Enhancement of Br(B_d -> mu^+mu^-)/Br(B_s -> mu^+mu^-) in Supersymmetric Unified Models

0.5 MB·English

by  Bhaskar Dutta

Enhancement of Br(B → µ+µ−)/Br(B → µ+µ−) in Supersymmetric Unified Models
d s
Bhaskar Dutta1 and Yukihiro Mimura2
1Department of Physics and Astronomy, Mitchell Institute for Fundamental Physics and Astronomy,
Texas A&M University, College Station, TX 77843-4242, USA
2Department of Physics, National Taiwan University, Taipei 10617, Taiwan
We explain the 2.3σ deviation in the recent measurements of the neutral B mesons decay into
muon pairs from the standard model prediction in the framework of supersymmetric grand unified
models using anti-symmetric coupling as a new source of flavor violation. We show a correlation
between the Bd → µ+µ− decay and the CP phase in the Bd → J/ψK decay and that their
deviationsfromthestandardmodelpredictionscanbeexplainedaftersatisfyingconstraintsarising
from various hadronic and leptonic rare decay processes, B-B¯, K-K¯ oscillations data and electric
5
dipole moments of electron and neutron. The allowed parameter space is typically represented by
1 pseudoscalar Higgs mass mA ≤ 1 TeV and tanβH(≡ vu/vd) <∼ 20 for squark and gluino masses
0
around 2 TeV.
2

r PACSnumbers: 12.10.Dm,12.10.Kt,12.60.Jv,12.15.Ff
p
A
I. INTRODUCTION measurements provide us a direction in which the SM
9
canbe extendedtothemodelsbeyondSM[4]. The devi-
2
Therecentmeasurementsofthebranchingfractionsof ation from the SM prediction is not very significant sta-
] the rare B meson decays, B0 →µ+µ− and B0 →µ+µ− tistically at present, however,it is meaningful to investi-
h showcase impressive achievesments of the LHdC experi- gate the models which canenhance the ratio R since the
p
ments [1]. The ratios of the experimental measurements usual source of flavor chaining neutral currents (FCNC)
-
p and the standard model (SM) predictions [2] are does not produce any enhancement naturally. In this
e paper, we suggest a possible source to explain the en-
h Br(B →µ+µ−) = 0.76+0.20, (1) hancement of the ratio naturally in the supersymmetric
[ s exp/SM −0.18
2 Br(Bd →µ+µ−)exp/SM = 3.7+−11..64. (2) (oSfUthSeYm)ostdaenlsdainrdthmeopdoesl,siabnleduinnvifiesetdigfartaemtehweoimrkps,liscuacthionass
v SU(5) and SO(10) grand unified models.
Both measurements are consistent with the SM predic-
4
tions within the errors, though Br(B → µ+µ−) seems InordertomodifytheratioRcomparedtotheSMpre-
4 d
0 to be a bit larger than the SM prediction. diction, one needs a new type of FCNC source which is
2 The ratio of the fractions, different from Cabibbo-Kobayashi-Maskawa (CKM) fla-
0 vor mixings. The main concerns regarding the enhance-
1. R≡ Br(Bd →µ+µ−), (3) ment of R are the followings:
0 Br(Bs →µ+µ−)
5 1. How natural is that to have a larger b → d transi-
1 has less theoretical errors in the SM compared to each
tion compared to the b →s transition in the pres-
: fractionbecause the ratioofthe decayconstantshas less
v ence of anew FCNC sourceto enhance R? Infact,
ambiguity compared to each decay constant in the lat-
i the B -B¯ mixings and the B → J/ψφ decay are
X tice calculation. The prediction for the SM (and for the s s s
consistentwiththe SMpredictions[5]anditseems
r models with minimal flavor violation [3]) is
a that there is not a large source of FCNC in the
τ M f2 V 2 b→s transition.
