Transcript Parity-violating electron scattering experiments @ JLAB Juliette Mammei Outline I. II. Introduction Theory A. Standard Model B. Madam Wu C.

Parity-violating
electron scattering
experiments @ JLAB
Juliette Mammei
Outline
I.
II.
Introduction
Theory
A. Standard Model
B. Madam Wu
C. Z’eldovich
D. Emmy Noether
III. Experimental Considerations
A. Beam quality
B. Target stability
C. Backgrounds
D. Apparatus symmetry
E. Detector linearity
F. Collimator precision
G. Magnet stability
H. Raster synchronization
IV. Past Experiments
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A. SLAC E158
B. SAMPLE
C. Mainz A4
D. G0
E. HappEx I-IV
F. Qweak
G. PREX
H. PVDIS
V. Future Experiments
A. PREX II
B. CREX
C. MOLLER
D. Qweak (Mainz)
E. PVDIS
F. SOLID
VI. Summary
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Introduction
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PVES
Historical view
Why Parity-Violating Electron Scattering
(PVES)?
o Search for physics Beyond the Standard Model (BSM) with low energy (Q2 <<M2) precision
tests complementary to high energy measurements
• Neutrino mass and their role in the early universe
0νββ decay, θ13, β decay,…
• Matter-antimatter asymmetry in the present universe EDM, DM, LFV, 0νββ, θ13
• Unseen Forces of the Early Universe
Weak decays, PVES, gμ-2,…
LHC new physics signals likely will need additional indirect evidence
• Neutrons: Lifetime, P- & T-Violating Asymmetries (LANSCE, NIST, SNS...)
• Muons: Lifetime, Michel parameters, g-2, Mu2e (PSI, TRIUMF, FNAL, J-PARC...)
• PVES: Low energy weak neutral current couplings, precision weak mixing angle (SLAC,
Jefferson Lab, Mainz)
o Study nuclear and nucleon properties
• Strange quark content of nucleon
• Neutron radii of heavy nuclei
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Standard Model
of Particles and Interactions
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http://www.cpepweb.org/cpep_sm_large.html
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Interactions
Particles
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Symmetries
Conservation laws imply symmetries
Conservation of:
Energy
Implies:
Time invariance
Linear momentum
Translational invariance
Angular momentum
Rotational invariance
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Emmy Noether
(18??-19??)
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What is unitarity and why is it required?
𝜙 𝜓 = 𝜙′ 𝜓′ = 𝜙 𝑈†𝑈 𝜓
The adjoint times the operator must be 1:
𝑈†𝑈 = 1
CKM matrix
𝑉𝑢𝑑
𝑑′
𝑠 ′ = 𝑉𝑐𝑑
𝑉𝑡𝑑
𝑏′
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𝑉𝑢𝑠
𝑉𝑐𝑠
𝑉𝑡𝑠
𝑉𝑢𝑏
𝑉𝑐𝑏
𝑉𝑡𝑏
𝑑
𝑠
𝑏
𝜈𝑒
𝑈𝑒1
𝜈𝜇 = 𝑈𝜇1
𝜈𝜏
𝑈𝜏1
𝑈𝑒2
𝑈𝜇2
𝑈𝜏2
𝑈𝑒3
𝑈𝜇3
𝑈𝜏3
𝜈1
𝜈2
𝜈3
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Parity
We describe physical
processes as interacting
currents by constructing
the most general form
which is consistent with
Lorentz invariance
quantum mechanical operator that
reverses the spatial sign ( P: x -> -x )
 
p s
T ermsof theform  (4  4) 
where  5  i 0 1 2 3
Parity
P

  5
Vector
  
Axial Vector     5
T ensor
   
Scalar
P seudoscalar
 
p s
𝑠∙𝑝
ℎ=
𝑠∙𝑝
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Note: P (V*V) = +1
1
1
 1

  1
 1  1
Charge
T Conjugation
C
Time
Reversal
1
1
 1
 1


  1  1
P (A*A) = + 1
P (A*V) = -1
1
1
1
1
1
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A brief history of parity violation
1930s – weak interaction needed to explain nuclear β decay
1950s – parity violation in weak interaction;
V-A theory to describe 60Co decay
R
L
L
R
1970s – neutral weak current events at
Gargamelle
late 1970s – parity violation observed in electron scattering - SLAC E122
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Nuclear beta decay
𝜈𝑒
e-
"Beta spectrum of RaE" by HPaul - Own work. Licensed
under CC BY-SA 4.0 via Wikimedia Commons
𝐺𝐹
p
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n
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EM and Weak Interactions : Historical View
EM: e + p  e + p elastic scattering
e-
p

