2. B Physics e+e- machine Hadron machine
CLEO(done), BaBar(1999-), Belle(1999-)
Hadron machine
CDF(2000-), D0(2000-), BTeV(2007-)

3. 1 1 CKM Matrix Status eig eib Vud/Vud 0.1% Vus/Vus =1% Vub/Vub 25%l e l
eig B n n n K n p p 
Free/bound
Vcd/Vcd 7%
Vcs/Vcs =15%
Vcb/Vcb 5% l l D n B n l D D n K p
Vtd/Vtd =36%
Vts/Vts 39%
Vtb/Vtb 29%
eib 1 Bd Bd Bs Bs
Vud, Vus and Vcb are the best determined due to flavor symmetries: I, SU(3), HQS. Charm (Vcd & Vcs) and rest of the beauty sector (Vub, Vtd, Vts) are poorly determined. Theoretical errors on hadronic matrix elements dominate.

4. Unitarity Constraints
|Vud|2 + |Vus|2 + |Vub|2 = = 1 ??
The normality test fails at 2.2
|Vcd|2 + |Vcs|2 + |Vcb|2 = = 1 ??
The error is too large for a meaningful test!
Orthogonality :
VudVcd* +VusVcs*+VubVcb* = 0
cu triangle

5. B Physics at BaBar and Belle
Light B quark
Upsilon(4S)

6. The b quark (anti b quark in [])
Charge 1/3e [-1/3e]
Baryon number 1/3 [-1/3]
Mass about 5.5 X the proton [same]
Decay lifetime 1.6X10-12 sec [same]
Beauty (bottom) quantum number -1 [+1]

7. CP Violation in B Decays (I)
Recall: In order to generate a CP violating observable, we must have the following conditions:
Interference between at least two different amplitudes
All 3 quark generations involved
In B decays, we can consider two different types of amplitudes:
Those responsible for decay
Those responsible for mixing d b W- u p+ p- B0
Decay Diagram
u,c,t
Mixing Diagram
For example …

8. If decays occur to a common CP eigenstate fcp, accessible to both B0 and B0, CP violation occurs via …
Mixing
Decay B0
Interference between
Mixing and Decay B0 B0
Squaring the amplitudes leads to CP violation effects
and
and

9. CP violating asymmetry
CP violating asymmetry is defined as
magnitude of l
phase of l

10. CP Violation in B Decays (II)
This gives rise to three possible manifestations of CP violation:
Direct CP violation
(interference between two decay amplitudes)
Indirect CP violation
(interference between two mixing amplitudes)
CP violation in the interference between mixed and unmixed decays

11. Three ways to measure CP (I)
From the decay of B mesons: Direct CP
It can occur in both neutral and charged B decays
Interference of several decay amplitudes gives CP asymmetries
e.g., G(B+  K+r0) = G(B-  K-r0)
Asymmetry is non-zero if
Amplitudes are similar
Have different CKM phases
Have different strong phases
But, it has large uncertainties on strong phase difference and decay amplitudes estimations.
Thus, it is difficult to extract
the value of the CKM angle
external spectator
internal spectator
annihilation
penguin
Feynman diagrams for B+  K+r0

12. Three ways to measure CP (II-1)
|B0 b d
u,c,t W-
From the B0 - B0 mixing
What is it?
The weak interaction allows |B0 to mix into |B0 through the box diagram.
A state the is initially |B0 will evolve in time, and eventually become |B0.
The stationary states are B1 and B2, and they have different masses:
Time evolution
Unmixed
Mixed

13. Three ways to measure CP (II-2)
The B0 - B0 mixing exists!
Unmixed B0
Mixed B0
p/Dmd

14. Three ways to measure CP (II-3)
CP from the B0 - B0 mixing:
e.g., B0 B l +l + + X = B0 B l -l - + X B0 B0
ACP/T = (0.5 ± 1.2 ± 1.4)%
|q/p| = ± ± 0.007
SM predict asymmetry < 10-3
Sizable asym. (~1%) signal NP

15. Three ways to measure CP (III)
CP From the interference between decay and mixing:
Large time dependent asymmetries expected in the SM
e.g., B0  p+ p- = B0  p+ p- d b W- u p+ p- B0
Decay Diagram
u,c,t
Mixing Diagram
For decays to CP eigenstates where one decay diagram dominates,
Asymmetries can be directly related to CKM parameters in many cases, without hadronic uncertainties

16. Three classes of final states
Class 1: CP eigenstates (e.g., J/ K0S)
Class 2: C eigenstates, but not CP eigenstates (e.g., J/ K*)
Class 3: Both and can decay to, but are not CP eigenstates (e.g., r+ p-): CP conjugate states
Golden Mode
Decay
Mode
|l|
Iml
Comments
b  ccs
J/Y Ks 1
Sin2b
Single weak phase.
Clean both theory & expt.
b  ccd
D*D(*) ?
sin2b if |l|=1
But, it has sizable Penguin
b  uud
p+p-
sin2a if |l|=1

17. Summary on CP violation in B decays
B system can measure all three CKM angles.
B system has the largest CP effects.
CP asymmetry caused by the interference between mixing and decay is the largest.
Clean CP violation signature in B decays will appear first in B0  J/ K0S channel.
Which experimental facility to choose?

