B中間子崩壊に潜む標準理論を超える物理の理論的探索

Systematic Analysis of
B  Ｋπll decays
Tadashi Yoshikawa
Nagoya U.
International Workshop
“Towards the Precise Prediction of CP violation”
Oct. 22 – 25, 2007
YITP, Kyoto University
To investigate CP phase is very important !
In SM and In New Physics !!
and
One of the most important aims
of B factories and super B factory.
It is very important to investigate by
using B meson decays (or τdecays ).
Kobayashi-Maskawa Theory ( CKM matrix) are almost confirmed !!
We are going to next stage to search for
New physics hiding well !
Unitarity Triangle :
Where are they hiding ?
Where can we find them in ?
direct search
tree
High energy exp.
VS
Indirect search
loop
High luminosity Exp.
Both approach are important to understand (find) new Physics .
B Physics are going to indirect search of New Physics .
They will give us some useful hints and strong constraints for new Physics.
Main Targets are in Penguin processes .
ｂ
s
u
Bd
d
u
d
b – s(d) gluon penguin
b – s(d) electro weak penguin
……..
They will give us some useful hints and strong constraints for new Physics.
As you know.
A few years ago, We had several excitingly large discrepancies
between the experimental data and theoretical expectations.
1) In CP asymmetries in b-sqq penguin decays, ex) B fK, h’K ….
2) In BKp decays, which are called “Kp puzzle”.(
=0
=0
Direct CP
=0
Time-dependent CP
=0
in SM)
Time-dependent CP Asymmetry :
Bigi and Sanda
c
J/j
b
BB
K
c
b
J/j
s
B
K
No CP phase in diagrams
cc mode
S penguin
s
b
B
Discrepancy of Scp between CC modes and b-s modes
in the SM
The EX. Data are moving to the SM direction !!
Present status of the Kp Puzzle
What was the Puzzle ?
Lipkin, Atwood-Soni
Yoshikawa( 03)., Gronau - Rosner, Buras-Fleischer et al ,
Li,
Mishima and Yoshikawa(04) …….
Many works.
. Discrepancies from expectations by Sum rule among the branching
ratios.
(Theory)
(After LP07)
Still remaining this Problem ??
History of Rc - Rn
0 or not
Rc – Rn
Rc
Rn
The EX. Data are moving to the SM direction !!
As you know.
A few years ago, We had several excitingly large discrepancies
between the experimental data and theoretical expectations.
1) In CP asymmetries in b-sqq penguin decays, ex) B fK, h’K ….
OK ?
2) In BKp decays, which are called “Kp puzzle”.
( = 0 )
= 0.14 ±0.10
Still remaining
small windows.
How do you think about this situation ?
Still remaining deviation.
There were many many works to explain these deviations,
SUSY, extra D model ………
It will give us several useful hints or constraint to build new model !!
New Physics is hiding in them !!
Where ?
The several relations comes from main contribution, which is QCD penguin.
The new contribution to explain these situations may be in EW penguin,
because it is the sub-leading contribution.
A possibility is new physics with new CP phase in EW Penguin!!
Gronau, Hernandez,London, Rosner
B decays ：topological diagram decomposition
b
b
B
B
Ｔｒｅｅ
b
QCD Ｐｅｎｇｕｉｎ
Color suppressed
ElectroWeak
tree
B
Annihilation
Penguin (PEW)
Singlet QCD Penguin
b
B
b
B
b
B
Color suppressed
EW Penguin
(PCEW )
b
B
What can we learn from the K pi puzzle ?
We should be investigate pure EW penguin processes
to find some evidences of New Physics (new CP phase ).
(Direct or indirect ) CP asymmetries of EW processes ( b->s gamma, b->s ll )
BUT
Tiny strong phase
difference
・Including both CP odd and even states
・Small interference term and X2 ∝ 1/q
Slightly difficult to investigate the CP asymmetries !!
CP Asymmetries
Direct CPA
Strong phase difference
CP phase
Need strong phase difference !!
eff
C9
Has imaginary part
Im[C9]
C9 is including strong phase
comes from CC resonances
However no phase in low q^2
region !!
Z ＝k^2
If EW Penguin : ( Z penguin ) : should include new phase,
the effect will appear in semi-leptonic decays .
But to investigate the effects in C10 process is slightly
difficult !!
CP asymmetry of B ll or B s gamma,
Small strong
tiny Br
phase.
B Xs ll
final states are both
CP odd and even .
Need angular analysis of B  K pi ll .
