Fundamental Symmetriesand

Weak Interaction through Parity Violation (Particularly with Polarized Electron Scattering)

Juliette Mammei

Modern Physics

July 8-19, 2019 NNPSS 2

speed

size

Classical (Newtonian) Mechanics

Relativistic Mechanics

QuantumMechanics

Relativistic Quantum Field Theory

10-9 m

100 m

3x108 m/s1 m/s (much slower than light)

109 m

Equivalence principle

Quantum Mechanics from Classical Mechanics

July 8-19, 2019 NNPSS 3

Matrix formulation of Hamiltonian in classical mechanicsCanonical invariants – Poisson brackets are invariant under canonical transformations

Poisson bracket is replaced by an appropriate commutator for quantum mechanicsMuch of the formal structure of quantum mechanics is a close copy of the Poisson bracket formulation of classical mechanicsPosition and momentum are conjugate variables (Heisenberg uncertainty principle)

𝑝 → Ƹ𝑝 = −𝑖ℏ𝜕

𝜕𝑥

Two components of L cannot simultaneously be canonical momenta → Li and Lj can’t have simultaneous eigenvalues but L2 can be quantized with any one of the Li

If I have seen further it is by standing on the

sholders [sic] of GiantsIsaac Newton, 1676

EM as a (Classical) Gauge Theory

July 8-19, 2019 NNPSS 4

(Lorenz gauge )

(Coulomb gauge )Scalar function 𝜓 Ԧ𝑟, 𝑡

Existence of arbitrary numbers of 𝜓 Ԧ𝑟, 𝑡 is the U(1) “gauge freedom”

Local vs. Global

July 8-19, 2019 NNPSS 5

Restore local symmetry; 𝐹𝜇𝜈 and Lagrangian are unchanged

Gauge fields – introduced to restore local symmetry – dictate the form of the couplings

Introduce covariant derivative:

Quantized EM → QED

July 8-19, 2019 NNPSS 6

Creation and annihilation of particles

The fields

The four-vectors are Lorentz covariant solutions to the Dirac equation (relativistic generalization of the Schrodinger equation)

The conserved vector current is:

Discrete symmetries

Charge

July 8-19, 2019 NNPSS 7

Credit: Quantum Field Theory for the Gifted Amateur

Parity

Time Reversal

𝑄 is an operator that can measure the “charge”, like the position and momentum operators ො𝑥 and Ƹ𝑝

The symmetries discussed so far were continuous:

SU(3), SU(2) or U(1)

Discrete symmetries are represented by finite groups

Not just EM charge, but also lepton number, hypercharge, etc.

Parity

July 8-19, 2019 NNPSS 8

quantum mechanical operator that reverses the spatial sign ( P: x -> -x )

s

p

s

p ( ) ( )

( ) ( )( ) ( ) ( ) ( ) 11111Tensor

111Vector Axial

111Vector

111arPseudoscal

111Scalar

CTP

5

5

−−−−−−

+−−−

−−−

+−−

+++

)44( form theof Terms

We describe physical processes as interacting currents by constructing the most general form which is consistent with Lorentz invariance

32105 where i

Note: P (V*V) = +1 P (A*A) = + 1 P (A*V) = -1

Parity Time ReversalCharge Conjugation

ℎ =റ𝑠 ∙ റ𝑝

റ𝑠 ∙ റ𝑝

EM and Weak Interactions : Historical View

July 8-19, 2019 NNPSS 9

( ) ( )eepp

eEMpEM

Q

eJ

Q

eJM

−=

−=

2

2, ,

2

2,

( ) ( )eeFnp

eweak

F

Nweak GJGJM

== , ,,

EM: e + p → e + p elastic scattering

Weak: n → e- + p + ҧ𝜈𝑒 neutron beta decay

Fermi (1932) : contact interaction, form inspired by EM

V x V

V x V

Parity Violation (1956, Lee, Yang; 1957, Wu)required modification to form of current - need axial vector as well as vector to get a parity-violating interaction

( )( ) ( )( )eeFnp

eweak

F

Nweak GJGJM

55, ,, 11 −−==

(V - A) x (V - A)

