Meson/baryon/tetraquark supersymmetry from superconformal algebra and light-front holography

Abstract

Superconformal algebra leads to remarkable connections between the masses of mesons and baryons of the same parity -supersymmetric relations between the bosonic and fermionic bound states of QCD. Supercharges connect the mesonic eigenstates to their baryonic superpartners, where the mesons have internal angular momentum one unit higher than the baryons: L M = L B + 1. The dynamics of the superpartner hadrons also match; for example, the power-law fall-off of the form factors are the same for the mesonic and baryonic superpartners, in agreement with twist counting rules. An effective supersymmetric light-front Hamiltonian for hadrons composed of light quarks can be constructed by embedding superconformal quantum mechanics into AdS space. This procedure also generates a spin-spin interaction between the hadronic constituents. A specific breaking of conformal symmetry inside the graded algebra determines a unique quark-confining light-front potential for light hadrons in agreement with the softwall AdS/QCD approach and light-front holography. Only one mass parameter √ λ appears; it sets the confinement mass scale, a universal value for the slope of all Regge trajectories, the nonzero mass of the proton and other hadrons in the chiral limit, as well as the length scale which underlies their structure. The mass for the pion eigenstate vanishes in the chiral limit. When one includes the constituent quark masses using the Feynman-Hellman theorem, the predictions are consistent with the empirical features of the light-quark hadronic spectra. Our analysis can be consistently applied to the excitation spectra of the π, ρ, K, K * and φ meson families as well as to the N, ∆, Λ, Σ, Σ * , Ξ and Ξ * baryons. We also predict the existence of tetraquarks which are degenerate in mass with baryons with the same angular momentum. The mass-squared of the light hadrons can be expressed in a universal and frame-independent decomposition of contributions from the constituent kinetic energy, the confinement potential, and spin-spin contributions. We also predict features of hadron dynamics, including hadronic light-front wavefunctions, distribution amplitudes, form factors, valence structure functions and vector meson electroproduction phenomenology. The mass scale √ λ can be connected to the parameter Λ M S in the QCD running coupling by matching the nonperturbative dynamics, as described by the light-front holographic approach. to the perturbative QCD regime. The result is an effective coupling defined at all momenta. The matching of the high and low momentum-transfer regimes determines a scale Q 0 proportional to √ λ which sets the interface between perturbative and nonperturbative hadron dynamics. The use of Q 0 to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combi-2 nation with the scheme-independent Principle of Maximal Conformality (PMC) procedure for setting renormalization scales, can greatly improve the precision of perturbative QCD predictions.

Spin effects in the pion holographic light-front wavefunction

“…[3] reports κ = 590 MeV for pseudoscalar mesons and κ = 540 MeV for vector mesons. A recent fit to the Regge slopes of mesons and baryons, treated as conformal superpartners, yields κ = 523 MeV [9]. On the other hand, the AdS/QCD scale κ can be connected to the scheme-dependent pQCD renormalization scale Λ QCD by matching the running strong coupling in the non-perturbative (described by light-front holography) and the perturbative regimes [17].…”

Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

“…Various interesting applications of the light-cone formalism to field theories such as QCD are discussed in refs. [24][25][26].…”

“…Zβ (β a , B a , α 12 , Z) , (F. 26) where G 1 , G 2 are given in (F.23)-(F.25). As the vertex V (2) Zβ is considered to be expandable in the B 3 we use the following power series expansion: 27) where V n is a degree-n monomial in B 3 .…”

Application of the light-front holographic wavefunction for heavy-light pseudoscalar meson in B d,s → D d,s P decays

“…In Refs. [9][10][11][12], with only one parameter λ = κ 2 , the observed light meson and baryon spectra are successfully described by extending superconformal quantum mechanics to the light-front and its embedding in AdS space. Moreover, very recently, the analyses are further extended to the heavy-light hadron family [13].…”