Let’s consider semi-leptonic decays
In this talk, I am going to introduce the following works:
1.New measurements using External Photon
Conversion at a High Luminosity B Factory
Ishino,Hazumi,Nakao, T.Y.
hep-ex/0703039
Low invariant mass region, z = (p+ + p-)^2 ~ 0
2.Systematic analysis of BKπｌｌ decays
C.S. Kim and T.Y,
preparing now
Using Photon Conversion
Ishino,Hazumi,Nakao, T.Y.
hep-ex/0703039
Using photon conversions in detector, we may measure
1. Time –dependent CP asymmetry of Bp0p0
2. BVg photon polarization
3.
4.
At Super B factory
Using Photon Conversion
1. Time –dependent CP asymmetry of Bp0p0 : Sp0p0
To find Sp0p0 , we need know the vertex position.
But it is difficult to find Bp0p0 decay vertex because the
final states are neutral pions which go to 2 photons.
Dt
g
g
B
p0
g
p0
B
g
m
Tag side
Can not trace to a vertex from 4 photons !
Using Photon Conversion
1. Time –dependent CP asymmetry of Bp0p0 : Sp0p0
Conversion : g + X  ｌ+ ｌDetector etal,
e
e
Dt
g
g
g
B
p0
p0
B
g
m
Tag side
Photon change to 2 leptons by conversion with some
material inside so that can trace to vertex!!
Sp 0 p 0
Can get one more information to
understand Bpp system !
Br(Bp p ), Br(Bp p ), Br(Bp p )
++0
00
+ Acp, Sp p ,
Acp,
Acp, Sp0p0
+ -
+ 0
0 0
New
6 measurements +
1 + 1  8 measurements
For Tree, Penguin, Color-suppressed tree , EW-Penguin,
strong phase differences (2 + 1), weak phase f2
After neglecting EW-penguin contribution,
6 measurements + 1 more
vs
6 parameters
?? We have several Questions.
1)
Is the isospin relation (triangle) exact one ?
Is Isospin triangle closed ?
or 0 ?
or
2)
How is EW Penguin dependence ?
3)
Can we remove the discrete ambiguity for the solution ?
PEW
which depend on how to use the 2 triangles
X = qpp - qpp or
B decay
A
B decay
A
qpp + qpp
B  V g using photon conversion
By photon conversion :
B  (K*Kp) + (g  l+ l- )
Semi-leptonic decay through Real photon,
We can do angular analysis by f .
φ
l+
K
qk
π
γ
K*
θl
z
B
l-
Can get information of Photon Polarization !!
Using Photon Conversion
2. BV gamma
photon polarization
Conversion : g + X  ｌ+ ｌDetector etal,
e
e
Dt
g
K
B
K*
B
p
m
Tag side
Real Photon change to 2 leptons by conversion with some
material inside so that can trace to vertex!!
The angular distribution : definition of the angles
φ
l+
K
qk
π
γ
K*
θl
z
B
l-
θl： angle between l+ momentum direction and z axis
at CM system of (l+ l- )
q K： angle between π direction and - z axis at CM of (K pi )
φ： angle between ２ decay planes
There are 3 angles.
Can not we use them ?
FB asymmetry
NEGLIGIBLE
b-s g
Tiny contribution in SM  ms/mb
Points: Using small-q^2 region, ( q^2 ~ 0 )
We can neglect
1) local interactions with O9, O10
2) longitudinal modes, A0
One can investigate B  Vγ
by using polarization analysis or angular distribution
Grossman and Pirjol, JHEP0006: 029 (2000)
Kim, Kim, Lu and Morozumi, PRD62: 034013 (2000)
Grinstein and Pirjol, PRD73 014013 (2006)
Q^2 ～０
ｑ＾２
After integrating angles and q^2 at small region, approximately,
Angler analysis
where
Small contribution in SM
From the distribution for angle φ + B->V γ、 one

can extract
C7 C7’
which may be including
new physics info.
Atwood, Gershon, Hazumi and Soni, PRD71:076003 (2005)
Combining with time dependent CP asymmetry :
Where f+ is a phase of decay amplitude
C7 or C7’
We can extract NEW CP Phase of EM penguins !!
After finding R and f+
We should investigate the phase of C10 or C9 as Z penguin .
2. Systematic Analysis of BKπll decays
Kim and T.Y.
To be appear soon.
investigate the contributions of the new CP phase
by using
angular analysis and the CP asymmetries for
B  Kπll 4 body decays .
We defined several partial angle integration asymmetries,
like Forward-Backward asymmetry (FB).
