Do all roads lead to a grand unification scale?
What might the cosmological observations and particle physics being telling us ? It is interesting that the dark energy or cosmological constant scale 0.002 eV ... is of the same order that we expect for the light neutrino mass [15, 46–49]. Light neutrino mass values ∼ 0.004-0.007eV are extracted from studies of neutrino oscillation data assuming normal hierarchy and values less than about 0.02 eV are obtained with inverted hierarchy [50, 51]. That is, one finds the phenomenological relation
where M∼3×1016 GeV is logarithmically close to the Planck mass MPl and typical of the scale that appears in Grand Unified Theories. There are also theoretical hints that this large mass scale might perhaps be associated with dynamical symmetry breaking, see below. The gauge bosons in the Standard Model which have a mass through the Higgs mechanism are also the gauge bosons which couple to the neutrino. Is this a clue? The non-perturbative structure of chiral gauge theories is not well understood. If taken literally Eq.(10) connects neutrino physics, Higgs phenomenon in electroweak symmetry breaking and dark energy to a new high mass scale which needs to be understood...
Vacuum stability is very sensitive to the exact values of the Higgs and top-quark masses. For the measured value of mt, mH is very close to the smallest value to give a stable vacuum with the vacuum being at the border of stable and metastable. With modest changes in mt and mH (increased top mass and/or reduced Higgs mass) the Standard Model vacuum would be unstable [70,71,72,73,74]. If the vacuum is indeed stable up to the Planck mass, perhaps there is some new critical phenomena to be understood in the extreme ultraviolet?
Radiative corrections to the Higgs mass in the ultraviolet are very interesting. The running Higgs mass mH is related to the bare mass m0H through
mH2 = m0H2 − δmH2, δmH2 = (MPl2/ 16πH2)C1 (16)where δmH2 is the mass counterterm andC1=6v2(MH2+MZ2+2MW2−4Mt2)=2λ+3/2g′2+9/2g2−12y2t (17)
Here v is the Higgs vacuum expectation value, λ is the Higgs self-interaction coupling, g′ and g are the electroweak couplings and yt is the top quark Yukawa coupling. The small value of mH2 relative to MPl2 is the hierarchy problem and connected to discussions  of naturalness. Taking the couplings in the formula for C1 to be renormalisation group scale dependent and the measured Higgs and top quark masses, Jegerlehner  has argued that C1 crosses zero at a scale ∼1016 GeV, logarithmically close to the Planck mass. He argues that the sign change in the Higgs bare mass squared triggers the Higgs mechanism with a first order phase transition if the Standard Model is understood as the low energy effective theory of some cutoff system residing at the Planck mass [74, 76, 77]. In this scenario the Higgs might act as the inflaton at higher mass scales in a symmetric phase characterised by a very large bare mass term [78, 79]. Note that the Higgs and top quark masses are taken to be time independent in these calculations. Further, the electroweak Higgs contribution to the vacuum energy density − λ/24v4 obeys a similar expression to Eq.(17) and crosses zero at a similar scale about 1016 GeV so the renormalised version of this quantity can be much less than the bare version at scales close to the Planck mass.
It is interesting that the scale ∼1016 GeV found in this calculation also arises (modulo Yukawa couplings) in the see-saw mechanism for neutrino masses. The scale of inflation is related to the tensor to scalar ratio r in B modes in the cosmic microwave background through Vinflation ∼ (r/0.01)1/41016 GeV . A finite value of r would be evidence of gravitational waves from the inflationary period. If ongoing and future measurements converge on a positive signal in the region 0.001<r<0.1, then this would point to a scale of inflation in the same region close to 1016 GeV.
What suppresses the very large vacuum energy contributions expected from particle physics? Is the accelerating expansion of the Universe really driven by a time independent cosmological constant or by new possibly time dependent dynamics? Experiments will push the high-energy and precision frontiers of subatomic particle physics. Is new physics “around the corner” or might the Standard Model work up to a very large scale, perhaps close to the Planck mass and perhaps hinting at critical new phenomena in the ultraviolet? Understanding the accelerating expansion of the Universe and the cosmological constant vacuum energy puzzle promises to teach us a great deal about the intersection of subatomic physics and dynamical symmetry breaking on the one hand, and gravitation on the other.
(Submitted on 18 Mar 2015)
Anyway a tentative coherent understanding of a connection between neutrino physics, Higgs phenomenon in electroweak symmetry breaking and dark energy (one can add dark matter as well) to a high mass scale ∼1016 GeV is available to the attentive reader of this blog!