Prishon said:
*If* you believe in the Higgs field in its present form (I dont) then its energy was high when the field was zero.
The "running" of the Higgs field at high energies to which you allude is really an "advanced" or "intermediate" level issue rather than one that makes much sense at a basic level, but since you mention it, I'll briefly sketch out these considerations.
Moreover, all statements about what happen at extremely high energies need to be taken with a grain of salt because we can't probe those energy scales experimentally, or with observational evidence.
Nonetheless, it is possible, consistent with the Standard Model of Particle Physics, for the Higgs field to go to zero for a very brief moment, but almost immediately, it goes from zero to non-zero but extremely small, which is qualitatively different (i.e., different in kind, and not just different in degree).
The Universe has an upper energy bound, i.e. the energy scale of the Big Bang itself, rather than admitting infinitely high energies. This is in the general vicinity of the GUT scale or the Planck scale:
The most powerful collider to date, the Large Hadron Collider (LHC), is designed to reach a center of mass energy of 1.4x10
4 GeV in proton-proton collisions. The scale 10
16 GeV is only a few orders of magnitude below the
Planck energy of 10
19 GeV[.]
So, above that threshold, describing the laws of physics in the Universe is basically a
category error, because there is no such Universe to have laws of physics. We don't know precisely what that threshold is, but it is undoubtedly finite, so any theory that is asymptotically safe as a result of an ultraviolet (i.e. high energy) upper bound at that scale, can be consistent and complete, even if it can't be generalized to arbitrarily high energy scales.
The mass of the Higgs boson and its beta function (i.e., the formula which governs how the strength of the Higgs field weakens at higher energy scales and can be determined exactly from first principles in the Standard Model) implies that the Higgs field weakens to zero in the general vicinity of the maximal Big Bang energy, although uncertainties in the Higgs boson mass and top quark mass which go into this calculation introduce considerable uncertainty into determining this threshold.
The beta function of the Higgs field used to determine when it reaches zero also omits the impact of gravity, which can safely be ignored at LHC energy scales, but which is material in determining at what energy scale the Higgs field weakens to zero at energies close to that of the Big Bang like the GUT scale, because if quantum gravity really exists, the existence of quantum gravity alters the exact terms of the Higgs field beta function, tweaking it in a way that is material in the extremely high energies of the first few moments of the Universe.
Note also, that even if the Higgs field went to zero (making the masses of all of the fundamental particles in the Standard Model zero), none of the three Standard Model forces (electromagnetism, the strong force, and the weak force) go to zero at these energies as shown in Figure 7a below. And, since hadrons (i.e. protons and neutrons and pions and kaons) all have masses that come from the strong force, rather than from the Higgs field, even in the theoretical limit of quarks with zero mass, the Universe would not cease to have massive particles interacting via the three Standard Model forces and gravity, even at this high energy threshold.
ADVANCED DETAILS
As the charts below illustrate, the Standard Model running of the Higgs field may be well defined and non-zero to a scale in excess of the GUT scale, but not quite to the Planck scale, although this could break down at a scale with a best fit value of 10
10 GeV (which is a million times higher in energy that the peak LHC energies and a million times lower than the GUT scale). But considerable uncertainty that could increase that threshold by many orders of magnitude.
This observation is closely related to the determination that
the Higgs vacuum is "metastable", although
within reasonable experimental and theoretical uncertainty (even before considering beyond the Standard Model physics at high energies that can't be ruled out from other observations) for the reasons set below which explain why the zero value of the Higgs field and metastability are so entwined:
Higgs vacuum sits very close to the border between stable and metastable within 1.3 standard deviations of being stable. . . .
Vacuum stability depends on the ultraviolet behaviour of the Higgs boson self-coupling
λ, that is, its behaviour at the maximum possible energy scales. The SM couplings evolve with changing resolution (energy scale) according to the renormalization group, as shown in Fig.
7a. The weak SU(2) and QCD SU(3) couplings,
g and
gs, are asymptotically free, with 𝛼𝑖=𝑔2𝑖/4𝜋 decaying logarithmically with increasing resolution, whereas the U(1) coupling 𝑔′ is non asymptotically free, rising in the ultraviolet. The top quark Yukawa coupling
yt decays with increasing resolution. The running of the Higgs boson self-coupling
λ determines the stability of the electroweak vacuum. Instability sets in if
λ crosses zero deep in the ultraviolet part of the spectrum and involves a delicate balance of SM parameters. With the SM parameters measured at the LHC,
λ decreases with increasing resolution. This behaviour is dominated by the large Higgs boson coupling to the top quark (and also QCD interactions of the top). Without this coupling,
λ would rise in the ultraviolet. In Fig.
7a, λ crosses zero around 10
10 GeV with the top quark pole mass of
mt = 173 GeV and
mH = 125 GeV. This situation signals a metastable vacuum with lifetime greater than about 10
600 years (ref.
137), much longer than the present age of the Universe, about 13.8 billion years (see also Fig.
1b). Figure
7b shows the sensitivity of vacuum stability to small changes in
mt. If the top mass is taken as 171 GeV in these calculations, the vacuum stays stable up to the Planck scale. The measured 125 GeV Higgs boson mass is close to the minimum needed for vacuum stability with the measured top quark mass.
So, the Higgs vacuum could be just barely stable at this upper bound. Similarly,
one published paper notes that:
Once
radiative corrections are taken into account, the stability of the Higgs vacuum is very sensitive to the value of the top quark mass.
The
the top quark pole mass has an experimental uncertainty about about 0.17% (about 300 MeV/c
2 according to direct measurements but realistically somewhat larger than that given the spread of determinations by different means) which is still material for many purposes including this one.
