Beauty In Physics Cheng-Wei Chiang ( 蔣正偉 ) National Central University & Academia Sinica Cheng-Wei Chiang ( 蔣正偉 ) National Central University & Academia Sinica Institute of Physics, NCTU October 11, 2007 Taiping Mt., April 29, 2007

C.W. ChiangBeauty in Physics2 Outline  Some cosmic questions  Standard Model of particle physics  CP violation in Standard Model  Beauty (bottom) mesons  Current status and my work in this direction  Summary

C.W. ChiangBeauty in Physics3 Some Questions Lingering In Our Minds…

C.W. ChiangBeauty in Physics4 Cosmic Questions  How does the Universe evolve?  What are the compositions and major activities of the Universe in the past, right now, and in the future?  Why is our Universe what we observe today?  Is it a pure accident or a delicate arrangement by God that we are here today?  Are we special in the Universe?

C.W. ChiangBeauty in Physics5 Standard Model of Cosmology Says

C.W. ChiangBeauty in Physics6 Why Not This One? Big Bang Where does the antimatter Universe go?

C.W. ChiangBeauty in Physics7 The Sakharov Conditions Antimatter → Matter if: (1) Baryon number violation (baryon # asymmetry) (2) Matter-antimatter asymmetry (CP Violation) (3) Departure from thermal equilibrium (preferential reaction direction) [Sakharov, JETP Lett 5, 24 (1967)] Particle Physics Astrophysics & Cosmology Must Understand CP Violation A.D. Sakharov 1975 Nobel Peace Winner

C.W. ChiangBeauty in Physics8 Little Do We Know of the Cosmos  Stars and galaxies are only ~0.5% (heavy elements are ~0.03%)  Neutrinos are ~0.3%  Rest of ordinary matter (electrons and protons) are ~4%  Dark Matter ~25%  Dark Energy ~70%  Anti-Matter ~0%

C.W. ChiangBeauty in Physics9 Standard Model Of Particle Physics

C.W. ChiangBeauty in Physics10 Standard Model of Particle Physics

C.W. ChiangBeauty in Physics11 Atomic Structure

C.W. ChiangBeauty in Physics12 Standard Model of Particle Physics Existent in usual matters Existent only in high-energy colliders and early Universe

C.W. ChiangBeauty in Physics13 Standard Model of Particle Physics  The famous Higgs boson, responsible for the masses of particles in the SM, has not been discovered yet. The existence and properties of such a particle will be a main task of CERN LHC and future colliders, and prove useful in our understanding of Nature.

C.W. ChiangBeauty in Physics14 Feynman’s Language of Interactions

C.W. ChiangBeauty in Physics15 Quantum Electrodynamics (QED)

C.W. ChiangBeauty in Physics16 Four Forces of Nature

C.W. ChiangBeauty in Physics17 Standard Procedure  Specify a scattering or decay process of interest.  Find all contributing Feynman diagrams.  Follow Feynman Rules to write down the amplitude for each diagram.  Sum over all contributing amplitudes coherently / incoherently as required by quantum mechanics.  Use Fermi’s Golden Rule to derive the scattering cross section or decay rate.

C.W. ChiangBeauty in Physics18 CP Violation In Standard Model

C.W. ChiangBeauty in Physics19 CP Transformation  In quantum mechanics, discrete symmetries  selection rules  P: parity transformation, reversing all coordinate axes; taking left to right, and vice versa.  C: charge conjugation; taking a particle to its antiparticle (reversing almost all quantum numbers except for mass, momentum, and spin), and vice versa.

C.W. ChiangBeauty in Physics20 Cabibbo-Kobayashi-Maskawa Matrix  Due to a mismatch between mass and flavor (interaction) eigenstates, the charged-current (W  ) weak interactions are  The CKM matrix is a 3 £ 3 unitary matrix connecting up-type and down-type quarks (cross-generation) in weak interactions.  It has 3 rotational angles and 1 CP-violating phase (3 families needed).  This mechanism gives CP-violating effects in the quark sector, and the only CP-violating source in the SM (insufficient for Sakharov though).

C.W. ChiangBeauty in Physics21 An Example: b → u Transition  The following processes are CP conjugate of each other.  The couplings are equal in strength, but opposite in phases.  This difference in weak phases is one ingredient for having unequal reaction rates for particles and their corresponding antiparticles. b u W − V ub / e − i  anti-b anti-u W + V * ub / e + i 

C.W. ChiangBeauty in Physics22 CKM Matrix Elements  The CKM matrix elements exhibit a hierarchical structure [Particle Data Group 2004]  Here is an order parameter of about O( )O(  ) OO OO O(  )

C.W. ChiangBeauty in Physics23 Wolfenstein Parameterization  Wolfenstein (1982) proposed the parameterization (four real parameters) to O( 3 ):  Wolfenstein parameters: ' 0.22, A ' 0.8,  ' 0.20,  '  Sizeable weak phases:  ' 22  and 40  ≤  ≤ 80 .  CPV is small due to the hierarchical structure, not the weak phase.  V ub and V td carry the largest weak phase, but are the least known elements due to their smallness.  e − i   e−i  e−i 

