CP Violation in B Decays Vivek Sharma University

CP Violation in B Decays Vivek Sharma University of California at San Diego http: //vsharma. ucsd. edu/marialaach 05. pdf

Outline Of The Four Lectures • • • Brief history of discrete symm. violation & KM Conjecture CKM Matrix, Unitarity triangle & the special place of B mesons Primer on B physics (to understand CPV discussion better) Quantum entanglement in (4 S) B 0 Need for Asymmetric energy colliders : PEP-II and KEK-B Critical features of Ba. Bar & Belle for CPV measurements Three types of CPV in B system : SM predictions Techniques in time-dependent CPV measurements Observables and hot new experimental results on CP violation Synthesis and summary of current experimental observations Future experimental directions Lectures intended for beginning graduate students in Particle and Particle Astrophysics kept simple and intuitive 2

Suggested Reading • Ba. Bar Physics Book available online at – http: //www. slac. stanford. edu/pubs/slacreports/slac-r-504. html • J. Silva’s lecture notes on CP Violation from Prague summer school 2004: – hep-ph/0410351 • Z. Ligeti’s SLAC Summer School Lectures 2002 – hep-ph/0302031 • Review articles on CP Violation, CKM Matrix and B Mixing in the Particle Data Book – http: //pdg. lbl. gov/ • B Physics at the Tevatron: Run II and Beyond : – hep-ph/0201071 Discovery Potential of a Super B factory: – http: //www. slac. stanford. edu/pubs/slacreports/slac-r-709. html • LHC-b “reoptimized” Detector TDR : – http: //lhcb. web. cern. ch/lhcb/TDR/reoptdr. pdf • Textbooks: – CP Violation: Branco, Lavoura, Silva; Published by Clarendon Press – CP Violation by Bigi & Sanda; Published by Cambridge Press – Heavy Quark Physics: Manohar & Wise; Published by Cambridge 3

Outline of Lectures: Lecture 1 • Brief History of Symmetry violations – Thru the looking glass With Alice : P, C and CP mirrors – CP Violation in Kaon system – The KM conjecture and the rise of three quark generations • The CKM Matrix and Unitarity Triangles – “The” Unitarity Triangle in B system • Three surprising discoveries that made B physics exciting • Prolific environments of b flavored hadrons • A quick primer on general B hadron properties (to understand the CP discussion better) • CP Violation as a Quantum Phenomenon • B 0 Meson time evolution and the special case of (4 S) B 0 • The need for an Asymmetric energy collider 4

Three Important Discrete Symmetries That Usually Work • Parity, P – Parity reflects a system through the origin. Converts right-handed coordinate systems to left-handed ones. – Vectors change sign but axial vectors remain unchanged • x x , L L • Charge Conjugation, C – Charge conjugation turns a particle into its anti-particle + • e+ e-, K- K+ , g g • Time Reversal, T – Changes, for example, the direction of motion of particles • t -t Gravitational, E&M and Strong Interaction indistinguishable under these transformations : but NOT Weak Interaction 5

A Shocker : Weak Interaction Violates Parity ! Observation of a spatial asymmetry in 1956 C. S. Wu the b-decay electrons from 60 Co 60 Ni + e + n • Cold 60 Co inside a Solenoidal B Field • 60 Co nuclei spin aligned with B field direction • 60 Co undergoes decay ……. electron emitted • Measure electron intensity w. r. t B field dir. • Result: Electrons preferentially emitted opposite spin dir. B Ve The fore-aft asymmetry of intensity Weak interaction violated Parity 6

Alice’s New Adventures Through The “Looking Glass” ! Real World Mirror World See Wigner, Adair ’s Articles (~1965) in Scientific American 7

Alice’s World “P Weak Interaction and a Journey” MThrough The irro r. W Symmetry -Mirror Worlds With Alice orl ! d e e Part I : Spatial Inversion as in a Regular B B e. Mirror e- Alice CAN differentiate between her world and the Parity Mirror World 8

Alice’s World “C ”M irro The C Mirror changes particles to anti-particles r W and Viceorl Verca d But maintains the orientation of objects it reflects e e- e+ Anti-Co Nuclei have Magnetic properties Opposite of Co So they are aligned opposite B field direction e+ Anti-Co Nuclei emit positrons in direction of the Nuclear Spin Alice Can differentiate between her world and the Charge Mirror World ! 9

