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Introduction to particle physics Part II

Physics 129, Fall 2010; Prof. D. Budker . Introduction to particle physics Part II. Intrinsic parity of particles. A brief history of parity: Concept found (no parity in everyday life): O. Laporte , 1924 Concept understood: Wigner, 1927 Concept becomes dogma

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Introduction to particle physics Part II

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  1. Physics 129, Fall 2010; Prof. D. Budker Introduction to particle physicsPart II

  2. Intrinsic parity of particles • A brief history of parity: • Concept found (no parity in everyday life): O. Laporte, 1924 • Concept understood: Wigner, 1927 • Concept becomes dogma • Dogma fails: Lee, Yang, Wu, 1956-1957 Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  3. Parity of atomic states • Spatial inversion (P) : • Or, in polar coordinates:

  4. Parity of atomic states • It might seem that P is an operation that may be reduced to rotations • This is NOTthe case • Let’s see what happens if we invert a coordinate frame : • Now apply a  rotation around z’ • Right-handed frame  left handed • P does NOTreduce to rotations !

  5. Parity of atomic states • An amazing fact : atomic Hamiltonian is rotationally invariant but is NOT P-invariant • We will discuss parity nonconservationeffects in detail later on in the course…

  6. This is because: Parity of atomic states • In hydrogen, the electron is in centro-symmetric nuclear potential • In more complex atoms, an electron sees a more complicated potential • If we approximate the potential from nucleus and other electrons as centro-symmetric (and not parity violating) , then : Wavefunctions in this form are automatically of certain parity : • Since multi-electron wavefunction is a (properly antisymmetrized) product of wavefunctions for each electron, parity of a multi-electron state is a product of parities for each electron:

  7. Comments on multi-electron atoms • Potential for individual electrons is NOT centrosymmetric • Angular momenta and parity of individual electrons are not exact notions (configuration mixing, etc.) • But for the system of all electrons, total angular momentum and parity are good ! • Parity of a multi-electron state: W A R N I N G

  8. Parity of atomic states • A bit of formal treatment… • Hamiltonian is P-invariant (ignoring PNC) : P-1HP=H •  spatial-inversion operator commutes with Hamiltonian : • [P,H]=0 •  stationary states are simultaneous eigenstates of H and P • What about eigenvalues (p; Pψ=pψ) ? • Note that doing spatial inversion twice brings us back to where we started • P2 ψ=P(P ψ)=P(pψ)=p(Pψ)=p2 ψ. This has to equal ψ p2=1  p=1 • p=1 – even parity; p=-1 – odd parity

  9. Intrinsic parity of particles Consider a reaction: a + b  c + d Initial wavefunction: Initial parity: Final wavefunction: Final parity: Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  10. Intrinsic parity of particles • Parity of proton is defined: p(p) = +1 • Parity of other particles is found from processes like a + b  c + d and parity conservation • Example: d + π- n + n • d : J=1; relative ang. moment. of p and n(mostly) 0 • The π–is captured from an l=0 orbit, so we have: Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  11. Intrinsic parity of particles • Whatcan we say about l’? • Total angular momentum of the two neutrons: 1 (because the dspin is 1, and the π-spin is 0) • Total wavefunction is antisymmetric (fermions) • If spin singlet  l’ = 0, 2, …  cannot be! (because the total angular momentum is 1) • If spin triplet  l’ = 1 • Neutron parity is chosen positive  • Gauge bosons, , Z, W+, W-, gnegative parity • Leptons: not much to talk about: disrespect of parity Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  12. Intrinsic parity of antiparticles • Not arbitrary! Must be related to that of particles • 0is its own antiparticle  allpions have odd parity • All antibosons have the same parity as their bosons • For fermions it is the opposite: opposite parity for particles and antiparticles • How do we know?  Dirac and Experiment • Consider para-Ps decay: e+e-(1S0)   • Possible amplitudes: • 1  2 scalar not observed • 1 2(k 1 - k 2)pseudoscalarobserved! • Only possible if p(e+)p(e-)= -1 Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  13. Charge conjugation (C) • A misnomer; better way to think about this: • All particles  antiparticles • If a particle is an eigenstateof C (most are not), • c=1 (because c2 = 1) • c() = -1 (this is e/m field, after all) • 0   +  allowed • 0   +  +  forbidden • Week interactions do not respect C Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  14. Parity-Violation:ParticlesNucleiAtomsMolecules

