Symmetry and Symmetry Violation in Particle Physics 违反对称 Lecture 4 March 28, 2008

Summary Lecture 3 CP is violated in Weak-Interactions –Neutral Kaon mass-matrix induced; scale    2x10 -3 –Direct CPV in K L   ; scale =  ’ = 1.6 x  Observing CPV requires: –Two interfering amplitudes –One with a CP-violating weak phase –Another “common” or “strong” phase In the W.I., the d and s quark mix  d’ & s’ – d’ =cos  c d +sin  s ; s’ =-sin  c d +cos  c s –  c  12 0 is the “Cabibbo angle If all quarks are in pairs, FCNC = 0 by Unitarity –(GIM Mechanism)

CP: matter  q q W g CP () =) = For CPV: g  g* (charge has to be complex) CP operator: “charge”  antimatter W†W† q g* q’q’ mirror some basic process

CP violating asymmetries in QM Even if CP is violated, generating matter-antimatter differences is hard –need a CP-violating phase (  ) –need 2 (or more) interfering amplitudes –+ a non-zero “common” phase (  ) (often called a “strong” phase)

Common and weak phases “Common” (strong) phase (  ): same sign for matter & antimatter  CP conserving Weak phase (  ): opposite sign for matter & antimatter  CP violating B A+B     A B |B|e i  i  B = |B|e i  -i 

How does CPV fit into the Standard model? Clue: CPV is seen in strangeness-changing weak decays. It must have something to do with flavor-changing Weak Interactions

CP Violation & Flavor mixing

d’ & s’ are mixed d & s Weak eigenstates Mass eigenstates 4-quark flavor-mixing matrix

how about a complex mixing matrix?   -  incorporate CPV by making  complex? (i.e.  ≠  *?) not so simple: a 2x2 matrix has 8 parameters unitarity: 4 conditions 4 quark fields: 3 free phases # of irreducible parameters: 1 Cabibbo angle s u GFGF WW  controls |  S|-1 where we see CPV

2-generation flavor-mixing  -  Only 1 free parameter: the Cabibbo angle  C  12 0 not enough degrees of freedom to incorporate a CPV complex phase d sd’ s’ cos  C  sin  C  sin  C cos  C

Enter Kobayashi Maskawa a 3x3 matrix has 18 parameters unitarity: 9 conditions 6 quark fields: 5 free phases # of irreducible parameters: 4 3 Euler angles +1 complex phase

Original KM paper (1973) From: Prog. of Theor. Phys. Vol. 49 Feb. 2, 1973 CP-violating phase3 Euler angles

3 quarks: q=  2/3 q=  1/ x3 matrix  3 generations, i.e. 6 quarks s  1/3 KM paper was in 1973, the 3-quark age Predicted by Glashow but not discovered until Nov.1974 These were not even in our 1973 dreams. 4 quarks: 6 quarks:

A little history 1963 CP violation seen in K 0 system 1973 KM 6-quark model proposed 1974 charm (4 th ) quark discovered 1978 beauty/bottom (5 th ) quark discovered 1995 truth/top (6 th ) quark discovered

CKM matrix (in 2008) CPV phases are in the corners       t d W+W+ V td b V ub W+W+ * u

The challenge b V ub W+W+ * t d W+W+ V td Measure a complex phase for b  u u or, even better, both or in t  d

The Key Use B 0 mesons B 0 = b d d b B 0 /B 0 similar to K 0 /K 0

Primer on B mesons 小学课本

What are B mesons? –B 0 = d b B 0 = b d –B  = u b B  = b u –J PC = 0  –  = 1.5 x s (c  m) How do they decay? –usually to charm: | b  c | 2  | b  u | 2  100 How are they produced? –e  e   (4S)  B B is the cleanest process Lesson 1: Basic properties u -2/3 b +1//3 u +2/3 b -1/3 d +1/3 b -1/3 b +1//3 d -1/3

Lesson 2: “flavor-specific” B decays In >95% of B 0 decays: B 0 and B 0 are distinguishable by their decay products X l  X l  B0B0 B0B0 semileptonic decays: D X B0B0 B0B0 hadronic decays: q C +2/3 D q D

Lesson 3: B  CP eigenstate decays In ~1% of B 0 decays: final state is equally accessible from B 0 and B 0 J/  K S J/  K L … B0B0 B0B0 charmonium decays: K+K…K+K… B0B0 B0B0 charmless decays: C -2/3 C +2/3 J/  J PC =1 -- CP=+

Lesson 4: The  (4S) resonance  (e  e   BB)  1nb B 0 B 0  B + B     good S/N: (~1/3) BB and nothing else coherent 1 -- P-wave 3 S bb bound states  (e  e  )  hadrons BB threshold e + e   qq continuum (u, d, s &c) 10.58GeV

