A comparison of system produced in the reactions meson +p→3 mesons + p

Critical mass renormalization in renormalized ϕ 4 theories in two and three dimensions

“…To compare with the results reviewed in [11], let us introduce the perturbatively renormalized mass µ 2 defined by…”

“…where the reported error is related to the uncertainty on D 2 . Taking into account the different normalization of the coupling constant, we obtain for the quantity f 0 defined in [11] f 0 = 1 6C = 11.00(4).…”

“…The quantity f 0 has been also computed by means of other techniques [5][6][7][8][9][10][11]. References [7,8,11] use Monte Carlo methods, while [9,10] consider the Hamiltonian quantum formulation in one dimension. Results are reviewed in [11].…”

“…The determination of µ 2 0c in the limit g → 0 is not an easy task as it represents a nonperturbative renormalization. In two dimensions it has been computed either by Monte Carlo simulations of lattice models or by an analysis of the corresponding Hamiltonian model defined in one dimension [5][6][7][8][9][10][11]. In three dimensions results, obtained by means of Monte Carlo simulations, are available for N = 2 [2].…”

Scaling and superscaling solutions from the functional renormalization group

“…Note that the definition (26) refers to renormalized quantities and bears an intrinsic local potential scheme dependence. The comparison of this critical coupling with analog definitions coming from a lattice's bare action (see for example [37] and references therein) might not be straightforward. The explicit relation between (26) and its lattice's counterpart could perhaps be computed along the lines of a non-perturbative generalization of [38].…”