Some speculations on the Higgs sector & ON the cosmological

constant A. Zee

Institute for Theoretical Physics University of California, Santa Barbara

WarsawAugust 26, 2011

Reversal of fortune

Dimension less than 4: super renormalizable Nice & EasyDimension equal to 4: renormalizableDimension greater than 4: non renormalizable Fear & Loathing

Then came a new (Wilsonian) way of looking at quantum field theoryField Theory as effective long distance expansionDimension less than 4: super renormalizable Fear & LoathingDimension equal to 4: renormalizableDimension greater than 4: non renormalizable To be expected

Two problems in fundamental physicsLow dimenional operators

Higgs problem (due to Brout, Englert; Anderson; Higgs; Hagen, Guralnik, & Kibble)

Cosmological constant problem

Private HiggsWith Rafael Porto, KITP Santa Barbara, now at IAS Princeton & Columbia

Hard to believe one single Higgs serves all, from electron to top quarkEach fermion should have its own private Higgs fields

Possible to construct model with workable parameter spaceSymmetry breaking in cascade driven by Higgs for the top quark; dark matter candidatesOne 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

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:

and compare with

assuming

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!!!

Proton Decay as a possible analogy!

Natural to write down

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

Modern notions of renormalization group flow and scaling

(Gell-Mann & Low, Wilson,...)

Remarkably, promotion from dimension 4 to 6 enough to solve the

problem (in the exponential!)

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 Yang-

Mills 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”

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.A25:2929-2932,2010, arXiv:1007.2971

We speculate gravity departs from general relativity at ultra-large distance scales.

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)

Observed: Rømer, tiny but not 0;

(as both Galileo and Newton thought)

How was this 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 non-relativistic theories.)

c becomes “part of the algebra”.

Flat earth: Algebra is E(2)={ }

Round earth: We realize that and are actually and . Together with , they form SO(3)

Change of algebra

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.

Perhaps this is similar to calculating the cosmological constant using quantum field theory.

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.

The cosmological constant would become a

fundamental constant of nature. (We then have to “explain” why the Planck

mass is so large.)

Perhaps we need to go one step farther and extend the Lorentz group

to the deSitter group!