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Discrete Space-Time Symmetries Xiao-Gang He USTC, Nanakai, and NTU 1. Discrete Space-Time Symmetries 2. The Down Fall of Parity P Symmetry 3. The Down Fall of CP and T Symmetries 4. CPT Symmetry and Its Violation 5. Discussions and Conclusions

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1. Discrete Space-Time Symmetries Symmetries : important for understanding the laws of Nature. -Simplify problems, classify complicated systems, determine conservation laws, even determine the dynamics of interactions. * SU(3) flavor symmetry -> Quark model and etc. *Continuous space-time symmetries, relativity (translational and rotational transformation) -> energy-momentum conservations. *Gauge symmetry -> electroweak and strong interactions. * General Relativity. -Some symmetries are exact and some are broken. All important. * SU(3) flavor symmetry – broken one. * Continuous space-time symmetries – exact. * Gauge symmetry – some part broken and some part still good symmetry We will discuss the properties of discrete space-time symmetries P-Parity, T-Time Reversal, and C-Charge Conjugation symmetries.

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Why discrete space-time symmetries are interesting? For a long time, it was believed that P, C, T symmetries are exact. In 1956, T.D. Lee and C.N. Yang : Parity violation in weak interaction => Nobel Prize. In 1964, Cronin and Fitch: CP violation in weak interaction => Nobel Prize. Parity violation => opened a new page in the understanding of symmetries, and led to the understanding of weak interaction: V-A theory, Standard Model of electroweak interaction (Glashow, Weinberg and Salam: Nobel Prize) CP violation => One of the basic ingredient why we are here in the Universe, explain why there is more matter than anti-matter in our universe (Sahkarov, 1966). The discovery of the Kobayashi-Maskawa (1973) model of the Standard Model of electroweak interaction. Excellent place for the study of New physics beyond the Standard Model! T violation? CPT violation? What do P, T, C do?

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Some basics of discrete space-time symmetries

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The CPT Theorem CPT is always conserved in the framework of quantum field theory with Lorentz invariance, Hermitian Hamiltonian, Spin-Statistics (Bose-Einstein statistics for bosons, and Fermi-Dirac statistics for fermions). (proven in the 1950’s). T is violated! Confirmed in 1998: CPLEAR. Some implications: particle and its anti-particle have the same mass and the same life-time, opposite additive quantum numbers. No experimental evidence for CPT violation.

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2. The Down Fall of Parity P Symmetry The Puzzle (the 1950’s) to pi+ pi0, to pi+ pi0 p0. and have the “same” mass. They look like the same particle! P(pi) = - pi. Pions in the final states are in S-wave, no relative angular momentum. P( ) = +, P( ) = -- Looks like two different particles. If and are actually are the same, => Parity is violated. T.D. Lee and C.N. Yang (1956) proposed Parity violation in weak interaction and several other experiments. Confirmed by Wu et al., Garwin et al., and Friedman et al. Wu et al.: Co (60) -> Ni (60) + e- + anti-nu

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Example Parity violating process

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Weak interaction is left-handed V-A theory, Feynman and Gell-Man SU(2)LxU(1)Y Standard Model of Electroweak Interaction (Glashow, Weinberg and Salam) Also predicted neutral current weak interaction, Z-interaction. Experimental data agree with data well, precision tests! LEP data But why only SU(2)L, not more symmetric SU(2)LxSU(2)R? (Pati-Salam, Mohapatra and Semjenovic…) Spontaneous symmetry breaking of left-right. Still a subject of interest to many!

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3. The Down Fall of CP and T Symmetries

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The first evidence of CP violation Cronin and Fitch (1964)

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The Standard Model of CP Violation Many models have been proposed. Kobayashi-Maskawa in 1973 proposed: V KM NxN unitary matrix: N(N-1)/2 rotation angles (N-1)(N-2)/2 phases. Non-zero phase CP violation! Three generations of quarks: U = (u, c, t), D = (d, s, b) ; One phase.

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Kaon and CP: classification CP violation in the decay amplitute CP eigenstates ≠ mass eigenstates CP violation from interference of “DIRECT and MIXING” DIRECT MIXING or INDIRECT INTERFERENCE DIRECT CP firmly established after more than 30 years Re( ’/ ) = (16.7 ± 2.3)x10 -4 KK Re( ’/ )

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CP from B decays ( Great achievements from BaBar and Belle )

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It is wrong to average different modes which have different sources of contaminations.

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All data are consistent with Kobayashi-Maskawa model!

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CP violation from Cosmology Our universe has more matter than anti-matter Not C symmetric, Not CP symmetric. Why such an asymmetric universe?

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Big-Bang Nucleosynthesis

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WMAP Results on CMB (2003)

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Why problem? If started with a symmetric initial condition, the expected ratio for is ~ 10^{-20} due to matter and anti-matter annihilation in the early epoch. This difference causes the universe to have more matter than anti-matter ---- the baryon (matter) asymmetry problem! Can this be created from a initially symmetric universe? To create baryon asymmetry 3 conditions (Sakharov 1966) Baryon number violation C and CP violation Deviation from thermal equilibrium

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New Physics Beyond Standard Model? SM not able to explain the baryon asymmetry in the Universe Too small CP violation! Need new physics, example SUSY. Effects in B decays: He, Li and Yang, hep-ph/0409338

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Electric dipole moment of elementary particles (Several experiments; A lot of theoretical activities) CP violation in hyperon decays (HyperCP; Donoghue, He and Pakvasa; Jiang and Yan, …) Other B decays At high energy colliders, CDF, LHC and etc. An exciting time for the study of CP violation. Other tests of CP and T violation

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4. CPT Symmetry and Its Violation No violation of CPT has been observed.

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Best test of CPT: Neutral Kaon system (again) Other tests particle and anti-particle lifetimes, magnetic dipole moment… No CPT violation is found. Theoretically CPT violations possible? Yes, violate some of the conditions For CPT theorem. String theory, 10 dimensions => 4 dimensions even in 10 dimensions CPT is a good symmetry, the vacuum may break CTP in 4 dimensions. Needs further study both experimentally and theoretically.

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5. Discussions and Conclusions C, P, T, CP symmetries are separately broken in nature. CP violation is a crucial condition for the dominance of matter over anti-matter in our universe. Understand the origin of CP violation will help understand of the matter-anti-matter asymmetry. CP and T violations have been studied in laboratory experiments, all are consistent with the standard CKM mechanism. Understand the matter-anti-matter asymmetry problem, new physics is needed. More experimental data needed. No direct evidence for CPT symmetry breaking. Further test of CPT needed. The studies of C, P, T symmetries have provided many understandings of the laws of nature. Future studies will continue to be important.

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