New CP phase of Bs  Bs mixing
on T violation in Bd ( s )  K *   

Chuan-Hung Chen
Department of Physics,
National Cheng-Kung U.,
Tainan, Taiwan
• Inspired & motivated by CDF & D0 experiments
• Z-mediated effects in vector-like quark model
• Summary
 What is mT2 and what is it for ?
cooperate with
C.Q. Geng & Lin Li
1
Foreword
 Definitely, SM is an effective model at electroweak scale. Our
universe should exist other unknown stuff
Hints: masses of neutrinos, matter-antimatter asymmetry,
dark matter, dark energy,… etc.
It is interesting to investigate the physics beyond the SM
 Where can we find the new physics (NP) ?
1. Rare decays :
• Loop induced processes, such as b  s , CP in Bs-Bsbar mixing
• tree processes but suppressed by CKM matrix elements
2. Precision measurements at high energy colliders :
Hereafter, we pay attention to CP in Bs symmetry
2
 In the SM, the CP violating source comes from CKM matrix
that appears associated with charged currents
Weak states:
d 
H C  J CW    u , c , t    PL  s W   U L  DLW 
b
 
After spontaneous symmetry breaking,
uL  VULU L ,
J  W  uL  V V d LW 
d L  VDL DL
C

L
U
L†
D
 VCKM
Flavor mixing matrices
theoretical constraint :
†
VCKMVCKM
1
 There is one physical phase (KM phase) in the SM
by Wolfenstein parametrization

 1 2 / 2

VCKM  

1 2 / 2
 A 3 1    i   A 2


A 3    i  


4

A 2
  O    

1


Vtd ei

Vts
Vub ei 
Vcb 



3
 the phase of Vtd could be determined through time-dependent
CP asymmetry of Bd-barBd mixing
e.g.
mixing
decay amp
Af 
CP
  B  fCP     B  f CP 
  B  fCP     B  f CP 
B1  p B0  q B0
B2  p B0  q B0
q
 p
 
M 12*
 exp(id )
M 12
12  M 12
Mixing-induced CPX
sin 2  0.668  0.026
Direct CPX
world average in
BJ/ K0 decay
4
 How is the CP in Bs system?
 Some observations in Bs mixing
 mixing of Bs , ms
ms  2 | M 12 | 2 Bs H  B  2  Bs
In 2006, CDF first observed the mixing effect
Now, the results of CDF and D0 in BsJ/  decay are
17.77  0.10  0.07 ps 1 (CDF)
ms  
1
18.56

0.87
ps
(D0)

 BR & Direct CP violation
B  Bs  K      5.00  1.25 10 6
ACP  Bs  K     0.39  0.17
It will be interesting if the BR (CPA ) is really so small (large)
5
 Time-dependent CP asymmetry in Bs
 According previous introduction, the ACP(t) is given by
B1  p B0  q B0
B2  p B0  q B0
q
 p
 
f  J / 
J / 
M 12*
M12
q

p
M12*
 exp[is ]
M12
M  Vts 
s
12
Vts*
*
2
6
 How large is the SJ/ in the SM ?
S J /  
2Im J / 
1  J /  
2
J / 
q

p
Vts
Vts*
 exp is 
SJ /   sin s
• with Vts= A2, s=0
• However, by including higher power of  where
Vtb  1  A2 4 / 2, Vts   A 2  A 4 / 2 1  2    i  
Vcb  A 4 , Vcs  1   2 / 2   4 1  4 A2  / 8
Buras, hep-ph/0505175
Vts   A 2 exp[is ], s   2
With =0.359 and =0.2272
  s   2  0.019

 s  2 s  0.038
Very small CPA in the SM
7
 preliminary results of CDF & D0
• to include the possible new physics effects, we write
at 68% C.L.
In addition, D0 also gives the result at 90% C.L. to be
8
 By combining other data of Bs decays, UTfit Collaboration finds that
the non-vanished phase is more than 3 from the SM prediction
Don’t take this too serious
9
 more than 30 citations since the paper is put on the arXiv
First Evidence of New Physics in b <---> s Transitions.
By UTfit Collaboration (M. Bona et al.). Mar 2008. 5pp.
e-Print: arXiv:0803.0659 [hep-ph]
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Cited 35 times
 Inspired by the results of CDF& D0 and UTfit collaboration,
If bs transition involves
new CP phase, can we
uncover it in other process?
and what is it?
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 Physical quantities related to CP violating phase
• CP-odd physical quantity: consider particle B decay, the
decay amplitude is written as
 : CPV phase
A  B   a  be
 iW
e
W
i
 : CPC phase
accordingly, the decay amplitude for its antiparticle is
A  B   a  bei ei
W
• A CP-odd quantity could be defined by
A  B   A B 
2
ACP odd 
A  B   A B 
2
2
2
A  B   A B 
2
A  B   A B 
2
2
2
A B   A  B 
2
CP


