Symmetry and Symmetry Violation in Particle Physics 对称 违反 Lecture 3 March 21, 2008

Summary Lecture 2 Antimatter predicted by Dirac & discovered by Chao & Anderson 1933 Nobel prize  Dirac 1936 Nobel prize  Anderson (but not Chao) Electron & positron have opposite parity Charge “reversal”  Charge “conjugation” Particle Antiparticle (not just charge) C=+1  even # of g’s; C=-1 odd # of g’s p and K mesons = qq with L=0, S=0 & P=-1

Summary Lecture 2 (pg 2) t+ = p+p+p- & q+p+p0 puzzle led Lee & Yang to question L-R symmetry of nature C.S. Wu discovered P viol. in Co60Ni60 e-n 1957 Nobel Prize to Lee & Yang (but not Wu) t+ and q+ are the same particle, the K+ meson C & P violation differences seen in m-/m+ decay But CP seems okay Large matter vs antimatter asymmetry in the present-day Universe implies CP is violated. K0K0 transitions possible @ 2nd-order W.I.

Reminder P C, P & CP for p and K mesons C CP Particle |p+ -1 +|p-

My tentative plan for this class is as follows: Lecture 1. Definition of symmetry, why they are important in physics. Symmetries of the laws of nature. Relation of symmetry and conservation laws. Discrete symmetries C, P & T. Violation of parity (P) in beta-decay Lecture 2. Antimatter, and matter-antimatter symmetry. Quark content of hadrons & discrete symmetries of hadrons. Violation of parity (P) and charge conjugation (C ) symmetry in beta-decay Particle- antiparticle mixing. Lecture 3. K0K0 mixing. CP violation in K decay. Difficulties with incorporating CP violation into a physics theory. KM 6-quark model for CP violation. Role of B mesons in the theory Lecture 4. Studying CP violation in the B meson system. Experimental techniques and results. What is left for the future. Lecture 5. Exam

Discovery of CP violation in the neutral K meson system outline Neutral K meson decay mechanisms K0 – K0 mixing  KS and KL mesons Discovery of KLp+p- CP violation in KLp+e-n/p-e+n decays “Direct” CP violation in KLpp decays

K0  p+p- decays via weak interaction u K0 d DS=-1 s W.I. d W+ p+ u

K0 also decays to p+p- p+ d u K0 d DS=1 S W.I. W- u p- d

K0 K0 possible as a 2nd order weak interaction process |DS|=2 p+ d W+ K0 d u W.I. S W.I. s u K0 W- d p- d This is a so-called “long-range” process. It occurs on a size scale determined by the p mesons: ~ 10-15m 1 fermi

K0 K0 in short-range quark |DS|=2 u c t W.I. W.I. S d W- W+ K0 K0 W.I. W.I. s d u c t This is a so-called “short-range” process. It occurs on a size scale determined by the t-quark: ~ 10-18 m 10-3 fermi

What happens when two identical systems are coupled? Energy transfers back-and-forth between the two oscillators

Steady-state “normal modes”

Shrodinger Equation: .. H Y = EY H Y Y If CP symmetry holds:

Eigenvalues and Eigenstates 特征值 Find the eigenvalues and eigenvectors for: Answer Homework: Please check that these answers are correct

In standard (textbook) notation

If CP symmetry is good:

CP of K1 and K2 Recall: CP = +1 CP = -1

K1 decays K1  p+ p- ? K1  p+ p- p0? CP= (-1)x(-1) = +1 OK CP= (-1)x(-1) = +1 CP +1 K1  p+ p- p0? NG CP = (-1)x(-1)x(-1) = -1

K2 decays K2 p+ p- ? K2  p+ p- p0? CP= (-1)x(-1) = +1 NG CP= (-1)x(-1) = +1 CP -1 K2  p+ p- p0? OK CP = (-1)x(-1)x(-1) = -1

K2  p+ p- p0 has little phase space K1 & K2 lifetimes 相空间 K2  p+ p- p0 has little phase space QK2 = MK – 3Mp  80 MeV K1  p+ p- has more phase space QK1 = MK – 2Mp  215 MeV tK1<<tK2 Easier for K1 to decay

1956: Search for long-lived K0 Brookhaven-Columbia Expt

Can you see it?

