Abstract
Light-front holographic QCD provides a successful first approximation to hadron spectroscopy in the chiral limit of $(3+1)$-dim light-front QCD, where a holographic Schr\"odinger-like equation, with an emerging confining scale, $\kappa$, governs confinement in the transverse direction. In its supersymmetric formulation, light-front holography predicts that each baryon has two superpartners: a meson and a tetraquark, with their degenerate masses being generated by the same scale, $\kappa$. In nature, this mass degeneracy is lifted by chiral symmetry breaking and longitudinal confinement. In this paper, we show that the latter can be successfully captured by the 't Hooft equation of $(1+1)$-dim, large $N_c$, QCD. Together, the holographic Schr\"odinger equation and the 't Hooft equation, provide a good global description of the data across the full hadron spectrum with a universal $\kappa$.
Highlights
Where Ψðx; b⊥Þ is the meson light-front wave function, x the light-front momentum fraction carried by the quark, and b⊥ the transverse
In light-front holography, the longitudinal mode, XðxÞ, is not dynamical, i.e., undetermined by Eq (6). It is instead fixed by the holographic mapping of the electromagnetic pion form factor in physical spacetime and AdS5 [5,6], resulting in χðxÞ 1⁄4 1, i.e., pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
The effects of nonzero quark masses were originally taken into account using a prescription by Brodsky and de Teramond (BdT) [12], which relies on the fact that the holographic ground state wave function depends on the invariant mass of the qqpair
Summary
In light-front (3 þ 1)-dim QCD, the mass of a quarkantiquark meson is given by [1]. × Ψðx; b⊥Þ þ interactions; ð1Þ where Ψðx; b⊥Þ is the meson light-front wave function, x the light-front momentum fraction carried by the quark, and b⊥ (or b⊥eiφ in polar representation) the transverse. In light-front holography, the longitudinal mode, XðxÞ, is not dynamical, i.e., undetermined by Eq (6) It is instead fixed by the holographic mapping of the electromagnetic (or gravitational) pion form factor in physical spacetime and AdS5 [5,6], resulting in χðxÞ 1⁄4 1, i.e., pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi. ST 2 þ ð18Þ where n⊥ is the principal quantum number that emerges when solving the holographic Schrödinger equation, and ST is total diquark-antidiquark spin It follows that baryons with quantum numbers, LB 1⁄4 LM − 1 and SD 1⁄4 SM, are superpartners to mesons with quantum numbers, LM and SM, and tetraquarks with quantum numbers ST 1⁄4 SD and LT 1⁄4 LB.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