Lesson 5: B 0  B 0 mixing V* td V* td These have a weak phase:  1 A B 0 can become a B 0 (and vice versa) _ u,c,t b d d b tb (only short-distance terms are important)

bud V ub V ud bcd V cb V cd btd V tb V td   *** b  d: Ά =V ub V ud f(m u ) + V cb V cd f(m c ) + V tb V td f(m t ) *** GIM: V ub V ud + V cb V cd + V tb V td = 0 ***  Ά = 0 if: m u = m c = m t

Large m t overides GIM but, m t >> m c & m u : GIM cancellation is ineffective B 0  B 0 mixing transition is strong (and this allows us to accesses V td ) V* td V* td t-quark dominates

Y.H. Zheng, PhD Thesis Also Y.H. Zheng et al., Phys Rev. D (2003) N(B) – N(B) N(B) + N(B)

The large t-quark mass: m t =174 GeV What makes B’s interesting?

Neutral meson mixing phenomenology Neutral B mesons are produced as flavor eigenstates: B 0 or B 0 B 0 (t) B 0 (t) B 0 (t) B 1 & B 2 |B 1 > = p |B 0 > + q |B 0 > |B 2 > = p |B 0 > - q |B 0 > If CPV is small: q ≈ p ≈1/  2

Time dependence of B 0 (B 0 ) mesons ( p  q  1/√2 ) |B 0 (t)> = ( |B 0 > (1+e i  mt )+ |B 0 >(1-e i  mt ))e -  t common phase  m = m 2 -m 1     

Can we measure  1 ? two processes: B 0  f cp & B 0  B 0  f cp weak phase: 2  1 common phase:  mt Yes!!

B0B0 Interfere B  f CP with B  B  f CP td  B0B0 V tb V* V cb KSKS J/  KSKS  V* 2 V tb V* tdtd td V cb B0B0 B0B0 Sanda, Bigi & Carter: + sin2  1 e i  mt

What do we measure? t   z/cβγ Flavor-tag decay (B 0 or B 0 ?) J/  KSKS B - B B + B ee ee more B tags zz t=0 f CP (tags) sin2  1 This is for CP=-1; for CP=+1, the asymmetry is opposite Asymmetric energies

Requirements for CPV Many B mesons – “B-factory” & the ϒ (4S) resonance Reconstruct+isolate CP eigenstate decays –Kinematic variables for signal +(cont. bkg suppr+PID). “Tag” flavor of the other B Measure decay-time difference –Asymmetric beam energies, high precision vertexing(Δz) –Likelihood fit to the  t distributions

PEPII B factory in California Stanford Linear Accelerator Ctr BaBar Detector

The PEPII Collider ( magnetic separation ) 9 x 3.0 GeV; L=(6.5 x )/cm 2 /sec On resonance:113 fb -1 Int(L dt)=131 fb -1

Cherenkov Detector (DIRC) [144 quartz bars, PMTs] Silicon Vertex Tracker (SVT)[5 layers] Instrumented Flux Return (IFR) [Iron interleaved with RPCs]. CsI(Tl) Calorimeter (EMC) [6580 crystals]. Superconducting Coil (1.5T) Drift Chamber [40 stereo lyrs](DCH) e - (9 GeV) e + (3 GeV) The BaBar Detector

KEK laboratory in Japan Tsukuba Mountain KEK laboratory KEKB Collider

Two rings e + : 3.5 GeV 1.5A e  : 8.0 GeV 1.1A E CM : GeV Luminosity: target: cm -2 s -1 ach’ved : cm -2 s -1 (~20 B’s/s  KEKB

elle A magnetic spectrometer based on a huge superconducting solenoid

Step 2: Select events B 0  J/  K s event Tracking chamber only  

Drift chamber for tracking & momentum measurement

Drift chamber cell E-field Charged particle track Drift speed  50  m/nsec Position resolution  150  m 16mm 17mm

Same event in the entire Detector B 0  J/  K s event J/     K S    

Kinematic variables for the ϒ (4S) invariant mass:  e+e- in CM: e+ e- B0B0 B0B0 E=E cm /2 Beam-constrained mass: J/  KSKS

Kinematic variables for the Υ(4S) Energy difference: Beam-constrained mass:    10MeV   2.5 MeV

B 0  ψ K L signal event p B * (cms) [2332 events with a purity of 0.60] Event display J/  K L 1399±67 signal K L “crash”

Step 3: Check the other tracks to see if the other meson is a B 0 or a B 0 ? ? ? ? ? ?