The angular distribution : definition of the angles
φ
l+
K
qk
π
γ
K*
θl
z
B
l-
θl： angle between l+ momentum direction and z axis
at CM system of (l+ l- )
q K： angle between π direction and - z axis at CM of (K pi )
φ： angle between ２ decay planes
There are 3 angles.
Can not we use them ?
FB asymmetry
B  K p l l mode Angular decomposition
Kruger,Sehgal, Shinha, Shinha
Kruger, Matias
Kim,Kim,Lu,Morozumi
The branching ratios is
Kim, T.Y.
After integrating all angles, G1 remains as the decay rate. The other
terms shown the angular distribution.
CP: odd
CP: even
CP: odd
CP: odd
CP: odd
CP: even
Z penguin
BK* l l decay matrix element
b-s g
Tiny contribution in SM
l^B
K
qK
K*
ql
l^+
B (K* K p) + l l
For example
Forward-Backward Asymmetry
l^+
B
K*
-
p
l^+
B
K*
How to detect the evidence of New Phys. by B K* ll .
We need to remove the hadronic uncertainty !!
V, Ti, Ai : B-K* Form Factors
We should use some asymmetries :
Using Forward-Backward asymmetry:
The zero of FB asymmetry is rather insensitive to hadron uncertainty .
AFB

AFB
B K* ll
C7
~
+4
Depend on C7 and C9.
-C7
How about BK pi l l decay ?
z = (pl^+ + pl^-)^2
Dilepton invariant mass
-C7
C7
If EW Penguin : ( Z penguin ) : should include new phase,
the effect will appear in semi-leptonic decays .
But to investigate the effects in C10 process is slightly
difficult !!
CP asymmetry of B ll or B Xs ll
final states are both
tiny Br
CP odd and even .
Need angular analysis of B  K pi ll .
Let’s consider semi-leptonic decays
B  K p l l mode
Decomposition by using 3 angle distribution
The branching ratios is
After integrating all angles, G1 remains as the decay rate. The other
terms shown the angular distribution.
CP: odd
CP: even
CP: odd
CP: odd
CP: odd
CP: even
If Possible, we would like to extract these contributions by
using FB asymmetries.
FB asymmetry for l^+
CP: odd
Triple FB asymmetry
CP: even
An asymmetry for f
CP: odd
Triple FB asymmetry
CP: odd
Double FB asymmetry for f and qk
CP: odd
CP: even
Usual FB asymmetry
Double FB asymmetry for f and qk
Proportional (C9* C10)
Double FB asymmetry for f and qk
Appear Im ( C10 C7 )
Note:
s = q^2 = (Pk + Pπ)^2
z = k^2 = (P+ + P- )^2
Imaginary part of C10
An asymmetry for f
Triple FB asymmetry
CP Asymmetries
Direct CPA
Strong phase difference
CP phase
Need strong phase difference !!
eff
C9
has imaginary part
Important points to use new FBs
Im[C9]
C9 is including strong phase
comes from CC resonances
no phase in low q^2 region !!
Z ＝k^2
And CP odd and even interference effect
is also existing in the new FBs.
The definition of direct and time-dependent CP asymmetries:
s, z distributions
A
FBi
FBi
cp
A
FBi[h Gi + Gi ]
( s, z ) 
B ( s, z ) + B ( s, z )
FBi[h Gi - Gi ]
( s, z ) 
B ( s, z ) + B ( s, z )
FB asymmetry
direct CPV of FB asymmetry
-2if1
2
FB
i
Im
[
e
M M *]
FBi
Scp ( s, z )  h
FBi [h Gi + Gi ]
 ＝－1
+1
（ＣＰ odd)
(CP even)
time-dependent CPV
FB asymmetry for l^+
FB2
FB2
Acp
C10  i |C10|
C7
-C7
FB4
If C7’ with CP phase exists,
the effect will appear in FB4.
FB4
C9  i |C9|
C7’ not =0
If C7’ with CP phase exists, the effect will appear in FB4 and Acp .
Triple FB asymmetry
FB5
FB5
If C7’ with CP phase exists, the effect will appear in FB5.
C7’ not =0
Double FB asymmetry for f and qk
FB6
FB6
C10  i |C10|
C7’ not =0
-C7
C7
FB7
Sensitive to
the phase of
C10 and C7
C10  i |C10|
An Example
FB2
FB2
Acp
The CP phase of C_9 are
０
π/８
π/４
π/2
FB2
FB2
Scp
－Sin2φ１
We need more strong phases .