C.W. ChiangBeauty in Physics24 Unitarity Triangle  V ub and V td can be related to each other through the unitarity relation V ud V ub * + V cd V cb * + V td V tb * = 0, which is often visualized as a triangle on a complex plane whose area characterizes CPV. (2)(2) (3)(3) (1)(1) (0,0) (1,0) A CP (t)[J/  K S,  ’K S,  K S (?),…]A CP [D CP K , K ,…]  M Bd and  M Bs BR(B  X c,u l ) A CP [ , ,  …] decay side oscillation side

C.W. ChiangBeauty in Physics25 Indirect CP Violation in Kaon System 1980 NOBEL PRIZE J. Cronin V. Fitch [Phys. Rev. Lett. 13, 138 (1964)]

C.W. ChiangBeauty in Physics26 K-(anti-K) Mixing  Here ,  = u, c, or t quarks.  The CP eigenstates are  But the mass (physical) eigenstates are not purely CP eigenstates and decay at different rates (resulting in different lifetime):

C.W. ChiangBeauty in Physics27 Kaon Decays  K L   +  – happens about once per 300 decays, indicating that the long-lived K is indeed a mixture of different CP eigenstates, indicating indirect CPV or CPV due to mixing.  This already provided some hint of the third-generation fermions.  One immediate explanation for this was a superweak model, which proposed a new |  S| = 2 interaction that had effects only on mixing but not decay. [Wolfenstein, PRL 13, 562 (1964)]  The model was put to rest after we observed direct CPV in the K system in [CERN-NA48, PLB 465, 335 (1999); FNAL-KTeV PRL 83, 22 (1999)]  Up to now, data from the K mesons, including rare decays, are consistent with the SM expectations.  Does the B meson system provide the same picture?

C.W. ChiangBeauty in Physics28 Beauty In Physics

C.W. ChiangBeauty in Physics29 Who’s the Beauty?

C.W. ChiangBeauty in Physics30 Three Generations of Fermions u d tc sb six quarks e     e six leptons Flavor

C.W. ChiangBeauty in Physics31 The Beauty Meson  The beauty of B mesons resides in its large mass: m u,d,s <<  QCD (~ 400 MeV) << m b (~ 4.4 GeV)  In the heavy quark limit, m Q  1, we discover extra symmetries not seen otherwise:  Flavor symmetry: strong dynamics unchanged under heavy flavor exchange (b  c), corrections incorporated in powers of 1/m b - 1/m c ;  Spin symmetry: strong dynamics unchanged under heavy quark spin flips, corrections incorporated in powers of 1/m b.  They provide an ideal system for:  studying heavy-to-heavy and heavy-to-light transitions,  testing QCD perturbation, and  probing new physics. b u,d,su,d,s B +, B d, B s

C.W. ChiangBeauty in Physics32 Different Approaches  Much progress has been made in understanding heavy-to-light transitions in recent years:  Perturbative approach:  generalized factorization,  QCD-improved factorization,  perturbative QCD (pQCD), and  soft-collinear effective theory (SCET);  Nonperturbative approach: flavor SU(3) symmetry.  In our approach, we employ as much as possible the symmetry principle to help us simplifying the analysis.

C.W. ChiangBeauty in Physics33 Strong Phases Matter  The strong phase (result of strong interactions) is another ingredient for having unequal reaction rates for particles and antiparticles. Particle Anti Particle

C.W. ChiangBeauty in Physics34 Noisy Strong Phases  We can compute and know that the perturbative strong phases are small. [BSS, PRL 43, 242 (1979)]  Large strong phases may come from long-distance final-state interactions, which however are nonperturbative effect that nobody knows how to compute from first principles.  It is of great importance to understand the patterns of the strong phases, even though what we really care about are weak phases (signals), not strong phases (noises).

C.W. ChiangBeauty in Physics35 Double-Slit Experiment in B Mesons [Bigi and Sanda, NPB 193, 85 (1981)]  The oscillation phase e –i  m t plays the role of the relative strong phase. Luckily, this is controllable.

C.W. ChiangBeauty in Physics36 B0B0 B0B0 B0B0 V cb V tb V* V tb J/  KSKS KSKS  V td * 2 / e +2i   td No CPV in B → J/  K S Decay M 12 CPV in B 0 → B 0 Mixing CPV in B 0 → B 0 Mixing V cs *

C.W. ChiangBeauty in Physics37 Precision Measurement of sin2  356 fb -1 ≅ 386M B pairs 7/002/013/027/01 Indirect CPV in the B system was firmly established in 2001, and now measured at <5% precision

C.W. ChiangBeauty in Physics38 Where Do the Data Come From? SLAC BaBar KEK Belle Mt. Tsukuba NCU, NTU, …

C.W. ChiangBeauty in Physics39 KEKB Accelerator 8 GeV electron3.5 GeV positron KEKB Collider B el le 美(人)美(人)

C.W. ChiangBeauty in Physics40 Direct CP Violation in B System  By 2004, we have also established direct CPV in the B system: A CP (B d  K   0 ) = –0.115  0.018[2004] = –0.108  0.017[2006]  This asymmetry is due to CP violation in the decay amplitudes.  The history repeats itself, but in just three years this time.  We hope to learn the other weak phases (e.g.,  ) from the direct CP asymmetry measurements of charmless B decays, which usually involve sub-processes with different weak phases.

