Contact interaction analysis of octet baryon axial-vector and pseudoscalar form factors

Octet baryon axial, induced pseudoscalar, and pseudoscalar form factors are computed using a symmetry-preserving treatment of a vector $\times$ vector contact interaction (SCI), thereby unifying them with an array of other baryon properties and analogous treatments of semileptonic decays of pseudoscalar mesons. The baryons are treated as quark-plus-interacting-diquark bound states, whose structure is obtained by solving a Poincaré-covariant Faddeev equation. The approach is marked by algebraic simplicity and involves no free parameters, and, since it is symmetry preserving, all consequences of partial conservation of the axial current are manifest. It is found that SCI results are consistent with only small violations of SU(3)-flavor symmetry, an outcome which may be understood as a dynamical consequence of emergent hadron mass. The spin-flavor structure of the Poincaré-covariant baryon wave functions is expressed in the presence of both flavor-antitriplet–scalar diquarks and flavor-sextet–axial-vector diquarks and plays a key role in determining all form factors. Considering neutral axial currents, SCI predictions for the flavor separation of octet baryon axial charges and, therefrom, values for the associated SU(3) singlet, triplet, and octet axial charges are obtained. The results indicate that, at the hadron scale ${\zeta }_{\mathcal{H}}$, valence degrees of freedom carry roughly 50% of an octet baryon’s total spin. Since there are no other degrees of freedom at ${\zeta }_{\mathcal{H}}$, the remainder may be associated with $\mathrm{quark}+\mathrm{diquark}$ orbital angular momentum.

Figure 1

Figurative representation of the integral equation for the Poincaré-covariant matrix-valued function $\mathrm{\Psi }$, which is the Faddeev amplitude for a baryon with total momentum $P=p_q+p_d=k_q+k_d$ constituted from three valence quarks, two of which are always contained in a nonpointlike, interacting diquark correlation. $\mathrm{\Psi }$ describes the relative momentum correlation between the dressed quarks and diquarks. Legend: shaded rectangle, Faddeev kernel; single line, dressed-quark propagator (Appendix pp1-s1); $\mathrm{\Gamma }$, diquark correlation amplitude; double line, diquark propagator (Appendix pp1-s2). Ground-state $J=1/2^{+}$ baryons contain both flavor-antitriplet–scalar and flavor-sextet–axial-vector diquarks (Appendix pp1-s3).

Figure 2

Currents that ensure PCAC for on-shell baryons which are described by the Faddeev amplitudes produced by the equation depicted in Fig. 1: single line, dressed-quark propagator; undulating line, axial or pseudoscalar current; $\mathrm{\Gamma }$, diquark correlation amplitude; double line, diquark propagator; $\chi$, seagull terms. A legend is provided in Table 1 with details in Appendix pp1-s4.

Figure 3

(a) $G_A^{pn}(x=Q^2/m_N^2)$: SCI result computed herein, solid red curve; prediction from Ref. [25], short-dashed purple curve within like-colored band; and dipole fit to data [68], long-dashed gold curve within like-colored band. (b) Complete array of SCI predictions for octet baryon axial transition form factors: $G_A^{B^{\prime }B}(x=Q^2/M_{B^{\prime }B}^2)$. (c) As in (b), but with each form factor normalized to unity at $x=0$. The thinner solid black curve is a pointwise average of the six transition form factors.

Figure 4

(a) $(m_l/M_N)G_P^{pn}(x=Q^2/m_N^2)$: SCI result computed herein, solid red curve; prediction from Ref. [25], short-dashed purple curve within like-colored band; and lQCD results [28], green points. (b) Complete array of SCI predictions for octet baryon axial transition form factors: $G_P^{B^{\prime }B}(x=Q^2/M_{B^{\prime }B}^2)/\mathcal{R}(x)$, Eqs. (b1b) and (b1c). (c) As in (b), but with each form factor normalized to unity at $x=0$. The thinner solid black curve is a pointwise average of the other six curves.

Figure 5

(a) $(m_l/M_N)G_5^{pn}(x=Q^2/m_N^2)$: SCI result, solid red curve; prediction from Ref. [25], short-dashed purple curve within like-colored band; lQCD results [28], green points. (b) Complete array of SCI predictions for octet baryon axial transition form factors: $G_P^{B^{\prime }B}(x=Q^2/M_{B^{\prime }B}^2)/\mathcal{R}(x)$, Eqs. (b1b) and (b1c). (c) As in (b), but with each form factor normalized to unity at $x=0$. The thinner solid black curve is a pointwise average of the other six curves.

Figure 6

Interaction vertex for the $J_1^{P_1}\to J_2^{P_2}$ diquark $+$ probe interaction (${\ell }^{\prime }=\ell +Q$): single line, quark propagator; undulating line, pseudoscalar or axial current; $\mathrm{\Gamma }$, diquark correlation amplitude; double line, diquark propagator; $\chi$, seagull interaction.