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Experimental tests of the SM (3):non-collider particle physics
FK8022, Lecture 7
Core text:
Further reading:
Collider vs non-collider physics (1)
Can see new physics ?
Max energy scale
Max precision Characterisation of new physics
Colliders
Good – precision measurements of particle masses/couplings.
Non-colliders
Poor
7 TeV2
s
7 TeV
(scenario-dependent)
~ 0.000001O
O
~ 0.001O
O
There is life beyond the large collaborations.
New physics often found at the high energy/high precision frontiers.Colliders and non-colliders offer complementarity .
Collider vis non-collider physics (2)Topic Scenario
Anomaous charge (q<<e)
Millicharged partices
Proton decay GUTs
Neutrinoless double b-decayAxions 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
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.
Major neutrino expts not listed (see Thomas’ lectures)
Dipole moments
• .
.
Magnetic dipole moment.
A particle, eg, electron picks up energy in a magnetic field: Magnetic dipole moment
Spin angular momentum
Spin quantum number Modern chemistry , eg, two
E B
S
s
1
• .
electrons in the shell etc.
Electric dipole moment
A particle, eg, electron picks up energy in an electric field:
Electric dipole moment
otherwise we'd need to invent a new quan
e
e
e
S
E d
d
d S
tum 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-invarianceMagnetic dipole moment along a -axis: ( =constant)
Measure spin-up or spin-down Moment parallel or antiparallel to spin, not both!
Electric dipole moment along a -axis: ( =constant
z z
ez z
z
aS a
z
d bS b
)
Measure spin-up or spin-down Moment parallel or antiparallel to spin, not both!
-transformation: Spin (odd), charge (even), distance (even), electric dipole moment (even)T
z zS zS
zz zS
z
zS
ezd zS zS
ezdezd zS
ezd
zS
OR
OR
ezd zS
ezd zS
TzS
ezd
ezd
zS
A non-zero permanent electric dipole moment violates T-invariance!
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
Electroweak 4 loops + cancellation needed.
Standard Model1 loop sufficient
CP-violating phase
Supersymmetry
40 3810 10 ecmed 29 2510 10 ecm
(selected SUSY models)ed
2
2
1.
40.1
4 130
Most new physics models have CPV phases . Assumed in models sin
EDM from typical new physics process at energy :
sin ; =number of loops
CP CP
n
effe eCP eff
d m cc n
e
x
y
z
1
2z
1.
2(1) 0
11(0)
12
(2) ( )
Consider spin- particle
At the spin is prepared along the -axisin an equally mixed spin-up/spin-down state.
X enters electric field along the -axis. electric + m
X
t z
z
1 1: ( )
2 2
agnetic dipole energy shifts.
At time ;
Ei i
e
E ii
e e dt t
ee
A simple generic EDM experiment (1)
x’
y’z’'z
-
21 11
( ) ( )12
s1
2
(3) To observe the phase difference a measurement is madeof the different up/down composition along a new ' axis
Rotate around -axis.
1
i i
i i
z
y
t t
e e i
e e
2
2
in
cos
sintan
cos
.
Relative populations in spin-up,spin-down states along '-axis
Measurement of measurement/limit on
e
e
z
dR
R d
A simple generic EDM experiment (2)
Experimental sensitivity
0
0
atan
, .
2
Increase sensitivity to small
It turns out number of particles in a pulse.
fields as high as 10000 GV/m obtained Eg ACME experiment to find an electron EDM.
Elect
e
e
e
d R
d
d NN
rons in polar ThO molecules. Internal field in molecule macroscopic fields. Eg thunder storm ~ 100 kV/m.
Worldwide EDM Community
Limits on particle EDMs Particle Upper limit on |
d| (ecm)SM prediction
(ecm)
n
em
p
26 34 316 10 10 10 10 29 40 38 8.7 10 10 10
28 40 3810 10 10 24 40 384 10 10 10
2
24
40.1
130
Searches still far from SM-sensitivity but sensitive to new physics.
sin
=number of loops
-EDM new physics scale > 3 TeV (1 loop), >1 TeV (2
n
effe eCP
eff
d m c
e
n
e
loops)
ACME (2013)
e-EDM predictions and limits
(D. DeMille)
Neutron EDM searches
7 orders of magnitude in precision gained. Eating into SUSY/exotic parameter space.
Gyromagnetic ratio in classical physics
2
,
ˆ
ˆˆ ˆ2 2
0)
A charged particle mass , in a loop or radius Magnetic moment:
normal
Independent of valid for point-like ( particle. Gyromagn
e m r
IA n
ev eI A r L mvr n L
r m
r r
ˆˆ 12
1
etic ratio of object with spin angular momentum
from classical arguments.
Intrinsic quantum mechanical spin has no true classical analogue.Naive to expect
g S
eg S g
m
g
Gyromagnetic ratio in quantum mechanics
2 0
1
2
1
2 2
Schrödinger-Pauli equation for point-like spin- particle in EM field.
Non-relativistic version of the Dirac equation.
=
Derived from Dirac equation or seen as an effec
A A
eP eA B eA E m
m m
• - •2
12
2 2 22
tive axiom of QM.
Identify term as energy due to magnetic moment ( )
S
. Holds in fully relativistic treatment.
eB U B
me e
Sm m
g
Gyromagnetic ratio in quantum field theory
2g
2g + infinite number of diagrams
= +
2g =
2Deviations from from loops. Sensitivity to heavier particles (SM and BSM) Precision test of the SM.
g
Quantum mechanics quantum field theory. The particle can take part in many self-interactions
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 QEDNucleon measurements complex substructure.Muon measurement possible discrepancies
2
410
active area of research/speculation.
-sensitivity to new physics ~
-sensitivity to new physics e
m
e m
Longitudinally polarised muons injected in storage ring. Follow circular orbit due to transverse -field.Vertical focusing quadropole -field
Spin precesses with frequency
Cyclotron frequency=s
c
a
B
E
12
2
.
anomalous -moment contribution
Measure -field and cyclotron frequency.
Measure
P-violating decay
spin-direction
s c
s
e
s
ea B
m
a g
B
e
E821 Experiment (Brookhaven)
Measuring the muon gyromagnetic ratio
Measurements of muon g-2
-10
-10
-10
11 659 208(6) 10 0.5
11 659 (7) 10 0.6
11 659 (8) 10 0.7
E821 Experiment
ppm
Theory:
196 ppm
181 ppm
~3 discrepancy.
µ
µ
µ
a
a
a
2
24
Generic model of new physics at energy scale : Contribution to
Observed discrepancy with experiment New physics at TeV scale Don't open the champagne just yet..
NP
a
ma
Theoretical uncertaintiesSource Contribution to am x 10-10 Contribution to dam x 10-10
QED 11000000 0.1
Hadronic vacuum polarisation 700 7
EW 15 0.3
Hadronic components dominate uncertainty.
QED had EWa a a a
QED Hadronic EW
.
hard to calculate ( soft strong processes).
Data-derived method with measurements
of hadrons and hadronic -decays. (lecture X)
New experiment underway at Fermilab to measure
New exper
hada
e e
a
iments to measure low energy hadrons.e e