  15. Outline • What is parity? Parity violation • Atomic parity violation (APV=PNC) • Optical-rotation expts • APV-Stark interference • Brief (personal) history of APV • APV in Yb • APV in Dy • Conclusions

  16. P x’ z’’ z’ y’ Rotation around y’ x’’ • Left hand cannot be rotated into right hand ! y’’=y’ What is parity? z y x

  17. Normal vs. axial vectors • Under Spatial Inversion (P): • V  -V r, p, E, d = er, … • A  A L = rp, S, B Similarly for scalars (pseudo-scalars) • Under Spatial Inversion (P): • S  S Energy, any VV’, AA’ … • PS  -PS any A V, …

  18. Discrete vs. Continuous Transformations and Symmetries • Continuous: • Translation → momentum conservation • Translation in time → energy conservation • Rotation → angular momentum conservation • Discrete: • Spatial Inversion (P) → P-invariance (parity) • Charge Conjugation (C) → C-invariance • Time reversal (T) → T-invariance • CP • CPT • Permutation of identical particles → PSP, spin-statistics

  19. The (broken) law of parity • Because the laws of Nature should be the same in the “real” world and its mirror image, no pseudo-scalar correlation should be observed in experiments, for example • Does not apply to cork-screws !

  20. The - paradox (the demise of parity) • Two particles with same mass and same lifetime… • But opposite parity ??? • In modern terminology: + = + = K+ ( ) • Resolution of the paradox: • parity violation inweak interactions Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  21. The theorists who said: check it ! Prof. T. D. Lee Prof. C. N. Yang

  22. Prof. C. S. Wu (1913-1997) The shatterer of the parity illusion (1956)…

  23. The Co-60 experiment

  24. Parity and Quantum Mechanics • If Hamiltonian is P-invariant  nondegenerate sate is eigenfunction of P • Atomic states are even or odd • If parity is violated  eigenstates are of mixed parity

  25. Atomic Parity Violation (APV) e g e Z Electromagnetic interaction (conserves parity) Weak interaction (violates parity) • APV = PNC = Parity Non-Conservation

  26. Atomic PNC: optical rotation PNC E1 M1 M1-E1PNC interference

  27. Optical Rotation Linear Polarization Medium  Circular Components

  28. PNC optical rotation: Tl Vetter, Meekhov, Lamoreaux, Fortson, PRL 74, 2658 (1995) Result: PNC to 1 % (exp); 3 % (theo) • 500 data hrs averaged • Many absorp. length →line wings • Polarimetric sensitivity: ~10-8rad • No reversals • New approaches needed for progress Prof. E. N. Fortson

  29. Atomic PNC: Stark interference PNC+EDC E1 M1 • E1Stark -E1PNC interference • Reversals !

  30. Atomic parity violation: the parents Profs. Marie-Anne and Claude Bouchiat

  31. Atomic PV landmarks • 1959Ya. B. Zel’dovich: • PNC (Neutr. Current)  Opt. Rotation in atoms • 1974M.-A. & C. Bouchiat • Z3enhancement PV observable in heavy atoms • 1978-9Novosibirsk, Berkeley • discovery of PV in OR(Bi) and Stark-interf.(Tl) • …1995Boulder, Oxford, Seattle, Paris • PV measured to 1-2% in Cs, Tl, Bi, Pb • 1997Boulder • 0.35% measurement, discovery of anapole moment

  32. A T O M E A T O M E Why the French? A T O M A T O M

  33. The Boulder Cs PNC Experiment 1982-1999 • P-odd, T-even correlation: • [E  B] • 5 reversals to distinguish PNC from systematics

  34. Prof. Carl E. Wieman The Champions of Parity violation

  35. Atomic PV landmarks • 1959Ya. B. Zel’dovich: • PNC (Neutr. Current)  Opt. Rotation in atoms • 1974M.-A. & C. Bouchiat • Z3enhancement PV observable in heavy atoms • 1978-9Novosibirsk, Berkeley • discovery of PV in OR(Bi) and Stark-interf.(Tl) • …1995Boulder, Oxford, Seattle, Paris • PV measured to 1-2% in Cs, Tl, Bi, Pb • 1997Boulder • 0.35% measurement, discovery of anapole moment 26 years • 2009Berkeley Large APV in Yb (personal landmark)

