FK8022, Lecture 7
Experimental tests of the SM (3):
non-collider particle physics
Core text:
Further reading:
Collider vs non-collider physics (1)
There is life beyond the large collaborations.
New physics often found at the high energy/high precision frontiers.
Colliders and non-colliders offer complementarity .
Can see
new
physics ?
Colliders
Non-colliders


Max energy
scale
s

 7 TeV
2
 7 TeV
(scenario-dependent)
Max precision
O
O
O
O
~ 0.001
Characterisation of
new physics
Good – precision
measurements of
particle
masses/couplings.
~ 0.000001 Poor
Collider vis non-collider physics (2)
Non-colliders also perform studies
for specific scenarios or (mad  )
speculative ideas which are
impossible for colliders to probe.
Impossible to cover all in one
lecture.
Neutrinoless double b-decay
covered by Thomas.
Dipole moment
measurements/searches among the
most high profile of non-collider
research (this lecture)
Give a flavour of the type of work
which is done and how its done.
Topic
Scenario
Anomaous
charge (q<<e)
Millicharged
partices
Proton decay
GUTs
Neutrinoless
double b-decay
Axions
Dark
matter/strong CP
problem
Electric dipole
moments
Precision SM test
– search for new
physics
Magnetic dipole
moments
Precision SM test
– search for new
physics
Major neutrino expts not
listed (see Thomas’ lectures)
Dipole moments
Magnetic dipole moment.
A particle, eg, electron picks up energy in a magnetic field: E    • B.
 Magnetic dipole moment 
 Spin angular momentum
  S 
 Spin quantum number s.
 Modern chemistry , eg, two electrons in the 1S shell etc.
Electric dipole moment
A particle, eg, electron picks up energy in an electric field: E   d e •  .
 Electric dipole moment d e
 d e  S otherwise we'd need to invent a new quantum number and the
world would change, eg, four electrons in the lowest level etc.
Spin angular momentum is the only preferred direction for a particle.
It defines the direction of the magnetic and electric dipole moments.
Electric dipole moments violate T-invariance
 zS z
Magnetic dipole moment along a z -axis:
Sz
 z  aS z (a=constant)
OR
 Measure spin-up or spin-down
 Moment parallel or antiparallel to spin, not both!
Electric dipole moment along a z -axis:
 zS z
z
Sz
d ezS z
d ez  bS z (b=constant)
 Moment parallel or antiparallel to spin, not both!
d ezS z
d ez
T -transformation:
Spin (odd), charge (even), distance (even), electric dipole moment (even)
T
d ezS z
Sz
d ez
OR
 Measure spin-up or spin-down
d ezS z
z
d ez
Sz
Sz
d ez
A non-zero permanent
electric dipole moment
violates T-invariance!
Sz
Electric dipole moment
• Similar argument can be made for Parity.
• A permanent EDM violates P and T.
– CP also violated (CPT invariance)
• Standard Mode CPV predicts tiny EDMs
• Searches for EDMs test strong CP sector of
the SM
• Sensitive to many exotics scenarios
SM and BSM contributions to electron-EDM
Standard Model
Supersymmetry
Electroweak
4 loops +
cancellation needed.
1 loop sufficient
CP-violating
phase
d e  10
40
 10
38
d e  1029  1025 ecm
ecm
(selected SUSY models)
Most new physics models have CPV phases CP . Assumed in models sinCP
EDM from typical new physics process at energy :
de
e
  eff   me c 2 
 c
  2  sinCP ;  eff
 4    
n
4

130
0.1 n=number of loops
1.
A simple generic EDM experiment (1)
1
z
Consider spin- particle X .
2
(1) At t  0 the spin is prepared along the z -axis  z 
1
  

2
in an equally mixed spin-up/spin-down state.
1 1
  (0) 
 
2 1
x
(2) X enters electric ( ) field along the z -axis.
 electric + magnetic dipole energy shifts.
 i E
1 e
At time t   :  (t ) 
2   i E 
e

i


e
1

  2  e  i 




y
; 
d e
A simple generic EDM experiment (2)
(3) To observe the phase difference a measurement is made
of the different up/down composition along a new z' - axis
 Rotate

2
x’
around y -axis.
1 1  1
  (t ) 