Alice’s World “C P” Mi rro The CP Mirror changes particles to anti-particles r. W orl and Vice-Versa, -flips the orientation of objects it d + reflects e e e Anti-Co Nuclei emit positrons in direction + of the Nuclear Spin e Alice Cannot differentiate between her world and the CP-Mirror World ! 10

Paradise Lost, Paradise Regained ? • While P & C Mirror Symmetry are each shattered • The combined CP Mirror seemed OK (1957) • Is CP the Universal Mirror ? • Will Alice be trapped forever in the Mirror World ? Luckily for Alice, the totally unexpected happened ! ! 11

CP Violation in Kaon System ! • CP conservation implies CP = +1 CP = 1 n CP violation in KL decay observed in 1964 0. 2% of the time! Theory in Turmoil ? How to explain this tiny CP Violation? Many models proposed …most fell by the way of experiments but One conjecture survived and grew in stature ! 12

What The Discoverers Of Kaon CP Violation Said 1980 Nobel Lecture These Lectures Examine CP Violation in the Context of the Standard Model developed since then 13

What Was Known about Quarks and Leptons Then Three Quarks for Muster Mark !…Joyce Cabibbo Angle (Flavor mixing flavor Weak state flavor Mass eigenstate 14

The Kobayashi-Maskawa Paradigm for CP Violation 1972 Two Young Postdocs at that time ! • Proposed a “daring” explanation for CP violation in K decay: • CP violation appears in the charged current weak interaction of quarks • There is a single source of CP Violation Complex Quantum Mechanical Phase KM in inter-quark coupling matrix • Need at least 3 Generation of Quarks (then not known) to facilitate this • CP is NOT an approximate symmetry, it’s MAXIMALLY violated ! 15

Generations of Quarks and Leptons Circa 2002 Since then, Experiments Show Three generations : no more, no less ! Just Enough to Make CP Violation Possible 16

Number of Light Neutrino Families: LEP@CERN Width of the Z resonance 17

The Weak Interaction Couplings of Quarks • The coupling strength at the weak vertex is given by g. Vij – g is the universal Fermi weak coupling W b g. Vcb c – Vij depends on which quarks are involved – For leptons, the coupling is just g • For 3 generations, the Vij can be written as a 3 x 3 complex unitary matrix (CKM) • View this matrix as rotating the quark states from a basis in which they are mass eigenstates to one in which they are Weak eigenstates 18

CP Violation In SM With 3 Generations • The CKM matrix 3 3 complex unitary matrix • Requires 4 independent parameters to describe it: – 3 real numbers & 1 complex non-trivial phase • The existence of the complex coupling (phase) gives rise to CP violation – If only 2 quark generations 2 2 matrix is all real No CP violation • Some Expectations: – CP violation is the result of interference between different decay amplitudes involving weak phase – CP violation is “built” into the Standard Model with 3 generations or more …or so Kobayashi-Maskawa wondered 19

CP Violation In SM With 3 Generations • The CKM matrix 3 3 complex unitary matrix • Requires 4 independent parameters to describe it: – 3 real numbers & 1 complex non-trivial phase • The existence of the complex coupling (phase) gives rise to CP violation – If only 2 quark generations 2 2 matrix is all real No CP violation • Some Expectations: quark decay q g. Vqp anti-quark decay q g. V*qp Wp W+ p – CP violation is the result of interference between different decay amplitudes involving weak phase – CP violation is “built” into the Standard Model with 3 generations or more …or so Kobayashi-Maskawa wondered Complex phases CP violation 20

Measurement of CKM Element Magnitudes eee e K n b u p el c b c l+ d D K l+ t b 21

A Convenient Parameterization of CKM Matrix Wolfenstein, saw interesting pattern with 4 numbers Relative magnitudes d s b u c t The four parameters are given by CPV phases in this parametrizatio 22

The (Many) Unitarity Triangles Unitarity condition of CKM Matrix orthonormality of rows & columns various relationship between elements, three of them are interesting for understanding SM predictions for CP violation Each relation requires sum of three complex quantities to vanish can be represented in the complex plane as a triangle known as Unitarity Triangles With the knowledge of |Vij| magnitudes, its instructive to draw the triangles 23

Three Unitarity Triangles drawn to Common scale ds One side is much shorter than the other two triangle collapses on a line sb db All sides of comparable length ( 3) All angles are large Experimentally hard to measure small numbers easier to measure larger numbers as in (c) 24

