Systematic Analysis of B K πll decaysSystematic Analysis of B K πll 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
VS Indirect search
tree loop
High energy exp. High luminosity Exp.
Both approach are important to understand (find) new Physics .
Physics are going to indirect search of New Physics .They will give us some useful hints and strong constraints for new
Physics.
B factory
→super B
factory
→ super-super B …
Main Targets are in Penguin processes .
b su
ud d
Bd
b – s(d) gluon penguin
b – s(d) electro weak penguin
……
..
They will give us some useful hints and strong constraints for new Physics.
A few years ago, We had several excitingly large discrepancies between the experimental data and theoretical expectations.
As you know.
1) In CP asymmetries in b-sqq penguin decays, ex) B ’K ….
2) In BK decays, which are called “K puzzle”. ( = 0 in SM)
Direct CP
Time-dependent CP
= 0
= 0
= 0
Time-dependent CP Asymmetry : Bigi and SandaBigi and Sanda
cc mode S penguin
No CP phase in diagrams No CP phase in diagrams
b
BB
c
B
b
c
s
J/
K
K
J/
B
b
s
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 Puzzle Lipkin, Atwood-Soni
Yoshikawa( 03)., Gronau - Rosner, Buras-Fleischer et al ,
Li, Mishima and Yoshikawa(04) ……. Many works.
What was the Puzzle ?
. Discrepancies from expectations by Sum ruleSum rule among the branching ratios.
(Theory)
(After LP07)
Still remaining this Problem ??
History of Rc - Rn
Rc – Rn Rc
Rn
The EX. Data are moving to the SM direction !!
0 or not
A few years ago, We had several excitingly large discrepancies between the experimental data and theoretical expectations.
As you know.
1) In CP asymmetries in b-sqq penguin decays, ex) B ’K ….
2) In BK decays, which are called “K puzzle”.
= 0.14 ±0.10
( = 0 )
OK ?
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 !!
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!!
Where ?
B decays : topological diagram topological diagram decompositiondecomposition
TTrreeee
QCDQCD PPengenguinuin
CColor olor suppressed suppressed
treetree
EElectrolectroWWeakeak
PPenguin (enguin (PPEWEW))
AAnnihilatinnihilationon SSinglet QCD inglet QCD
PenguinPenguin
CColor suppressed olor suppressed
EWEW PPenguinenguin
((PPCCEWEW ))
Gronau, Hernandez,London, Rosner
b
B
B
B
BB
B
B
bb
b
b
bb
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 !!
Ceff9 Has imaginary part
C9 is including strong phase comes from CC resonances
However no phase in low q^2 region !!
Z = k^2
Im[C
9]
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, B Xs ll
tiny Br
final states are both CP odd and even .
Need angular analysis of B K pi ll .
Let’s consider semi-leptonic decays
Small strong phase.
In this talk, I am going to introduce the following works:
1.New measurements using External Photon Conversion at a High Luminosity B Factory
2.Systematic analysis of BKπ ll decays
Ishino,Hazumi,Nakao, T.Y. hep-ex/0703039
C.S. Kim and T.Y, preparing now
Low invariant mass region, z = (p+ + p-)^2 ~ 0
Using Photon Conversion
Using photon conversions in detector, we may measure
Using photon conversions in detector, we may measure
1. Time –dependent CP asymmetry of B
2. Vphoton polarization
3.
4.
At Super B factoryAt Super B factory
Ishino,Hazumi,Nakao, T.Y. hep-ex/0703039
Using Photon
Conversion 1. Time –dependent CP asymmetry of
BS
To find S we need know the vertex position.
But it is difficult to find Bdecay vertex because the final states are neutral pions which go to 2 photons.
Tag sideBB
BB
t
Can not trace to a vertex from 4 photons !
Using Photon
Conversion 1. Time –dependent CP asymmetry of
BS
Tag side
BB
BB
t
Photon change to 2 leptons by conversion with some material inside so that can trace to vertex!!
Detector etal, e
e
Conversion : X l + l -
SS
Can get one more information to understand Bsystem !
Br(B), Br(B), Br(B)Acp, S, Acp, Acp, SS
6 measurements + 1 + 1 8 measurements
For Tree, Penguin, Color-suppressed tree , EW-Penguin,
strong phase differences (2 + 1), weak phase 2
After neglecting EW-penguin contribution,
6 measurements + 1 more vs 6 parameters 6 measurements + 1 more vs 6 parameters
NewNew
?? We have several Questions. Is the isospin relation (triangle) exact one ? Is the isospin relation (triangle) exact one ?
Is Isospin triangle closed ? Is Isospin triangle closed ? or 0 ?
or
1)1)
2) How is EW Penguin dependence ? 2) How is EW Penguin dependence ?
