Kobe KaiseiCollege
Kobe
Kaisei College

Phenomenologyofquarksinglet models
KatsuichiHiguchia Masato Senamib
and KatsajiYamamotoc,

Kbbe Kttisei
Collage,
Kbbe 657-0805
ofLiterat"re,blnstitutefbrCosnricRay Research, U)iiversdyofIbdyo,Chiba277-8582,
aDepartment

eJopaneltrpanCDapartment

Engineeritrg,
1<YotoUhiversity,
606-8501,
K5totoofNueiear

tJopanAbstract
Recent developmentin flavorphysics is described.We show the elementsof the quark mixing
matrix,
Cabibbo-Kobayashi-Maskawa (CKM)
matrixIn addition, we discussthe Bs physics,and then the phe[1,2].
nomenaappearingin quark singlet models.
1. Introduction
The CKM matrix

by a 3 × 3 uniin the Standard Model (SM)is given

tary matrix,

K, K, PZ,
4d Ks Vcb

pJbKM

=:

(1.1)

PIh P'1, P:,
This matrix
tion [3]as

%KM

=

may

be written

by using the Wolfeinsteinparameteriza-

1-A2/2A

AZ3(p-in)-A

1- Z2 /2

AA2

A13(1-p-ii7)
The unitarity
anglesas shown

constraints

are

dAA2

represented+

O(A4) .(L2)1by the six independent tri-in Fig.1.

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bs triangle

bd triangle
i7in7latriangle

sd

.P:,

K,

K,"PZ,
P'lrd

tu triangle

cu triangle

K,'P:,

P:,'C,

P;,7c
r
.

r

PZ,

%Pla

tc triangle

K,'
K,

*P1,

pla

*wr

*Kb

PZ,'PZ,.q

PZb'PZs

K,Z,Si]J]i)#'=)

Z,Pl,

% Pla
-

-

.4

Pts
Fig.1. The CKM

Especially,theunitarity

triangles.

triangle" has been investigatedso far,and"bd

the corre-detemiined experimentally. Each result shows the
successof the SM, but phenomena
by New Physics (NP) may not be
excluded.
Now we are at the stage for precisemeasurementof thistrianFor the Bs physics, the mass
dithreneeAm4 is
gle at the B factories.
experimentally
determined by CDF and DO, and the other parameters wi11
be measured
by LHCb in the near future.
This article is organized
as fbllows.The experimentally
determinedvaluesof the CKM
matrixelements
are reviewed
in Sec. 2. Then, theexperimental
resultsand expectations
fbrthe Bs physics are describedin
Sec.3. In Sec. 4, possible NP in quark singlet models
is discussed.
Sec,5isdevotedto summary.
sponding

elementsare2. The CKM matrix
elements
2-1.The sides
2'1-1･
The magnitudeof Kd isdetermined from the nuclear

IVudl( O' - O' ) andsemileptoni

IK,l=O.97377¢

chargedbeta decayspion decay(n' - rcOe'v) as(nuclearbeta decays)[4,s],± O.OO027

O.O026 (piondecay) [6].
IK,I=O.9728
±

(2.1)

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P decaypion decay

d

u

d

u

e-

e"

v-t

v

c

Fig.2.Nuclearbetadecayand pion decay.

These results
will be small.

agree

with

each

in high accuracy.

other

The effect ofNP

IPlsl

2'i-2.
The most traditional measurementkaon decay(K' -> nOe+v ).Itprovides

ofK, is from the semileptonic

o.oo21 [7].
IVI,l=o.22s7

(2.2)

±

The

other

measurementsfrom the Ieptonic kaon decaysare(K -> "v(7) ),hyperon decays, anddecays. From the kaon decays
the ratio
1PLd1isdeterminedto pro-

hyperon decays,respeetively,
vide
and

T

1Pl.

+O.OO12

lK,1 O･224s-O.O031 (kaondecays)[8],"O,O025 (hyperondecays)[9].
IPZ.l=O.2250
±

These

results

agreewith eachotherin high accuracy.

(2.3)

The effect of NP

wi11be small.

IK,I
lagdlbe2-1.3.

canfrom theextracted

semileptonic

charm

decay

(DO -> zme'v )with IatticeQCD as
O.O08 O.021 [lo].
IPZ,I=O.213
±

(2.4)

±

The diffk)renceof the ratios of the double-muon to single-muontions by neutrino
andantineutrino
beams is proponional toproduc--89-

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B,
Then, using(o.463o.o34) lo-2 [11].
IpinI2
±

==

(2.s)

×

QCD analysis,

the next-to-leading-orderweobtainO.Oll[11].
IVL,1=O.230

(2.6)

±

d

c

e'

Vc

decay (P;F- e"v).

