Test of fundamental symmetries

1. Test of fundamental symmetries from an atomic physics perspective With thanks to Antoine Weis Mike Tarbutt Sumerian, 2600 B.C. (British Museum)

2. The plan… Introduction to symmetry Mirror symmetry – parity – P Puzzles Time-reversal symmetry – T CPT

3. What is symmetry? Thing, T Property, P Take a ‘thing’ Do something to it Symmetry operation, O Does the thing remain the same? New thing, T’ Property, P’ If P’ = P We say “T is invariant under the symmetry operation O” We say “O is a symmetry of T” • Examples of a ‘thing’: • Macroscopic object • Particle \ atom \ molecule • Process • Elementary force \ interaction

4. Symmetry operations • Continuous symmetries • Space translation • Time translation • Orientation • Boosts (Lorentz transformation) • Discrete symmetries • Space reflection (parity) • Time reversal • Charge conjugation • Interchange of identical particles The laws of nature (or in some cases, a subset of them) are invariant under these operations (as far as we can tell). Note – this is an experimental matter! “In all physics nothing has shown up indicating an intrinsic difference of left and right. The same problem of equivalence arises with respect to past and future, and with respect to positive and negative electricity. A priori evidence is not sufficient to settle the question; the empirical facts have to be consulted.” Hermann Weyl (1951)

5. Some counter-examples • You can tell when a system is rotating, without looking from the outside (e.g. the earth) • No invariance under a change of scale

6. No scale invariance – why giants don’t exist From Galileo’s “Two New Sciences” “To illustrate briefly, I have sketched a bone whose natural length has been increased three times and whose thickness has been multiplied until, for a correspondingly large animal, it would perform the same function which the small bone performs for its small animal.” “From the figures here shown you can see how out of proportion the enlarged bone appears….the smaller the body the greater its relative strength. Thus a small dog could probably carry on his back two or three dogs of his own size; but I believe that a horse could not carry even one of his own size. “

7. Noether’s theorem For every continuous symmetry of the laws of physics, there must exist a conservation law. For every conservation law there must exist a continuous symmetry. Symmetry Space translations Rotations Time translations Conserved quantity Momentum Angular momentum Energy Emmy Noether, 1882-1935

8. Parity and mirror symmetry Mirror reflection Parity operation Reflect P {x,y,z} {x,y,-z} y {x,y,z} {-x,-y,-z} y y z z -z x x x r -r Parity operation = mirror reflection + rotation by p around the z-axis

9. Parity conservation and violation When a thing looks the same after reflection in a mirror we say: “this thing conserves parity” When the mirror image of a thing is not the same as the thing itself we say: “this thing is chiral” “it has handedness” “it has helicity” “it violates parity”

10. Rotations, axial vectors, polar vectors & handedness A A -V V Polar vector: rank 1 spherical tensor, odd under parity Axial vector: rank 1 spherical tensor, even under parity Rotation + Axis = Handedness Axial vector A Polar vector V Helicity . A V |V| |A| Pseudoscalar: odd under parity

11. 1957: weak interactions violate parity January 1957 - 3 papers appear in Physical Review proving that weak interactions violate parity. C.S. Wu, E. Ambler, R.W. Hayward, D.D. Hoppes and R.P. Hudson, Physical Review 105, 1413 (15 January 1957) R.L. Garwin, L.M. Lederman and M. Weinrich, Physical Review 105, 1415 (15 January 1957) J.I. Friedman and V.L. Telegdi, Physical Review 105, 1681 (17 January 1957) 1956 - Lee & Yang - no experimental evidence for parity conservation in weak interactions; suggest possible experiments. T.D. Lee & C.N. Yang, Physical Review 104, 254 (June 22 1956) C.S. Wu, in the lab Lee and Yang awarded the 1957 Nobel prize in Physics

12. Weak interactions violate parity Beta-decay 60% 40% 60Co Neutrino helicity 100% 0%

13. Is parity violation possible in atoms? N N N N • Electromagnetic • Mediated by exchange of photons • Conserves parity • Weak • Mediated by exchange of Z0 • Violates parity • In b-decay, parity violation is mediated by the weak charged currents, W+/- • Identity of interacting particles changes at the vertex (they carry charge) • Cannot occur for stable atoms • No atomic parity violation mediated by weak charged currents • Atomic parity violation CAN be mediated by weak neutral currents Two types of neutral-current interaction between a nucleon and an electron in an atom:

14. How to search for parity violation in atoms Circular dichroism Optical rotation IL IR Measure plane of polarization of incident and transmitted plane-polarized light. Is there a difference? Measure absorption of left-handed and right-handed circularly polarized light. Is there a difference?

