Gauge loops select the Standard-Model direction of a Pati–Salam triplet vacuum from a shape-blind start

Abstract. In left–right-symmetric Pati–Salam models the scalar that gives the right-handed neutrinos their Majorana mass, the (10,1,3) triplet, has many inequivalent vacuum directions. Only one orbit of them leaves the Standard-Model gauge group unbroken. Usually that orbit is reached by choosing the quartic couplings. We record a result in which it is selected instead. Start
the scalar quartic at a high scale Λ as a pure function of the total field norm, blind to the direction. Run it down at one loop. Then the direction that first becomes flat, and so hosts a Gildener–Weinberg vacuum, is the Standard-Model direction, at every point of a large grid of couplings and scales. No tachyon appears there. The cause is a representation-theory fact: the gauge-boson contribution 3/2 trM^4V is largest on that orbit. The selection survives adding a (15,2,2) scalar. We also state plainly what the result does not do. It does not fix the breaking scale without strong coupling near Λ, it leaves a light electroweak doublet unstable, and it is generic to this class of models.

What the result is. In many extensions of the Standard Model, a heavy field fills empty space and breaks a larger symmetry down to the one we see. It also gives neutrinos their tiny masses. That field could settle in many different ways, and only one of them leaves the familiar forces of the Standard Model intact. Usually theorists choose parameters so that the field settles in the right one. This note shows that the choice can be left to physics instead. Start with no preference at all: the field’s energy depends only on its overall size, not its direction. Then let quantum effects of the force-carrying particles act as the energy scale drops. Those effects alone steer the field into the Standard-Model arrangement. This happened at every point we tested, and it holds up when extra fields are added.

Why it matters. It turns an assumption into an outcome. Which symmetry survives at low energies is normally an input to such models. Here it follows from the gauge forces themselves, through a simple mathematical fact: the force carriers’ contribution peaks on the Standard-Model direction. That removes one arbitrary choice from this class of theories. The note is also clear about its limits. The energy scale of the breaking, the mass of the Higgs boson and some other details do not come out right without further assumptions. So this is a step toward explaining the vacuum, not a complete explanation.