Transcript Scalars 2011

Some speculations
on the Higgs sector & ON the
cosmological constant
A. Zee
Institute for Theoretical Physics
University of California, Santa Barbara
Warsaw
August 26, 2011
Reversal of fortune
Dimension less than 4: super renormalizable Nice & Easy
Dimension equal to 4: renormalizable
Dimension greater than 4: non renormalizable Fear & Loathing
Then came a new (Wilsonian) way of looking at quantum field
theory
Field Theory as effective long distance expansion
Dimension less than 4: super renormalizable Fear & Loathing
Dimension equal to 4: renormalizable
Dimension greater than 4: non renormalizable To be expected
Two problems in fundamental physics
Low dimenional operators
Higgs problem (due to Brout,
Englert; Anderson; Higgs; Hagen,
Guralnik, & Kibble)
Cosmological constant problem
Private Higgs
With Rafael Porto, KITP Santa Barbara, now at IAS Princeton & Columbia
Hard to believe one single Higgs serves all, from electron to top
quark
Each fermion should have its own private Higgs fields
Possible to construct model with workable parameter space
Symmetry breaking in cascade driven by Higgs for the top
quark; dark matter candidates
One difficulty: flavor changing neutral interactions
Neutrino mixing and the private Higgs
Porto & Zee, Phys. Rev. D79
Electron special in lepton sector just as top special in quark
sector
Combined with an earlier radiative neutrino mass model (Zee,
Phys. Lett. 1980), we obtain some interesting mixing matrices
The cosmological
constant paradox poses a
serious challenge to our
understanding of
quantum field theory.
The so-called naturalness
dogma may be out the
window (with implications
for the hierarchy problem.)
Assume dark energy represents
the cosmological constant
Expected:
, enormous even if m is
electron mass, let alone Planck mass; robust!
Decreed: mathematically 0, but an exact
symmetry was never found
Observed: tiny ~
but not 0
Can we learn something arguing by analogy?
Cf history of physics
Proton Decay as a possible analogy!
A. Zee, Remarks on the Cosmological Constant Paradox, Physics in Honor of P. A. M. Dirac
in his Eightieth Year, Proceedings of the 20th Orbis Scientiae (1983) ~28 years ago!!!
Suppose that long ago, in the pre-quark era, perhaps in
another civilization in another galaxy, a young theorist
decided to calculate the rate for proton decay into:
Natural to write down
and compare with
assuming
The story of the proton decay rate
~ the story of the cosmological constant???
Expected: Enormous
Decreed: proof by authority (Wigner?),
words like baryon number conservation
Observed: suppose that the particle
physicists in the other galaxy were not as
unlucky as we were, tiny rate but not 0
As is often the case in physics, the solution did not
come from thinking about the mechanism for proton
decay, but from hadron spectroscopy
Quarks! (Gell-Mann, Zweig)
Proton decays via a dimension 6
rather than dimension 4 operator
in the effective Lagrangian
so that
Remarkably, promotion
from dimension 4 to 6
enough to solve the problem
(in the exponential!)
Modern notions of renormalization
group flow and scaling
(Gell-Mann & Low, Wilson,...)
Could we promote the dimension of the cosmological
constant term to make it less relevant at large distances
compared with the curvature piece?
How did we avoid promoting this term? The “secret”:
it metamorphosized into a term involving a YangMills gauge field, with dimension staying at 4.
See A. Zee, Gravity and Its Mysteries: Some Thoughts and Speculations, Int. J. Mod. Phys. 23
(2008) 1295, hep-th/0805.2183 C. N. Yang at 85, Singapore, November 2007
How do we promote the dimension 0
cosmological constant term to
dimension p > 4?
The reason is that, in our current
understanding of gravity, the
cosmological constant enters in the
Lagrangian as a dimension-0 operator
Therefore we’d expect:
Einstein said:
“Physics should be as
simple as possible,
but not any simpler”
We say: “The solution to the
cosmological constant paradox
should be as crazy as possible,
but not any crazier”
We speculate gravity departs from general relativity at ultralarge distance scales.
Quantum gravity and string theory
focussed on UV thus far.
It is highly speculative but not outrageous.
My talk at Murray Gell-Mann's 80th Birthday Conference, Singapore 2010
Porto & Zee, Class. Quant. Gravity, 27(2010)065006; Mod.Phys.Lett.A25:29292932,2010, arXiv:1007.2971
Another relevant historical analogy?
Expected: enormous even if the ether is
similar to ordinary material (“naturalness”)
Decreed:
Mathematically 0,
Newton
(He knew that it was not 0)
How was this
Observed: Rømer, tiny but not 0;
(as both Galileo and Newton
thought)
paradox resolved???
My talk at Murray Gell-Mann's 80th Birthday Conference,
Porto & Zee, Mod.Phys.Lett.A25:2929-2932,2010, arXiv:1007.2971
We made c part of the
kinematics, by going
from the Galilean to the
Lorentz group; c became
a ‘conversion-factor’
between space and time.
The unification of
spacetime allows us to
chose units in which
c=1, which is protected
by Lorentz invariance.
In other words, it does
not get renormalized!
(contrary to nonrelativistic theories.)
c becomes
“part of the
algebra”.
Change of algebra
Flat earth: Algebra is E(2)={
Round earth: We realize that
and
. Together with
}
and
are actually
, they form SO(3)
The algebra SO(3) reduces
(Inönü-Wigner
contraction) to E(2) as the
radius of the earth R goes
to infinity, just as the
Lorentz algebra reduces to
the Galilean algebra as c
goes to infinity.
R is not a dynamical quantity
that could be calculated by flat
earth physicists.
For example, using flat earth
physics, calculate the rate at which
ships disappear over the horizon.
Perhaps this is similar to calculating the
cosmological constant using quantum field theory.
Perhaps we need to go one step farther and
extend the Lorentz group to the deSitter
group!
The cosmological constant would
become a fundamental constant of
nature. (We then have to “explain”
why the Planck mass is so large.)