observed value within reasonable
ranges of SSM parameters. The EDMs are predicted to be slightly smaller than
their experimental upper limits.
(cid:3)
To be published in the Proceedings of the International Workshop on Physics beyond the
Standard Model: from Theory to Experiment.
y
Research Fellow of the Japan Society for the Promotion of Science.