Symmetry and the Origin of Mass

1
Symmetry and theOrigin of Mass
Christopher T. Hill Theoretical Physics
Department Fermilab
2
In 10 years the written laws of physics will be
different than they are now.
3
The Energy Frontier will reveal new organizing
principles of nature
Conventional Wisdom

• Supersymmetry
• Extra Dimensions

4
(a heretic)
5
All theoretical candidate organizing principles
of nature, in our modern perspective, involve
hypothetical new symmetries.
Symmetry is fundamental to our understanding of
the basic laws of physics
6
Mass is always associated with symmetry breaking
7
Symmetry was (sort of) a Twentieth Century
Revelation
Noethers Theorem ConnectsSymmetry to Laws of
Physics
8
Noethers Theorem is as important to us now as
the Pythagorean Theorem
Emmy Noether 1882-1935
9
Symmetry is

• Invariance of a system or object under a
  transformation or collection of transformations.

Symmetry Groups
10
Symmetry Groups

• A group G is a collection of elements rj
• G has a multiplication operation rj x rk rk
  where rk is in G
• There is a unique identity in G, 1, such that 1
  x rk rk x 1 rk
• Each element rk has a unique inverse rk-1 such
  that rk-1 x rk rk x rk-1 1
• Group multiplication is associative

11
Commutation generally doesnt hold in nature
A x B B x A
/
B
A
A
B
B x A
A x B
12
Continuous (simple, compact) Symmetry
GroupsCartan Classification

• Spheres in N dimensions O(2),
  O(3), ..., SO(N)
• Complex Spheres in N dimensions U(1), SU(2),
  ..., SU(N)
• N dimensional phase space Sp(2N)
• Exceptional Groups
  G2, F4, E6, E7, E8

Continuous symmetries for the basis of Noethers
Theorem, and the fundamental forces in nature
described as local gauge symmetries.
13
Noethers Theorem
For every continuous symmetry there is a
conservation law
For every conservation law there is a continuous
symmetry
Conservation law
conserved current
Space Translations (3 d.o.f.)
Momentum (3 d.o.f.)
Time Translations (1 d.o.f.)
Energy (3 d.o.f.)
Rotations (3 d.o.f.)
Angular Momentum (3 d.o.f.)
Boosts (3 d.o.f.)
Relativistic Angular Momentum (3 d.o.f.)
14
Electricity and Magnetism
Electric charge
Electric charge is conserved
15
What is the continuous symmetry that leads, by
Noethers Theorem, to electric charge
conservation?
16
What is the continuous symmetry that leads, by
Noethers Theorem, to electric charge
conservation?
Defines the full structure of electrodynamics
17
Local Gauge Symmetry U(1)
phase of electrons wave function is strictly
unobservable
electron electron collinear gauge field
18
(No Transcript)
19
Electromagnetic force U(1)
Quark color force SU(3)
20
Local U(1) Gauge Invariance Wallet Card
21
Standard Model

• Weak Force (left-handed fields)