3) Can we remove the discrete ambiguity for the solution ? 3) Can we remove the discrete ambiguity for the solution ?
which depend on how to use the 2 triangles which depend on how to use the 2 triangles
X = orX = or
PPEWEW
B decay
A
B decay
A
V V using photon using photon conversionconversion
By photon conversion : B B (K* (K*KK + ( + (ll++ l l--Semi-leptonic decay through Real photonthrough Real photon,
z
l+
l -
K
π
K* γB
θl
φ
We can do angular analysis
by .
Can get information of Photon Polarization !!
Using Photon
Conversion 2. BV gamma photon polarization
Tag side
BB
BB
t
Real Photon change to 2 leptons by conversion with some material inside so that can trace to vertex!!
Detector etal, e
e
Conversion : X l + l -
The angular distribution : definition of the angles
z
l+
l -
K
π
K* γB
θl
φ
θl : angle between l+ momentum direction and z axis
at CM system of (l+ l- )
: angle between π direction and - z axis at CM of (K pi )
φ : angle between 2 decay planes
FB asymmetry
There are 3 angles. Can not we use them ?
q^2
Q^2 ~0
b-s Tiny contribution in SM ∝ ms/mb
Points:Using small-q^2 region, ( q^2 ~ 0 )
One can investigate B Vγ by using polarization analysis or angular distribution
We can neglect 1) local interactions with O9, O10
2) longitudinal modes, A0
NEGLIGIBLE
Grossman and Pirjol, JHEP0006: 029 (2000)
Kim, Kim, Lu and Morozumi, PRD62: 034013 (2000) Grinstein and Pirjol, PRD73 014013 (2006)
After integrating angles and q^2 at small region, approximately,
From the distribution for angle φ + B->V γ 、 one can extract
which may be including new physics info.
Angler analysis
C7 C7’
whereSmall contribution in SM
Combining with time dependent CP asymmetry :
Where is a phase of decay amplitude
C7 or C7’
We can extract NEW CP Phase of EM penguins !!
After finding R and
We should investigate the phase of C10 or C9 as Z penguin .
Atwood, Gershon, Hazumi and Soni, PRD71:076003 (2005)
2. Systematic Analysis of BKπll 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
z
l+
l -
K
π
K* γB
θl
φ
θl : angle between l+ momentum direction and z axis
at CM system of (l+ l- )
: angle between π direction and - z axis at CM of (K pi )
φ : angle between 2 decay planes
FB asymmetry
There are 3 angles. Can not we use them ?
The branching ratios is
After integrating all angles, remains as the decay rate. The other terms shown the angular distribution.
B K l l mode
CP: odd
CP: even
CP: odd
CP: odd
CP: odd
CP: even
Kruger,Sehgal, Shinha, Shinha
Kruger, Matias
Kim,Kim,Lu,Morozumi
Kim, T.Y.
Angular decomposition
BK* l l decay matrix element
b-s Tiny contribution in SM
Z penguin
B (K* K ) + l l
l^-
l^+
l
K
Forward-Backward Asymmetry
l^+ l^+
For example
How to detect the evidence of New Phys. by B K* ll .
Using Forward-Backward asymmetry:
The zero of FB asymmetry is rather insensitive to hadron uncertainty .
We need to remove the hadronic uncertainty !!
We should use some asymmetries :
C7
-C7
AFB
z = (pl^+ + pl^-)^2 Dilepton invariant mass
AFB
V, Ti, Ai : B-K* Form Factors
B K* ll
How about BK pi l l decay ?
Depend on C7 and C9.
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
tiny Br
final states are both CP odd and even .
Need angular analysis of B K pi ll .
Let’s consider semi-leptonic decays
The branching ratios is
After integrating all angles, remains as the decay rate. The other terms shown the angular distribution.
B K l l mode
CP: odd
CP: even
CP: odd
CP: odd
CP: odd
CP: even
Decomposition by using 3 angle distribution
If Possible, we would like to extract these contributions by
using FB asymmetries.
FB asymmetry for l^+
Triple FB asymmetry
An asymmetry for
Triple FB asymmetry
Double FB asymmetry for and
CP: odd
CP: even
CP: odd
CP: odd
CP: odd
CP: even
Usual FB asymmetry
Double FB asymmetry for and
Proportional (CProportional (C99* * CC1010))
Double FB asymmetry for and
Appear Im ( C10 C7 ) Imaginary part of C10
Note: s = q^2 = (Pk + Pπ)^2
z = k^2 = (P+ + P- )^2
An asymmetry for
Triple FB asymmetry
CP Asymmetries
Direct CPA
Strong phase difference CP phase
Need strong phase difference !!
Ceff9has imaginary part
C9 is including strong phase comes from CC resonances
Z = k^2
Im[C
9]
no phase in low q^2 region !!
