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Time-reversal symmetry violation
in heavy atoms
Zakład Optyki
Jacek Bieroń
Atomowej
Uniwersytet Jagielloński
Kraków, 24 IV 2008
Instytut Fizyki
Parity
Chen Ning Yang Tsung-Dao Lee
Parity violation
parity reversal
Parity
Chen Ning Yang Tsung-Dao Lee
a comment on (non)equivalence
of mirror and parity transformations
Parity violation
Chien-Shiung Wu
Charge conjugation
• C operation - interchange of particle with its antiparticle.
• C symmetry in classical physics - invariance of Maxwell’s
equations under change in sign of the charge, electric and
magnetic fields.
• C symmetry in particle physics - the same laws for a set of
particles and their antiparticles: collisions between electrons
and protons are described in the same way as collisions
between positrons and antiprotons. The symmetry also applies
for neutral particles.
• Cy =  y: even or odd symmetry.
• Example: particle decay into two photons, for example p o 
2g, by the electromagnetic force. Photon is odd under C
symmetry; two photon state gives a product (-1)2 and is even.
So, if symmetry is exact, then 3 photon decay is forbidden. In
fact it has not been observed.
• C symmetry holds in strong and electromagnetic interactions.
C-symmetry violation
• C invariance was violated in weak interactions because parity
was violated, if CP symmetry was assumed to be preserved.
• Under C operation left-handed neutrinos should transform into
left-handed antineutrino, which was not found in nature.
However, the combined CP operation transforms left-handed
neutrino into right-handed antineutrino, which does exist.
CP and Time-reversal symmetry
• CP invariance was violated in neutral kaon system.
• T operation - connects a process with a reversed process
obtained by running backwards in time, i.e. reverses the
directions of motion of all components of the system.
• T symmetry: "initial state  final state" can be converted to
"final state  initial state" by reversing the directions of
motion of all particles.
CPT theorem
• Define product symmetries, like CP (parity and charge
conjugation)  a system of antiparticles in the reverse-handed
coordinate system symmetry
• Combined CPT symmetry is absolutely exact: for any process,
• its mirror image with antiparticles and time reversed
• should look exactly as the original  CPT theorem
• If any one individual (or pair) of the symmetries is broken, there
must be a compensating asymmetry in the remaining operation(s)
to ensure exact symmetry under CPT operation
• CPT symmetry was checked through the possible difference in
masses, lifetimes, electric charges and magnetic moments of
particle vs antiparticle and was confirmed experimentally with
10-19 accuracy (relative difference in masses)
„Proof” of CPT
y
y
rotation
=
reflection
x
x
j = ( jx , j y )
C
j = (  j x , j y )
P
T
j  = (  , j )  (   , j )  (   , j )  (   , j )
Howto observe
Time Reversal Violation
1.
Compare cross sections of a scattering
process [running in ‘real’ time]
and ‘time-reversed’ scattering process
[running in ‘reversed’ time]
2.
Detect an Electric Dipole Moment
of an elementary particle
Time Reversal Violation
in atoms
…………
enhancement mechanisms
of
Electric Dipole Moments
in atoms
• A neutral system composed of
charged objects re-arranges in an
external electric field such that the
net force on it cancels on average.
• This may give rise to
– significant shielding of the field at the
location of the particle of interest
– (strong) enhancement of the EDM effect
• “Schiff corrections” - need for
theoretical support
Schiff theorem violation mechanisms:
magnetic shielding
volume shielding
de K 

2
c
E
2
 d e  Eint
 dr
3
Z

E
3
2
T-odd atomic beauty contest:
heavy
close levels of opposite parity
deformed nucleus
Role of atomic theory

E (atom) =   (nucl )  B(el )

hyperfine
structure
magnetic dipole
electric quadrupole
2

V
(
el
)

E
=
Q
(
nucl
)
 2

z
…
Enhancement of electron EDM
in paramagnetic atoms
d atom
=
de
2
v c
N
j
2e 
 (g
i =1
i
0
2
 1)  E
i
i
int
N
k k
z
i
j
i =1
E j  Ek
k
Z

E j  Ek
3
2
opposite parity
states mixed
by EDM
Enhancement of nuclear EDM
in diamagnetic atoms
d (atom) = d (nucl )  K
P,T-odd
interactions
E
Schiff moment
MQM
E octupole
atomic enhancement factor
Schiff moment
Schiff x K

j d z k k  4p S   i  (ri ) j
N
d atom = 2
k
Z 

E j  Ek
2
2
i =1
E j  Ek
opposite parity
states mixed
and the winner is … by EDM
so, what do we know about radium ?
1
7s7p P1
2 1
7s S 0 rate in
213
88
Ra
3
7s6d D2
2 1
7s S 0 rate in
213
88
Ra
3
7s7p P1
2 1
7s S 0 rate in
225
88
[PRL 98 (2007) 093001]
Ra

j d z k k  4p S   i  (ri ) j
N
d atom = 2
k
i =1
E j  Ek
Co-Producers
(in alphabetical order)
Jacek Bieroń Uniwersytet Jagielloński (300-400)
Charlotte Froese Fischer Vanderbilt University (38) & NIST
Stephan Fritzsche GSI
Gediminas Gaigalas Vilniaus Universitetas
Ian Grant University of Oxford (9)
Paul Indelicato l’Université Paris VI (41) & ENS
Per Jönsson Malmö Högskola
T-foils = thanks to Klaus Jungmann & Hans Wilschut (KVI)
YbF foils = thanks to Ed Hinds (University of Sussex)
T-foils & YbF foils = conditions of use