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HUGS 2
Outline
June 1-19, 2015
I. IntroductionII. Theory
A. Standard ModelB. Madam WuC. Z’eldovichD. Emmy Noether
III. Experimental ConsiderationsA. Beam qualityB. Target stabilityC. BackgroundsD. Apparatus symmetryE. Detector linearityF. Collimator precisionG. Magnet stabilityH. Raster synchronization
IV. Past ExperimentsA. SLAC E158
B. SAMPLEC. Mainz A4D. G0E. HappEx I-IVF. QweakG. PREXH. PVDIS
V. Future ExperimentsA. PREX IIB. CREXC. MOLLERD. Qweak (Mainz)E. PVDISF. SOLID
VI. Summary
HUGS 5
Why Parity-Violating Electron Scattering(PVES)?
June 1-19, 2015
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
HUGS 6
Standard Modelof Particles and Interactions
June 1-19, 2015
http://www.cpepweb.org/cpep_sm_large.html
9
Symmetries
HUGS
Emmy Noether(18??-19??)
June 1-19, 2015
Conservation laws imply symmetries
Conservation of:
Linear momentum
Angular momentum
Energy
Implies:
Rotational invariance
Translational invariance
Time invariance
HUGS 10
What is unitarity and why is it required?
June 1-19, 2015
(𝑑′
𝑠′
𝑏′ )=(𝑉 𝑢𝑑 𝑉 𝑢𝑠 𝑉 𝑢𝑏
𝑉 𝑐𝑑 𝑉 𝑐𝑠 𝑉 𝑐𝑏
𝑉 𝑡𝑑 𝑉 𝑡𝑠 𝑉 𝑡𝑏)(𝑑𝑠𝑏)
CKM matrix
(𝜈𝑒𝜈𝜇
𝜈𝜏)=(𝑈𝑒1 𝑈𝑒2 𝑈𝑒3
𝑈𝜇1 𝑈𝜇2 𝑈𝜇3
𝑈𝜏 1 𝑈𝜏 2 𝑈𝜏 3)(𝜈1
𝜈2
𝜈3)
The adjoint times the operator must be 1:
HUGS 11
Parity
June 1-19, 2015
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=�⃑� ∙ �⃑�|�⃑� ∙ �⃑�|
HUGS 12
A brief history of parity violation
June 1-19, 2015
R
R
L
L
1930s – weak interaction needed to explain nuclear β decay
1950s – parity violation in weak interaction; V-A theory to describe 60Co decay
1970s – neutral weak current events at Gargamelle
late 1970s – parity violation observed in electron scattering - SLAC E122
HUGS 13
Nuclear beta decay
June 1-19, 2015
"Beta spectrum of RaE" by HPaul - Own work. Licensed under CC BY-SA 4.0 via Wikimedia Commons
e- 𝜈𝑒
p n
𝐺𝐹
HUGS 14
EM and Weak Interactions : Historical View
June 1-19, 2015
eeppeEMpEM
Q
eJ
Q
eJM
2
2, ,
2
2,
eeFnp
eweakF
Nweak GJGJM
, ,,
EM: e + p e + p elastic scattering
Weak: n e- + p + 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
eweakF
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
HUGS 15
Parity-violation in charge current maximal
June 1-19, 2015
Madam Wu
Bleckneuhaus, with English language captions by Stigmatella aurantiaca
electrons favored the direction opposite to that of the nuclear spin
HUGS 16
What about a neutral weak current?
June 1-19, 2015
e- p
n
𝐺𝐹𝜈𝑒
e- p
p
𝐺𝐹e-
Zel’dovich – 1959
Is there a neutral analog to decay?
Would determine the sign of
?
HUGS 17
Neutral weak currents observed
June 1-19, 2015
The prediction of the Z0 implied the existence of previously unobserved neutral current processes like:
These processes were first discovered in 1973:
Z0
e- e-
+ e- + e-
What about parity violation?
HUGS 18
The neutral weak current, Zel’Dovich
June 1-19, 2015
parity non-conservation via weak – EM interference
parity-violating asymmetry
𝐴𝑃𝑉 ≤10−6−10− 4
≈𝐺𝐹𝑄
2
4𝜋𝛼𝑄2 0.1−1𝐺𝑒𝑉 2
𝐴𝑃𝑉=𝜎+¿−𝜎−
𝜎+¿+𝜎−≈𝑀𝑤𝑒𝑎𝑘
𝑀𝛾
¿¿
e-
e-
0,Z
longitudinally polarized e-
Four drops of ink in a 55-gallon barrel of water would produce an "ink concentration" of 1 ppm!!!
HUGS 19
Magnetic spectrometer
Background and kinematic separation
SLAC Experiment E122
June 1-19, 2015
Polarimetry
Integrating detectors
• High luminosity from photoemission from NEA GaAs cathode• Rapid helicity-flip (sign of e- polarization)Huge achievement!