And CP odd and even interference effect is also existing in the new FBs.
Important points to use new FBs
The definition of direct and time-dependent CP asymmetries:
s,s, z distributionsz distributions
),(),(
][),(
zsBzsB
FBzsA
iiiFBicp
][
*][2),(
12Im
iii
iiFBicp
FB
MMeFBzsS
= = === odd)
+1 (CP even)
direct CPV of FB asymmetry direct CPV of FB asymmetry
time-dependent CPVtime-dependent CPV
),(),(
][),(
zsBzsB
FBzsA
iiiFBi
FB asymmetryFB asymmetry
FB asymmetry for l^+
C7
-C7
C10 i |C10|
AcpFB2
FB2
C9 i |C9|
FB4
If C7’ with CP phase exists, the effect will appear in FB4 and Acp .
C7’ not =0
If C7’ with CP phase exists, the effect will appear in FB4.
FB4
FB5
Triple FB asymmetry
C7’ not =0
If C7’ with CP phase exists, the effect will appear in FB5.
FB5
C10 i |C10|
FB6
Double FB asymmetry for and
C7’ not =0
C7
-C7
FB6
C10 i |C10|
Sensitive to the phase of
C10 and C7
FB7
An Example FB2
The CP phase of C_9 are
π/ 80
π/ 4
π/2
FB2
2FBcpA
2FBcpS
- Sin2φ1
We need more strong phases .
How about interferences between K^* and scalar resonance as intermediated states ?
We may get many fruitful information from B K pi ll decay modes.
Angular analysis
CP asymmetries
l
l
S (scalar) K0*(800)
We can define new FB like asymmetries!!There is another strong phase source by the resonance effects.
We used
Im partsDescotes-Genon, Moussallam
EPJ C8, 553
Here we are using and start frommost 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
UP-Down asymmetry for angle
Triple asymmetry
L-R for phi, FB asymmetry for lepton
If there is such scalar resonance effects, these new FBs will appear!!
FB 2^s
FB 4^s
2FBcpSA
4FBcpSA
π/ 80
π/ 4
π/2
C9 の CP 位相 を
K meson FB asymmetry
UP-Down asymmetry for angle
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
= =
We are using =→= as a very strict constraints to new physics.
As you know well,
Nakao( ====
Charged Higgs mass
)%95(295 CLGeVM
Constraint for SUS Y
======= et al (06)
HFAG06
For example
|A +- ||A +ー|
√ 2 |A+0 |= √ 2 |A - 0 |
Isospin analysis :Isospin analysis :
Relation:Relation:
Extract 2
By using 2 triangles, the angle between A and Ais extracted .
X
where
Isospin Triangles
Gronau and London
Where does new S appear in the triangles ? :
|A +- ||A +=|
√ 2 |A+0 |= √ 2 |A - 0 |
X
Isospin Triangles
Y
As the same sense,
one can extract 2 .
As the same sense,
one can extract 2 .
then
2 = or not 22 = or not 2
New check item ! New check item !
3) Can we remove the discrete ambiguity ?
YX
X and Y have 4 fold ambiguity
1 2 3 4
2 ambiguity to find 22 – x from
22 - X, –22 + X
total 4 x 2 = 8 fold ambiguity
Using Using 22(() = ) = 22(() , one can reduce the ambiguity !) , one can reduce the ambiguity !
Z() + Xi
– z() - Xi----
Z() + Yi
– z() - Yii = 1 ~ 4
At each “ I ”, by comparing each solution, if they are same, then
it will remain as the solution.
An example:An example:
From the present data, one can predict some region of Sfor 2.
From recent HFAG data, S for 2 is shown in Figure.
Note that this is not 2 fitting
Within the 1 error for
all experimental data .
Within the 1 error for
all experimental data .
There are 8 regions
for each solution.
S
2
By using
Br() = 5.2 0.20, Br()= 1.31 0.21, Br) = 5.7 0.4
Acp(+-) = 0.39 0.07, Acp(00) = 0.36 0.32, Acp(+0) = 0.04 0.05
S = -0.59 0.09
22
S
If we find If we find SS, we can reduce, we can reduce
the ambiguity of the solutionsthe ambiguity of the solutions
for for 22..
Br() = 5.21 0.10, Br()= 1.31 0.10, Br) = 5.7 0.2
Acp(+-) = 0.39 0.04, Acp(00) = 0.36 0.16, Acp(+0) = 0.04 0.03
S = -0.59 0.005
After reduce the error (up to 1/2) :
Almost 2 hold ambiguity for SAlmost 2 hold ambiguity for S
One can reduce the ambiguity!!One can reduce the ambiguity!!22
S
Once we find S,
1) Is the isospin relation (triangle) exact one ? 1) Is the isospin relation (triangle) exact one ?
