1. Intro to Symmetries Gene Golowich Physics (UMass) Talk at NEPPSR-04
August 23, 2004
Goals of this Talk
1] Set table for talks by:
a] Dallapiccola (Fri 8/27)
b] Morii (Fri 8/27)
2] Motivate study of C,P,T, etc

2. Why C,P,T? Standard Model Remaining Issues? Constructed (1967-1974)
Experimentally Tested (1967-Now)
Remaining Issues?
CP-violation (BaBar, BELLE)
Higgs boson (TEVATRON, LHC)

3. Defining C,P,T Parity Time-reversal Charge Conjugation
X = (t,x)  (t,-x )
Particles unaffected
Time-reversal
X = (t,x)  (-t,x )
Charge Conjugation
Matter  Antimatter
Spacetime unaffected

4. Effect on Classical Particles
Spatial Momentum (P = mv)
P: p = mdx/dt  -p
T: p = m dx/dt  -p
Angular Momentum (L = x x p)
P: L = x x p  L
T: L = x x -p  -L

5. Ex: Massless Spin ½ Particles
RH Particle:
Spin, momentum are parallel. p s
LH Particle:
Spin, momentum are antiparallel.
s p

6. Parity & QM in One Dim. (x) = Bound state wave function
i(x)/t = -”(x) + V(x) (x)
Consider P-reversed equation:
i(-x)/t = -”(-x) + V(-x)(-x)
V(-x) = V(x)  (-x) =  (x)
Ex: d=1 Infinite Well
1(x) = N cos(x/a)
2(x) = N sin(x/a)
etc

7. T-reversal & QM Schrodinger Equation i (t)/t = -2(t)/2m + V (t)
T-reversed Equation
i *(-t)/t =
-2*(-t)/2m + V *(-t)
(But V must be real-valued!)
Parameterizing T-violation
Let V = Vei. Then the phase 
indicates T-violation!

8. E=+mc2____________________ E=-mc2____________________
Dirac Energy Spectrum
E>+mc2
E=+mc2____________________
E=-mc2____________________
E<-mc2

9. E=+mc2____________________ E=-mc2____________________
Dirac Ground State
E>+mc2
E=+mc2____________________
E=-mc2____________________
E<-mc2

10. E=+mc2____________________ E=-mc2____________________
Antimatter!
E>+mc2
E=+mc2____________________
E=-mc2____________________
E<-mc2

11. Symmetry in QFT Input: Lagrange density L Symmetry possibilities:
1] Continuous: Gauge, Flavor, etc
2] Discrete: C,P,T, etc
Symmetry breaking:
1] Ground state?
2] Quantum corrections?
CPT Theorem: CPT is a symmetry operation in standard QFT!

12. Predictions of CPT Testing for CPT

13. C,P,T: Partial Summary
Thus Far:
C,P,T defined ()
Some examples ()
To Do:
Standard Model
C,P,T: Symmetry or not?
Experimental tests?

14. A Bit of History C and P Violation: Prediction: 1956 Discovery: 1957
CP Violation:
Prediction: None!
Discovery: 1964

15. Standard Model Structure
Part 1 (inputs)
Particles (massless spin ½)
Interactions (gauge)
Strong
Electroweak (flavor basis).
Part 2 (getting mass)
Introduce scalar Higgs field.
Higgs breaks gauge symmetry.
Particles get mass (mass basis).

16. Quark Flavors & Generations
Up-type (Q = +2/3):
Up u Charm c Top t
Down-type (Q = -1/3):
Down d Strange s Bottom b
Generations
Up-type uk Down-type dk
Label k = 1,2,3
Why ‘generations’? Nobody knows!

17. One Picture = 103 Words

18. C,P,T Scorecard EM and Strong* Weak (charged) P,C,T all conserved!
(*Theoretical ‘strong CP problem’?)
Weak (charged)
Std. Mdl. Part 1:
C,P violated but CP conserved.
Std. Mdl. Part 2:
CP becomes violated (‘CPV’)
due to a single phase .

19. Charged-weak: Part 1 Interaction Particles can carry weak charge.
W-bosons ‘smell’ weak charge.
Fermions are massless (LH,RH).
Only LH,anti-RH are charged!
P and C
P violated! (P LH = RH)
C violated! (C LH = anti-LH)
….. But ...
CP OK at this stage!
(CP LH = C RH = anti-RH)

20. Again: ‘LH’,’RH’ Particles
Spin, momentum are parallel. p s
LH Particle:
Spin, momentum are antiparallel.
s p

21. Charged-weak: Part 2 Flavor & Mass Bases Quark Transitions
(u’L)+ d’L = uL+ [K(u)+K(d)] dL
u’La = K(u)abuLb d’La = K(d)abdLb
= uL+ [V] dL (VV=1)

22. CKM & Experiment

23. CKM Revealed

24. CKM Notations
Euler
Wolfenstein

25. CPV in the Standard Model
Source of CPV:
Just one* source of CPV: .
Often plot in the (,) plane.
*(i) Ignore strong-CP problem.
(ii) No CPV for two generations.
Magnitude of CPV:
Note: The CPV is NOT maximal!

26. CPV and New Physics
Experimental Opportunities
Kaons or B-mesons
Electric dipole moments
Neutrinos
Antimatter in the Universe
Theoretical Opportunities
What will supplant the SM?
Everybody loves SUSY!
But SUSY has 44 CPVs!!

27. CPV is Crucial in Cosmology!
Protons vs Antiprotons
Early:
Today:
Sakharov’s Criteria
1] Baryon number violation
2] CP,C-violating physics
3] Lack of thermal equilibrium

28. Electric Dipole Moments
An EDM Violates P,T

29. Conclusions 1] CPV seen in kaon, B systems.
2] Existing results agree with SM.
3] Await additional B-meson data.
4] Further avenues to explore:
a] Electric Dipole Moments
b] Neutrinos
c] Cosmology
5] Will CPV lead to New Physics?