C.W. ChiangBeauty in Physics41 The FCNC effect in b-s sector of the SM was recently confirmed in the B s meson mixing observed by both CDF and D0 in 2006: Within the SM, this implies: |V td /V ts | = In comparison, the latest Belle results for b → d  and b → s  give a 95% CL range of ~ [0.201  0.030] for the above ratio. New Results From D0 and CDF

C.W. ChiangBeauty in Physics42 Status Of Constraining Unitarity Triangle

C.W. ChiangBeauty in Physics43 My Recent Works In Constraining Unitarity Triangle (For Those of You Who Are Still Awake…)

C.W. ChiangBeauty in Physics44 Flavor Diagram Approach  This approach is intended to rely, to the greatest extent, on model independent flavor SU(3) symmetry arguments, rather than on specific model calculations of amplitudes. [Zeppenfeld (1981); Chau + Cheng (1986, 1987, 1991); Savage + Wise (1989); Grinstein + Lebed (1996); Gronau et. al. (1994, 1995, 1995)]  The flavor diagram approach:  is diagrammatic (can be formulated in a formal way);  only concerns the flavor flow (arbitrary gluon exchange among quarks);  has a clearer weak phase structure (unlike isospin analysis where different weak phases usually mix).  The three light quarks (u, d, s) ~ 3 under SU(3) F.  In any process, one can freely replace one by another whenever allowed by the dynamics without changing the magnitude of its probability amplitude, except for obvious CKM factor and electric charge changes.

C.W. ChiangBeauty in Physics45 Tree-Level Diagrams q = u,d,s q 0 = d,s  All these tree-level diagrams involve the same CKM factor. annihilation (charged mesons only)exchange (neutral mesons only) tree (external W emission)color-suppressed (internal W emission) 1/m b suppressed due to f B.

C.W. ChiangBeauty in Physics46 Loop-Level (Penguin) Diagrams QCD (strong) penguin (internal gluon emission) penguin annihilation (neutral mesons) S, S' flavor singlet (external gluon emission)  All these loop-level diagrams also have the same CKM factor. q = u,d,s q 0 = d,s

C.W. ChiangBeauty in Physics47 Next-to-Leading Order Flavor Diagrams EW penguin color-suppressed EW penguin appear together with C and S in decay amps appear together with T and P in decay amps  Nothing forbids you from drawing one of the following diagrams whenever you see T, C, or P in your amplitude list. They involve two weak boson propagators.

C.W. ChiangBeauty in Physics48 Little Story About Penguin Diagrams Shifman, ITEP Lectures On Particle Physics And QFT

C.W. ChiangUT from Rare B Decays49 Hierarchical Structure And An Example  Without factoring out CKM factors, we have for the flavor diagrams:  As an example, the decay of B d →  +  – can be decomposed as – (T +P), where the minus sign comes from our convention for the meson wave functions. BdBd BdBd -- ++ ++ -- T P +-+-

C.W. ChiangBeauty in Physics50 Charmless (Rare) Decay Modes largely unexplored territory, waiting for LHC data

C.W. ChiangBeauty in Physics51 Global Fits  Objectives of the global fits:  Check if the SM offers a consistent picture for all available data;  Check the working assumption of SU(3) F ;  Extract  and  and thus the weak phases ,  and  ;  Extract strong phases;  Make predictions of unseen modes based upon current data.  Parameters involved in the fits include:  Amplitude sizes;  Weak phases;  Strong phases.  Data points used in the  2 fits include:  Branching ratios and CP asymmetries (time-dependent and -independent).

C.W. ChiangBeauty in Physics52 Old Results  charmless V P modes,  。  。 ; charmless P P modes,  。   。 ; both consistent with constraints from other observables. VP PP [CWC, Gronau, Luo, Rosner, and Suprun, PRD 69, (2004); PRD 70, (2004)]

C.W. ChiangBeauty in Physics53 New Fitting Results (P P Modes Only)  In this new analysis, we partially relax the flavor SU(3) assumption by putting in extra SU(3) breaking parameters.  Comparing our global fits with other methods: [CWC and Zhou, JHEP 12, 027 (2006)]

C.W. ChiangBeauty in Physics54 Concluding Remarks  CP violation remains one of the biggest mysteries in particle physics. We would like to understand more about its origin(s), within and beyond the Standard Model.  B meson physics provides a good opportunity at low energies for us to determine important parameters in the CKM mechanism (magnitudes and weak phases of the elements).  Currently, everything seems to fit into a consistent picture.  Rare decays of B mesons may provide us with hints of new physics (NP) at higher energy (e.g, TeV) scales because the SM contributions are much suppressed.  Once the Large Hadron Collider (LHC) turns on, we will be able to study more about the B s meson (particularly its rare decays) that are not currently probed at B factories.