15. The parity violating potential Interaction is mediated by a massive particle Yukawa potential r0 is the “range” of the potential The coupling of a Z0 to an e is proportional to the e helicity Parity-violating potential Electromagnetic potential Z – electric charge e – coupling constant Qw – weak nuclear charge g – coupling constant (~e, unification) What is the form of the potential responsible for parity violation in atoms?

16. What is QW? QW Weak nuclear charge Additive – just add together the weak charges for all the quarks in the nucleus Neutron – ddu Proton – uud Number of protons Weak charge of down-quark Weak charge of up-quark Number of neutrons Standard model gives us Primary aim of atomic parity violation experiments – measure QW

17. How to search for Atomic Parity Violation I Electromagnetic process: Assign an amplitude Aem Weak process: Assign an amplitude AW N N N N First idea: The brute force approach Look directly at a “pure” parity-violating signal e.g. drive a transition that is otherwise completely forbidden Rate is proportional to | AW |2. Relative to an allowed E1 transition, suppressed by 20-30 orders of magnitude! Completely impossible.

18. How to search for Atomic Parity Violation II Electromagnetic process: Assign an amplitude Aem Weak process: Assign an amplitude AW N N Since AW<<Aem N N Try to measure this interference term N.B. Linear in Aw A good measure of the degree of Left-Right asymmetry is These two processes have identical initial and final states. The probability for the process is given by: Sign depends on handedness of experiment

19. How big is it? For both types of interaction, the amplitude is g1, g2 - coupling constants at the vertices, q - momentum transfer M – mass of the mediating gauge boson For the electromagnetic interaction, g1= g2= e M = Mg = 0 q= electron momentum= ma c For the weak interaction, g1=g2 = g M = MZ q << M c Electroweak unification: g = e Consider the hydrogen atom

20. All is not lost 7S An example – 6S1/2 – 7S1/2 in Cs: E1 – strictly forbidden by parity (in absence of parity violation!) M1 –approximately forbidden by Dn=0 selection rule E2 – J=1/2 – J=1/2 transitions are strictly forbidden M2, E3 – parity forbidden… 6P Excite Detect 6S Enhancements can result in Enhance AW by using heavier atoms – turns out that AW ~ Z3 Suppress Aem by using forbidden transitions (i.e. not E1) Beware – forbidden transitions allow for much larger Left-Right asymmetry, but result in very small signals. Is it better to measure 10-8 of something, or 10-4 of nothing?

21. Stark-induced E1 transition Stronger signal Smaller asymmetry Search for the parity-violating 6S – 7S E1 transition In presence of electric field, there is a Stark-induced component to the 6S-7S rate This allows the transition rate to be controlled Trade-off between size of signal and size of asymmetry can be controlled using an electric field

22. Colorado Cs experiment I 7S 6P Excite Excite 6S-7S transition Observe resulting fluorescence Does excitation rate change when apparatus handedness is reversed? Detect 6S Reversals -E E Coordinate system defined by electric field, magnetic field and photon angular momentum vectors – defines the handedness. -B B -s s -m m

23. Colorado Cs experiment II Electric field plates divided into 5 segments Build-up cavity, F=30000 Intensity stabilizer Optical isolator Half-wave plate Pockels cell 4 lasers – Df/f=10-14, DI/I=10-6 31 servo-loops 23 magnetic field coils 32 switch states 7 years of development 5 years on systematic effects 8 months of data-taking 1 result, 0 Nobel prizes!

24. Colorado Cs experiment - results Experimental result Atomic physics calculations Combine Compare to Standard Model: Agree within 1s The absorption coefficient of Cs depends on the handedness of the apparatus Difference is about 6 parts per million, measured to 0.35% precision

25. What does a parity violating atom look like? Example – the 2p1/2 state of hydrogen Calculate the current density: e ~ 10-11 – too small to visualize. Artificially increase it by 10 orders of magnitude N.B. You could solve this problem yourselves, with the help of Am. J. Phys. 56, 1086 (1988)

26. Shoes More left shoes are washed up on Dutch beaches, more right shoes on Scottish beaches! Results of a 1997 study: Texel, Holland: 68 left, 39 right Shetland islands: 63 left, 93 right

27. Chiral molecules Limonene Carvone Tastes of spearmint Tastes of caraway Smells of oranges Smells of lemons (or turpentine!) Thalidomide (R) (S) Sedative. Treatment of morning sickness Malformations in over 10,000 children

28. Biological homochirality Chiral molecules synthesized in the lab Racemic mixture Equal mixture of left and right handed enantiomers All amino acids found in life are left-handed Biologically relevant sugars are right-handed Not so in life… Maximal parity violation How did it happen? Is the weak interaction involved?