18. Experimental Consideration (I)
B-FACTORY GOAL: performing a comprehensive study of the CP violation phenomena such as angle b measurement.
Ideal place is e+e- collider at (4S) resonance
Very clean environment
- No extra particles produced in
association with the Bs
Possible to produce many Bs
- Large cross section
- High luminosity
BB threshold

19. Experimental Consideration (II)
VudV*ub+ Vcd V*cb+ VtdV*tb = 0
B0 ,  a
Need high luminosity (~500fb-1)
B-factories!
B.R. ~ few 10- 6
Theoretically uncertain
Vtd
Vub b g
B0J/K0s
B0DK, D*
Vcb
Very clean,
Eff B.R. ~
Eff B.R ~10- 7; tough!!

20. Experimental Consideration (III-1)Dt
l -
Asymmetry vanish
if one integrates over Dz(Dt)

21. Experimental Consideration (III-2)
Asymmetry possible if one is able to distinguish positive and negative Dt
Since the velocity of the Y(4S) frame (center-of-mass frame for the B meson pairs) is very small, produced B meson pairs are almost at rest until they decay. Therefore, measuring Dz(Dt) is hopeless  Need Asymmetric B factory of moving center-of-mass frame!

26. B Physics at CDF, D0 and BTeV
Heavy B quark

27. The Tevatron is a Full Service B Factory
B production rate is high: ~ 20 L = 2 x 1032 cm-2s-1
Data collection limited by offline bandwidth of ~50Hz
All B species are produced
B mixing measurements:
- Bd , Bs access to |Vtd|/|Vts|
CP violation:
- Bo  J/y Ks , Bs  J/y f , …
Rare decays:
- B/Bs->Kmm/em, B/Bs->K*/r/fg,
B hadron spectroscopy with Bc
- Bc J/yln
- Bc J/yp, J/y a1, J/yDs, Bsp
Lb->pln and Lb->Lcln
QCD production studies… ps

28. B physics Lightest B Mesons Heavier B Mesons Baryons: bu bd bs bc bud
Antimesons:
Antibaryons: bu bd bs bc
b u d B- B0 Bs Bc
Upsilon:
B Factory Energy is too low to make these modes! bb

29. CKM Quark Mixing VCKM : 3 X 3 Unitary Matrix (V†V=I)
The Cabibbo-Kobayashi-Maskawa (CKM) matrix relates quark
mass eigenstates to weak eigenstates
VCKM : 3 X 3 Unitary Matrix (V†V=I)
Vij has a real part + imag phase
CP violation due to imag phase

30. CKM Matrix Wolfenstein parameterization to order 4
4 parameters (A, , , )
=sinC = ±
A =0.81 ± 0.04
To O( 4 ) ~ 10-3

31. The Unitary Triangle B0→pp B0→rp etc. B0→J/Y Ks B0→D(*)D(*) etc.
with l = and A = ,
Im (r , h)
a with l Vcb* = A l3
Vub* / l Vcb* Vtd / l Vts and l Vts = - A l3
g b Re
B0→pp
B0→rp
etc.
B0→J/Y Ks
B0→D(*)D(*)
etc.
B0→D*p
B0→D*r

32. Current allowed r - h region
Heavy flavor decay
measurements, together
with CP violation in
K decay restrict the
unitary triangle apex
to an allowed region

33. CP Violation in B physics
To Measure differences or asymmetry between B’s and anti-B’s are the goal.
To show the evidence of matter-antimatter asymmetry of universe
Up to now, CP violation is observed only Kaon system.
However, Standard Model predicts CP violation in B physics.
Both will be carried at CDF
Bd will complement measurements at Belle and Babar
Bs will be unique to the Tevatron for the near future

34. B – B mixing
Vtd controls Bo - Bo mixing via box diagram. The oscillation frequency
can be measured and used to determine Dmd = m(BH) -m(BL)
Then Dmd can be used to calculate |Vtd| from :

35. Mixing angles a , b , g
Measure direct interference between neutral B and B decays to
CP eigenstates
Measured ACP lowered
by effects of flavor
tagging efficiency:
ACPobs = D ACP
Mixing of different
samples different
CKM angles

36.  B0  J/Y Ks (sin2b) V*2 td J/y B0 KS J/y B0 B0 KS V* td V* td Vcb
Vtb td B0 B0 KS
Vtb V* td

37. References
Dr. S.W. Yang
Prof. Tom Browders