Do all roads lead to a grand unification scale?

Experimental and phenomenological hints 

I continue my trip to a grand unified view of physics started this summer (see the Grand Loop of Physics). I have chosen to quote today an article that provides a simple summary about numerous experimental and phenomenological interesting facts pointing to the relevance of a grand unification energy scale close but below the Planck one:

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 

µ_vac∼m_ν∼Λ²_ew/M   (10) 

where M∼3×10¹⁶ GeV is logarithmically close to the Planck mass M_Pl 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 m_t, m_H 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 m_t and m_H (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?

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Radiative corrections to the Higgs mass in the ultraviolet are very interesting. The running Higgs mass m_H is related to the bare mass m_0H through

m_H² = m_0H² − δm_H²,    δm_H² = (M_Pl²/ 16π_H²)C₁    (16) 

where δm_H² is the mass counterterm and 

C₁=6v²(M_H²+M_Z²+2M_W²−4M_t²)=2λ+3/2g′²+9/2g²−12y²_t    (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 m_H² relative to M_Pl² is the hierarchy problem and connected to discussions [75] 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 [74] 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 [80]. 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.

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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.

Vacuum energy and the cosmological constant

Steven D. Bass

(Submitted on 18 Mar 2015)

Let's make the educated wish that the spectral noncommutative geometrization of physics has already taught us enough about the intersection of subatomic physics and dynamical symmetry breaking on the one hand, and gravitation on the other to start to investigate soon more thoroughly the accelerating expansion of the Universe and the cosmological constant vacuum energy puzzle...

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!