SU(2)L x U(1)
d
What gives rise to the masses of W and Z boson?
nu
W
e
u
22
Can a gauge field have a mass and still have
gauge symmetry?
23
Can a gauge field have a mass and still have
gauge symmetry?
massless scalar field
24
(No Transcript)
25
Where can we find a massless scalar?
Spontaneous Continuous Symmetry Breaking
26
Goldstone Theorem
U(1) symmetry
Nambu-Goldstone Boson angular motion with no
cost in energy massless mode
Higgs Boson small radial oscillations
massive mode
27
Fermion Mass and Chirality
28
Fermion Mass and Chirality
time
light cone
z axis
29
A massless right-handed fermionsz 1/2
time
momentum
spin
z axis
30
A massless left-handed fermionsz 1/2
time
momentum
spin
z axis
31
Couple electron to the photon
time
right-handed
right-handed
z axis
Chirality is conserved!
32
Couple electron to the photon
time
left-handed
left-handed
z axis
Chirality is conserved
33
The left-handed and right-handed electrons have
the same electric charge
QED is vectorlike
34
How do we make a massive electron?
time
light cone
z axis
35
A massive fermion oscillates inchirality through
spacetime
right-handed
electric charge is conserved
m
left-handed
m
right-handed
m
left-handed
spin is conserved
m
right-handed
Chirality is not conserved by mass!
36
Only left-handed fermions have electroweak charge
and form doublets under SU(2) Right handeds
are sterile under SU(2)
37
Reflection Symmetry
doublets
singlets
38
Parity is violated in pion decay (Lederman)
39
Helicity of decay products in pion decay
?
Mirror Images
?
40
Couple LH fermions to the W-boson
time
left-handed
left-handed
z axis
41
How do we make a massive fermionbut conserve
weak charge?
left-handed
right-handed
mass violates weak charge!!!
left-handed
right-handed
left-handed
Mass Violates Electroweak Gauge Symmetry!!!
42
Couple to the Higgs
time
right-handed
Higgs boson
left-handed
z axis
Weak charge is conserved !
43
Higgs Boson Condenses in vacuum
time
Higgs boson vacuum expectation value 175 GeV
z axis
Weak charge is hidden in vacuum !!
44
Fermion Masses in Electroweak Theory
left-handed
right-handed
left-handed
right-handed
left-handed
Fermion Mass requires Higgs to maintain Electrowea
k Gauge Symmetry!!!
45
Searching for the Higgs (Vacuum Electroweak
Superconductivity)
114 GeV lt mH lt 260 GeV
46
(No Transcript)
47
Extra DimensionsProvide Organizing PrinciplesA
Context for the Higgs boson
48
(No Transcript)
49
Supersymmetry Boson Fermion
Name Spin Superpartner Spin
Graviton 2 Gravitino 3/2
Photon 1 Photino 1/2
Gluon 1 Gluino 1/2
W,- 1 Wino,- 1/2
Z0 1 Zino 1/2
Higgs 0 Higgsino 1/2
Name Spin Superpartner Spin
Electron 1/2 Selectron 0
Muon 1/2 Smuon 0
Tau 1/2 Stau 0
Neutrino 1/2 Sneutrino 0
Quark 1/2 Squark 0
50
SUSY Higgs
In SUSY, two Higgs doublets are needed. 8 DoF, 3
eaten up by the W and Z gt 5 Higgs fields
h0, A0, H0, H
Tree level connection between Higgs masses and
gauge boson masses M2H M2A M2W gt MH gt
MW Mh lt MZ
51
Probe in Flavor PhysicsIndirect constraint BS
???

• Rare decay, SM branching frac 10-9
• Loop diagrams with sparticles (or direct
• decay if RPV) enhance orders of magnitude

Important at high tan?

• Look for excess of µµ events in Bs and Bd
• mass windows
• Background estimation linear extrapolation
• from sidebands
• Results compatible with SM backgrounds
• Br(Bs???)lt1.010-7 _at_ 95CL
• --- Closing in on SUSY! ---

52
MSSM is squeezed
Fine Tuning lt few precision
53
Does MSSM Unify?
S. Raby PDG, 2002
Two Loops
One Loop
4 discrepancy 3 sigma discrepancy predicting
a(MZ)
54
Supersymmetry is still our best operational
hypothesis !!!

• Perturbative -gt Calculable
• Unification works pretty well
• rich spectroscopy to probe, LHC, ILC and flavor
  physics
• fits into string theory envelope
• Offers a hierarchy custodial symmetry

55
But....

• It (probably) wont be MSSM !!!

56
If Not SUSY then What?
Conventional Extra Dimensions?
57
3rd KK mode
Kaluza-Klein Modes
2nd KK mode
1st KK mode
zero mode
58
Composite Higgs Cooper Pair of L-R Chiral
Fermions
59
Top Quark Seesaw Model
60
(No Transcript)
61
Mass is always associated with conformal
symmetry breaking
62
Broken Scale SymmetryThe Origin of the Nucleon
Mass(aka, the visible mass in the universe)
63
Murraypalooza July 2005
64
Gell-Mann and Low
Gross, Politzer and Wilczek
65
(No Transcript)
66
A Puzzle Murray Gell-Mann lecture ca 1975
!???
QCD is scale invariant!!!???
67
Resolution The Scale Anomaly
Origin of Mass in QCD Quantum Mechanics
68
A very heretical conjecture
69
Predictions of the Conjecture
We live in D4!
Cosmological constant is zero in classical limit
QCD scale is generated in this way Hierarchy is
naturally generated
Testable in the Weak Interactions?
Weyl Gravity in D4 is QCD-like
Is the Higgs technically natural?
On naturalness in the standard model.William A.
Bardeen (Fermilab) . FERMILAB-CONF-95-391-T, Aug
1995. 5pp.
Conjecture on the physical implications of the
scale anomaly.Christopher T. Hill (Fermilab) .
hep-th/0510177
70
Symmetry Principles Define Modern Physics
71
The mission Statement of particle physics
72
The mission Statement of particle physics
Find the symmetries
Discover what breaks them
73
Symmetry
Beauty
Physics