How about interferences between K^* and scalar resonance
as intermediated states？
K
K*
l
B
S (scalar)
l
K0*(800)

We used
Im parts
Descotes-Genon, Moussallam
EPJ C8, 553
We may get many fruitful information from B  K pi ll decay modes.
Angular analysis
CP asymmetries
We can define new FB like asymmetries!!
There is another strong phase source
by the resonance effects.
Here we are using and start from
most general 4-fermi interaction
C9, C10, C7
: SM parameters
C9’, C10’, C7’ : L-R model
et.al.
R current
Css, CAs, CsA, CAA : scalar type interactions
CT, CTE : tensor type interactions
Br
With scalar resonance
We can define new type FBs.
K meson FB asymmetry
L-R asymmetry for angle f
UP-Down asymmetry for angle f
Triple asymmetry
L-R for phi, FB asymmetry for lepton
If there is such scalar resonance effects, these new FBs will appear!!
FB２＾ｓ
C9 の CP位相を
K meson FB asymmetry
FB2
AcpS
０
π/８
π/４
π/2
FB４＾ｓ
UP-Down asymmetry for angle f
FB4
AcpS
Summary
There are several discrepancies between Ex. and theory in B decays.
But some ones seem to be moving to SM prediction.
Still remaining the region for New Physics in
EW penguin as the new CP phases.
To understand and find the evidence of NP, we should
investigate semi-leptonic rare decays.
At Low invariant mass k^2 ~ 0 region
Using photon conversions technique
C7’ and the CP phase
Angular analysis and the CP asym.
C10 or C9 CP phase
With Scalar resonance effect
New information
Buck up
As you know well,
We are using ｂｓ as a very strict
constraints to new physics.
For example
Charged Higgs mass
M   295GeV (95%CL)

Ｂ
Ｓ
HFAG06
Constraint for ＳＵＳY
Ｉｓｉｄｏｒｉ et al (06)
Nakao( ＬＰ０７)
Isospin analysis :
Gronau and London
Relation:
By using 2 triangles, the angle between A+- and A+- is extracted .
where
|A＋－|
|A＋ー｜
X
Isospin Triangles
√２|A+0 |= √２|A－0 |
Extract f2
!!!
Where does new Sp0p0 appear in the triangles ? :
As the same sense,
one can extract f2 .
|A＋－|
|A＋ー｜
then
f2(p+p- )
X
= or not
f2(p0p0)
Y
Isospin Triangles
√２|A+0 |= √２|A－0 |
New check item !
3)
Can we remove the discrete ambiguity ?
X
X and Y have 4 fold ambiguity
1
Y
2
3
4
2 ambiguity to find 2f2 – x from
Z  2f2 - X,
total
Using
f2(p+p-)
p –2f2 + X
4 x 2 = 8 fold ambiguity
=
f2(p0p0) ,
Z(p+p-) + Xi
p–
z(p+p-)
- Xi
----
one can reduce the ambiguity !
Z(p0p0) + Yi
p–
z(p0p0)
- Yi
i=1~4
At each “ I ”, by comparing each solution, if they are same, then
it will remain as the solution.
An example:
From the present data, one can predict some region of Sp0p0 for
f2 .
From recent HFAG data, Sp0p0 for f2 is shown in Figure.
There are 8 regions
for each solution.
Sp0p0
Within the 1 s error for
all experimental data .
f2
Note that this is not c2 fitting
By using
Br(p+p-) = 5.2  0.20, Br(p0p0)= 1.31  0.21, Br(p+p0) = 5.7  0.4
Acp(+-) = 0.39  0.07,
Acp(00) = 0.36  0.32,
Acp(+0) = 0.04  0.05
Sp+p- = -0.59  0.09
If we find Sp0p0, we can reduce
the ambiguity of the solutions
Sp0p0
for F2.
2f2
After reduce the error (up to 1/2) :
Br(p+p-) = 5.21  0.10, Br(p0p0)= 1.31  0.10, Br(p+p0) = 5.7  0.2
Acp(+-) = 0.39  0.04,
Acp(00) = 0.36  0.16,
Acp(+0) = 0.04  0.03
Sp+p- = -0.59  0.005
Once we find Sp0p0,
Sp0p0
Almost 2 hold ambiguity
for Sp0p0
2f2
One can reduce the ambiguity!!
1) Is the isospin relation (triangle) exact one ?
Is Isospin triangle closed ?
or 0 ?
D
or
To use Sp0p0 is only method to check the situation about isospin triangle
!
