EDM as a Probe of Physics Beyond EDM as a Probe of Physics Beyond SMSM
Isabella Masina (Fermi Ctr. Rome)
OUTLINE:
* Introduction
- EDMs of elementary s=1/2 particles
- EDMs in the SM
1* EDM probe of SM or NP beyond SM?
2* Which NP scales and couplings are probed?
3* SUSY is a NP candidate. Which constraints from EDMs on:
3a) ?
3b) the relevant phases in SUSY SU(5) ?
* Conclusions
EDMs of elementary EDMs of elementary particlesparticles
Dirac equation for s=1/2, charged e, massive m, elementary particle interacting with an e.m. field
g B s dNP 0
P T=CP
50’s: Purcell & Ramsey look for dn (not elementary!) as a probe of P,T in strong interaction
dn < 3x10-18 e cm = 3x10-5 e fm dn/(e rn) < 3x10-5 , like 100m/Rearth ...now 1m (Ellis)
rn Also de/(e re) < 10-17 , like 0.1nm !
Beyond SM: d=5 [NP, dNP]=M-1
EDMs in the SMEDMs in the SM
2 sources of CPV:
one strongly constrained by EDM, one measured to be large but
uneffective for EDM
d4
STRONG CP PROBLEM:
=0 due to PQ? MULTI-LOOP<<EXP
and of UMNS with m
present planned
upp. limit pr. SM+m with =0
dn 1.5 x 10-26 10-28
O(10-10) 10-31
dHg 2 x 10-28 10-28 O(10-9-10-10) ?
dD ? 10-29 O(10-13) plnd ?
dp 5 x 10-24 10-28 O(10-8) ?
dTl 0.9 x 10-24 O(10-4) ?
de 1.6 x 10-27 10-30 10-38
d 10-19 10-24 10-35
of VCKM
=60°14°
...which generically contains MANY fundamental sources of CPV (resulting in eff. op of d>4 at l.e.)
At least one NP CPV source is NECESSARY to explain matter-antimatter asymmetry!!!
NP if measure: d dTl dHg dD > 10-26(-28) e cm dp > 5x10-26(-28) e cm
if below there is ambiguity
As EDMs probe in general different combinations of CPV sources they are ALL IMPORTANT
DIFFERENT EDM measurements are NECESSARY to understand NP CPV
....but also upper limits are strongly welcome!
EDM probe of SM or NP beyond SM?
With present (planned) dn
Planned dD will be the most sensitive to :
NP if measure: d dTl dHg dn dp with dD < 10-29 e cm
see for instance the present limits on leptonic sector
Which NP scales and couplings are to be probed?
d=5 ij
coupling of NP with leptons:
e.m.chargechirality flip
mass of NP in loops
loop factor
adimensional and naturally O(1)
MDM EDM LFVdecays
probe NPij , hence NP
ij/ MNP2
Consider possible 1-loop NP
Where i,j =e,,
present planned at present MNP > planned
de [e cm] 1.6x10-
27
10-30 (Imee)1/2 x 6 TeV -> 250 TeV
d [e cm] 10-19 10-24 (Im)1/2 x 10 GeV -> 3 TeV
ae 6x10-11 (Reee)1/2 x 30 GeV
a (1-3)x10-9 (Re)1/2 x 0.2 TeV th?
BR(->e ) 10-11 10-14 (PSI) |e|1/2 x 4 TeV -> 20 TeV
BR(->) 10-6 10-8 (LHC) ||1/2 x 0.1 TeV -> 0.5 TeV
N.B.: 0) if NP = O(1) -> EDM, LFV , MDM, probe now MNP at O(TeV), in future at O(10 TeV)
1) if MNP TeV (like susy) -> constraint on from de and ->e (susy CP and flavour problems)
2) if ImRe-> CP must be a good symmetry also for NP!
3) if Imee=Im(universality) then d< m/me de < 3x10-25 e cm , below planned...
...but violation of universality is reasonable!!!Unfortunately, extracting a bound on MNP from hadronic EDMs is much more
involved ......
Hence NP CPV sources MUST be SUPPRESSED (like in
susy)
EDM
LFV
MDM
EDM of NON-elementary particles EDM of NON-elementary particles
MNP
1 GeV
nuclear
atomic Measure: dTl , dHg , dD
E
N-EDMs-N interactions e-N interactions
New Phys fundamental CPV phases (e.g. and A in susy)
-termEDM & CEDM
Weinberg & 4-fermion op’s
dd
ddTl Tl = -585 d= -585 dee – e 43 GeV C – e 43 GeV CSS atomic matrix elements known with 20%
accuracy
E
MNP
1 GeV
nuclear
atomic Measure: dTl , dHg , dD
-termEDM & CEDM
Weinberg & 4-fermion op’s
N-EDMs-N interactions e-N interactions
ddHgHg==EVEN EVEN
WORSE!WORSE!