RSM ≃ τBd MBd fB2d (cid:12)(cid:12)Vtd(cid:12)(cid:12) , (4)
Bs Bs Bs (cid:12) ts(cid:12) 2. The mass difference of B and the CP violation
(cid:12) (cid:12) d
wcohnesrteanτBt,ofMthBe, arensdpefcBtivaeremtheseolnifse,taimnde,[m1,a2s]s, and decay imneathsuereBmd-eBn¯tdsmofixtinhgesBfrdo-mB¯dthoescitlhlaetieoxnpserainmdentthael
B →J/ψK decayareconsistentwiththeSMpre-
d
R =0.0295+0.0028. (5) diction. How can large modifications of them be
SM −0.0025
avoided if the Br(B → µ+µ−) is enhanced by a
d
The ratio using the experimental measurements is new FCNC source?
R =0.14+0.08, (6) The SM prediction of sin2β has a slight differ-
exp −0.06
ence from the experimental measurements1 from
andtheexperimentalresultshowsdeviationfromtheSM
prediction at 2.3σ.
These rare decays are induced radiatively in the SM,
andthus,theyaresensitivetothenewphysics,andtheir 1 Recently, LHCbreleasedtheirnewanalysisoftheCPviolation
2
the B →J/ψK decay [6]: squarks and gluino are O(10) TeV, it is hard to extract
d
the off-diagonalelements from the flavordata. However,
sin2β = 0.692+−00..002108 (BaBar & Belle exp.), (8) if the squark and gluino masses are about 2 TeV, the
sin2β = 0.774+0.017 (SM prediction). (9) scalartrilinear coupling A0 has to be large (∼ 5 TeV) to
−0.036
obtain the Higgs mass to be 125 GeV, and then, the off-
Canthe slightdifference be consistentwitha mod- diagonalelementsaregenerated(evenifm0 issmall)and
ification of R? the FCNCs are induced slightly. Therefore, the SUSY
contribution can be consistent with the experimental re-
3. The experimental results of the b → sγ and b → sults of many ofthe FCNC processes,but a slightexcess
dγ decays are consistent with the SM prediction. canbeobservedinaprocesswhoseamplitudecanhavea
The ratio of Br(b→dγ)/Br(b→sγ) in SM is also enhancement factor. We remark that the circumstances
relatedto|Vtd/Vts|2 uptohadronicuncertainty[8]. are changed from the literatures a few years ago.
Theratio,byusingtheexperimentalmeasurements
TheRGE-inducedoff-diagonalelementsarecharacter-
[9,10],isBr(b→dγ)/Br(b→sγ)=0.040±0.009± ized by YY†, and it can be parameterized as
0.010. How natural can the enhancement of B →
d
µ+µ− be without enhancing b→dγ? YY† ∝Udiag.(k ,k ,1)U†, (11)
1 2
whereU isadiagonalizingunitarymatrixofY,andk ,k
1 2
II. FCNC INDUCED BY ANTI-SYMMETRIC are the ratios ofeigenvalues of YY†. Using usualmixing
COUPLINGS
parameterization in U, the off-diagonal elements can be
expressed as
In SUSY models, too much FCNCs are generated in
general, and thus, the flavor universality of the SUSY 1
M2 ∝− sin2θ , (12)
breaking mass parameters are often assumed. In such a 23 2 23
framework,therenormalizationgroupevolutioncangen- 1
M2 ∝− k sin2θ sinθ +eiδsinθ cosθ , (13)
erateoff-diagonalelementsinthesfermionmassmatrices 13 2 2 12 23 13 23
andFCNCsareinduced. IftheCKMquarkmixingisthe 1
onlysourcetogeneratetheoff-diagonalelements,Risnot M122 ∝−2k2sin2θ12cosθ23−eiδsinθ13sinθ23, (14)
modified even though the individual branching fractions
can be modified. In unified models, new particles can where the hierarchy of eigenvalues k ≪ k ≪ 1 is as-
1 2
propagate in the loops and it can generate a new type sumed. The popular source of the flavor violation is
of flavor violation source [11–13]. In simple models, this the Dirac neutrino Yukawa coupling matrix Y , which
ν
new FCNC source can induce b-s transitions, and thus, can contain the large mixing angles realigning to neu-
the ratio R is rather reduced. In this paper, we suggest trino mixings. In SU(5) GUT models, Y can also in-
ν
a model to provide a possible explanation for enhancing ducetheoff-diagonalelementsintheright-handeddown-
