Higgs potential

Because of the spontaneously broken U 1) x 0(3) symmetry in Eq. (3), for A / 0 there should be collective Nambu-Goldstone excitations in the spectrum. However, due to the Lorentz non-invariance of the system there can be subtleties [19, 28-30], The NG spectrum can be analyzed within an underlying effective Higgs potential... 

There are also theoretical arguments which place some constraints on mn. In Section 3.1 we discussed the Higgs potential V p) = + Xp ... 

Fig. 6.4. The shaded area shows the permitted range of m.H vs rfh in order that the Higgs potential has an acceptable shape (see text).

As a consequence of one loop quantum correction the effective Higgs potential is modified to... 

Recall that, in the SM, a natural scale is set by the vacuum expectation value of the Higgs field v, related to the parameters of the Higgs potential, and it has a rather precise value (4.2.38)... 

Figure 25. Illustrative view of the scalar Higgs potential (Eq. 24), the Mexican hat, added to the vacuum to explain the origin of the nonzero mass of bosons. At each point along the bottom of the trough the symmetry is spontaneously broken and the Higgs field has a fixed nonzero value, the same in all these points, reahzing the continues degeneracy. The Higgs potential coincides with the Mexican-hat potential of the ITE problem E e in Fig. 2, except for the conical intersection ai.cp =cp =(i in the latter.

The Higgs potential is introduced ad hoc, and its reality cannot be confirmed experimentally directly, but the consequences of its existence were confirmed by observing the Higgs boson in experiments with the Large Hadron Collider at CERN in 2012. This indirectly confirmed also the idea that aU our observations are about one of the degenerate states of the broken symmetry of the Universe. Similar Higgs-field behavior was observed in superconductors [84] (coherent excited states in superconducting condensates with SSB were predicted earlier [85]). 

For the purpose of this chapter it is important to state that the very existence and properties of elementary particles are due to SSB associated with degeneracy. But it may be also interesting to compare the physical background similarities and differences between atomic system ( geometric ) and elementary particle (field) SSB. By comparing the theoretical Higgs potential (Fig. 25) with the JTE... 

It was demonstrated by Higgs [50] that the appearance of massless bosons can be avoided by combining the spontaneous breakdown of symmetry under a compact Lie group with local gauge symmetry. The potential V() which is invariant under the local transformation of the charged field... 

The gauge potentials and are 2x2 Hermitian traceless matrices, and the Higgs fields and % are also 2x2 matrices. These expectations are real-valued, and the nonzero contributions of the Higgs field on the physical vacuum are given by the diagonal matrix entries [95] ... 

From the foregoing, it becomes clear that fields and potentials are freely intermingled in the symmetry-broken Lagrangians of the Higgs mechanism. To close this section, we address the question of whether potentials are physical (Faraday and Maxwell) or mathematical (Heaviside) using the non-Abelian Stokes theorem for any gauge symmetry ... 

It is seen that the acquisition of mass by the photon is the result of an equation of superconductivity, and this is, of course, the basis of spontaneous symmetry breaking and the Higgs mechanism (Section XIV). Beltrami equations account for all these phenomena, and are foundational in nature. Note that the London equation (919) is not gauge-invariant on the U(l) level because aphysical gauge-invariant current is proportional to the vector potential, which, in the received view, is gauge-noninvariant. This is another flaw of U(l) electrodynamics in the... 

Perry, M. J., Higgs, G. A. (1998) Chemotherapeutic potential of phosphodiesterase inhibitors. Curr Opin Chem Biol 2(4), 472-481. 

Hobbs, A. J., Higgs, A., Moncada, S. Inhibition of nitric oxide synthase as potential therapeutic target, Annu. Rev. Pharmacol. Toxicol. 1999, 39, 191-220. 

The equations of motion of the held at the Higgs minimum (the minimum potential energy of the vacuum) are the Euler-Lagrange equations... 

To take this theory further would be to embed it into an 517(4) gauge theory. The gauge potentials are described by 4 x 4 traceless Hermitian matrices and the Dirac spinor has 16 components. The neutrality of the photon is then given by the sum over charges, which vanishes by the tracelessness of the theory. The Higgs field is described by a 4 x 4 matrix of entries. 

Ghafourifar P, Saavedra-Molina A. Functions of mitochondrial nitric oxide synthase. Oxidative Stress and Disease 2006 19 77-98. Su Y, Kondrikov D, Block ER. Cytoskeletal regulation of nitric oxide synthase. Cell Biochem. Biophys. 2005 43(3) 439-449. Hobbs AJ, Higgs A, Moncada S. Inhibition of nitric oxide synthase as a potential therapeutic target. Annu. Rev. Pharmacol. Toxicol. 1999 39 191-220. 

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