1. Prepared By A.K.M. Moinul Haque Meaze Student ID: 2003419008 Center for High Energy Physics Kyungpook National University Daegu Daegu 702-701 Republic of Korea Course Title: Phenomenology Honorable Professor Kihyeon Cho DISCRETE SYMMETRIES November 11, 2003

2. Symmetry is usually associated with an action or transformation of a system or object such that after carrying the operation the system or object in a state indistinguishable from that which it had prior to carrying out the action or transformation. The existence of symmetries implies that it is impossible to devise an experiment to distinguish before and after the situation. So the symmetry or invariance, of physical laws describing a system undergoing some operation is one of the most important concepts in physics. Discrete symmetries, such as reflections, inversions, time reversal, charge conjugation, parity, finite rotations, permutations etc. associated with multiplicative or phase-like quantum numbers Continuous symmetries, such as translations and rotations are associated with additive quantum numbers (e.g., angular momentum J or linear momentum p) SYMMETRIES Types of Symmetries * Global, Local, Dynamical, Internal-are also classes of symmetries. November 11, 2003

3. Charge conjugation C transforms each particle into its antiparticle. Here C 2 =1, So C=±1, i.e., it has eigen value ±1 Any particle that is an eigen state of C must be its own anti particle, since C|particle>=|anti particle>=±|particle> Charge Conjugation November 11, 2003

4. Parity is the act of reflecting a system in a mirror. Parity invariance means the probability of a particle process occurring is exactly the same as the probability of the same process occurring with the position vector and directions of travel of all particle reversed. Parity P=±1 November 11, 2003

5. This doodle pad was used by T.D. Lee during talks with C.N. Yang, while both were visiting scientists at Brookhaven in the summer of 1956. These discussions led to questioning the conservation of parity in weak interactions and resulted in their being awarded the Nobel prize in1957 November 11, 2003

6. Time reversal invariance is a theory predicting that if a process is governed by a physical theory, then the same physical theory applied in the reverse direction of time. Time Reversal Invariance Time reversal invariance, T reverses the time coordinate. But T does not satisfy the simple eigen value equation Instead here K is the complex conjugation operator. * For example direction of motion of particles T violation means that the rate for a particle interaction is different for the time reversal process. November 11, 2003

7. CP Violation Must Exist! Our planet is made out of matter and a block of antimatter can not exist. In fact we have not found any evidence of anti matter in the whole universe! If this universe originated from the big bang, which creates equal amount of matter and anti matter, the forces responsible for the expansion and cooling of our universe must violate particle-antiparticle symmetry. CP violation must exit!!! If Big Bang is to produce unequal amount of matter and anti matter CP must be violated. November 11, 2003

8. CP In Weak Interaction Fig. Transformations on pion decay Under a combined operation CP LH Neutrino RH Anti neutrino So CP is conserved in weak interaction even though C and P separately are not conserved November 11, 2003

9. Then CP|K1>=|k1> CP|K2>=-|K2> CP Violation in K Meson November 11, 2003

10. CP Violation in K Meson The short lived kaon decay into two pions while long lived pions would decay into three pions, but in some cases two pions, thus violating the CP symmetry. November 11, 2003

11. CPT Theorem * This is one of the most important and generally valid theorems in quantum field theory. * This appears to be an exact invariance of all process. This means that any process has a related process which an identical rate, the process to which it is converted by making three replacements of C,P & T. * All interactions are invariant under combined C, P & T. * Invariance under Lorentz transformation implies CPT invariance showed by George Luders, Wolfgang Pauli and Julian Schwinger. * Implies particle and antiparticle have equal masses and lifetimes. * Implies all the internal quantum numbers of antiparticles are opposite to those of particles. November 11, 2003

12. QuantitySymbolTP Position rr-r Momentum p-p Spin σ- σσ Electric FieldEE-E Magnetic field B-BB Magnetic dipole moment σ.B Electric dipole moment σ.E-σ.E Longitudinal polarization σ.p -σ.p Transverse polarization σ.(p 1 ×p 2 )-σ.(p 1 ×p 2 )σ.(p 1 ×p 2 ) Common Quantities under T & P November 11, 2003

13. We can write the Hamiltonians H M, H E that describe the interaction of μ with B, and of D with E, in the non relativistic limit Under space inversion (P) the axial vector σ and B remain unchanged, but the polar vector E changes sign. Hence under P, H M is invariant, while H E is not. Under time reversal (T), σ and B changes sign, while E remains unchanged. Hence under T, H M is once again invariant, but H E changes sign. Therefore, non zero EDM violates both T and P symmetries General Remark on EDM November 11, 2003

14. Fig. A bit history of EDM [Ref. E. A. Hinds, Electric dipole moments: Theory and Experiment http://blois.in2p3.fr/2002/plenary/friday21/ cpt/Blois2002Hinds.pdf ] The limits of neutron electric dipole moments are: d n <1.2x10^ -25ecm [Ref. P.F. Smith et al, Phy Lett B234(1990)19] d n <6.3x10^ -25ecm [Ref. P. G. Harris et al, Phy Rev Lett 82(1999)904] November 11, 2003

15. Symmetry Obeyed By Strong Force Electromagnetic Force Weak Force Gravitational Force Charge Conjugation, C Yes NoYes Parity, P Yes NoYes Time Reversal, T Yes AlmostYes CP Yes AlmostYes CPT Yes Symmetries on Forces

16. SYMMETRIES-AT A GLANCE SymmetryAction Charge Conjugation, CParticle→ Anti-particle Parity, Px→-x, y→-y, z→-z Time reversal, Tt→-t CPParticle→ Anti-particle x→-x, y→-y, z→-z CPTParticle→ Anti-particle x→-x, y→-y, z→-z, t→-t Symmetry Action On PositionTimeVelocity, MomentumSpin Charge Conjugation, C Unchanged Parity, P ReversedUnchangedReversedUnchanged Time reversal, TUnchangedReversed CP ReversedUnchangedReversedUnchanged CPTReversed UnchangedReversed November 11, 2003