symmetry and the origin of mass -...
TRANSCRIPT
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Symmetry and the
Origin of Mass
Christopher T. Hill
Theoretical Physics Department
Fermilab
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In 10 years the written laws of
physics will be different than
they are now.
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The Energy Frontier
will reveal new organizing principles
of nature
Supersymmetry
Extra Dimensions
Conventional Wisdom:
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(a heretic)
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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
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Mass is always associated with
symmetry breaking
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Symmetry was (sort of) a Twentieth Century
Revelation
“Noether’s Theorem” Connects
Symmetry to Laws of Physics
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Emmy Noether 1882-1935
Noether’s Theorem is as important to us now
as the Pythagorean Theorem
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Symmetry is:
Invariance of a system or object under a
transformation or collection of
transformations.
Symmetry Groups
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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
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A x B = B x A/
A x B B x A
Commutation generally
doesn’t hold in nature:
A
B A
B
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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
Noether’s Theorem, and the fundamental forces in
nature described as local gauge symmetries.
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Noether’s Theorem
Space Translations (3 d.o.f.)
Time Translations (1 d.o.f.)
Rotations (3 d.o.f.)
Boosts (3 d.o.f.)
For every continuous symmetry there is a conservation law
For every conservation law there is a continuous symmetry
Momentum (3 d.o.f.)
Energy (3 d.o.f.)
Angular Momentum (3 d.o.f.)
Relativistic Angular Momentum
(3 d.o.f.)
Conservation law conserved current
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Electricity and Magnetism
Electric charge:
Electric charge is conserved:
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What is the continuous symmetry that
leads, by Noether’s Theorem, to electric
charge conservation?
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What is the continuous symmetry that
leads, by Noether’s Theorem, to electric
charge conservation?
Defines the full structure of
electrodynamics
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Local Gauge Symmetry U(1):
electron = electron + collinear
gauge field
phase of electron’s
wave function is
strictly unobservable
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Electromagnetic
force U(1)
Quark color
force SU(3)
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Local U(1) Gauge Invariance Wallet Card
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Standard Model
Weak Force (left-handed
fields):
u
d
e
nuW What gives rise to
the masses of
W and Z boson?
SU(2)L x U(1)
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Can a gauge field have a
mass and still have gauge symmetry?
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Can a gauge field have a
mass and still have gauge symmetry?
massless
scalar
field
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Spontaneous Continuous Symmetry Breaking
Where can we find a massless scalar?
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Higgs Boson: small radial oscillations massive mode
Nambu-Goldstone Boson:
angular motion with no cost
in energy massless mode
Goldstone TheoremU(1) symmetry
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Fermion Mass and Chirality
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Fermion Mass and Chirality
+z axis
time
light cone
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A massless right-handed fermionsz = +1/2
+z axis
time
spin
momentum
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+z axis
time
spin
momentum
A massless left-handed fermionsz = +1/2
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Couple electron to the photon
+z axis
time
right-handed
right-handed
Chirality is conserved!
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Couple electron to the photon
+z axis
time
left-handed
left-handed
Chirality is conserved
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The left-handed and right-handed
electrons have the same electric charge
QED is “vectorlike”
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How do we make a massive electron?
+z axis
time
light cone
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A massive fermion oscillates in
chirality through spacetime:
right-handed
right-handed
right-handed
left-handed
left-handed
Chirality is not conserved by mass!
electric charge is
conserved
spin is
conservedm
m
m
m
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Only left-handed fermions have
electroweak charge and form doublets
under SU(2)
Right handed’s are “sterile”
under SU(2)
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Reflection Symmetry
doublets singlets
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Parity is violated in pion decay:
(Lederman)
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Helicity of decay products in pion decay:
?
?
Mirror Images
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Couple LH fermions to the W-boson
+z axis
time
left-handed
left-handed
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How do we make a massive fermion
but conserve weak charge?
right-handed
right-handed
left-handed
left-handed
left-handed
Mass Violates Electroweak Gauge Symmetry!!!
mass violates
weak charge!!!
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Couple to the Higgs
+z axis
time
left-handed
right-handed
Weak charge is conserved !
Higgs boson
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Higgs Boson Condenses in vacuum
+z axis
time
Weak charge is hidden in vacuum !!
Higgs boson
vacuum expectation
value = 175 GeV
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Fermion Masses in Electroweak Theory
right-handed
right-handed
left-handed
left-handed
left-handed
Fermion Mass requires Higgs to maintain
Electroweak Gauge Symmetry!!!
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114 GeV < mH < 260 GeV
Searching for the Higgs
(Vacuum Electroweak Superconductivity)
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Extra Dimensions
Provide Organizing Principles:
A Context for the Higgs boson
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1/2Higgsino0Higgs
1/2Zino1Z0
1/2Wino+,-1W+,-
1/2Gluino1Gluon
1/2Photino1Photon
3/2Gravitino2Graviton
SpinSuperpartnerSpinName
0Squark1/2Quark
0Sneutrino1/2Neutrino
0Stau1/2Tau
0Smuon1/2Muon
0Selectron1/2Electron
SpinSuperpartnerSpinName
Supersymmetry: Boson Fermion
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SUSY Higgs
Tree level connection between Higgs
masses and gauge boson masses:
M2H±= M2
A + M2W
=> MH± > MW Mh < MZ
In SUSY, two Higgs doublets are needed.
8 DoF, 3 eaten up by the W± and Z
=> 5 Higgs fields: h0, A0, H0, H±
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Probe in Flavor Physics:Indirect constraint: BS →µµ
• 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�µµ)<1.0×10-7 @ 95%CL
--- Closing in on SUSY! ---
Rare decay, SM branching frac ~10-9
→Loop diagrams with sparticles (or direct
decay if RPV) enhance orders of magnitudeImportant at high tanββββ
Previous limit:
hep-ph/0507233
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MSSM is squeezed
Fine Tuning
< few % precision
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Does MSSM Unify?
One Loop
Two Loops
4% discrepancy = 3 sigma discrepancy predicting α(MZ)
S. Raby PDG, 2002
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Supersymmetry is still our best
operational hypothesis !!!
• Perturbative -> Calculable
• Unification works pretty well
• rich spectroscopy to probe, LHC, ILC and
flavor physics
• fits into string theory envelope
• Offers a hierarchy custodial symmetry
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But....
It (probably) won’t be MSSM !!!
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Conventional Extra Dimensions?
If Not SUSY then What?
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zero mode
1st KK mode
2nd KK mode
3rd KK modeKaluza-Klein Modes
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Composite Higgs
“Cooper Pair” of L-R Chiral Fermions
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Top Quark Seesaw Model
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Mass is always associated with
conformal symmetry breaking
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Broken Scale Symmetry
The Origin of the Nucleon Mass
(aka, the visible mass in the
universe)
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Murraypalooza July 2005
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Gell-Mann and Low:
Gross, Politzer and Wilczek:
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A Puzzle: Murray Gell-Mann lecture ca 1975
!???
QCD is scale invariant!!!???
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Resolution: The Scale Anomaly
Origin of Mass in QCD = Quantum Mechanics
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A very heretical conjecture:
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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
We live in D=4!
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 D=4 is QCD-like:
Is the Higgs technically natural?
“Predictions” of the Conjecture:
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Symmetry Principles Define Modern Physics
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The mission Statement of particle physics:
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Find the symmetries
Discover what breaks them
The mission Statement of particle physics:
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Symmetry
Beauty Physics