“The” CKM Unitarity Triangle In B Decays Angles of Unitarity Triangle Rescaling, aligning All lengths involve b decays Large CP Asymmetries predicted , UT angles 25

Is CKM Matrix the (only) Source of CP Violation? • Observed CP violation in Kaon decays is consistent with the KM conjecture but this could have been a fluke (post-prediction) ! – needs new& many rigorous experimental tests • KM paradigm quantitatively predicts large CP violating asymmetries in the decays of the B meson system • In addition, New Physics sources of CP violating phases which can substantially alter the CPV asymmetries in B decays – B Mesons provide a good laboratory for searches for NP – emphasis on experimental observables which have “clean” theoretical interpretation Large B mass helps ! 26

1980 s: When b quark Became Special ! With CPV measurements at B factories currently in full swing, It is perhaps useful to look back at the three surprising experimental results which have paved the way towards measurement of CP Violation in B meson decays 1. B Lifetime (1983) 2. B 0 Oscillation (1986) 3. b u Transitions (1988) 27

The Large Lifetime of B Mesons • 1983: MAC and MARKII B lifetime 1. 6 ps !! detectors at SLAC • Measure signed impact parameter of leptons in semileptonic b hadron decay • Impact Parameter Resolution – MAC ~ 600 micron – MARK II ~ 200 micron • Results – MAC : 1. 8 +- 0. 6 +- 0. 4 ps – MARKII: 1. 2+. 45 -. 36+-. 3 ps • Confirmed by TASSO & JADE @PETRA • Subsequently measured very precisely at LEP@CERN decay 28

DESY’s discovery: The Large B 0 Oscillation Rate ARGUS • • • Mixing rate depends on Top quark mass Inspired by PEP/PETRA nonobservation of the top quark, many theorist assured as that “Top could not be heavier than 40 -50 Ge. V. . conservatively speaking” !! Definitive results from ARGUS(1987) showed B mixing to be large, if we could calculate better, could have shown that top quark is as heavy as it really is ! 29

Vub: The Magnitude of b u Transition • • • Must have Vub 0 for SM with 3 generations to accommodate CP Violation seen in K 0 decays and expect CP violation in B decays The magnitude has too be just-right for measurable CP asymmetries in B decays No theory could predict the magnitude of b u transition Observed excess of leptops beyond b cl kinematic endpoint Vub 0. Thus, stage was set for probing CP violation in B decays all over the world b cl b u l 30

CPV Studies in B decays is a Worldwide effort 2002 BABAR 1999 2001 CLEO A T L A S 2007 1999 BELLE 1999 Primary Goal Precision measurements of charged weak interactions as a test of the CKM sector of the Standard Model and a probe of the origin of the CP violation 31

An Express B Meson Primer Where are the b hadrons produced copiously ? What does the Environment Look Like ?

Where the B’s are : In Electron-Positron Collisions 33

The Upsilon resonances as seen in e+ e- Collisions e+ (4 S) Ebeam= 5. 29 Ge. V e- Ebeam= 5. 29 Ge. V e+ g e- Enough energy to barely produce 2 B mesons, nothing else! B Mesons produced with ~ 300 Me. V momentum Moving very slowly, don’t travel much before decay 34

The Magnificent Z Resonance All types of B hadrons produced in Z bb hadronization Average B momentum ~ 35 Ge. V ( )B 7 (highly relativistic) LEP/SLD Program ended in ‘ 95, made important contributions to b physics 35

In pp Collisions at the Tevatron (& LHC soon !) Tevatron 36

Where the B’s are: In pp collisions At the Tevatron 37

Advantages And Disadvantages of (4 S) Machines • Advantages: – Low interaction rate (~102 Hz) , possible to trigger on, and record, essentially every BB event – High Signal/Background – Events clean to interpret, mean multiplicity~11 – One B and one B produced per event (and nothing else) – Clean environment Possible to reconstruct 0 & capability to make measurements in many different channels – Happening now ! • Disadvantages: – Low cross-section, produce ~108 BB /year (107 seconds) – Only Bd and Bu mesons produced, Not enough energy to make Bs. Bs mesons or b baryons 38