Note: weak interaction process here is charged current (CC)

e-

e- p

p

𝐽𝜇𝐸𝑀,𝑝𝐽𝜇

𝐸𝑀,𝑒

𝐽𝜇𝑤𝑒𝑎𝑘,𝑁𝐽𝜇

𝑤𝑒𝑎𝑘,𝑒

e- p

n

𝐺𝐹𝜈𝑒

Experiment

July 8-19, 2019 NNPSS 10

Can only measure something if it is “observable”

The incident flux times the differential cross section is proportional to the product of the square of the matrix element and the Lorentz invariant phase space

|| 2M

dQMFd || 2=

All the physics is in the matrix element

Transition rates or scattering cross sections

“Fermi’s Golden Rule”

The Dirac Equation

July 8-19, 2019 NNPSS

0)( =− mi

( )

−=

−==

0

0

10

01, 00

space 3,2,1 time,0 ==

ej −=

0= j

Dirac equation for free electron:

0 +

where:

with:

leads to electron four-vector current density:

where the adjoint is:

satisfies the continuity equation:

11

the matrix element

July 8-19, 2019 NNPSS

xppiepu − )()( )'( puie ][2q

ig−

external lines

vertex factors

propagator

)(ku xkkieku − )()'(

pEMeEM

EM JJQ

M ,,

2

1~

12

Further reading: Looking for consistency in the construction and use of Feynman diagrams

Peter Dunne , Phys. Educ. 36 No 5 (September 2001) 366-374

external lines

the matrix element

July 8-19, 2019 NNPSS

xppiepu − )()( )'( pu

)sin41(cos4

52

−− W

W

gi

][22

2 )/(

ZMq

Mkkgi

−

−−

vertex factors

propagator

)(ku xkkieku − )()'(

pNCeNC

NC JJG

M ,,

22~

eNCe

A

eNCe

V

eNC AgVgJ ,,,

+= NNCNNCNNC AVJ ,,,

+=

13

Atomic Parity Violation

July 8-19, 2019 NNPSS 14

nucl. spin independent

interaction coherent over

all nucleons

Cs: 6s → 7s osc. strength f ≈ 10-22

use interference:

f ∝ | APC + APNC |2

≈ APC2 + APC APNC cos φ

Z-boson exchange between atomic electrons and the quarks in the nucleus

nucl. spin dependent,

interaction only with

valence nucleons

HPNC mixes electronic s & p states

< n’s’ | HPNC | np > ∝ Z3

Drive s → s E1 transition!

Credit: Gerald Gwinner

July 8-19, 2019 NNPSS 15

excitation rate per atom: 30 s-1

APNC possible with 106 - 107 atoms!

Credit: Gerald Gwinner

1010 excitations /sec

July 8-19, 2019 NNPSS 16Credit: Jason Fry

July 8-19, 2019 NNPSS 17Credit: Jason Fry

July 8-19, 2019 NNPSS 18

Credit: Jason Fry

PVES Experiment Summary

July 8-19, 2019 NNPSSsize of the asymmetry

size of the uncertainty

relative uncertainty(log scale)

19

How does PVES measure ?

July 8-19, 2019 NNPSS

2

+

= + +

2 2

2

eh

𝐴𝑃𝑉 =𝜎+ − 𝜎−𝜎+ + 𝜎−

≈ ++

= 2

4

2

F

4

G-QBQ

Q p

W

ppm1011010 56 −− −−

20

Hand-waving derivation of the parity-violating asymmetry in electron-proton scattering

