Toshihide Maskawa

Structure of non-linear realization in supersymmetric theories

Abstract We clarify the origin of massless particles which come out when an internal symmetry breaks down preserving supersymmetry. A special feature is that even if original and final symmetries are fixed, there exist many inequivalent non-linear realizations. We present the theorems which make clear the essential structure of the phenomena. The (non-linear)_transformation law for the massless particles is accurately defined and it is shown how to construct the supersymmetric non-linear lagrangian.

Light composite scalar in eight-flavor QCD on the lattice

We present the first observation of a flavor-singlet scalar meson as light as the pion in

Walking signals in Nf=8 QCD on the lattice

N_f=8

Singular Lagrangian and the Dirac-Faddeev Method Existence Theorem of Constraints in 'Standard Form'

QCD on the lattice, using the Highly Improved Staggered Quark action. Such a light scalar meson can be regarded as a composite Higgs with mass 125 GeV. In accord with our previous lattice results showing that the theory exhibits walking behavior, the light scalar may be a technidilaton, a pseudo Nambu-Goldstone boson of the approximate scale symmetry in walking technicolor.

The scalar spectrum of many-flavour QCD

We investigate walking signals of Nf = 8 QCD through meson spectrum using the HISQ (highly improved staggered quark) action. Our data (the pion decay constant, the p and r meson masses and the chiral condensate) for theNf =8 QCD are consistent with the spontaneously broken chiral symmetry in the chiral limit extrapolation of the chiral perturbation theory (ChPT). Remarkably enough, while the Nf = 8 data near the chiral limit are well described by the ChPT, those for the relatively large fermion bare mass mf away from the chiral limit actually exhibit a finite-size hyperscaling relation, suggesting a large anomalous dimension g m � 1. This implies that there exists a remnant of the infrared conformality, and suggests that a typical technicolor, “one-family model”, as modeled by the Nf = 8 QCD can be a walking technicolor theory.

Study of the conformal hyperscaling relation through the Schwinger-Dyson equation

Rigorous basis is given to the Dirac-Faddeev method, i.e., the Feynman integral with constraints (1st-class and/or 2nd-class), by proving existence theorem of constraints in ‘standard form’ for the restricted submanifold of definite dimension. The theorem states that such canonical variables exist for a given restricted submanifold that the submanifold is specified by putting those canonical variables equal to zero. This theorem will also give straightforward understanding of concepts in the Dirac formalism, e.g., Dirac bracket.

Topological insights in many-flavor QCD on the lattice

The LatKMI collaboration is studying systematically the dynamical properties of N_f = 4,8,12,16 SU(3) gauge theories using lattice simulations with (HISQ) staggered fermions. Exploring the spectrum of many-flavour QCD, and its scaling near the chiral limit, is mandatory in order to establish if one of these models realises the Walking Technicolor scenario. Although lattice technologies to study the mesonic spectrum are well developed, scalar flavour-singlet states still require extra effort to be determined. In addition, gluonic observables usually require large-statistic simulations and powerful noise-reduction techniques. In the following, we present useful spectroscopic methods to investigate scalar glueballs and scalar flavour-singlet mesons, together with the current status of the scalar spectrum in N_f = 12 QCD from the LatKMI collaboration.

Conformality in twelve-flavor QCD

We study corrections to the conformal hyperscaling relation in the conformal window of the large Nf QCD by using the ladder Schwinger-Dyson (SD) equation as a concrete dynamical model. From the analytical expression of the solution of the ladder SD equation, we identify the form of the leading mass correction to the hyperscaling relation. We find that the anomalous dimension, when identified through the hyperscaling relation neglecting these corrections, yields a value substantially lower than the one at the fixed point \gamma_m^* for large mass region. We further study finite-volume effects on the hyperscaling relation, based on the ladder SD equation in a finite space-time with the periodic boundary condition. We find that the finite-volume corrections on the hyperscaling relation are negligible compared with the mass correction. The anomalous dimension, when identified through the finite-size hyperscaling relation neglecting the mass corrections as is often done in the lattice analyses, yields almost the same value as that in the case of the infinite space-time neglecting the mass correction, i.e., a substantially lower value than \gamma_m^* for large mass. We also apply the finite-volume SD equation to the chiral-symmetry-breaking phase and find that when the theory is close to the critical point such that the dynamically generated mass is much smaller than the explicit breaking mass, the finite-size hyperscaling relation is still operative. We also suggest a concrete form of the modification of the finite-size hyperscaling relation by including the mass correction, which may be useful to analyze the lattice data.

Flavor-singlet spectrum in multi-flavor QCD

LatKMI Collaboration discusses the topological insights in many-flavor QCD on the lattice. We explore walking/conformal/confining phase in

Topological observables in many-flavour QCD

N_\mathrm{f}