Fig.3.Semileptoniccharm
v, +N

->

#- +c(-> p' +v, )+X

v-, +N->"' +c-(-> u- +v-, )+X

Fig.4.Muon productionsby neutrino

andantineutrino

beams.

'

IL[

2-,-,.
is obtained

17Ly1

M ± decays (rv' -> cS,M-

from the on-shell->liy)as+O.32

IPL,1=

O･94-o.26± O･i3 [i2]･(2.7)

Another determinationis possible from leptonic
the Ds decays (P;-> e'v)
and semileptonic
D decays (D -> Kev,D --->nev ) with lattieeQCD calculation.Itprovides
O.O17 O.093 [13].
IK,1=O.957±

These results

agree

with

each

other,

thus NPwill

affect

not

these

'

processes.
c

(2.s)

±

c

t+

s

e+
I

v

v

Fig.5.LeptonicDs decay(4' -> e"v ). Fig.6.Semileptonicchami

deca:sr(D - Key ).

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2-1-5. K,1
is
IP;bI

from the inclusiveandmeasured

The inclusivedecays(b -> cevM,b

exclusive-> s7)provide

decays of B mesons.

[14]O.7) 10-3,
IK,1=(41.7
±

while

the exclusive

(2.g)

×

decays(B -> D'ev )provide

1K,1:(40.9±1.8)
× 1O".

(2.Io)

is givenas

The averageO.6) 10-3.
iPl,,l=(41.6±

These results

agreewith each

IP:,,lis
IKbl

other.

(2.11)

×NP contribution

wi11be negligible.

2-i-6.

preciselybecause it is hard to distinguishcomb -> u from b -) e transitions. This is due to the smallnessof. Measurementsof the inclusive decayspared withdecays (B-nev) have been per(b -> uev-,b -> s7 ) and exelusivenotmeasured

so

IPZbl

IP;bl

fbrmed. These results

are

shown

in Table 1-1 and 1-2 [15].

from the inclusivedecays [HFAG
2006].
IPZbl
Group(analysis)lV.,I

Table 1-1.

winter

CLEO(endpoint)

4.09± O.48± O.36

BELLE(endpoint)

4.82± O.45± O.30

BABAR(endpoint)

4.41± O.29± O.31

BABA[R(E.,q2)

4.10± O.27± O.36

BELLE(M.)

4.06± O.27± 024

BELLE(m.,g2)

4.37 ± O.46± O.29

BABAR(m.,q2)

4.75 ± O.35± O.32

Average4.45± 020 ± O.26
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Table1-2.IPZb1firomthe exclusive decays [HFAG winter 2006].

lVubl

Group(analysis)Ball-Zwicky(g2<16)+O.55

3.36± O.15-O.37

HPQCD(q2<16)+O.63

4.20±029-Oi43

FNAL(q2<16)+O.65

3.75±O.26-O.43

APE(g2<16)+1.45

3.78± O.26n.67[PZbI

The annihilation
can be used
to constrain
process for B- -T-vDue to the helicitysuppression
term, there is practically no possibility
toof B --> u(e)vat the B factoperfbrm branching fractionmeasurements
ries. The constraint
is givenas(1-m)xL,2IV.,1

GF2 M'2

Iili#

B(B--T-v-)=

M

<26

,

×

10-`[16] (212).'2

The result

of

IKbl

is not precise enough to confirm
room
forNP in these processes.

measurement

prediction. There may

be some
b

T-

"-

v-

Fig.7.Annihilationprosess for B- -->T-vM

IVI,]

2-i-7.
The magriitude

Ama measuredofthe SM.

Pld is determined by the BOB-Ooscillation

frequency

at the B factories.
The resultis

Ania,=O･507±O.O04 ps-i [17].

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O.505± O.O05 ps-i.)
Then,oneobtains=

O.8) 10-3.
IK,1:(7.4±

In the BOBO mixing,
the SM [18].

NP

may

(2.14)

×levelup to 20% ofat the tree

contribute

IP2yl

2-i-8.

The magnitudeofoscillation
freK, is determined by the 19,eBM,O
result from CDF and DO measurements
isquency Am4 . The combined

Am44± o.o7 ps-i[lg].
o12i=17.33tO'(2.ls)

at the B faetories.
A conThis quantity, however, cannot be measured
A,ne, 1 Am4] is instead obtained
strainton[asfrom B-> p(to)7and B-K7

Zdll[Vl,1(IP[dlllP7,])2oc*'+O.O18+O.026lZd1/lv2,1 (exp)=o.1gg-O.025-O.O15[Belle][20],(theo)

1K,11[pj2,l<o.1g[BABrm][21].(2.16)

These results are consistent with the measurements
B mesonmixings.
Possibilityof NP in the neueralhowever, may not be excluded yet.