R. typesquarkmassmatrixviacoloredHiggsloopdiagram.
In general, the Yukawa coupling Yij to the quarks can Thus, in the popular scenario, the b-s FCNC is induced
induceoff-diagonalelementsinthesquarksmassmatrices relating to the large atmospheric neutrino mixing. How-
by RGE in the form of ever, it turns out that via the measurements of B -B¯
s s
oscillations the new FCNC contribution in the mixing
C M
(M2) =− Y Y∗(3m2+A2)ln ∗ , (10) amplitudeshouldbesmall[5]. Inadditiontothat,the12
q˜ i6=j 8π2 ik jk 0 0 MX and13elements arenaivelysameorderif the mixing an-
glesinU arerelatedtotheneutrinomixings,andthusthe
where m is a universal scalar mass, A is a universal
0 0
large b-d FCNC needs a cancellation between two terms
scalar trilinear coupling, M is a cutoff scale, M is the
∗ X in M due to the experimental results of K-K¯ mixing.
mass of a heavy field which propagate in the loop, and 12
Surely,themixinganglesinY isnotdirectlysameasthe
C is a group weight factor. It is important to note that ν
neutrino mixing since the neutrino mass matrix is pro-
thegluinoandsquarkmassesshouldbeheavyduetothe
portional to Y M−1Y†, where M is the right-handed
LHCresults,andthus,theamountoftheinducedFCNC ν R ν R
neutrinomassmatrix. Therefore,therecanbeasolution
becomes less. The discovery of the 125 GeV Higgs bo-
to enlarge the ratio R for the B → µ+µ− decays, but
sonalso pushes up the squarkmasses. If the mass of the d,s
one should admit that it is not a natural solution in this
popular source of the Dirac neutrino coupling. We thus
suggest a new source of flavor violation to enlarge R.
intheBd→J/ψK decay[7]: Wenowconsiderthefollowinganti-symmetriccoupling
matrix h′ under the flavor indices for the left-handed
sin2β=0.746±0.030. (7) quark doublet q:
The world average of the CP phase becomes larger by the new
LHCbresult,andthedeviationfromtheSMpredictionbecomes h′ q q (3,3,−1), or h′ q q (6,1,−1). (15)
less,thoughitisstillasmallervaluethanit. ij i j 3 ij i j 3
3
Here, (3,3,−1) and (6,1,−1) are new fields whose rep- 6.´10-10
3 3
resentations are denoted under the SM gauge group,
5.´10-10
SU(3) ×SU(2) ×U(1) . They canarise in granduni-
c L Y
fied models, SU(5), SO(10), and so on, as we will study
4.´10-10
later. Denoting -LΜ
+Μ
® 3.´10-10
0 a −b Bd
h′ =−a 0 c , (16) HBr 2.´10-10
 b −c 0 
1.´10-10
one obtains
|a|2+|b|2 −bc∗ −ac∗ 0
h′h′† = −b∗c |a|2+|c|2 −ab∗ . (17) 0 2.´10-9 4.´10-9 6.´10-9 8.´10-9
 −a∗c −a∗b |b|2+|c|2  BrHBs®Μ+Μ-L
FIG. 1: Bs → µ+µ− and Bd → µ+µ− induced by the anti-
We then find interesting features in the off-diagonal ele-
symmetric FCNC source are shown. The setup is detailed in
ments arising from the anti-symmetric coupling:
thetext. Thebluepointscorrespondtothecaseofrandomly
generated a,b,c (with phases) using the anti-symmetric cou-
1. In the case of a naive hierarchy |b| < |c| in the
h′ coupling, one obtains an inverted hierarchy in pling, and the green points satisfy K-K¯ mixing data (∆MK
and ǫK). The red point shows theSM prediction.
the off-diagonal elements using the RGEs since
|(h′h′†) |>|(h′h′†) |,andthusitcanbeexpected
13 23
that the b-d FCNC is larger than the b-s FCNC.
2. The magnitudes of two out of three off-diagonal
elements (12, 13 and 23) in h′h′† are correlated.
Forexample,if12elementiszero,oneof13and23
elements of h′h′† is zero. One can easily enhance
b → d transition (but not b → s) after satisfying
K-K¯ data.