Advantages And Disadvantages of Hadron Colliders • Advantages: – HUGE bb cross-section ! b=100 b (Tevatron), x 5 (LHC) – Bs mesons produced (1/3 of Bd rate) – Long B decay distance (~mm) before decay – Very energetic particle in the final state • Disadvantages: – Very high multiplicity event – poor S/N 0. 002 (Tevatron)--0. 006 (LHC) – Difficulty in triggering and recording (need lifetime trigger) – High interaction rate (~20, 000 Hz!) – Possible asymmetries in production rates of B Vs B – Tevatron luminosity finally improving, LHC experiments begin > 2008 (future) 39

Characteristic Parameters of (4 S) Machines & Hadron Colliders Ultimately both environments are complementary and essential for complete understanding of the CPV Phenomenon Because (4 S) Machines are currently producing exciting results at a furious pace, I will concentrate on that environment during these lectures and comment on Interesting measurements from Hadron machines at the 40 end

B Meson Properties (To follow the CP Violation Discussion Better)

Some Lowest B Hadron Masses and Lifetimes Particle, I(JP) Mass ( in Me. V/c 2) Lifetime =1/ (in 10 -12 s) B 0 d =(bd) , I(JP)=½ (0 -) 5279. 4 0. 5 1. 536 0. 014 & (c =460 m) B- = (bu), I(JP)=½ (0 -) 5279. 0 0. 5 1. 671 0. 018 & (c =501 m) B 0 s =(bs), I(JP)=0(0 -) 5369. 6 2. 4 1. 461 0. 057 & (c =438 m) b = (bud), I(JP)=0(1/2+) 5624. 0 9. 0 1. 229 0. 080 & (c =368 m) 42

Mass Measurement: Reconstruct All p in Decay 43

ps Lifetime Measurement is a Distance Measurement A Z 0 bb event c 2000 m measurable by silicon detectors proper time distribution Measure distance between production and decay Measure B momentum Fit proper time distribution to exponetial detector resolution 44

Many Ways That a B Mesons Transform or Decay (Introduction to the Jargon relevant for CPV discussion)

B 0 Oscillation Start with a pure beam of B 0 mesons Probability a B 0 component automagically develops with time-dependent oscillation B 0 QM Two-state system Oscillation rate dominated by tt (off-shell) intermediate states Scope for heavy New Physics particles to contribute additionally (e. g. SUSY) 46

“Tree Level” Diagrams For B Hadron Decays Spectator Semileptonic W- WColor Suppressed W- Annihilation W-Exchange W 47

Penguin Decays of B Mesons Radiative Penguin EW Penguin Gluonic Penguin 48

Penguins Observed in B Decay !! (1993) CLEO B K* Important window to New Physics 49

Penguins In B Decays? 50

Summary of b-quark Decay 51

CP Violation • CP violation can be observed by comparing decay rates of particles and antiparticles • The difference in decay rates arises from a different interference term for the matter vs. antimatter process. Analogy to double-slit experiment: source Classical double-slit experiment: Relative phase variation due to different path lengths: interference pattern in space 52

CP Violation Is a Quantum Phenomenon • CPV is due to Quantum interference between > two amplitudes • Phases of QM amplitudes is the key • Need to consider two types of phases – CP-conserving phases: don’t change sign under CP (Sometimes called strong phases since they can arise from strong, final-state interactions) – CP-violating phases: these do change sign under CP transformation (originate in the Weak interaction sector) 53

How can CP asymmetries arise ? • Suppose a decay can occur through two different processes, with amplitudes A 1 and A 2. • First, consider the case in which there is a (relative) CP-violating phase between A 1 and A 2 only. No CP asymmetry! (Decay rate is different from what is would be without the phase) 54

How can CP asymmetries arise ? • Next, introduce a relative CP-conserving phase in addition to the relative CP-violating phase • Now have a CP asymmetry 55

Definition of CP Asymmetry To extract the CP-violating phase from an observed CP asymmetry, we need to know the value of the CP-conserving phase difference B system: extraordinary laboratory for quantum interference experiments: many final states, multiple “paths” Lots of channels for CP Violation 56

End of Lecture 1 Tomorrow: QM of neutral B Mesons & EPR at (4 S) CPV Observables and requirements Asymmetric Energy Colliders and Detectors –requirements –performance

A Convenient Parameterization of CKM Matrix • Wolfenstein, saw a pattern with 4 numbers Relative magnitudes d s b u c t • The four parameters are given by: parametrization and the CPV phases in this 58