B s B B 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

cooperate with C.Q. Geng & Lin Li



What is m T2 and what is it for ?

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 B s -B s bar mixing

• tree processes but suppressed by CKM matrix elements 2. Precision measurements at high energy colliders : Hereafter, we pay attention to CP in B s symmetry 2

 In the SM, the CP violating source comes from CKM matrix that appears associated with charged currents Weak states:

H C



C J W

     

P L d

     

U L

 

D W L

 After spontaneous symmetry breaking,

u L



L V U U L

,

d L



L V D D L

Flavor mixing matrices

C J W

 

u L

 

L V V U D L

† 

V CKM d W L



theoretical constraint :

V CKM

†

V CKM

 1  There is one physical phase (KM phase) in the SM by Wolfenstein parametrization

V CKM

   1   2 / 2

A

 3  1       1   2 / 2 

A

 2

A



A

 2 

i

1    

O

      

V td e



i



V ts V ub e



i



V cb

     3

 the phase of V td could be determined through time-dependent CP asymmetry of B d -barB d mixing e.g.

mixing decay amp

A f CP

    

B B

 

f CP f CP

       

B B

 

f CP f CP

 

B B

2 1 

p B

0 

p B

0 

q B

0 

q B

0

q

  *

M

12

M

12  exp(

i



d

)   12

M

12 Mixing-induced CPX Direct CPX

sin 2

 

0.668



0.026

world average in B



J/



K 0 decay

4



How is the CP in B s system?

 Some observations in B s mixing 

mixing of B s ,



m s



m s



2 |

M

12

B s H

 2 

B s

In 2006, CDF first observed the mixing effect Now, the results of CDF and D0 in

B s



J/

 

decay

are 

m s

 

17.77



0.10

18.56

   1

0.07 ps (

CD  1

0.87 ps (

D0

)

F

)



BR & Direct CP violation

A CP



s



B s

 

K

 

K

            6 0.39

 0.17

It will be interesting if the BR (CPA ) is really so small (large)

5

 Time-dependent CP asymmetry in B s  According previous introduction, the A CP (t) is given by

V ts

*

f



J

/  

B B

2 1 

p B

0 

p B

0 

q B

0 

q B

0

q p



J

/   

q p

*

M

12

M

12 *

M

12

M

12  exp[

i



s

]

M

12

s

   2 6

 How large is the S J/  in the SM ?

S J

/    2Im 1  

J



J

/   /   2 

J

/   

q p V ts

*

V ts

 exp • with V ts =  A  2 ,  s =0 • However, by including higher power of  where

S J

/    sin 

s V tb V cb



A

2  4 / 2,

V ts A

 4 , V c s  

A

 2  2 / 2    4 

A

 4 /  2  

A

2  / 8 

i

  

Buras, hep-ph/0505175

V ts

 

A

 2 exp[

i



s

],

s

With  =0.359 and  =0.2272

  





s s





2



 2 

s

 0 .019

 0 .0

38 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 B s the

non-vanished phase

decays, UTfit Collaboration is more than

3

 finds that 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?

10



Physical quantities related to CP violating phase

•

CP-odd physical quantity

: consider particle B decay, the decay amplitude is written as  

be



i



W e i

  W : CPV phase  : CPC phase accordingly, the decay amplitude for its antiparticle is

i



be e i

 • A CP-odd quantity could be defined by

A

 2  2  2 2 2  2  2 2 2  2  2 2

A

 

A

• Such kind of physical quantities need CP violating and conserving phases at the same time • The quantity is also called direct CP violation 11

• ˆT -odd physical quantity:

t t

 Triple-product spin-momentum correlation in 3-body decay

s B





p C



p D



T

ˆ

s B



p C



p D



A



BCD

    

s p p p

B C D



A d





Im  †  '  1.

CPV ph ase

2 .

C PC pha se

 Triple-product momentum correlation in 4-body decay

p B





p C



p D

     

p p p p

B C D



A p B





p C



p D



A



BCDE

12

 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  

K

*  

p

 

p K



T-odd

Dominant effect 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 consider the extension of the SM  s, we need to 14

 We consider the so-called vector-like quark model (VQM) VQM: add a pair of L and R quarks to the SM 

L R L 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

H C



C J W

     

SP L d s b

 

W



S

 1 0 New 4  4 CKM is not an unitary matrix 0 0  

L V SV U D L

† 

V CKM

For Z-coupling

FCNC induced at tree 15

• We only pay attention the Z-mediated FCNC

L

V X V

D D F

† 

L

V X

D D

V

F

† 

sb



V

D L



X

D

 2 4 

X D



F

† 

I

 44  

F

† 43 16

Current limit < CDF 17

18

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 B s mixing, it helps to know whether there exists a new CP phase in b  s transition 

B



K

* to observe the new phase   19

A brief introduction to

m T2

 The definition:

p

: missing transverse momentum

p

T

:

m

T

: visible transverse momentum transverse mass  A method to determine the mass of unknown particle when invisible particle appears in the final state for instance: m T2 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 m T2 , we need to know the definition of transverse mass • set a particle A decaying to B and C, if B and C are visible

P A

2 

m A

2  

p B



p C

 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

E T

  

p T

 1 ln 2

E E

 

m p

2

p z z

example:

P

W

2 

m

2 

m

2 

m

2

W

  

m

W

2    

m

2

m

2

m

2    

p



p

 2 2   2 

E E E

T E T

 2

E

T E T

 cosh 

p

p T



p

 

p T

p

T

 

m T

2 

p

T



= is satisfied when the rapidity difference vanishes

22

 Using the concept of transverse mass, Lester & Summers proposed m T2 variable to determine the mass of new particle which is produced in pair at collider • m T2 is a variable that is calculated with event by event

m

2

T



m

2 

m

2  2 

E E T T



p T



p T

 neutralino

m

2 

m T

2 • the total missing momentum is fixed

p

T



p

1 

p

2 known and fixed 23

 How powerful is the m T2 ?

very sharp at the end-point, i.e.

the error of the determined mass is very small

A.

B.

Barr, C. Lester, P. Stephens, 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 m T2 variable cannot determine the mass of invisible 

How to determine the mass of missing particle by using m T2 ?

W.S. Cho, K. choi, Y.G. Kim, C.B. Park, PRL100:171801,2008

25

m invis



m vis

26

27