Is Isospin triangle closed ? Is Isospin triangle closed ? or 0 ?
What is the origin of “” ?
= 5/2 contribution no such diagram in the SM !!
1. New Physics contribution ?
2. Final state interaction ?
3. ’ mixing ?
or
To use S is only method to check the situation about isospin triangle ! To use S is only method to check the situation about isospin triangle !
quite tiny contribution O(1/100)
Gronau and Zupan, PRD71,074017,(05)Gronau and Zupan, PRD71,074017,(05)
2 = 22 = 2
To extract a correct 2 and get some information about the discrepancy from the SM, we have to check the relation. To extract a correct 2 and get some information about the discrepancy from the SM, we have to check the relation.
Real situationfake situation
SummarySummaryIn (super) B factory, S will be measured !! -----> Ishino-san’s talk
You can be going to get one more information about B decays system . You can be going to get one more information about B decays system .
How to use the new measurement ?How to use the new measurement ?
1. To remove the discrete ambiguity.
2. To check the isospin triangle.
New Physics ? Final state int. ? ’mixing ?
The other effects we do not know ?
With BKpi gamma, we can extract New physics information in b-s gamma interaction by using polarization of gamma (=angular analysis of
We can find the magnitude of A_R coupling and the CP phase as a New physics evidence.
Application of PCApplication of PCBy using Photon Conversion Technique,
1. Can trace (find) to the decay vertex including et al.
at good accuracy.)
B
B
B
2.Can use angular analysis
B V
……
.
Please consider what we can do by using this new Please consider what we can do by using this new technique !!!technique !!!
New Physics search
The branching ratios is
After integrating all angles, remains as the decay rate. The other terms shown the angular distribution.
B K l l mode
CP: odd
CP: even
CP: odd
CP: odd
CP: odd
CP: even
Kruger,Sehgal, Shinha, Shinha
Kruger, Matias
If Possible, we would like to extract these contributions by
using FB asymmetries.
FB asymmetry for l^+
Triple FB asymmetry
An asymmetry for
Triple FB asymmetry
Double FB asymmetry for and
CP: odd
CP: even
CP: odd
CP: odd
CP: odd
CP: even
CP Asymmetries
Direct CPA
Strong phase difference CP phase
Need strong phase difference !!
Ceff9 の imaginary part (Buchalla 00)
C9 is including strong phase comes from CC resonances
However no phase in low q^2 region !!
FB asymmetry for l^+
C7
-C7
C10 i |C10|
Acp
FB2
CP: oddExample:
Buck up 2
system, decay amplitudes: T (tree), P (penguin), C (color suppressed )
6 measurements for 6 parameters = solve (can extract 2
Isospin analysis to remove penguin pollution.Isospin analysis to remove penguin pollution.
+ 1 measurement ( S
To check the SM, New Phys. And to solve discrete ambiguityTo check the SM, New Phys. And to solve discrete ambiguity
3 Br, 2 Acp, 1 Sfor T, rp, rc, 2 23 Br, 2 Acp, 1 Sfor T, rp, rc, 2 2
22 – X1
- 22 + X1
22 – X2
– 22 – X2
- 22 + X1
- 22 + X2
22 + X1
22 + X2
Z for each regionZ for each region
X1 = X2=
X3 = X1 , X4 = X2
2) How is EW Penguin dependence ? 2) How is EW Penguin dependence ?
Note that is not changed !!
We need a correction in the bottom line, which shows B.
|T+C||PEW|
22
rotate a triangle by angle to fit the botom linesrotate a triangle by angle to fit the botom lines
so that we cam use same isospin analysis to extract 2eff .
X
where
One can find “ 22“ by using isospin analysis
and can reduce the ambiguity as the same sense with no EWP case.
One can find “ 22“ by using isospin analysis
and can reduce the ambiguity as the same sense with no EWP case.
have to be determine by the other method !! have to be determine by the other method !!
In this case, there are 8 measurements
( Br+-, Br+0, Br00, Acp, Acp, Acp, S, S
for
( T, rp, rc, rEW, p, c, EW, 2 ) 8 parameters
may solve if we can get enough data.
b
u, d
B0 decay
B+ decay
=?
New Physics?New Physics? usual case = b -- 3 light quarks vertex
spectator is free !! spectator is free !!
Not changed by the interactions
Isospin relaion
= 1/2 or 3/2 interactions
Usual type new physics can not break the isospin relation !!
b
d
d
d
d
d
?π 0
π 0
Bbresaking of isospin relation
New Physics?New Physics? an example of 5/2 interaction: b – 5 dquarks interaction
Which type seems to be quite exotic model.
New Physics ?
or
Final state interactions ?
PointPointTo extract a correct result as the weak phase 2, 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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