IK,Iof the above

B meson2-1-g.
There are two measurements
to constrainof R = B(t -> P7b)/B(t Mg) by CDF
the measurement

mixings is,

is
IZbl.one

-->

and

1Pl,
l

+O.48

o.77

-O.24

are expected

-

DO as

(2.17)to r(Z -> bb) as

The other is from the top-loop contribution=

fromobtained[22].
IPI,[>O.78

More precise measurements

neutral[23].

(2.18)

to be performed in future.

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2-2.The complex phases fbrCP violation
2-2-1.fi(q)Measurements of the angle
fiare separated into two classes. One isthe class in which
both tree and penguin diagrams exist for the decaysa charmonium.
The other is the one in which pen(b- c-as)including
guin diagramsare dominant forthe decays (b -> sg4 )ineludinga strange
The' theoreticallycleanest
exampleofquark (no tree levelcontribution).
the fbrmer class is BO --> JlqKO mode ( BO -> J/ipKk and BO -> JlqKi ).
In thismode, we are not suflbred from penguin pollutionbecausethe penas the tree one. This is the so ealled
guin weakphase is the sameplated mode", and precise determinations of sin 2fi are performed at BelleandBABAR. These experimentallymeasuredvaluesof sin2fi agreewitheach other very well. The averagedvalue
is givenas"Gold

sin2fi=O.69± O.03 [HFAG2006].

(2.19)The penguin dominated decay b -> sqq- involvesthe same CKM phaseas the tree leveldecay b-->c-cs. There are a lot of modes
through thisdeeayto measure sin2fi. In table3,the values of sin2P determined fromthese measurements
are shown[24].
In Be-ipKa
at BABAR,
BO->nOKS at BABAR,
BO->toK,at->
BABAR, BOat both,and
BO -K'K-KO
at]3K, at Belle, BO ->zOzOK,BABAR, significant derivations
from the result of the charm decay are
seen.

Especiallyin BO ->zOzOl(k
b

mode,

derivation
exists.

alarge

m

c

b

t

:g:

i
s

s

a
e

Fig.9.Penguindiagramfbr
b-s(b->
sg4)･

Fig.8.Tree diagram fbrb-.s( b -> cds )･-94-

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Table 3.The sin 2P from the penguin decays [HFAG2006i.

Mode
Cf.b->cEstreemode

Group

sin2P

Worldaverage

O.69± O.03

BABAR

O.50± O.25-O.04

Belle

O.44± 027 ± O.05

BO->n'KD

BABAR
Belle

O.36± O.13±O.03
O.62± O.12± O.04

BO->f,K,throughthis
decay

BABAR

O.95 --O.32 ± O.10

Belle

O.47± O.36± O.08

BABA[R

O.35-O.33

Belle

O.22± O.47± O.08

BO->nOnOKs

BABAR-O.84 ± O.71± O.08

BO->tuKs

BABAR± O.02050 -O.38+O.12

Belle

O.95± O.53-O.15

BO-pOKs

BABAR

O.17± O.52± 026

BO->K+K-KO

BABAR

OAI ± O.18± O.07± O.11+O.19

Belle

O.60± O.18± O.04-O.12

BABAR

O.63 -O.32

Belle

058 ± O.36± O.08

Naiveaverage

O.50 ± O.06

Be->J/qKo
BO-ipKO

BO-zOKs

BO-KsKsKs

C £ b-->sgg-penguin

+o.e7

+O.23

+O.30

± o.oa

+O.34

+028

± O.04mode

2-2-2.a(%)
is dominated by the amplitude
with
The decay mode
BO -JlqKO
one weakphase because the penguin diagram ihvolves the same weakphase as the tree diagram. In contrast, the tree and penguin diagrams
contributions
with different
weak phases in B - mprovide comparable

decays.
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Theis extracted
from BO->n'n', BO--nOnO
by using isospinanalysis. A constraint isobtained as

angle

B' --> z'nOa

OO<a<170, 730<a<1800
In spiteand(2.20)[25].

the smallnessof amplitude,
BO -> p'p' provides the besta, FromBO-)p'p-,
BO->pOpeand
precision to determine
B' --> p'pO one obtains with isospinanalysis
of

a=96e

From
with

with
BO -p'nisospinanalysis

BO ->pezO

the above

130 [25],

-17o

± 60

one

[25].