These two features nicely explain how R is enhanced
naturally using the RGE-induced FCNC. In order to
illustrate these features, we plot B → µ+µ− vs
d
B →µ+µ− by imposing the anti-symmetric coupling h′
s
(Fig.1). We use universal scalar masses for squark and
sleptonfields,m =2TeVandtheunifiedgauginomass,
0
m =1TeV.TheuniversalscalartrilinearcouplingA
1/2 0
is chosen to make the Higgs mass to be 125 GeV (A ≃
0
5 TeV). However, we use non-universal SUSY breaking FIG. 2: The illustration of the SM and SUSY contribution
Higgs masses, and we choose the Higgsino mass µ = 3 ofthemixingamplitudeofB-B¯ mixinginthecomplexplane.
The detail is explained in the text.
TeV and the CP odd Higgs mass m =1 TeV. The val-
A
ues ofa, b andc are< 1. The ratio ofthe Higgs vacuum
expectation values,tanβ is chosennotto be very large
H
(here weuse tanβ =20)to makeitconsistentwiththe
H andthe massdifferenceofthe B mesonandaCPphase
experimental measurement. We will explain the reason d
of B → J/ψK decay are obtained as ∆M = 2|Meff|,
for these choices later. In this plot, the naive hierarchies d 12
and 2β = argMeff. We show a geometrical illustration
among a, b and c (such as |a|,|b| < |c|) is not assumed 12
in the complex plane of the mixing amplitude M in
to illustrate the second feature. As it is expected, the 12
Fig.2. The magnitude ofMSUSY canbe calculatedwhen
green points (which correspond to the choice of small 12 12
the SUSY particle spectrum is fixed, while the phase of
off-diagonalelement)appearlikeacrossor†symbol. We
MSUSY is free depending on the phase parameter of the
notethateveninthecasewherethereisnonew23FCNC 12
new source for FCNC. Therefore, the arrowheadof Meff
source,B →µ+µ− isenhancedduetothecharginocon- 12
s tracks the circle shown in the figure. We comment that
tribution.
argMSUSY =argMSM issatisfiedinthe caseofminimal
12 12
flavor violation, and thus the CP phase of the mixing
A. Bd-B¯d mixings amplitude is not changed from SM prediction.
To satisfy the experimental results of the B -B¯ oscil-
d d
The B -B¯ mixing amplitude is given as lation,|M1S2USY|hastobesufficientlysmall,butacontri-
d d bution of small size can be expected due to a slight dis-
Meff =MSM+MSUSY, (18) crepancy of the sin2β measurement in Eqs.(8),(9). We
12 12 12
4
remark that the modification of the magnitude of Meff 6.´10-10
12
(i.e., the mass difference of B-B¯ mesons) is expected to
berathersmallinthedirectionofthephasemodification 5.´10-10
by MSUSY as illustrated in Fig.2. On the other hand, to
12 4.´10-10
enhance the ratio R, a sizable SUSY contribution to the -LΜ
Bd → µ+µ− decay amplitude. We need to explain how +®Μ 3.´10-10
such a situation is reproduced by the left-handed quark Bd
FCNC source. We note that the SUSY contribution of HBr 2.´10-10
the box diagram for the B-B¯ mixing amplitude is now
suppressed(roughly 10% of SM contribution) due to the 1.´10-10
LHC constraint of qluino and squarks. The key is thus
how the SUSY contribution of the B → µ+µ− decay is 0
0.5 0.6 0.7 0.8 0.9 1.0
enhanced even when the SUSY particles are heavy ∼ 2
sin2Β
TeV. The SUSY contributions to the B →µ+µ− ampli-
tudes are dominated by the Higgs-penguin diagram[14]. FIG. 3: We show the correlation between Bd → µ+µ− and
TheHiggsFCNCcouplingviathenon-holomorphicfinite Bd-B¯d mixing for the choice of SUSY parameters described
correctionterms due to SUSY breakingareenhancedfor in the text. The blue plots are for the randomly generated
a large tanβ since the mass eigenstates of the down- a,b,c in the anti-symmetric coupling, and the green points
typequarksaHremodifiedbythenon-holomorphiccorrec- satisfy all the experimental data, such as K-K¯ mixing, Bs-
tion terms. As a result, the Higgs-penguin contribution B¯s mixing, and b → dγ, b → sγ. The red point shows the
SM prediction. The dashed lines show the 2σ region of the
can be the same order of the SM contribution even with
experimental measurement of sin2β.
the heavy gluino and squarks masses.
