Variational mass perturbation theory for light-front bound-state equations

Abstract

We investigate the mesonic light-front bound-state equations of the 't Hooft and Schwinger model in the two-particle, i.e. valence sector, for small fermion mass. We perform a high precision determination of the mass and light-cone wave function of the lowest lying meson by combining fermion mass perturbation theory with a variational approach. All calculations are done entirely in the fermionic representation without using any bosonization scheme. In a step-by-step procedure we enlarge the space of variational parameters. We achieve good convergence so that the calculation of the meson mass squared can be extended to third order in the fermion mass. Within a numerical treatment we include higher Fock states up to six particles. Our results are consistent with all previous numerical investigations, in particular lattice calculations. For the massive Schwinger model, we find a small discrepancy ( < ∼ 2%) in comparison with known results. Possible resolutions of this discrepancy are discussed. PACS number(s):where all masses are measured in units of the basic scale µ 0 = e/ √ π, the mass of the boson in the massless Schwinger model, which is thus represented by the '1' in (1.1). The first order coefficient M 1 was obtained analytically in [12] via bosonization, M 1 = 2e γ = 3.56215 . (1.2) with γ = 0.577216 being Euler's constant. Shortly afterwards Bergknoff, using light-cone Hamiltonian techniques (see below), found a value [13] M 1 = 2π/ √ 3 = 3.62760 , (1.3)

New basis function approach to the ’t Hooft-Bergknoff-Eller equations

“…An almost identical result has been obtained by Harada et al [15], in which they have restricted themselves to a case where γ 0 = β 0 , and γ j = β 0 + j. Our conclusion is a generalization of Harada et al's result.…”

Bosonized massiveN-flavour Schwinger model

“…Adam's mass perturbation theory fails for m > .5µ. [20] There is ambiguity in the definition of the composite operator ψ − ψ(x). It diverges in perturbation theory.…”

“…[13,14] Investigation in the light-cone quantization method has been pushed forward both on the analytic and numerical sides. [15]- [20] The bound state spectrum has been evaluated in the entire range of a fermion mass at θ = 0 and T = 0. Subtleties in the chiral condensate in this formalism has been noted.…”

Schwinger Mass in Renormal-Ordered Chiral Perturbation Theory

“…is the lowest curve. We use the rescaled Schwinger mass M ′ = M/(1 + m 2 ) 1/2 , like in [25,26], and choose units µ = 1. to the lattice data of [29] (small dots, for larger m) and [30] (fat dots, for small m, with rather large errors). We again use the rescaled Schwinger mass M ′ = M/(1 + m 2 ) 1/2 and units µ = 1.…”

“…For an overview on additional data for the Schwinger mass (e.g., from light-front computations) we refer to [25] (especially their Fig. 2 and Table 16), and to [26].…”