  36. What were we doing all this time? • 1983-1988 Bi, diatomic molecules, Sm (Novosibirsk) with L. M. Barkov and M. Zolotorev • 1989-1994 Tl (Berkeley) with E. D. Commins, D. DeMille, and M. Zolotorev • 1989- Dy M. Zolotorev, D. DeMille, E. D. Commins, A.-T.Nguyen, A. Cingoz, N. Leefer • 1995-1997 Sm S. M. Rochester • 1995- Yb S. J. Freedman, C. J. Bowers, G. Gwinner, J. E. Stalnaker, D. F. Kimball, V. V. Yashchuk, K. Tsigutkin, A. Family, D. Dounas-Frazer,…

  37. Why did it take so long to detectPNC? Dr. A.-T. Nguyen says: it was deposited

  38. Parity Violation in Yb: motivation Atomic Physics: • Verification of large predicted atomic PV effect (x100 Cs; DeMille, Kozlov et al, Das et al) Nuclear Physics: • Nuclear spin-dependent PV – anapole moments (valence neutrons) • Isotopic ratios and neutron distributions (6 stable isotopes; N=8)

  39. Anapole Momentof a current distribution (e.g., a nucleus) Ya. B. Zel’dovich T-conserving; P-violating

  40. Anapole Moments Ya . B. Zel’dovich, V. G. Vaks • 1959 AM first introduced V.V. Flambaum, I.B. Khriplovich & • 1980 - 84 O.P. Sushkov Nuclear AM detectable in atoms E.N.Fortson and co-workers • 1995 Tl AM – small… C. E. Wieman and co-workers • 1997 Cs AM detected ! PNC within nucleus! probe of weak meson couplings

  41. Atomic Yb: energy levels and transitions +5d6p PV amplitude: 10-9e·a0 DeMille (1995) |M1|10-4 μB J.E. Stalnaker, et al, PRA 66(3), 31403 (2002) β2·10-8ea0/(V/cm) C.J. Bowers et al, PRA 59(5), 3513 (1999); J.E. Stalnaker et al, PRA 73, 043416 (2006)

  42. Stark-PV-interference technique (invented by the Bouchiats in 1970s)

  43. The Yb PV Experiment Electric and magnetic fields define handedness

  44. PV effects on rates m = +1 m = 0 m = -1 3D1 R+1 R0 R-1 1S0 Transitionrates interference E-field modulation Compute ratio for 1st and 2nd harm. signal Ratio difference yields PV asymmetry:

  45. Typical Stark-induced signal • 174Yb resonance split by B70 G; E=3 kV/cm • PV asymmetry: • ~ 2·10-4/ E/(kV/cm) • Asymmetric lineshape← • ACStark effect DC bias 43 V/cm

  46. Atoms in electric field: the Stark effectorLoSurdophenomenon Johannes Stark (1874-1957) Nazi Fascist

  47. Reversals andpseudo-reversals • E-field reversal (14 ms: 70-Hz modulation) • Lineshape scan (200 ms/point x 100 pts/lineshape = 40 s) • B-field reversal (every few minutes) • Polarization angle (occasionally) • E-field magnitude • B-field magnitude • Angle magnitude For θ=/4→

  48. Systematics control strategy • APV is mimicked by combinations of two or more imperfections • Enhance one imperfection; measure the other • Adapted from the Berkeley eEDM • expt. of Prof. Commins et al

  49. Yb PV Amplitude: Results z/b=39(4)stat.(5)syst.mV/cm  |z|=8.7±1.4×10-10 ea0 Accuracy is affected by HV-amplifier noise, fluctuations of stray fields, and laser drifts → to be improved

  50. Progress in Yb APV • Completed Work • Lifetime Measurements • General Spectroscopy (hyperfine shifts, isotope shifts) • dc Stark Shift Measurements • Stark-Induced Amplitude (β): 2 independent measurements • M1 Measurement (Stark-M1 interference) • ac StarkShift Measurements • Verification of APV enhancement • Near Future… • Verification of expected isotopic dependence • PV in odd isotopes: NSD PV, Anapole Moment • PV in a string of isotopes; neutron distributions, … • Further Ahead (?) • Testing the Standard Model [Brown et al PHYSICAL REVIEW C 79, 035501 (2009)]

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