A B   A  B 
2
2
2
CP
ACP odd 
 ACP odd
• Such kind of physical quantities need CP violating
and conserving phases at the same time
• The quantity is also called direct CP violation
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T̂  t
• T̂-odd physical quantity: t 
 Triple-product spin-momentum correlation in 3-body decay
Tˆ
sB   pC  pD   sB   pC  pD 
ABCD
  sB pC pD pA
1. CPV phase
d  Im  M  M  '  
2. CPC phase
†
 Triple-product momentum correlation in 4-body decay
Tˆ
pB   pC  pD   pB   pC  pD 
ABCDE
  pB pC pD pA
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 semileptonic B decays might be a good environment to probe
the new phase in bs transition
e.g. b  s


;B  K*



K
K*
B

Dominant effect
 K   p  pK 
*

T-odd

13
• To explore the effects, we examine the T-odd observable,
defined by
The statistical significance is given by
• Since s is small, to obtain large phase in bs, we need to
consider the extension of the SM
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 We consider the so-called vector-like quark model (VQM)
VQM: add a pair of L and R quarks to the SM
 D , D  ; U
L
R
L
,U R 
SU(2)L singlet
• Since the new particles are SU(2)L singlet, they don’t couple to
charged W-boson, but they couple to Z-boson
For W-coupling
d 
s
H C  J CW    u , c , t ,U    SPL  W 
b
 
 D
133
S 
 0
0
0 44
L
U
L†
D
V SV
 VCKM
New 44 CKM is not an unitary matrix
For Z-coupling
FCNC induced at tree
15
• We only pay attention the Z-mediated FCNC
VDL X DVF†  I  VDL  X D  I VF†
V
L
D
X DVF† sb  VDL 24  X D  I 44 VF† 43
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Current limit <
CDF
17
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Summary:
 Although CKM matrix provides a unique phase in the SM,
due to the failure to explain the matter-antimatter asymmetry,
it is important to find out other new CP violating phase at colliders
 b s transition could be the good candidate to look for the new
CP phase
 By studying time-dependent CPA of Bs mixing, it helps to
know whether there exists a new CP phase in bs transition
T-odd effects of Bd ( s )  K *  
to observe the new phase


decay provide another chance
19
A brief introduction to mT2
 The definition:
p : missing transverse momentum
pT : visible transverse momentum
mT : transverse mass
 A method to determine the mass of unknown particle
when invisible particle appears in the final state
for instance:
mT2 could be used to determine
the mass of gluino
20
 Original question: how to determine the mass of new particle
that is produced in pair at collider, where the particle decays to
a visible and an invisible particles
Lester & Summers, PLB463 (99)
example:
Mass of slepton ?
A. Barr, C. Lester, P. Stephens, J. Phys. G29 (2003)
21
 To understand mT2, we need to know the definition of transverse mass
• set a particle A decaying to B and C, if B and C are visible
PA2  mA2   pB  pC 
2
can be observed
no problem to know the mass of A particle
• Now, if C is an invisible particle and escapes the detection from detector
example:
W 
PW2  mW2   p  p 
ET 
1
2
pT  m
  ln
2
E  pz
E  pz
2
 m2  m 2  2  E E  p  p 
 m 2  m 2  2  ET ET cosh   pT  pT 
 m 2  m 2  2  ET ET  pT  pT   mT2
= is satisfied when the rapidity difference vanishes
22
 Using the concept of transverse mass, Lester & Summers proposed
mT2 variable to determine the mass of new particle which is produced
in pair at collider
• mT2 is a variable that is calculated with event by event
mT2  m2  m 2  2  ET ET  pT  pT 
neutralino
m2  mT2
• the total missing momentum is fixed
pT  p1  p2
known and fixed
23
 How powerful is the mT2 ?
very sharp at the end-point, i.e.
the error of the determined mass
is very small
A. Barr, C. Lester, P. Stephens,
B. J. Phys. G29 (2003)
• Now, you can see that the 2 in the subscript means the number of
missing particles
24
• error of the mass of invisible particle
 The original mT2 variable cannot determine the mass of invisible
 How to determine the mass of missing particle by using mT2 ?
W.S. Cho, K. choi, Y.G. Kim, C.B. Park, PRL100:171801,2008
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minvis  mvis
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