𝐽𝜇𝐸𝑀,𝑒
M  J
EM , p
𝐸𝑀,𝑝
𝐽𝜇
 e 2   , EM ,e
  2  J
  p  p 
 Q 
 e2 
  2   e  e
 Q 

V
x

V
p
ee-
p
𝐽𝜇𝑤𝑒𝑎𝑘,𝑒
𝐺𝐹
𝐽𝜇𝑤𝑒𝑎𝑘,𝑁
𝜈𝑒
n
Weak: n  e- + p + 𝜈𝑒 neutron beta decay
Fermi (1932) : contact interaction, form inspired by EM

M  J weak , N GF J  , weak ,e   p  n  GF  e  e
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


  

 
M  J weak , N GF J  , weak ,e   p  1   5  n GF  e  1   5   e
(V - A)
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x
(V - A)
Note: weak interaction process here is charged current (CC)
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Parity-violation in charge current maximal
electrons favored the
direction opposite to
that of the nuclear spin
Madam Wu
Bleckneuhaus, with English language captions by Stigmatella aurantiaca
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What about a neutral weak current?
Zel’dovich – 1959
Is there a neutral analog to 𝛽 decay?
Would determine the sign of 𝐺𝐹
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e-
?
𝐺𝐹
𝜈𝑒
e-
p
n
p
𝐺𝐹
e-
p
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Neutral weak currents observed
The prediction of the Z0 implied the
existence of previously unobserved
neutral current processes like:
These processes were
first discovered in 1973:
 + e-   + e

Z0
e-
e-
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What about parity violation?
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The neutral weak current, Zel’Dovich
elongitudinally polarized ee-
,Z0
parity non-conservation via
weak – EM interference
𝐴𝑃𝑉
𝜎+ − 𝜎− 𝑀𝑤𝑒𝑎𝑘
=
≈
𝜎+ + 𝜎−
𝑀𝛾
𝐺𝐹 𝑄 2
≈
4𝜋𝛼
parity-violating asymmetry
Four drops of ink in a 55-gallon 𝑄
barrel of water would produce an
"ink concentration" of 1 ppm!!!
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2 ~0.1
− 1 𝐺𝑒𝑉 2
𝐴𝑃𝑉 ≤ 10−6 − 10−4
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SLAC Experiment E122
Polarimetry
• High luminosity from
photoemission from NEA
GaAs cathode
• Rapid helicity-flip (sign of
e- polarization)
Magnetic spectrometer
Background and
kinematic separation
Integrating
detectors
Huge achievement!
Highest P2I ever, by far. Developed for this
experiment at SLAC and used ever since
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SLAC Experiment E122
Parity Non-Conservation in Inelastic Electron
Scattering, C.Y. Prescott et. al, 1978
APV ~ 100 ± 10 ppm
Left
Right
γ Charge
0, ±1, ±1/3, ±2/3
0, ±1, ±1/3, ±2/3
W Charge
T=±1/2
0
Z Charge
T-qsin2θW
-qsin2θW
sin2θW=0.20±0.03
GWS --‐ Nobel Prize 1979
Deep inelastic scattering:
Y dependence reflects quark axial/electron vector
coupling strength
3GF Q 2
ax   bx Y 
A PV 
10 2
At high x
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a x   2 g Vug Ae  g Vd g Ae
u e
d e


b
x

2
g
g

g
A V
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Standard Model of Electroweak Interactions
Glashow-Weinberg-Salam Model (1967): unified EM and weak forces as an electroweak force
 SU(2)L x U(1) gauge theory with spontaneous symmetry breaking
 e   u 
   ,   , ...
e 
 L  d ' L
fermions:
eR , uR , d ' R , ...
Interaction of fermions with gauge bosons:
e 
g
2 2



