EDM and CPV in the t system
Gabriel González Sprinberg
Instituto de Física, Facultad de Ciencias
Montevideo Uruguay
[email protected]
DIF06 INFN
Laboratori Nazionali di Frascati
Outline
1.
Electric Dipole Moment
1.1 Definition
d
B
f
B = , Z, g, …
f = e, , t, ..., b, t
1.2 Experiments
2.
Observables
2.1 High energies
2.2 Low energies
3.
Conclusions
1. EDM
1.1Definition
P and T-odd interaction of a fermion
with gauge fields:
Classical electromagnetism
Ordinary quantum mechanics
H EDM
 
 d  E ,


dd s
Relativistic quantum mechanics: Dirac equation
i
 )  m    d  5  F
H    i (  eA
2
Non-relativistic limit:
H  H EDM
 
 d  E
1. EDM
1.1Definition
SYMMETRIES:
Time reversal T, Parity P
Besides, chirality flip (some insight into the mass origin)
EDM
t  t
LANDAU 1957
T , P odd interactions


: E  E,
H EDM
In QFT:


s  s
  H EDM
CPT Invariance
CP  T
1. EDM
1.1Definition

t
t
EDM
SM :
• vertex corrections
• at least 4-loops
Beyond SM: • one loop effect (SUSY,2HDM,...)
• dimension six effective operator
1. EDM
SM :
1.1Definition
= 0 !!!
V
V*
E.P.Shabalin ’78
We need 3-loops for a quark-EDM, and 4 loops for a lepton...
J.F.Donoghue ’78
I.B.Khriplovich,M.E.Pospelov ‘90
A.Czarnecki,B.Krause ‘97
1. EDM
1.1Definition
Fermion of mass mf generated by physics at
L scale has
EDM  mf/L2
T-odd tEDM has particular interest and
depends on the underlying physics of CP
violation
1. EDM
Effective Lagrangian:
CPV:
Operators:
Other operators:
1.1Definition
1. EDM
1.1Definition

Z
t
t
t
WEDM
t
EDM
More sensitivity
HIGH ENERGY (Z-peak)
LOW ENERGY
1. EDM
1.1Definition
5 ( p , p )  ie    5 aV (q 2 )     5 q dV (q 2 ) 
V = , Z
For
q2=0
EDM
q2=MZ2 WEDM
t
d
t
dZ
GAUGE INVARIANT
OBSERVABLE QUANTITIES
Beyond SM EDM: Loop calculations
1. EDM
PDG ’06
1.2 Experiments
95% CL
EDM BELLE ‘02
Re(d ) : ( 2.2 to 0.45)  1016 e cm
t

Im(d ) : (0.25 to 0.008)  10
t

WEDM ALEPH 1990-95 LEP runs
Re(d )  0.50  10 e cm
t
Z
17
Im(d )  1.1  1017 e cm
t
Z
16
ecm
1. EDM
1.2 Experiments
For other fermions….
e

d  (0.069  0.074)  10
26
e cm
d  (3.7  3.4)  1019 e cm


dn  0.63  1025 e cm, 90% CL
2. Observables
SM for EDM is well below within present experimental
limits:
dq  1032  1034 ecm
CKM 3-loops
de  1038 ecm
CKM 4-loops
Hopefully
SM prediction
mt e
d 
d  1033  1034 ecm in the SM
me
t

…15 orders of magnitude below experiments...
2. Observables
Currents limits on electron EDM gives:
dt  2.4  1024 ecm
However, in many models the EDM do not necessarily
scale as the first power of the masses.
Multihiggs models 1-loop contributions
Vectrolike leptons
EDM scale as the cube of the mass!
BSM t-EDM can go up to 10-19 e cm
2. Observables
Non-vanishing signal in a
tEDM observable
NEW PHYSICS
mt
One expects: d  e 2
L
t

special interest in
heavy flavours
tEDM: In order to be able to measure a
genuine non-vanishing signal one has
to deal with a CP -observable
2. Observables
Indirect arguments:
2.1 High energies
(e e  t t )


 
(Z  t t )
 
 d
t 2
Z
any other physics may
also contribute…
Look for P , CP
linear effects
Genuine CPV observables in t–pair production:
SPIN TERMS
and/or
SPIN CORRELATIONS
2. Observables
Spin terms
CP :
2.1 High energies
angular distribution
decay products
of
• Asymmetries in the decay products
• Expectation values of tensor observables
2. Observables
2.1 High energies
x: Transverse y: Normal z: Longitudinal
2. Observables
2.1 High energies
Tensor observables: T  (q  q ) (q  q )  (i  j)
ij

 i

 j


mZ
t
t
Z-peak:
T ij 
c   s ij dZ

 (q )

e
W.Bernreuther,O.Nachtmann ‘89
Normal polarization:
P Nt  T  odd, P  even
(and needs helicity-flip)
Genuine CPV if
P
t
N
P
t
N
2. Observables
2.1 High energies
d
P  a   sin qt 2v  (v  a )  cos qt  mt
e
t
EDM (and P N ) is proportional to angular asymmetries,
t
N
2
to extract sinqt cosqt sinfh
2
t
Z
2


   (more details latter..)
A 
  


One can measure A for t and/or t
CP :
A
CPV
1 
 (A  A )
2
2. Observables
2.2 Low energies
e  e   ,   t  (s ) t  (s )
Diagrams:
dt
dt
2. Observables
2.2 Low energies
What about the linear terms?
Interference with the axial
part of Z-exchange,
suppressed by q2/MZ2
2. Observables
2.2 Low energies
2. Observables
2.2 Low energies
2. Observables
T ,P
CPV
2.2 Low energies
2. Observables
2.2 Low energies
2. Observables
2.2 Low energies
2. Observables
2.2 Low energies
+
2. Observables
2.2 Low energies
2. Observables
2.2 Low energies
Bounds:
For 106/7 t and at low/U energies
upper bound
Re(d t )  1016 / 17 e cm
3. Conclusions
 Polarized beams open the possibility for new
observables
 Improving the number of t–pairs ( ...1011? )
allows to lower the EDM bound by many (...2?)
orders of magnitude
 These new bounds may be important for
beyond the SM tphysics
3. Summary
Discussions with J.Bernabeu, J.Vidal and A.Santamaría
are gratefully acknowledged
SOME REFERENCES
 J. Bernabeu, G.S., Jordi Vidal
Nuclear Physics B 701 (2004) 87–102
 Daniel Gomez-Dumm, G.S.
Eur. Phys. J. C 11, 293{300 (1999)
 W. Bernreuther, A. Brandenburg, and P. Overmann
Phys. Lett. B 391 (1997) 413; ibid., B 412 (1997) 425.