Flavor-tagging the other B  Inclusive Leptons:  high-p l  b  c l   intermed-p l + s l    Inclusive Hadrons:  high-p  - B 0  D (*)+  -, D (*)+  -, etc.  intermed-p K - K - X,      low-p  + D 0  + Belle: effective efficiency = 30 % Figure of merit(Q) =ε(1-2 w) 2 a.k.a effective tagging efficiency

Distinguishing different particle types dE/dx Ionization density in the drift chamber (dE/dx)

Distinguishing different particle types (Cherenkov) When  (=v/c) > 1/n, “cherenkov” light is produced Only particles with b>0.99 count in these

K meson identification from dE/dx, Cherenkov & TOF

Distinguishing different particle types (time-of-flight) Time = L/v x x Scintillation Counter barrel

TOF measurements of particle mass Time = L/v   = v/c = p/ √ (p 2 +m 2 )  m Mass from TOF measurements

A K - tag event means the other meson is (probably) a B 0 (not a B 0 )     K-K-  Identify the other tracks in the event D  K - not K + D  K + not K - B  D >> B  D

Silicon detectors measure Δz (typically ~200  m) Beam spot: 110 μm x 5 μm x 0.35 cm Step 4. Find decay time difference

Silicon vertex detector 50  m

Silicon detector E-field Charged particle track position resolution  20  m 300  m

Magnified vertex K s  +   ~7cm

y-z vertices

A Fully-reconstructed Event Human hair ~200 

Event-by-event Likelihood background frac Sidebands & MC resolution function B-lifetime studies  f = ±1 for CP=  1 PDG wrong-tag frac. lone free parameter b-flavor tag

sin2  1 measurement by Belle (2003) sin2  1 measurement by Belle (2003)  “Raw” asymmetry BELLE-CONF evts Poor tags Good tags

Results (2007) Belle BaBar sin2  1 = ± CP=-1 CP=+1 CP=-1 CP=+1  1 = ± 1.0 0

The “Unitary Triangle”

Unitary triangle: ~1  |V td | measured by B 0 -B 0 mixing |V ub | measured in b  uℓ - decay |V cb | measured in b  cℓ - decay |V cd |=sin  C luckily: otherwise, the triangle would be flat Overconstrained!!

Unitary triangle constraints 2007 SM+CKM is verified

CP is violated in B decays ~70% effect in B  J/  K S decays –compared to ~0.2% effect in K 0 decays Kobayashi-Maskawa mechanism verified. After 35 years, 3 new quarks &, happily,

Next Step Check the Unitary Triangle with Penguins b  s FCNC decay t-quark is the dominant contributor Why is he so happy?

SM FCNC: i.e.> ~10% for M X,Y LHC t at least V New heavy Particles? 2 nd -order weak process with t & W in the loop New Physics?: X Y

sin2  1 with b  s penguins (SM) Example: no CP phase SM: sin2  1  sin2  1 from B  J/  K S (b  c c s) eff V td + 11 B B,  ’,     11 _ * *

B0  'K0B0  'K0 (bkg subtracted) B 0 mass B 0 momentum hep-ex/ K0KSK0KS K0KLK0KL 1421 ± 46 signal evts 454±39 signal evts

TCPV in B 0   'K 0 “sin2  1 ” =  0.64  0.11 hep-ex/ SM: 0.681±0.025 (from B  K S J/  )

B0  K0B0  K0 B 0 mass B 0 momentum (bkg subtracted) hep-ex/ K0KSK0KS K0KLK0KL 307 ± 21 signal evts 114±17 signal evts

TCPV in B 0   K 0 “sin2  1 ” =  0.50  0.22 hep-ex/ SM: 0.681±0.025 (from B  K S J/  )

 1 with b  s Penguins Naïve average of all b  s modes sin2  eff = 0.52 ± 0.05 Naïve average of all b  s modes sin2  eff = 0.52 ± 0.05 SM: ± ~2.6  difference  Hint, but not strong evidence for new physics.  Need more precision (data)  M X,Y > M top

Brief summary 得了

Symmetries are important in: –Life –Art –Nature

Space time symmetries  conservation laws –Space translation symm  Conser. of momentum –Rotational symm  Conserv of angular momentum –Time translation symm  Conserv. of Energy E. Noether

Discrete symmetries are important in QM –Parity –Charge Conjugation –Time Reversal Man P Man C

P (and C ) are strongly violated in W.I. But C P looks  OK  e-e-  e+e+ CPCP “charge conjugate” mirror

C P is violated in neutral K decay –Small effects: –  (K L   )/  (K S   ) =  2  4x10 -6 –  (K L   e + )/  (K L   e - ) =   2x10 -3 M(  +  - )<M(K L ) M(  +  - )>M(K L ) M(  +  - )=M(K L ) cos  K0K0 K0K0

Kobayashi Maskawa (1973) 6-quark model –Needs 3 more quarks than are known at the time –Predicts large C P violation in B-meson decays. 3 more quarks discovered –c (1974) –b(1978) –t(1995) CP phases go here

Large C P violation found in B meson decays –~70% effect KM predictions validated sin2  1 = ± 0.025

C P measurements for Penguin (loop) processes can search for new particles at high mass scales –Even higher than the LHC New heavy Particles? X Y

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