   5
+,-
W

g
2 cosW
Z
0
c 
f
V

 c Af   5 
cVf  t3f  2 sin 2 W Q f
c Af  t3f
2
sin W – “weak mixing angle”, parameterizes the
mixing between the two neutral currents
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Running of coupling constants
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What about sin2θW?
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Running of sin2θW
+
+ 
Present:
“d-quark dominated” : Cesium APV (QAW): SM running verified at ~ 4 level
“pure lepton”:
SLAC E158 (QeW ): SM running verified at ~ 6 level
Future:
“u-quark dominated” : Qweak (QpW): projected to test SM running at ~ 10 level
“pure lepton”: MOLLER (QeW ): projected to test SM running at ~ 25  level
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Width of the Z0
Production of real Z0 bosons in e+eannihilation
Γ𝑡𝑜𝑡 𝑍 0 =
Γ 𝑍 0 → 𝑓𝑓
𝑎𝑙𝑙 𝑓𝑒𝑟𝑚𝑖𝑜𝑛𝑠 𝑓
• Measure a variety of electroweak processes with couplings to all
possible fermions
2
• Extract values of (sin W )eff in a consistent renormalization scheme
from all processes
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Spontaneous symmetry breaking
Why do the weak bosons have mass?
Higgs mechanism
𝑊+
𝑊− , 𝛾
𝑍0
Higgs field – scalar (not a vector)
field that permeates all of space
As universe cooled, symmetry was
broken and 3 of the electroweak
bosons absorbed 3 of the Higgs
bosons, gaining mass
but leaving the photon massless
and one Higgs boson to be discovered at CERN
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Low Energy Weak Neutral Current
Standard Model Tests
Z
Low energy weak charge
“triad” (M. Ramsey-Musolf)
probed in weak neutral
current experiments
Cesium Atomic Parity Violation
primarily sensitive to neutron
weak charge
QWA   N  Z (1  4 sin 2 W )   N
parity-violating
Moller scattering
e+e e+e
QWe  (1  4 sin 2 W )
e
N
JLAB Qpweak: parity-violating
e-p elastic scattering
e+p e+p
QWp  1 4 sin 2 W
These three types of experiments are a complementary set for exploring new
physics possibilities well below the Z pole
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Some PVES Experiments
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PVES Experiments at JLAB
JLAB has a rich program of PVES experiments to measure
nuclear and nucleon properties and to perform precision tests
of the Standard Model to search for new physics
Nuclear properties
PREX
CREX
SM Tests
Nucleon properties
G0
Happex
Qweak
MOLLER
SOLID
PVDIS
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Feynman Diagrams
Further reading: Looking for consistency in
the construction and use of
Feynman diagrams
Peter Dunne , Phys. Educ. 36 No 5 (September 2001) 366-374
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The Dirac Equation
Dirac equation for free electron:
where:
   ,  

0

with:
(i     m)   0

1 0 
0
 
  
 0  1

 0 

   
 0 

  0 time,   1,2,3 space
leads to electron four-vector current density:
j    e   
where the adjoint is:
satisfies the continuity equation:
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  

0
 j   0
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Cross section
Fd
M | dQ
||M
2
All the physics is in the matrix element
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
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the matrix element
external lines
vertex factors
propagator

u(k ) ie u(k ' )e
i ( k k ) x
q
M EM
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 ig 
2
i ( p p ) x
u( p )e
1 EM ,e EM , p
~ 2 J J
Q
[
] u( p' )
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the matrix element
external lines
vertex factors
g
i
  (1  4 sin 2 W   5 )
4 cosW
propagator
2

i
(
g

k
k
/
M
)
NC

 
i ( ,kek ) x
NC ,e
e NC ,e
uJ(k
u(gkAe'A
)e
 )  gVV
q2  M Z
M NC
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,N
p p )NC
uJ( pNC)e,Ni ( 
Vx [ ,N  ]ANC
u( p' )
G NC ,e NC , p
~
J J
2 2
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How do we measure
?
2

+
2
2
+ he
=
𝐴𝑃𝑉
𝜎+ − 𝜎−
=
≈
𝜎+ + 𝜎−
+
2


- G FQ 2

QWp  B4Q 2  
4 
 10 6  10 5  1  10 ppm
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Hand-waving derivation of the parity-violating
asymmetry in electron-proton scattering
J EM ,e  Qe e  e  QeVEM ,e
J EM , N  VEM , N

M EM ~
1 EM ,e EM , p 1
EM ,e EM , N
~
Q
V
V
J
J
e



2
2
Q
Q

J NC ,e   1  4 sin 2 W  e  e  e 5  e  gVe VNC ,e  g Ae ANC ,e
J NC , N  VNC , N  ANC , N
M NC
G NC ,e NC , p
~
J J
2 2

G
~
gVe VNC ,eVNC , N  g Ae ANC ,eVNC , N  gVe VNC ,e ANC , N  g Ae ANC ,e ANC , N
2 2
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
Asymmetry
𝜎± ∝ 𝑀𝐸𝑀 ± 𝑀𝑁𝐶 2 = 𝑀𝐸𝑀
𝐴𝑃𝑉

2
∗
± 2𝑅𝑒 𝑀𝐸𝑀
𝑀𝑁𝐶 + 𝑀𝑁𝐶
2
∗
𝜎+ − 𝜎− 2𝑅𝑒 𝑀𝐸𝑀
𝑀𝑁𝐶
=
≈
𝜎+ + 𝜎−
𝑀𝐸𝑀 2 + ⋯
EM ,e EM , N e NC ,e NC , N
g A A V
 QeVEM ,eVEM , N gVe VNC ,e ANC , N
GF Q 2 QeV V

EM ,e EM , N 2
4 2
QeV V
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


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