The Higgs FCNC coupling can also contribute to the
B-B¯ mixingamplitudeviathedoubleHiggs-penguinme-
diated diagram [15]. In fact, the SUSY contribution 2 TeV, m1/2 = 1 TeV) in order to make Bs → µ+µ−
MSUSY is enhanced if there are FCNC sources in both consistent with the experiment. Then, the SUSY con-
12
left- and right-handed quarks. However, if it is in only tribution to Bd → µ+µ− amplitude in the case of no
one of left- and right-handed sector, the mixing am- new FCNC source is also small because the ratio of the
plitude is not enhanced and the box contribution be- branching fraction is fixed for the minimal flavor viola-
comes dominant. On the other hand, the amplitudes tion. In that case, the enlarged SUSY contribution of
of B → µ+µ− decay can be enhanced (compared to the Bd → µ+µ− amplitude from the flavor violation is al-
SM amplitude) even if there is only left-handed quark most directly related to the phase in the FCNC source.
FCNCs arising due to the off-diagonal elements in the For making one round of the circle in the M1e2ff plane in
squarkmassmatrices. Since thereareFCNCsoriginated Fig.2,thephaseoftheSUSYcontributionofBd →µ+µ−
from CKM mixings in the left-handed squarks sector, ischangedahalfround. Asaresult,atypicalcorrelation
the off-diagonal elements in the right-handed down-type betweenBd →µ+µ−andsin2βmodificationsisobtained
squarks should not be there in order to naturally satisfy asshowninFig.3. The Fig.3 is drawnby using the same
the experimental results for the B -B¯ mixings and the SUSY parameters before. Interestingly, for smaller val-
d d
phase in the B → J/ψK decay if there is a sizable b- ues of the effective sin2β (which is consistent with the
d
d transition to enhance the amplitude of Bd → µ+µ−. measured value), two distinctive regions of Bd → µ+µ−
If this is the case, the SUSY contribution to the B -B¯ appear,andwe find thatsin2β is decreasedfor the most
d d
mixing amplitude is dominated by a box diagram, and enhanced values of Br(Bd →µ+µ−). We note that such
|MSUSY|/|MSM| is roughly 10% for squark and gluino qualitative behavior (namely, the “shape” of the plots
12 12
masses around2 TeV, whichcan explainthe slight mod- in Fig.3) is not sensitive to the SUSY mass parameters
ification of the CP phase of Bd →J/ψK decay. under the above setup to make Br(Bs → µ+µ−) con-
sistent with the experiment (though the shape can be
The flavor violating mass (i.e., off-diagonal element of
squark mass matrix) is inserted twice in the B-B¯ mix- collapsed depending on the size of the anti-symmetric
FCNC source) as far as the size of MSUSY/MSM is up
ing amplitude from the box diagram, while it is inserted 12 12
to 10% to satisfy the mass differences of B-B¯ mesons.
once in the Higgs-penguin diagram for the B → µ+µ−.
This can be easily understood by the simple geometrical
Therefore,thephasesoftheSUSYcontributionstothose
explanationaboveandthereisonlyonephaseinthenew
two amplitudes are different but related. The experi-
left-handed b-d FCNC.
