Dynamical consistency of the Pati-Salam-Strathdee dual electric-magnetic charge preon model (1981): binding, emergent gauge symmetry, and composite spectroscopy

In 1981 Pati, Salam, and Strathdee proposed that quarks and leptons are bound states of scalar preons (a flavon f, a chromon C, and a third species S) held together by a primordial abelian U(1) x U(1) force whose two charges, with couplings g and h, are hidden reciprocal electric-type and magnetic-type charges satisfying the Dirac-like quantization condition gh/4pi = 1/2. The half-integer spins of the composite fermions were to come from angular momentum stored in the field of dual charge pairs, the observed non-abelian gauge symmetry was conjectured to emerge as an effective low-energy symmetry of the composites, and the graviton was speculated to be composite. The construction left its dynamical core open: a consistent Lorentz-invariant field theory for the dual-charge binding; a nonperturbative demonstration that such forces bind scalar preons into the small, light spin-1/2 composites observed in nature; a derivation of the emergent non-abelian symmetry and its anomaly cancellation; the compatibility of massless composite spin-1 and spin-2 particles (including a composite graviton) with the Weinberg-Witten theorem; and the resulting spectroscopy of composite Z bosons and proton-decay mediators. This dynamical core is not settled by the subsequent literature: the formal quantum field theory of electric plus magnetic charges is well developed (Zwanziger's two-potential theory with proven Lorentz invariance) and composite-gravity research is active, yet the central nonperturbative binding and emergence questions of this specific construction remain neither demonstrated nor refuted.

Background

By the late 1970s the proliferation of quarks and leptons - three nearly identical fermion families plus gauge bosons and Higgs particles - motivated preon (subquark) models, in which the observed fermions are bound states of a smaller set of more fundamental constituents. Two obstacles recur in such models: ordinary abelian binding forces appear too weak to confine preons into composites far smaller than hadrons (sizes below $10^{-16}$ cm, as required by the absence of any measured substructure of quarks and leptons), and it is difficult to obtain half-integer composite spins if the preons are taken to be spinless, even though scalar preons are the most economical choice.

Pati, Salam, and Strathdee (1981) attacked both obstacles at once. Their preons - the flavon $f$ (so named because it carries the flavor, i.e. family, quantum numbers), the chromon $C$ (carrying color), and a third species $S$ - are scalar (spin-0) fields bound by a primordial abelian gauge interaction $U(1)_A\times U(1)_B$ with two charges $Q_A$ and $Q_B$ coupled through constants $g$ and $h$ and realized in the model by a single primordial gauge boson $A'_\mu$ coupled to both charge types, with a subsidiary condition that reduces the two $U(1)$ symmetries to one. Their charge assignments are $f:(g,0)$, $C:(0,h)$, and $S:(-g,-h)$, so that the three-preon composites $fCS$ are neutral under both binding charges. The key postulate is that these two charges are reciprocal: they are hidden electric-type and magnetic-type charges, like the electric charge and the magnetic charge of a monopole (a hypothetical particle that is a source of magnetic field). A quantum theory containing both charge types must obey the Dirac quantization condition, which fixes the product of any electric and magnetic charge to half-integer units, $gh/4\pi=n/2$. The model takes the minimal case $\frac{gh}{4\pi}=\frac{1}{2}$: the angular momentum stored in the gauge field of a pair carrying one electric-type and one magnetic-type charge is then exactly one half, so a two-preon core acquires half-integer angular momentum from the field itself, and the three-preon composites $fCS$ can be spin-$\frac{1}{2}$ fermions even though every constituent is a scalar. With the magnetic-type coupling strong at short distances ($h^2/4\pi\sim 1$ in the estimates of reference [1]), the model estimates a compositeness scale $M_0=1/r_0$ with $r_0\lesssim 10^{-17}$-$10^{-18}$ cm, corresponding to $M_0$ of order 1-10 TeV.

