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Intro to Symmetries

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. Why C,P,T?. Standard Model Constructed (1967-1974)

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Intro to Symmetries

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  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 Constructed (1967-1974) Experimentally Tested (1967-Now) Remaining Issues? CP-violation (BaBar, BELLE) Higgs boson (TEVATRON, LHC)

  3. Defining C,P,T Parity X = (t,x)  (t,-x ) Particles unaffected Time-reversal X = (t,x)  (-t,x ) Particles unaffected 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. Dirac Energy Spectrum E>+mc2 E=+mc2____________________ E=-mc2____________________ E<-mc2

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

  10. 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. CPT 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 Flavors 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* 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 RH Particle: 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?

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