What is the origin of “D” ?
DI = 5/2 contribution
no such diagram in the SM !!
1. New Physics contribution ?
2. Final state interaction ?
3.
p0-h-h’
mixing ?
quite tiny contribution O(1/100)
Gronau and Zupan, PRD71,074017,(05)
Real situation
fake situation
f2(p+p- )
=
f2(p0p0)
To extract a correct f2 and get some information about the discrepancy from the
SM, we have to check the relation.
Summary
In (super) B factory, Sp0p0 will be measured !! -----> Ishino-san’s talk
You can be going to get one more information about B  pp decays system .
How to use the new measurement ?
1. To remove the discrete ambiguity.
2. To check the isospin triangle.
New Physics ? Final state int. ? p-h-h’ mixing ?
The other effects we do not know ?
With BKpi gamma, we can extract New physics information in b-s gamma
interaction by using polarization of gamma (=angular analysis of f )
We can find the magnitude of A_R coupling and the CP phase as a New physics evidence.
Application of PC
By using Photon Conversion Technique,
1. Can trace (find) to the decay vertex including p0, h et al.
( at good accuracy.)
B  p0 p0
B  K0 p0
B f p0
…….
2. Can use angular analysis
B V g
t m g
New Physics search
Please consider what we can do by using this new technique !!!
Kruger,Sehgal, Shinha, Shinha
B  K p l l mode
Kruger, Matias
The branching ratios is
After integrating all angles, G1 remains as the decay rate. The other
terms shown the angular distribution.
CP: odd
CP: even
CP: odd
CP: odd
CP: odd
CP: even
If Possible, we would like to extract these contributions by
using FB asymmetries.
FB asymmetry for l^+
CP: odd
Triple FB asymmetry
CP: even
An asymmetry for f
CP: odd
Triple FB asymmetry
CP: odd
Double FB asymmetry for f and qk
CP: odd
CP: even
CP Asymmetries
Direct CPA
Strong phase difference
CP phase
Need strong phase difference !!
eff
C9
の imaginary part (Buchalla 00)
C9 is including strong phase
comes from CC resonances
However no phase in low q^2
region !!
Example:
CP: odd
FB asymmetry for l^+
FB2
Acp
C10  i |C10|
C7
-C7
Buck up 2
pp system, decay amplitudes: T (tree), P (penguin), C (color suppressed )
6 measurements for 6 parameters
3 Br, 2 Acp, 1 Sp+p-
=
solve (can extract f2)
for T, rp, rc, 2 d, f2
Isospin analysis to remove penguin pollution.
+ 1 measurement
( Sp0p0 )
To check the SM, New Phys. And to solve discrete ambiguity
X1 = qpp - qpp , X2= qpp + qpp
Z for each region
p- 2f2 + X2
X3 = - X1 ,
X4 = - X2
2f2 – X2
2f2 – X1
p- 2f2 + X1
p – 2f2 – X2
2f2 + X1
2f2 + X2
p- 2f2 + X1
2)
How is EW Penguin dependence ?
Note that
is not changed !!
so that we cam use same isospin analysis to extract f2eff .
We need a correction in the bottom line, which shows Bp+p0 .
rotate a triangle by angle df
to fit the botom lines
2f2
df
|T+C|
|PEW |
X
where
One can find “ 2f2 + df “ by using isospin analysis
and can reduce the ambiguity as the same sense with no EWP case.
df have to be determine by the other method !!
In this case, there are 8 measurements
(
for
Br+-,
Br+0,
Br00,
+-
00
+0
Acp, Acp, Acp, Sp+p-, Sp0p0 )
8 parameters
( T, rp, rc, rEW, dp, dc, dEW,
may solve if we can get enough data.
f2 )
New Physics?
usual case = b -- 3 light quarks vertex
ｂ
？
= D1/2 or D3/2 interactions
B0 decay
=
u, d
B+ decay
spectator is free !!
Isospin
relaion
Not changed by the interactions
Usual type new physics can not break the isospin relation !!
New Physics?
an example of D5/2 interaction:
b – 5 dquarks interaction
ｄ
ｂ
B
π０
ｄ
？
ｄ
ｄ
ｄ
π０
Which type seems to be quite exotic model.
New Physics ?
or
Final state interactions ?
bresaking of isospin relation
Point
To extract a correct result as the weak phase f2, we have to remove all ambiguities.
To do so, the first
we have to check whether the isospin triangle is closed or not.
After that we can move to search for new physics including in
the loop contributions as QCD, EW- Penguins.

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