Abstract
Through the embedding of superconformal quantum mechanics into AdS space, it is possible to construct an effective supersymmetric QCD light-front Hamiltonian for hadrons, which includes a spin-spin interaction between the hadronic constituents. A specific breaking of conformal symmetry determines a unique effective quark-confining potential for light hadrons, as well as remarkable connections between the meson, baryon, and tetraquark spectra. The pion is massless in the chiral limit and has no supersymmetric partner. The excitation spectra of relativistic light-quark meson, baryon and tetraquark bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. Although conformal symmetry is strongly broken by the heavy quark mass, the basic underlying supersymmetric mechanism, which transforms mesons to baryons (and baryons to tetraquarks) into each other, still holds and gives remarkable connections across the entire spectrum of light, heavy-light and double-heavy hadrons. Here we show that all the observed hadrons can be related through this effective supersymmetric QCD, and that it can be used to identify the structure of the new charmonium states.
Highlights
Superconformal algebra allows the construction of relativistic light-front (LF) semiclassical bound-state equations in physical spacetime which can be embedded in a higher dimensional classical gravitational theory
This holographic approach to hadronic physics gives remarkable connections between the light meson and nucleon spectra [2], and even though heavy quark masses break conformal invariance, an underlying dynamical supersymmetry still holds in the light-heavy sector [3,5]
Supersymmetric quantum mechanics together with lightfront holography can account for principal features of hadron physics, such as the approximatively linear Regge trajectories with nearly equal slopes for all mesons, baryons and tetraquarks in both L and n
Summary
Superconformal algebra allows the construction of relativistic light-front (LF) semiclassical bound-state equations in physical spacetime which can be embedded in a higher dimensional classical gravitational theory. The emerging dynamical supersymmetry between mesons and baryons in this framework is not a consequence of supersymmetric QCD at the level of fundamental fields, but it represents the supersymmetry between the LF boundstate wave functions of mesons and baryons This symmetry is consistent with an essential feature of color SUðNCÞ: a cluster of NC − 1 constituents can be in the same color representation as the anti-constituent; for SUðNc 1⁄4 3Þ this means 3 ̄c ∈ 3c × 3c and 3c ∈ 3 ̄c × 3 ̄c.
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