The further ambition is that all low-energy structure is emergent. Since the low-energy theory of composites much lighter than $M_0$ must be renormalizable (its ultraviolet divergences absorbable into finitely many measured parameters), and the only renormalizable interacting theory of charged spin-1 fields is a (possibly spontaneously broken) Yang-Mills theory - the generic non-abelian gauge theory - the electroweak and color gauge bosons are conjectured to be six-preon (preon-antipreon) bound states, with the observed non-abelian gauge symmetry and its anomaly cancellation - the required cancellation of quantum-loop contributions that would otherwise break the gauge symmetry and render the theory inconsistent - emerging at the composite level rather than being postulated; candidate low-energy symmetry groups discussed in reference [1] are $\mathrm{SU}(2)_L\times\mathrm{SU}(2)_R\times\mathrm{SU}(4)^C$, SO(10) and SU(16), with the caveat that a large group such as SU(16) may contain triangle anomalies (quantum symmetry violations), in which case the realized symmetry would be an anomaly-free subgroup. The model predicts three universal neutral composite gauge bosons $Z_f$, $Z_C$, $Z_S$, each coupled to the conserved preon-number current of one preon species, as a distinctive experimental signature; the graviton is speculated to be composite, its weak low-energy coupling damped by composite form factors (the modification of point-particle interactions due to finite spatial size); and proton decay is mediated either by superheavy six-preon composites (requiring $M_0\gtrsim 10^{14}$ GeV to respect proton-lifetime limits) or by effective multi-preon transitions at scales of order $10^3$-$10^4$ GeV.

Two consistency issues are intrinsic. First, a quantum field theory with both electric and magnetic charges needs a nonstandard formulation. The working assumption of reference [1] is a single primordial gauge boson $A'_\mu$ (a field distinct from the ordinary photon) coupled to both charge types, but the existence of a consistent Lorentz-invariant quantum theory realizing the dual-charge assignment with a single boson was itself left open. The established alternative is the two-potential formalism of Zwanziger (1971), in which electric and magnetic currents couple locally to two gauge potentials at the cost of a fixed reference direction (the Dirac-string direction - an unphysical line singularity attached to each monopole, along which its magnetic flux is transported) that hides manifest Lorentz invariance; Brandt, Neri, and Zwanziger (1978) proved that the gauge-invariant Green's (correlation) functions of this theory are nevertheless Lorentz invariant. Second, the Weinberg-Witten theorem (Weinberg and Witten, 1980) forbids massless particles of spin $j>\frac{1}{2}$ that carry a Lorentz-covariant conserved charge current, and massless particles of spin $j>1$ with a Lorentz-covariant conserved energy-momentum tensor, in theories such as ordinary renormalizable field theories - which directly constrains massless composite gauge bosons and any composite graviton unless the theorem's assumptions fail at the fundamental level. Reference [1] engages both issues, and its open questions are precisely whether its construction can be made dynamically real.

Problem Statement

The problem is the unresolved dynamical core of the 1981 Pati-Salam-Strathdee construction, as left open by reference [1] and not settled by subsequent literature: establish, by controlled dynamical argument rather than conjecture - or refute - the consistency and viability of the dual-charge preon model. The objective comprises, jointly: (1) a Lorentz-invariant, consistent quantum field theory of the reciprocal electric-type and magnetic-type abelian charges with the quantization condition $\frac{gh}{4\pi}=\frac{1}{2}$, either in the single-gauge-boson realization envisaged in the model or in a formulation (such as the two-potential formalism) shown to reproduce its dynamics, suitable for computing binding; (2) a nonperturbative demonstration that such interactions with the proposed strong short-distance couplings bind scalar preons into small ($r_0\lesssim 10^{-17}$-$10^{-18}$ cm in the estimates of reference [1]), light spin-$\frac{1}{2}$ three-preon composites reproducing the quark-lepton spectrum, including the binding of systems that contain both electric-type and magnetic-type charges; (3) a derivation, from the microscopic preon dynamics, of the emergent low-energy non-abelian gauge symmetry with its anomaly cancellation (the identification of the anomaly-free subgroup being part of the derivation, not an input); (4) a determination of whether massless composite spin-1 particles and a composite graviton are consistent with the Weinberg-Witten theorem, with a concrete dynamical evasion if so; and (5) the resulting spectroscopy - whether six-preon spin-1 composites form, the masses of the composite $Z_f$, $Z_C$, $Z_S$ bosons, and the proton-decay scale - confronted with experiment. The construction is refuted by an inconsistency or exclusion in any one of (1)-(5) - which jointly constitute its dynamical core - and established only if all five are realized with computable scales. Reference [1] also raised the further speculation of whether the compositeness hierarchy terminates in a single deepest constituent of possible topological character; this facet lies outside items (1)-(5).

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