Some speculations on the Higgs sector & ON the cosmological constant

1. 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

2. 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

3. Two problems in fundamental physics Low dimenional operators Higgs problem (due to Brout, Englert; Anderson; Higgs; Hagen, Guralnik, & Kibble) Cosmological constant problem

4. 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

5. 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

6. 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.)

7. 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

8. 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

9. 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

10. 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

11. 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,...)

12. 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

13. 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:

14. 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 ultra-large 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.A25:2929-2932,2010, arXiv:1007.2971

15. 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

16. 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”.

17. Change of algebra Flat earth: Algebra is E(2)={ } Round earth: We realize that and are actually and . Together with , 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.

18. 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.

19. 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.)