mental result of B → µ+µ− branching fraction is con-
s
sistent with the SM prediction. Therefore, we choose
the SUSY parameters to make the SUSY contribution
to B → µ+µ− less if the new FCNC source is absent B. Constraints from b→dγ/b→sγ
s
(namely, at the center of the cross in Fig.1). More con-
cretely, for example, we choose tanβ to be a value for The b → dγ and b → sγ processes are also important
H
benchmark SUSY mass parameters (m =1 TeV, m = for constraining the flavor violations beyond the stan-
A 0
5
dard model. Even in the minimal flavor violation, each
c.c. SU(5) SU(5)×U(1)X SO(10)
branching fraction can be modified compared to the SM
prediction, but the ratio of the fractions is same as the (qq)a (3,3,−13) qℓ 45 (45,−2) 120
SM.IftheratioofthebranchingfractionsofBd →µ+µ− (qq)a (6,1,−13) ucdc 45 (45,−2) 120
and Bs → µ+µ− is modified, the ratio of the branching quc (8,2,12) qdc 45 (5,2) 120
fractionsofb→dγ andb→sγ isalsomodifiedinprinci- qνc (3,2,−1) ℓdc 10 (45,−2) 120
6
ple. The experimental measurements of those branching qec (3,2,−7) ℓuc 45 (10,−6) 120
6
fractions are consistent with the SM prediction within
the experimental errors. Since the CP phases of the fla-
TABLE I: Five candidates for the anti-symmetric bi-fermion
vor violating decays are not yet observed, we can have
couplingtoenhancetheratioRinunifiedmodels. TheHiggs
solutions for the partial decay widths to satisfy the ex-
representation and bi-fermion of its conjugate representation
perimental results, even though there are sizable contri-
are also listed.
bution to the amplitudes from new physics. However, if
the experimental results are naturally satisfied, the new
physics contribution should be small. The amplitude for
the b → qγ (q = d,s) process is roughly proportional to should choose another gauge symmetry in the same row
tanβ . Therefore, if tanβ is not as large as 30-50,the of the list.
H H
SUSYcontributioncanbesmallevenifthesquarkmasses
As described, the right-handedFCNC shouldbe small
are then at the edge of the current LHC bounds in the duetotheconstraintsarisingfromtheB -B¯ mixingam-
minimal supergravity scenario. The amplitudes for the s s
plitudes. Since each Higgs representation has a conju-
B →µ+µ− processis proportionalto tan3β /m2, and
q H A gate representation which can also have bi-fermion cou-
thus, the SUSY contribution can be comparable to the
pling,welistthecorrespondingconjugatebi-fermioncou-
SM prediction for smaller CP odd Higgs mass m < 1
A plings. The conjugate bi-fermion couplings include the
TeVevenforsmalltanβH <20. Thesearchprospectfor right-handeddown-typequarkdc,barring(3,3,−1)and
a CP odd Higgs boson is given in [16, 17]. 3
(3,2,−7). In SU(5) or flipped-SU(5) model, the con-
We note that for the minimal supergravity SUSY 6
jugate bi-fermion couplings are 10·5·45 and they are
breaking boundary conditions, where the SUSY break-
not necessarily unified to the anti-symmetric coupling,
ing Higgs masses are same as the other SUSY breaking
and the right-handed FCNC can be free in principle.
scalar masses at the grand unified scale, m is roughly
A
In SO(10), the conjugate coupling matrices are unified
sameasthesquarkmasses(exceptforlargetanβ ∼50).
H to the 120 Higgs coupling, and thus, the antisymmetric
Therefore,inordertoobtainlargeRwithnaturalfitsfor
couplings are naively given by (3,3,−1) and (3,2,−7)
b → dγ/b → sγ, we need the non-universal Higgs scalar 3 6
reps in SO(10) model. However, since the same reps.
mass scenario for the SUSY breaking.
are included in 126 and 126 (45⊂126, 45⊂126, and
45+45⊂120)andtheycanmix,thelinearcombination
III. UNIFIED MODELS AND IMPLICATIONS of the light fields to generate the FCNC can be different
betweenthe conjugateandunconjugate reps.,by adjust-
The fields (3,3,−1), (6,1,−1) which provide the an- ing the λ120·126·210 and λ¯120·126·210 couplings
3 3 using λ≫λ¯. Therefore, in general, all the five cases are
tisymmetric couplings to the left-handed quark doublets
possible in SO(10).
can be unified with the Higgs representations in unified
theories, such as SU(5) and SO(10). In SU(5), The (3,3,−1) +c.c. can give rise to the proton de-
3
cay operator qqqℓ, and it may not be a good choice to
10×10=5¯s+45a+50s, (19) makethisrep. lighttogenerateFCNC.Inflipped-SU(5),
(3,2,−1)+c.c. have the same quantum numbers as the
6
and in SO(10),
would-be-Goldstone modes to be eaten by the SU(5)
gaugebosons. Therefore,in the flipped-SU(5)-like vacua
16×16=10 +120 +126 , (20)
s a s in SO(10), this rep. can be a good candidate to gener-
atetheFCNC.Wepointoutthat(6,1,−1)and(8,2,1)
where s and a stand for symmetric and anti-symmetric, 3 2
respectively. Therefore,theYukawacouplingswith45in reps. aregoodcandidatestoincreasetheunificationscale
SU(5)and120inSO(10)canprovidetheanti-symmetric and relax the bound due to the proton lifetime [13].
