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