  (t )
2 1 1 
i
 i
1  e  e   i sin  
  i


 i 
2  e  e   cos  
 z'
z’
Relative populations in spin-up,spin-down states along z'-axis
2
 sin  
2  d e 
R

tan



cos





 Measurement of R  measurement/limit on d e .
y’
Experimental sensitivity
de 

atan
 R
Increase  ,  sensitivity to small d e .
It turns out  d e
2 N 0
N 0  number of particles in a pulse.
  fields as high as 10000 GV/m obtained
Eg ACME experiment to find an electron EDM.
 Electrons in polar ThO molecules.
 Internal   field in molecule
 Eg thunder storm  ~ 100 kV/m.
macroscopic   fields.
Worldwide EDM Community
Limits on particle EDMs
Particle
Upper limit on
|d| (ecm)
SM prediction
(ecm)
n
 6  10  1026
e
8.7 1029
1034  1031
1040  1038

1028
1040  1038
p
4 1024
1040  1038
Searches still far from SM-sensitivity but sensitive to new physics.
  eff 


e
4



4
 eff

130
 e-EDM 
de
n
 me c 2 
 2  sinCP
  
0.1 n=number of loops
new physics scale > 3 TeV (1 loop), >1 TeV (2 loops)
e-EDM predictions and limits
ACME
(2013)
(D. DeMille)
Neutron EDM searches
7 orders of magnitude in precision gained.
Eating into SUSY/exotic parameter space.
Gyromagnetic ratio in classical physics
A charged particle e, mass m, in a loop or radius r
Magnetic moment:   IA nˆ
ev
 e ˆ
2
I
A   r L  mvr nˆ  normal  ˆ  
L
2 r
 2m 
Independent of r  valid for point-like ( r  0) particle.
Gyromagnetic ratio g of object with spin angular momentum S
 e ˆ
ˆ  g 
 S  g  1 from classical arguments.
 2m 
Intrinsic quantum mechanical spin has no true classical analogue.
Naive to expect g  1
Gyromagnetic ratio in quantum mechanics
1
Schrödinger-Pauli equation for point-like spin- particle in EM field.
2
Non-relativistic version of the Dirac equation.
e
2
 1
0
P

eA



B

eA



 A =  E  m  A
2m
 2m

Derived from Dirac equation or seen as an effective axiom of QM.
e
 • B as energy due to magnetic moment (U  - • B)
2m
e
1
e

 S      2
S
2m
2
2m
 g2.
Identify term
Holds in fully relativistic treatment.
Gyromagnetic ratio in quantum field theory
Quantum mechanics  quantum field theory. The particle
can take part in many self-interactions
g2
=
g2
=
+
+ infinite number
of diagrams
g2
Deviations from g  2 from loops.
 Sensitivity to heavier particles (SM and BSM)
 Precision test of the SM.
Some more Feynman diagrams…
Subset of the SM processes which need to be calculated.
Sensitivity to a range of TeV-scale BSM
scenarios Eg SUSY
Measurements of g
Measurements have extraordinary precision.
Electron measurement and theory  a triumph for QED
Nucleon measurements  complex substructure.
Muon measurement  possible discrepancies
 active area of research/speculation.
 m 

~

e-sensitivity to new physics  me 
 -sensitivity to new physics
2
104
Measuring the muon gyromagnetic ratio
Longitudinally polarised muons injected in storage ring.
Follow circular orbit due to transverse B -field.
Vertical focusing quadropole E -field
Spin precesses with frequency s
Cyclotron frequency=c
 a   s  c 
e
a B
m
1
a   g  2  anomalous  -moment contribution
2
Measure B-field and cyclotron frequency.
Measure s
 P-violating decay   e      e
 spin-direction  s .
E821 Experiment (Brookhaven)
Measurements of muon g-2
E821 Experiment
aµ  11 659 208(6)  10-10  0.5ppm 
Theory:
aµ  11 659 196(7)  10-10
aµ  11 659 181(8)  10-10
 0.6ppm 
 0.7ppm 
~3 discrepancy.
Generic model of new physics at energy scale :
Contribution to a
 NP  m
 2
4  

 a


Observed discrepancy with experiment  New physics at TeV scale
2
Don't open the champagne just yet..
Theoretical uncertainties
Contribution to a x 10-10
Contribution to da x 10-10
11000000
0.1
Hadronic vacuum polarisation
700
7
EW
15
0.3
Source
QED
a  aQED  ahad  aEW
Hadronic components dominate
uncertainty.
QED
Hadronic
ahad hard to calculate (  soft strong processes).
Data-derived method with measurements
of e   e   hadrons and hadronic  -decays.
(lecture X)
New experiment underway at Fermilab to measure a .
New experiments to measure low energy e   e   hadrons.
EW