Download Some basics of discrete space

Discrete Space-Time Symmetries
Xiao-Gang He
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
Talk at NCKU, 5/5/5
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.
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?
Some basics of discrete space-time symmetries
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.
2. The Down Fall of Parity P Symmetry
The
Puzzle (the 1950’s)
to pi+ pi0,
and
to pi+ pi0 p0.
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
Example Parity violating process
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!
3. The Down Fall of CP and T Symmetries
The first evidence of CP violation
Cronin and Fitch (1964)
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.
Kaon and CP: classification
MIXING or INDIRECT
DIRECT
CP violation in the
decay amplitute
Re(e’/e)
DIRECT CP firmly
established after more
than 30 years
Re(e’/e) = (16.7±2.3)x10-4
CP eigenstates ≠ mass
eigenstates
INTERFERENCE
CP violation from
interference of “DIRECT and
MIXING”
eK
CP from B decays (Great achievements from BaBar and Belle)
It is wrong to average different modes which have different sources of contaminations.
All data are consistent with Kobayashi-Maskawa model!
CP violation from Cosmology
Our universe has more matter than anti-matter
Not C symmetric, Not CP symmetric. Why such an asymmetric universe?
Big-Bang Nucleosynthesis
WMAP Results on CMB (2003)
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
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
Other tests of CP and T violation
• Electric dipole moment of elementary particles (Several
experiments; A lot of theoretical activities)
• CP violation in hyperon decays
• Other B decays
• At high energy colliders, CDF, LHC, ILC and etc.
An exciting time for the study of CP violation.
4. CPT Symmetry and Its Violation
No violation of CPT has been observed.
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.
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.