sources for the FCNCs. We note that the 45 rep. in SU(5) and 120 rep. in
In Table 1, we list five possible bi-fermion couplings SO(10) contain the MSSM Higgs doublets and the anti-
to the Higgs representations for the anti-symmetric cou- symmetriccouplingisapartofthelinearcombinationof
plings to generate the off-diagonal elements in the left- the Yukawa couplings to generate the quark and lepton
handed squarks in SU(5), flipped-SU(5) (whose gauge masses. Since the mixings of the doublets are multiplied
symmetry is SU(5)×U(1) ) and SO(10). If the Higgs in the linear combination of the Yukawa couplings, the
X
representationis not 45(for example, 10 for (3,2,−1)), original anti-symmetric couplings can be O(1) and can
6
the Yukawa coupling is not anti-symmetric, and one provide large off-diagonal elements via RGE.
6
A. Neutron and electron EDM the currentexperimentalbound |d |<8.7×10−29 e·cm
e
[19].
The enhancement of the ratio R can impact the t →
uγ(g) and τ → eγ decays rather than the t → cγ(g)
and τ → µγ decay processes. However, both t → cγ(g) IV. CONCLUSION
and t → uγ(g) branching fractions are tiny due to the
current bound on gluino and squark masses, and it will
In conclusion, the anti-symmetric Yukawa interaction
be hard to observe them. The τ → eγ process can be
as a new source of FCNC can explain the enhance-
generated for (3,3,−1) and (3,2,−7) couplings. If the
3 6 ment for the ratio of the branching fractions Br(Bd →
13 off-diagonal element in the left-handed slepton mass µ+µ−)/Br(B →µ+µ−) and the deviation of the exper-
s
matrix is turned on, the chargino loop contribution can
imental result from the SM prediction of the CP phase
generate the branching fraction of τ → eγ to be several
in the B → J/ψK decay. The new interactions can be
times 10−9, by using the parametersfrom Figs. 1 and 2. d
described by grand unified models, e.g., SO(10), SU(5),
The other impact of 13 generation mixings is that
flipped SU(5) etc. The enhancement of the ratio and
they can generate neutron and electron electric dipole
natural realization of the b → dγ and b → sγ data force
moments (EDM). The up and down quark EDM can
the choice of the CP odd Higgs mass to be less than 1
be induced from the chargino diagrams due to the 13 TeVandtanβH <∼20forsquarkandgluinomassestobe
off-diagonalelementsinleft-handed squarkmassmatrix.
around2TeV.Theallowedparameterspacesatisfiescon-
SinceV orV ismultipliedtotheamplitude,theSUSY
ub td straints arising from various hadronic and leptonic rare
contribution is not very large (∼ 10−28 e·cm), but it is decayprocesses,B-B¯, K-K¯ oscillationsdataandelectric
muchlargerthanthe SMpredictions. If there are13 off-
dipole moments of electron and neutron.
diagonal elements in both left- and right-handed squark
massmatricesduetothe (8,2,1)FCNCsource,the am-
2
plitude can be much enhanced by a gluino diagram, and
V. ACKNOWLEDGEMENT
itcanmaketheneutronEDMcomparabletothecurrent
bound, |d |<2.9×10−26 e·cm [18]. The electronEDM
n
can also be enhanced by a neutralino diagram (for Bino The work of B.D. is supported by DOE Grant DE-
components),ifFCNCcontributionsarisefrombothleft- FG02-13ER42020. The work of Y.M. is supported by
andright-handedcharged-sleptonmassmatricesinduced the ExcellentResearchProjectsofNationalTaiwanUni-
by(3,2,−7)+c.c.couplings,anditcanbecomparableto versity under grant number NTU-EPR-104R8915.
6
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