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

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.

Unitarity Constraints |Vud|2 + |Vus|2 + |Vub|2 = 0.9959+-0.0019 = 1 ?? The normality test fails at 2.2 |Vcd|2 + |Vcs|2 + |Vcb|2 = 1.13+-0.33 = 1 ?? The error is too large for a meaningful test! Orthogonality : VudVcd* +VusVcs*+VubVcb* = 0 cu triangle

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

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]

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 …

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

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

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

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

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

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

Three ways to measure CP (II-3) CP from the B0 - B0 mixing: e.g., B0 B0 l +l + + X = B0 B0 l -l - + X B0 B0 ACP/T = (0.5 ± 1.2 ± 1.4)% |q/p| = 0.998 ± 0.006 ± 0.007 SM predict asymmetry < 10-3 Sizable asym. (~1%) signal NP

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

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

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?

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

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. ~ 10- 4 Eff B.R ~10- 7; tough!!

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

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!

B Physics at CDF, D0 and BTeV Heavy B quark

The Tevatron is a Full Service B Factory B production rate is high: ~ 20 KHz @ 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

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

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

CKM Matrix Wolfenstein parameterization to order 4 4 parameters (A, , , ) =sinC = 0.2205 ± 0.0018 A =0.81 ± 0.04 To O( 4 ) ~ 10-3

The Unitary Triangle B0→pp B0→rp etc. B0→J/Y Ks B0→D(*)D(*) etc. with l = 0.2205 + 0.0018 and A = 0.81 + 0.04, Im (r , h) a with l Vcb* = A l3 Vub* / l Vcb* Vtd / l Vts and l Vts = - A l3 g b 0 1 Re B0→pp B0→rp etc. B0→J/Y Ks B0→D(*)D(*) etc. B0→D*p B0→D*r

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

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

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 :

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

 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

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