the angle

measurements,(2.21)

BO ->p-n'

and

+27o

a=1130

By combining

±

also

obtains(2.22)
ais determined as [25](2.23)

a=ggo+120.
-9o2-2-3.7(¢ 3)
The angle 7 can be measured
directlyin the tree-Ievel B decays,
which
is unlikely to be affbctedby NP. From the interferenceterms in± -)B
DOK' and B' -> DeK itis extracted as [25],±

7= 680+14o-15o± 130± 110[Belle],7=670 ± 280± 130± 110[BABAR].
The decaysB' - DO'K"

and

B

±

be'K"

->

also

+15o

7= 630-12e [25]'(2.24)

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3. Bs physics
3-1.Am Bs
While the B,OB,O
oscillation
caimotLEP and SLAC, itisrneasured
by CDF

be measured
andin the B factories
at
DO at Tevatoron.The result is.grvenas

Zim4

On the other hand, owing
mated

±

=17.33(3,1)

O.10± O.07 ps-i[17].

to the CKM

unitarityin the SM, Zim4 is esti-

as

+3.6

AnlB.

=17･9-1.4(3.2)

ps-i[261･

be done in B,O ->P,'K"and
statistical
B,O-> D,"K-decays observed at LHCb. The estimated
precibeThen, ifthe measurement
result of AmB. ission mayps'i[27].
inconsistentwith the prediction of the SM, we will expect to see an effectA

precisemoremaymeasurement

-O.Ol

of NP

in this mixing.

3-2. B,O--)}Jlip¢
In the SM, the phasesmall

A of the ll,OR,Omixingasis expected

to be very*

¢ ,=arg

P;b,.lll

K(3.3)=O.04-O

will be measured
Then this phase is sensitive to NP. At LHCb sin 4Z,
fiveyears ofrunning.
sensitivity
up to O.O13 after firstwith

3-3. 7

B,O-> 4K

decays are not sensitive to NP because they occur at thethese decays the phase 7+q istree level in the SM. By measuring
extracted.
In the SM, because q =O,thephase 7+q simply corre±
spondsto 7 B, --> P,K is also dominated by the same tree diagram as
7.
This decay provides a clean
measurement
ofB,e->DO,KO.
±

.

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B.O -K'K-

is dominated by a penguin diagram.The measurement
7 with thisdecay isthus sensitive to NP.
3-4. B,O-> pt'ptIn the SM, BR(B," -to be very smallp'"-) is estimatedofas± O.1) 10"9 [28].
(3.5

(3,4)

×

limiton the branchingratio at present comes from theat Tevatron, reaching
fewX10-7. More precise experiments

The best upper
experiments
will

be perfbrmed at LHCb.
"'

b

GF
5

"

Fig.10.Leptonic decay B,e--) It'It-･

4. Quark singiet models
Flavor changing
neutralcurrents (FCNC's)at the tree levelare present in quark singlet models
[29],
while
they are absent in the SM. In thissort of models
the 3 × 3 submatrixof quark mixing
corresponding
to the
CKM matrix in the SM is no longer unitary. Then Z mediatedand neutral
scalarmediated
FCNC's are present at the tree level.
Typicaldiagramswith the FCNC's relevant fbrthe B and Bs physicsare shown in Fig.11.

E

4oao ( a,o4o)mixing><

Es-(d-)

i(d-)

s

s(d)

s(d)

b -> sqd e-dbatsdecayb

the tree level
bv

s

( Z,
d

4,

,

gd

"

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Kobe KaiseiCollege
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Kaisei Collegeb -> sqdijd decay via penguin diagramszIt.-i---NNxS

D:g:

b

s

b

D

:g:

a-d

s

ia
ed

qd

B,O-> p. p- leptonicdecayat the tree level

1 :> <II

E

-

'

--E-

s

Fig.11. FCNC's in quark singlet

5. Summary
We have describedthe experimental
physics with quark mixing. The CKM
physics are

considered

specifically.

modelsstatussee

the flavor

Bs
that the possibilityof NP isThe
andoscillation.
BIOB-,O

elements,

We

concerning

unitarity triangles andIPZbl

in the measurementsofdecays B- ->T"v- 40 --> Jlq ¢ , JEI,O -> P,OKO,
B,O ->K'K',
ll,O-> u'#and
neuandare sensitive
to NP. In quark singlets models, Z mediated
FCNC's are really present, contributing
to these B
tral scalar mediatedmeson
decays as NP.
notexcluded,Acknowledgement
We would liketo thank Kobe Kaisei college
ence

for providingsome

refer-

books.

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