KS & KL mesons Two neutral K mesons were discovered: KS  p+p- tKS  0.1 nanosecs (10-10s) 500x bigger KL  p+p-p0 tKS  50 nanosecs (5x10-8s) (Are they the CP eigenstates K1 and K2?)

KL & KS mesons in e+e- annihilation KS = K-short pS = 110 MeV <l> = 6mm p+ p- f 510MeV e+ e- 510MeV p+ pL = 110 MeV <l> = 3.4m f = ss M(f) = 1020 MeV p0 KL = K-long p-

KLOE Experiment in Italy KS In this event the KL only travels ~1m before it decays

Usually, the KL traverses to entire 2m radius of the drift chamber KL “crash” b= 0.22 (TOF) KS  p-e+n KL “crash” 2m KS

Neutral K mesons “Basis” sets These have a well defined quark structure K0-K0 Flavor States These are the Particles that exist in Nature K1-K2 CP eigenstates KS-KL Mass eigenstsate are these the same?

Does KS=K1 & KL=K2? (i.e. is CP conserved?) These are the particles that are observed in nature express them in terms of K1 and K2:

invert

e If CV is conserved: e=0, KS=K1 & KL=K2

Does KL p+p- ? |e|2 =0 if CP is conserved Remember, p+p- has CP=+1 Forbidden(?) Forbidden(?) |e|2 =0 if CP is conserved

Christenson-Cronin-Fitch-Turlay Experiment (1964) KL p-

|e|2 = 4x10-6 p+ KL p- p+ q cosq small,but not 0 M(p+p-)<M(KL) p+p- “invariant mass” M(p+p-)=M(KL) |e|2 = 4x10-6 small,but not 0 p+ KL q p- p+ M(p+p-)>M(KL) cosq

CP is violated!! James Cronin Val Fitch 1980 Nobel Prize for Physics No prizes for Christenson or Turlay

Flavor-non specific K0 (K0) decays 特定 Decays that are equally likely for K0 and K0 If you see p+p-, you don’t know if it was from a K0 or a K0 K0 p+ p- K0 p+ p- K0 p+ p-p0 Same for p+p-p0, (& p0p0 & p0p0p0) K0 p+ p-p0

Flavor specific K0 (K0) decays 特定 Decays that can only come from a K0 or K0, but not both d p- d p+ u d u d K0 K0 W.I. n W.I. n s s W+ W- e+ e- DS=-1 DQ=-1 DS=+1 DQ=+1 Rule: K0 p- e+ n K0 p+ e- n only DS=DQ If you see p-e+n, you know it must be from a K0, not K0 If you see p+e-n, you know it must be from a K0, not K0

K0 & K0 in terms of KS & KL invert

Start with a K0 at t=0 KS & KL have different t-dependence using and

Similarly:

K0K0 Oscillations GS>>GL (GS500xGL) Expt NA48 (CERN) K0 K0 CP is violated in KLp+e-n/p-e+n decays t=t/g (“proper time”)

Search for direct CPV in KLpp In 2002,after 20 yr searches, NA48 (CERN) & KTeV (Fermilab) found direct |DS|=1 CPV in K2pp CP violation from |DS|=2 transition Mass Matrix Forbidden(?) Is this true? Can there be a “direct” CP violation in |DS|=1 K2pp? = e’  1.6 x 10-3 x e Small, but establishes existence of “direct” |DS|=1 CP violation.

CPV in neutral K meson system summary Neutral K mesons mix: K0  K0 CP is violated in the K0-K0 mass-mixing matrix scale  e  2x10-3 CPV is seen in flavor non-specific & flavor specific modes KL  pp (CPV  e2  4x10-6) KL  p+e-n / p-e+n (CPV  e = 2x10-3) Direct CP is seen in KLpp decays scale = e’ = 1.6 x 10-3 e

CP is violated in the Weak Interactions Observation of both Mass-Matrix CPV (|DS|=2) & direct CPV (|DS|=1) rule out theories where CPV comes from a previously unknown “fifth” force characterized by |DS|=2

C P and the forces of Nature Slide from last weak Force C P CP Gravity √ Electro-magnetic Strong-nuclear Weak-Interaction ╳ Force C P CP Gravity √ Electro-magnetic Strong-nuclear Weak-Interaction ╳ OK?