July 8-19, 2019 NNPSS

NEMeEM

e VVQQ

,,

2

1~

pNCeNC

NC JJG

M ,,

22~ NNCeNCe

A

NNCeNCe

V

NNCeNCe

A

NNCeNCe

V AAgAVgVAgVVgG ,,,,,,,,

22~ +++

eEM

eeee

eEM VQQJ ,,

==

NEMNEM VJ ,,

=

NNCNNCNNC AVJ ,,,

+=

( ) eNCe

A

eNCe

VeeeeW

eNC AgVgJ ,,

5

2, sin41 +=++−=

pEMeEM

EM JJQ

M ,,

2

1~

21

Asymmetry

July 8-19, 2019 NNPSS

𝜎± ∝ 𝑀𝐸𝑀 ±𝑀𝑁𝐶2= 𝑀𝐸𝑀

2 ± 2𝑅𝑒 𝑀𝐸𝑀∗ 𝑀𝑁𝐶 + 𝑀𝑁𝐶

2

𝐴𝑃𝑉 =𝜎+ − 𝜎−𝜎+ + 𝜎−

≈2𝑅𝑒 𝑀𝐸𝑀

∗ 𝑀𝑁𝐶

𝑀𝐸𝑀2 +⋯

( )( )2,,

,,,,,,,,2

24 NEMeEM

e

NNCeNCe

V

NEMeEM

e

NNCeNCe

A

NEMeEM

eF

VVQ

AVgVVQVAgVVQQG

+

22

Elastic Scattering

NNPSS

2sin

21

2sin4

sin'42

22

222

e

N

e

e

M

E

E

EEQq

+

=

==−

Q2 is related to the wavelength of the virtual photon probe -

from 208Pb or 48Caor

from p or d or Heor

from e

e + N → e + N

qh /=

N N

N N

July 8-19, 2019 23

Polarimetry

Polarimetry

detectors

detectors

spectrometer

Cartoon Experiment

July 8-19, 2019 NNPSS

beam target

spectrometer

Collimators Magnets

main detector

electronics

accelerator

Position monitors

tracking detectors

luminosity monitors

RasterPhoto-

cathode

continuous

invasive

Pockellscell

At injector

Wien filters

Energy measurements

background determination

targetbeampolarized

beampolarized

beam

Charge monitors

Halo monitors

coolingposition

24

July 8-19, 2019 NNPSS

Quantity of interest

Typical Corrections:

Helicity Correlated CorrectionsBackground Asymmetry

Beam PolarizationEM Radiative corrections

Raw Asymmetries

Ameas

Analysis OverviewBlindingFactors

Other Measurements

Physics Asymmetries

Aphys

Unblind

Q2

25

Blinding

July 8-19, 2019 NNPSS 26

Why would anyone want to “hide” the result from oneself?

Suggestions for further reading*:

- Joshua R. Klein, Aaron Roodman, Annu. Rev. Nucl. Part. Sci. 2005. 55:141- P. F. Harrison, J. Phys. G: 28 2679 (2002)- F.G. Dunnington, Phys. Rev. 43, 404, (1933).- R. Feynman, “Surely You’re Joking, Mr. Feynman!” New York: W.W. Norton (1985)

*much of this talk shamelessly borrowed from these sources

The need for blind analysis (in fact, double-blind analysis in which the subject (the patient)

and the researcher are both unaware of who is getting the medicine and who is getting the

placebo) is well established in medicine – no clinical trial is taken seriously unless it is double-blind.

Double-blind technique first used in 1942

But, you say, we are physicists – rigorous, objective, unbiased...

Why should we want to blind?

Credit: D. Armstrong

Examples

July 8-19, 2019 NNPSS 27

The speed of light vs. year

Just a coincidence that there are several measurements in a row that have close to the same central values?

Even with such large uncertainties?

Credit: D. Armstrong

When to Blind

Armstrong’s criterion:

Blinding is a good idea* for any analysis in which:

a) there is judgment involved - eg. setting cuts, choosing data sets, deciding on background subtraction techniques, which polarimeter to trust, linear regression vs. beam modulation, Q2

ambiguities, GEANT 3 vs GEANT 4 radiative corrections, etc.

and

b) there is an “expected” answer, eg. from precise previous experiments or theoretical prediction –eg. Standard Model tests!

*translation: absolutely flipping essential

July 8-19, 2019 NNPSS 28

Credit: D. Armstrong

Unconscious (?) bias

An experimenter’s natural tendency is to looks for bugs or additional systematic errors when a result does not agree with expectation, and to not look so hard if it does…as well, to only look for those systematic errors that will work in the “right direction” to “explain” the deviation….

Blinding prevents this from happening – all systematics are treated in an unbiased, objective manner

But, you say, what if I remove the blinding, and my result is “crazy” (say, 6 from Standard Model) – aren’t there lots of checks I should do before I publish?

Answer: make a list of all those checks and studies and do them all before you unblind – if you haven’t done them all, you don’t deserve to publish a test of the Standard Model !!

