Is the quantum-chromodynamic gluon a composite object?

Abstract

It is shown that the compositeness conditions required for ihe equivalence or quantum chromodynamics and the corresponding four-fernlion theory rnay be den~onstrated for a large class of gauges. + A unification of interparticle forces may be &,= & ( i d -m , )~, -$G,(l&,~,+Xdj,)~.(1) brought about by reducing the number of fundaHere, X a r e the generators of the local color group. mental fields in interaction, One attempt in this By introducing auxiliary fields K,, C, can be direction is the nonlinear spinor theory of Heisenequivalently written a s b e r & in which the physical fields a r e regarded a s composites of one fundamental self-coupled spinor --.-. -C;=I,(i$-~n,)b,-g,i,y,~X$,.~,,+~6y2A,b.A,b,field. In the past two decades there have been several attempts t o derive both Abelian2 and non-(2) Abelian3'4 gauge fields a s collective modes of a quartically self-coupled spinor field. The condition for the equivalence of these four-fermion and Yukawa-type Lagrangians, a s i s well known, is that the effects of the b a r e Yukawa field vanish. This i s realized by the vanishing of certain r enormalization constants of the corresponding Yukawa theorye5 Recently, it has been ~l a i m e d~'~ that f o r quantum chromodynamics (QCD) this happens automatically; it i s , therefore, suggested that the gluon field is nonelementary and that QCD is equivalent to a four-fermion theory with a single elementary field. In this note, we reexamine the arguments of Refs. 3 and 6 wherein it has been claimed that the compositeness conditions need only be verified in the Landau gauge [ a ( y ) = 0] since it is argued therein that the renormalized gauge parameter a ( k ) vanishes in the limit of an infinite ultraviolet cutoff A. We note, however, that although a ( y ) vanishes when the renormalization point y moves to infinity, it does not vanish f o r finite y even when -=, contrary to what has been stated by these authors. A s a result, the gauge independence of the compositeness conditions cannot b e concluded from the arguments of Refs. 3 and 6. Our study of the gauge dependence of the renormalization constants, however, indicates that it may indeed be possible to satisfy the compositeness conditions in a wide variety of gauges. We a l s o r e m a r k that, in spite of this, the present proofs of equivalence of four-fermion-type and Yukawa-type theories may not be complete. Alternatively, we may recognize that two theories may be equivalent with certain prescriptions f o r renormalizing while being not equivalent f o r other equally consistent renormalization schemes.Following E g~c h i ,~ we begin with the non-Abelia n four-fermion Lagrangian with ~,=g,2/6~~. The suffix b indicates b a r e quantities. The Lagrangian (2) can be formally r ewritten in t e r m s of the renormalized quantities defined by ,+g.A,xA,. The separation of t e r m s in Eq. (5) i s performed to facilitate the comparison to be made l a t e r [see Eq. ('7)s with the QCD Lagrangian. We a l s o note the m a s s t e r m for the field A,, that occurred in Eq.(2...

Relativistic five-quark equations and the nature ofθpentaquarks

“…qq and qq ! qq are calculated in the framework of the dispersion N/D method with the input four-fermion interaction [35][36][37] with quantum numbers of the gluon [31]. The regularization of the dispersion integral for the D-function is carried out with the cutoff parameters n .…”

“…In our relativistic quark model with four-fermion interaction [35][36][37], the octet color qq bound state was found, which corresponds to the constituent gluon G with a mass M G 0:67 GeV [31]. This approach is similar to the large N c limit [38][39][40].…”

Baryonium X(1835)

“…We derived the relativistic six-quark equations in the framework of the dispersion technique. The pair quarks amplitudes qq → qq and q q → q q are calculated with the dispersion N/D method using the input four-fermion interaction [22,23] with the quantum numbers of the gluon [24,25].…”

“…As explained in the previous paper [21] the relativistic generalization of the three-body Faddeev equations was obtained in the form of dispersion relations in the pair energy of two interacting quarks. The pair quarks amplitudes qq → qq are calculated in the framework of the dispersion N/D method with the input four-fermion interaction [22,23] with quantum numbers of the gluon [24,25].…”

Negative Parity Tetraquarks With the Open Charm

“…In order to represent the subamplitudes , , [31,32] with the quantum numbers of the gluon [33]. The regularization of the dispersion integral for the D-function is carried out with the cutoff parameters Λ .…”