the standard model of electroweak physics christopher t. hill head of theoretical physics fermilab
TRANSCRIPT
![Page 1: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/1.jpg)
The Standard Model of Electroweak Physics
Christopher T. Hill Head of Theoretical
PhysicsFermilab
![Page 2: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/2.jpg)
Lecture I: Incarnations of Symmetry
![Page 3: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/3.jpg)
Emmy Noether 1882-1935
Noether’s Theorem is as important to us now as the Pythagorean Theorem
![Page 4: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/4.jpg)
Electricity and Magnetism
Electric charge:
Electric charge is conserved:
![Page 5: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/5.jpg)
What is the Symmetry that leads, by Noether’s Theorem to electric
charge conservation?
![Page 6: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/6.jpg)
In Five Easy Pieces
![Page 7: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/7.jpg)
electron = electron + gauge field
Local Gauge Symmetry of Electrodynamics
I.
![Page 8: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/8.jpg)
![Page 9: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/9.jpg)
Electromagnetic force
![Page 10: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/10.jpg)
Electromagnetic force
Quark color force
![Page 11: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/11.jpg)
Weak Force:
u
d
e
nu
W
What gives rise to masses ofW and Z boson?
Higgs Field?
SU(2)xU(1) is“Spontaneously broken
Symmetry”
SU(2) x U(1)
![Page 12: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/12.jpg)
U(1) Local Gauge Invariance on a Wallet Card
covariant derivative
![Page 13: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/13.jpg)
U(1) Local Gauge Invariance on a Wallet Card
field strength
invariants
![Page 14: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/14.jpg)
Yang-Mills Local Gauge Invariance on a Wallet Card
![Page 15: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/15.jpg)
Homework:
Verify all of the transformations laws stated on the previous pages for U(1) and Yang-Mills
gauge theories.
![Page 16: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/16.jpg)
Can a gauge field have a mass?II.
![Page 17: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/17.jpg)
Can a gauge field have a mass? Yes!
![Page 18: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/18.jpg)
![Page 19: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/19.jpg)
Superconductivity === Massive Gauge Field
![Page 20: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/20.jpg)
Cartoon Feature: Gauge Boson Mass
+z axis
time
light cone
![Page 21: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/21.jpg)
Massless Photon
+z axis
time
light cone
![Page 22: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/22.jpg)
A massive photon
+z axis
time
light cone
![Page 23: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/23.jpg)
A massive photon oscillates through spacetime,colliding withthe condensate andmixing with phasedegree of freedom:
spin isconserved
Charge condensate
![Page 24: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/24.jpg)
Superconductivity === Massive photon Field
![Page 25: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/25.jpg)
Our vacuum is an electroweak
superconductorMassive W and Z bosons
Superconductivity === Massive photon Field
![Page 26: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/26.jpg)
Homework:
Consider a charged scalar field coupled to the photon and described the Lagrangian:
Show that this is gauge invariant under:
Show that if :
then the photon acquires a gauge invariant mass:
![Page 27: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/27.jpg)
III. Massless Fermions and Chiral Symmetry
![Page 28: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/28.jpg)
Massless Fermions have Chiral Symmetry
![Page 29: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/29.jpg)
Both currents are conserved when fermions are massless and chiral
symmetry is exact(modulo anomalies)
![Page 30: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/30.jpg)
Each chiral current corresponds to a different
“chiral charge”
e.g., L couples to W-bosons
while R does notStandard Model is “flavor
chiral”
![Page 31: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/31.jpg)
Cartoon Feature: Fermion Mass and Chirality
+z axis
time
light cone
![Page 32: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/32.jpg)
A massless right-handed fermion sz = +1/2
+z axis
time
spin
momentum
![Page 33: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/33.jpg)
+z axis
time
spin
momentum
A massless left-handed fermion sz = +1/2
![Page 34: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/34.jpg)
Can couple fermions to gauge bosons and preserve chiral symmetry:
+z axis
time
right-handed
right-handed
Chirality is conserved
![Page 35: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/35.jpg)
e.g., couple electron to the photonin a L-R symmetric way
+z axis
time
left-handed
left-handed
Chirality is conserved
![Page 36: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/36.jpg)
The left-handed and right-handedelectrons have the same electric charge
QED is “vectorlike”
![Page 37: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/37.jpg)
Only left-handed fermions haveelectroweak charge and form doublets
under SU(2)
Right handed’s are “sterile” under SU(2)
Standard Model is not “vectorlike” !!!
![Page 38: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/38.jpg)
only L fermions couple to the W-boson
+z axis
time
left-handed
left-handed
![Page 39: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/39.jpg)
Reflection Symmetry (parity)
doublets singlets
![Page 40: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/40.jpg)
Helicity of decay products in pion decay:
?
?
Mirror Images
![Page 41: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/41.jpg)
Parity is violated in pion decay:(Lederman)
![Page 42: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/42.jpg)
Chiral symmetry is broken by mass
![Page 43: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/43.jpg)
Chiral symmetry is broken by mass
![Page 44: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/44.jpg)
Cartoon: a massive electron
+z axis
time
light cone
![Page 45: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/45.jpg)
A massive fermion oscillates inchirality through spacetime:
right-handed
right-handed
right-handed
left-handed
left-handed
Chirality nonconservation by the mass term
electric charge isconserved
spin isconserved
![Page 46: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/46.jpg)
![Page 47: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/47.jpg)
Homework:
Verify that:
Hint: use the Dirac equation
![Page 48: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/48.jpg)
How do we make a massive fermionbut conserve weak charge?
right-handed
right-handed
left-handed
left-handed
left-handed
Mass Violates Electroweak Gauge Symmetry!!!
mass violatesweak charge!!!
![Page 49: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/49.jpg)
Spontaneous Symmetry BreakingIV.
![Page 50: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/50.jpg)
![Page 51: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/51.jpg)
![Page 52: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/52.jpg)
Nambu-Goldstone Boson
“Higgs” Boson
![Page 53: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/53.jpg)
![Page 54: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/54.jpg)
Engineer a Coupling to a Complex ScalarBoson that conserves chirality
![Page 55: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/55.jpg)
Couple to a Complex Scalar
+z axis
time
left-handed
right-handed
Chiral charge is conserved
complex boson
![Page 56: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/56.jpg)
Can we have a massive fermionbut conserve chirality?
right-handed
right-handed
left-handed
left-handed
left-handed
![Page 57: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/57.jpg)
Boson Condenses in vacuum!
+z axis
time
Chiral charge is hidden in vacuum !!
Complex bosonvacuum expectation
value = f
![Page 58: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/58.jpg)
Fermion Masses generated spontaneously
right-handed
right-handed
left-handed
left-handed
left-handed
![Page 59: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/59.jpg)
Ungauged Spontaneously Broken Chiral Symmetry
![Page 60: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/60.jpg)
Gauged Spontaneously Broken Chiral Symmetry
![Page 61: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/61.jpg)
![Page 62: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/62.jpg)
Putting it all together:Gauged Spontaneously Broken Chiral Symmetry
V.
![Page 63: The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab](https://reader037.vdocuments.mx/reader037/viewer/2022110101/56649e7e5503460f94b81ac7/html5/thumbnails/63.jpg)
We’re ready for the Standard Model !!!
Weak Force:
u
d
e
nuW
What gives rise to masses ofW and Z boson?
Higgs Field?
SU(2)xU(1) is“Spontaneously broken
Symmetry”
SU(2) x U(1)