Highest P2I ever, by far. Developed for this experiment at
SLAC and used ever since
HUGS 20
SLAC Experiment E122
June 1-19, 2015
sin2θW=0.20±0.03
GWS --‐ Nobel Prize 1979
Parity Non-Conservation in Inelastic Electron Scattering, C.Y. Prescott
et. al, 1978
Deep inelastic scattering:Y dependence reflects quark axial/electron vector coupling strength
YxbxaQG
A FPV
210
3 2
At high x eA
dV
eA
uV ggggxa 2
eV
dA
eV
uA ggggxb 2
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
APV ~ 100 ± 10 ppm
HUGS 21
Standard Model of Electroweak Interactions
June 1-19, 2015
5
22
g
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
fermions:
...,',,
...,'
,
RRR
LL
e
due
d
u
e
Interaction of fermions with gauge bosons:
e
W+,- Z0
5
cos2
f
AfV
W
ccg
ffA
fWff
V
tc
Qtc
3
23 sin2
sin2W – “weak mixing angle”, parameterizes the mixing between the two neutral currents
HUGS 23
Running of sin2θW
June 1-19, 2015
Present:“d-quark dominated” : Cesium APV (QA
W): SM running verified at ~ 4 level“pure lepton”: SLAC E158 (Qe
W ): SM running verified at ~ 6 levelFuture:“u-quark dominated” : Qweak (Q
pW): projected to test SM running at
~ 10 level“pure lepton”: MOLLER (Qe
W ): projected to test SM running at ~ 25 level
+ +
24
Width of the Z0
HUGSJune 1-19,
2015
• Measure a variety of electroweak processes with couplings to all possible fermions
• Extract values of (sin2W )eff in a consistent renormalization scheme from all processes
Production of real Z0 bosons in e+e- annihilation
25
Spontaneous symmetry breaking
HUGSJune 1-19,
2015
Why do the weak bosons have mass?
Higgs mechanism
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
(𝑊 +¿ ¿𝑊−
𝑍0 ) ,𝛾
but leaving the photon massless
and one Higgs boson to be discovered at CERN
HUGS 26
Low Energy Weak Neutral Current Standard Model Tests
These three types of experiments are a complementary set for exploring new
physics possibilities well below the Z pole
Low energy weak charge “triad” (M. Ramsey-Musolf) probed in weak neutral current experiments
Z
N e
NZNQ WAW )sin41( 2
parity-violating Moller
scattering e
+ e e + e
Cesium Atomic Parity Violation primarily
sensitive to neutron weak charge
JLAB Qpweak: parity-violating
e-p elastic scattering
e + p e + p
)sin41( 2W
eWQ
WpWQ 2sin41
June 1-19, 2015
28
PVES Experiments at JLAB
June 1-19, 2015
HUGS
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
SM TestsNuclear properties Nucleon properties
Qweak MOLLERPREXCREX
G0Happex
PVDIS
SOLID
HUGS 29
Feynman Diagrams
June 1-19, 2015
Further reading: Looking for consistency in the construction and
use of Feynman diagramsPeter Dunne , Phys. Educ. 36 No 5 (September 2001) 366-374
HUGS 30
The Dirac Equation
June 1-19, 2015
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:
HUGS 31
Cross section
June 1-19, 2015
dQMFd || 2
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
All the physics is in the matrix element
HUGS 32
the matrix element
June 1-19, 2015
xppiepu )()( )'( puie ][2q
ig
external lines
vertex factors
propagator
)(ku xkkieku )()'(
pEMeEMEM JJ
QM ,,
2
1~
HUGS 33
external lines
the matrix element
June 1-19, 2015
xppiepu )()( )'( pu
)sin41(cos4
52
WW
gi
][22
2 )/(
ZMq
Mkkgi
vertex factors
propagator
)(ku xkkieku )()'(
pNCeNCNC JJ
GM ,,
22~
eNCeA
eNCeV
eNC AgVgJ ,,, NNCNNCNNC AVJ ,,,
HUGS 34
How do we measure ?
June 1-19, 2015
2
+
= + +
2 2
2
eh
𝐴𝑃𝑉=𝜎+¿−𝜎−
𝜎+¿+𝜎−≈ ¿
¿
24
2F
4
G-QBQ
Q pW
ppm1011010 56
35
Hand-waving derivation of the parity-violating asymmetry in electron-proton scattering
June 1-19, 2015
HUGS
NEMeEMe VVQ
Q,,
2
1~
pNCeNCNC JJ
GM ,,
22~
NNCeNCeA
NNCeNCeV
NNCeNCeA
NNCeNCeV AAgAVgVAgVVg
G ,,,,,,,,
22~
eEMeeee
eEM VQQJ ,,
NEMNEM VJ ,,
NNCNNCNNC AVJ ,,,
eNCeA
eNCeVeeeeW
eNC AgVgJ ,,5
2, sin41
pEMeEMEM JJ
QM ,,
2
1~