New Phys fundamental CPV phases (e.g. and A in susy)
ddnn==DIFFICULT NON PERT DIFFICULT NON PERT
PROBLEM!PROBLEM!
ddDD== NOT NOT
BADBAD
ddpp LIKELIKE ddnn
EDM of NON-elementary particles EDM of NON-elementary particles
Models for hadronic EDMs
Generically it turns out that the sensitivity of hadronic EDMs to NP is also around TeV
...and they also depend on which contribution dominates, hence depend on NP itself!
Assume =0
Combining chiral and SR techniques
UNCERTAINTIES are LARGE ~ factor of 2 (hopefully overall for Hg, D)
Agree within a factor of 2
Chiral lagrangian: + 0.26 ds e cm
~
from
Supersymmetry
FC = diag : =Arg() & ai=Arg(ai)
FV = off-diag : phases of LLij RR
ij LRij RL
ij. EDM probe combinations like Im(LLij mj
RRji)
Always the best for hierarchy, gcu,dark matter candidate, connection with string, ...
....but LFV and EDM are a problem
Universal: can compare EDMs sensitivities on eq grounds
The SUSY Flavor & CP problems: msusy =O(TeV) ijsusy
<<1
Amplitudes arise from Loops of Sfermions &
Gauginos
M2sferm
misalignment in flavour between f e sf mass matrices and can contain many CPV sources
Consider here...
NON universal: different EDMs probe different phases
ALL EDMs are IMPORTANT
(assuming no cancellations) Which EDM better constrain ? Take mSugra with
tg=10
2x10-2
[IM and C. Savoy, hep-ph/0211283]
10-2
10-5
5x10-6
4x10-3
10-3
2x10-6
5x10-7
NOW
g -2
PRESENTPRESENT PLANNEDPLANNED
A measure of d would be a signal of
a non universal source of CPV ( )
@ 3x10-25 ecm
e
LHC
(assuming no cancellations) Which EDM better constrain ? Take mSugra with
tg=10
2x10-2
[IM and C. Savoy, hep-ph/0211283]
10-2
10-5
5x10-6
4x10-3
10-3
0.10.1
1010-2-2
3x103x10-2-2
2x10-6
5x10-7
1010-2-2
4x104x10-3-3
5x10-6
10-4
10-6
3x10-5
5x10-7
10-5
NOW
g -2
PRESENTPRESENT PLANNEDPLANNED
[Olive, Pospelov, Ritz and Santoso, hep-ph/0506106
-updated by IM for n, D]
A measure of d would be a signal of
a non universal source of CPV ( )
@ 3x10-25 ecm
e
LHC
Hgn
Dpn
PRESENT: ne
Remember factor of
2
PLANNED: De
A-term and FV A-term and FV ’s a source of EDM’s a source of EDM
susy GUTs (R+HT): yes for both LFV and EDM
Could perfectly be =0 .
THEN ?
= (0) (rad)
Misalignment INDUCED in soft masses running from MPl to msusy
by LFV&CPV Yukawas of NP Heavy States
Misalignment in soft masses at MPl
NOT present in mSUGRA because an INHIBITION mechanism is at
work
Idem for CEDMs
Notice also
Are exp’s are ALREADY TESTING it?
susy seesaw (R): LFV yes, EDM no [Borzumati Masiero; Hisano; etc...] [Ellis Hisano Raidal; IM; etc]
[Barbieri Hall; Mohapatra; Hisano; IM Savoy; etc ]
SUSY SU(5)+seesaw
Relevant phase which is constrained by de :
Im(LL13 m RR
31) Im(e-i VL13)
yD32Where VL yD VR = diag(yD)
In the basis where ch. leptons and R-’s are diagonal
IF VR = 1 -> VL = UMNS & yD32 =
MN3/1015GeV(Strong assumption!!)
MT=2x1016 GeV MN3=1015 GeV
3x10-2
10-2
3x10-3
tg=10
Assuming also Im=O(1),
CEDM of d puts a bound on Ue3 as a function of MN3
tg=10
MT=2x1016 GeV
[IM, hep-ph/0304299]
[Hisano Kakizaki Nagai Shimizu, hep-ph/0407169]
de
dD
dp
N.B.: SU(5) just toy because ruled out by p-decay
In realistic SO(10) where p is ok, EDMs are even larger as there are more heavy states
[for de : IM Savoy, hep-ph/0309067]
de |Vtd| Im(e-i VL13)
d |Vts| Im(VL23)
=
5 >40?
Conclusions
EDMs are effective probes of TeV-scale NP beyond SM
- in particular SUSY
Even thought is interesting to compare their sensitivities by considering just ONE CPV source...
- like in SUSY
...in general different EDMs probe different CPV sources
- like d and de in SUSY SU(5)
ALL EDMs SEARCHES are SIGNIFICANT
- much work to do also in the theory sector!