Aside: blinding, of course, is no protection against deliberate fraud by experimenter…

July 8-19, 2019 NNPSS 29

Credit: D. Armstrong

• unpolarized target

• high current

• highly polarized beam

• polarimetry

• elastic electrons from target

(resolution of the spectrometers)

• beam property monitoring

• active feedback to minimize helicity correlations

• rapid helicity reversal

• slow helicity reversal as a cross check −+

−+

+

−=

YY

YYAmeas

( )

−−+=

=

−=

PPiΔP where

1

21

N

i

iPY

Ymeascorr PAAi

sig

backbackcorrsig

f

fAAA

−=

beam

sig

PVP

AA =

Measuring APV with ES

NNPSSJuly 8-19, 2019 30

Statistical Uncertainty on APV

July 8-19, 2019 NNPSS

𝐴𝑚𝑒𝑎𝑠 =𝑁1 − 𝑁2𝑁1 + 𝑁2

The statistical uncertainty in a counting experiment is given by

𝜎𝑁 = 𝑁𝛿𝑁

𝑁=

𝑁

𝑁=

1

𝑁

The expected width, 𝜎𝐴, is calculated from

𝜎𝐴2 = 𝑁1

2𝑁2𝑁1 + 𝑁2

2

2

+ 𝑁2−2𝑁1

𝑁1 + 𝑁22

2

=4𝑁1𝑁2 𝑁1 + 𝑁2

𝑁1 + 𝑁22

𝜎𝑁𝑖 = 𝑁𝑖

𝜕𝐴

𝜕𝑁1=

2𝑁2𝑁1 + 𝑁2

2

𝜕𝐴

𝜕𝑁2=

−2𝑁1𝑁1 + 𝑁2

2

𝜎𝐴2 =𝜎𝑁𝑖

2𝜕𝐴

𝜕𝑁𝑖

2

31

𝑁1~𝑁2 =𝑁

2

Hint:

Statistical Uncertainty

Gaussian

𝜎𝐴2 =

4𝑁1𝑁2 𝑁1 + 𝑁2𝑁1 + 𝑁2

4 𝑁1~𝑁2 =𝑁

2𝑁 = 𝑁1 + 𝑁2

𝜎𝐴2 =

4𝑁2

4𝑁

𝑁4=1

𝑁𝜎𝐴 =

1

𝑁

The expected width, 𝜎𝐴, is:

𝜎𝐴 =1

1𝑓𝑙𝑖𝑝 𝑟𝑎𝑡𝑒

× 𝑏𝑒𝑎𝑚 𝑐𝑢𝑟𝑟𝑒𝑛𝑡(𝜇𝐴) × 𝑅𝑎𝑡𝑒 Τ𝐻𝑧 𝜇𝐴 × #𝑓𝑙𝑖𝑝𝑠 × # 𝑑𝑒𝑡𝑠

=1

1120𝐻𝑧

50𝜇𝐴34𝑀𝐻𝑧𝜇𝐴

×1𝑒6𝐻𝑧1𝑀𝐻𝑧

(4)(1)

= 132𝑝𝑝𝑚

July 8-19, 2019 NNPSS 32

Jefferson Lab

July 8-19, 2019 NNPSS 33

Parity quality beam >85% using strained GaAs photocathodes

~100 μA max (multi-hall running)

After upgrade to 12 GeV beam energy, addition of a new Hall D

photoemission of electrons from GaAs

→"Bulk" GaAs typical Pe ~ 37%theoretical maximum - 50%

→ "Strained" GaAs = typical Pe ~ 80% theoretical maximum - 100%

"Figure of Merit" I Pe2

Polarized Electron Source

July 8-19, 2019 NNPSS 34

Helicity reversals

July 8-19, 2019 NNPSS

Double-wien

• Rapid, random helicity reversal

• Electrical isolation from the rest of the lab

• Feedback on Intensity Asymmetry

35

Precision Polarimetry

July 8-19, 2019 NNPSS

Require measurement of the beam polarization to sub-

Strategy: use 2 independent polarimeters

Møller Polarimeter

Compton Polarimeter

• Use Compton polarimeter to provide continuous, non-destructive measurement of beam polarization

• Known analyzing power provided by circularly-polarized laser beam

• Use existing Hall C Møller polarimeter to measure absolute beam polarization to <1% at low beam currents

• Known analyzing power provided by polarized Iron foil in high magnetic field

36

Compton Polarimeter

July 8-19, 2019 NNPSS 37

= 346.1c

me 802 =

m 802 =

kWPL 10=

nm532=

249 −= fmtot

False asymmetries from helicity correlated beam properties

July 8-19, 2019 NNPSS 38

The width of human hair is

50,000 nanometers!!!

Average position differences at the

target controlled to order ~10 nm