Next: How are CP-violating asymmetries generated in QM? How does CP violation fit into the Standard Model for particle physics? Brief review of flavor mixing/GIM-mechanism Kobayashi 6-quark model

Generating CPV asymmetries in QM

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

 matter- symmetry is ~“automatic” QM: processes go as |A|2 Phases tend to cancel out in rate calculations  g*g  gg* 2 2 g q’ q’ = g* q q J J† mirror even for g* = g (i.e with CPV)  matter- symmetry is ~“automatic” antimatter

Phase measurements in QM: need interference 干扰 need a process with 2 competing mechanisms: Amplitudes should have similar magnitudes: phase angle A & Beif: |A+B|2=|A|2+|B|2+2|A|B|cosf 2|B| 2|A|B|cosf cosf if |A|>>|B| |A| |A|2+|B|2 Small number Relative size of the interference effect

Even this doesn’t work for CPV!! B A A+B f f B A+B A = |A+B| |A+B| still! matter antimatter symmetric

need a “common phase” d between A & B 合用 same sign eg A=real: B = |B|eid+if & B = |B|eid-if f f A+B A+B B B d d A A = |A+B| |A+B| matter antimatter difference

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

Common and weak phases B = |B|eid-if |B|eid+if f f A+B A+B B B d d A “Common” (strong) phase (d): same sign for matter & antimatter  CP conserving Weak phase (f): opposite sign for matter & antimatter  CP violating B = |B|eid-if |B|eid+if f f A+B A+B B B d d A

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

Flavor mixing & CP Violation

s Brief review of weak int’s in the 3-quark era 3 quarks: 4 leptons: 1964--1974 3 quarks: q=+2/3 |DS|=1 s q=-1/3 Weak interactions 4 leptons:

Problems Problem 1: Different weak interaction “charges” for leptons & hadrons: Fermi Constant m- GF su Gs 0.21GF du Gd 0.98GF nm Gs Gd s d K- n u u p0 p

Cabibbo’s sol’n: flavor mixing Weak Int flavor state Flavor mass eigenstates d = a d + b s b=sinqc=0.21 a=cosqc=0.98 bGF aGF u GF u u = + s d’ d W- W- W- Unitarity: |a|2 + |b|2 = 1 a=cos qc; b = sin qc qc=“Cabibbo angle”

Missing neutral currents Problem 2: no flavor-changing “neutral currents” seen. Discovered At CERN s GN K- d d,u d,u p- flavor-changing neutral currents (e.g. Kp l+l-) are strongly supressed flavor-preserving neutral currents (e.g. nNnX) are allowed

GIM sol’n: Introduce 4th quark 2 quark doublets: charmed quark Weak eigenstates Mass eigenstates

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

Mixing matrix must be Unitary UU† = 1 |a|2 + |b|2 = 1 & a*b - ab* =0

Charged currents (u-quark) |DS|=1 aGF u(c) u(c) bGF d(s) s(d) W- W- GF modified by a GF modified by b

Charged currents (c-quark) |DS|=1 |DC|=1 |DS|=0 -bGF c c aGF d s W- W- GF modified by b GF modified by a

Flavor preserving Neutral Current =1 d,(S) |a|2+|b| 2GN d,(s) Z0 =1 =0 =0 =1 From Unitarity =1 OK

Flavor changing Neutral Current =0 (a*b+ba*)GN d(s) s(d) Z0 =0 =1 =0 =1 =0 From Unitarity GIM- Mechanism FCNC forbidden by Unitarity

GIM Mechanism FCNC forbidden by Unitarity if quarks come in pairs of 2 GIM: Glashow Iliopoulis Maiani No prize for Iliopoulis & Maiani Glashow won 1979 Physics Nobel prize

Next Friday: Incorporating CPV into flavor mixing

Summary Lecture 3 CP is violated Weak-Interactions Mass-matrix induced; scale  e  2x10-3 Direct CPV; scale = e’ = 1.6 x 10-3 e 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’ =cosqcd +sinq s; s’ =-sinqcd +cosqcs qc  120 is the “Cabibbo angle If all quarks are in pairs, FCNC = 0 by Unitarity (GIM Mechanism)