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T. Shinohara

Publications and source records attributed to T. Shinohara.

31 records · Page 2Linked to original sources
arXiv2006

Gluon mass generation and infrared Abelian dominance in Yang-Mills theory

The dual superconductivity is believed to be a promising mechanism for quark confinement. Indeed, what this picture is true has been confirmed in the maximal Abelian (MA) gauge. However, it is not yet confirmed in any other gauge and the MA gauge explicitly breaks color symmetry. To remedy this defect, we propose to use our compact formulation of a non-linear change of variables on a lattice. This formulation has succeeded to extract the magnetic monopole with integer-valued magnetic charge in the gauge-invariant way. In this talk, we present measurements of various correlation functions for the operators constructed from the CFN variables in SU(2) Yang-Mills theory. Some of our results reproduce previous results obtained in MA gauge, e.g., DeGrant-Toussaint monopole, infrared Abelian dominance and off-diagonal gluon mass generation. These studies preserve color symmetry, in sharp contrast to the conventional MA gauge. We argue the gauge fixing independence of these results and the implications to quark confinement

hep-lat↗
arXiv2006

Yang-Mills theory constructed from Cho--Faddeev--Niemi decomposition

We give a new way of looking at the Cho--Faddeev--Niemi (CFN) decomposition of the Yang-Mills theory to answer how the enlarged local gauge symmetry respected by the CFN variables is restricted to obtain another Yang-Mills theory with the same local and global gauge symmetries as the original Yang-Mills theory. This may shed new light on the fundamental issue of the discrepancy between two theories for independent degrees of freedom and the role of the Maximal Abelian gauge in Yang-Mills theory. As a byproduct, this consideration gives new insight into the meaning of the gauge invariance and the observables, e.g., a gauge-invariant mass term and vacuum condensates of mass dimension two. We point out the implications for the Skyrme--Faddeev model.

hep-th↗
arXiv2005

Lattice construction of Cho-Faddeev-Niemi decomposition and gauge invariant monopole

We present the first implementation of the Cho--Faddeev--Niemi decomposition of the SU(2) Yang-Mills field on a lattice. Our construction retains the color symmetry (global SU(2) gauge invariance) even after a new type of Maximally Abelian gauge, as explicitly demonstrated by numerical simulations. Moreover, we propose a gauge-invariant definition of the magnetic monopole current using this formulation and compare the new definition with the conventional one by DeGrand and Toussaint to exhibit its validity.

hep-lat↗
arXiv2005

Numerical evidence for the existence of a novel magnetic condensation in Yang-Mills theory

We present a first numerical evidence for the existence of a novel magnetic condensate proposed recently by one of the authors in SU(2) Yang-Mills theory. In our framework, the spontaneously generated color magnetic field identified with the Savvidy vacuum has the microscopic origin and is a consequence of the intrinsic dynamics of the Yang-Mills theory. It strongly suggests the Nielsen--Olesen instability of the Savvidy vacuum disappears and the stability is restored without the need of the Copenhagen vacuum. The implications to the Faddeev-Skyrme model are also discussed. These results are obtained through the first implementation of the Cho--Faddeev--Niemi decomposition of the Yang-Mills field on a lattice.

hep-ph↗
arXiv2005

BRST symmetry of SU(2) Yang-Mills theory in Cho--Faddeev--Niemi decomposition

We determine the nilpotent BRST and anti-BRST transformations for the Cho--Faddeev-Niemi variables for the SU(2) Yang-Mills theory based on the new interpretation given in the previous paper of the Cho--Faddeev-Niemi decomposition. This gives a firm ground for performing the BRST quantization of the Yang--Mills theory written in terms of the Cho--Faddeev-Niemi variables. We propose also a modified version of the new Maximal Abelian gauge which could play an important role in the reduction to the original Yang-Mills theory.

hep-th↗
arXiv2003

Renormalizable Abelian-projected effective gauge theory derived from Quantum Chromodynamics II

In the previous paper\cite{KS00b}, we derived the Abelian projected effective gauge theory as a low energy effective theory of the SU(N) Yang-Mills theory by adopting the maximal Abelian gauge. At that time, we have demonstrated the multiplicative renormalizability of the propagators for the diagonal gluon and the dual Abelian anti-symmetric tensor field. In this paper, we show the multiplicative renormalizability of the Green's functions also for the off-diagonal gluon. Moreover we complement the previous results by calculating the anomalous dimension and the renormalization group functions which are undetermined in the previous paper.

hep-th↗
arXiv2003

The Most General and Renormalizable Maximal Abelian Gauge

We construct the most general gauge fixing and the associated Faddeev-Popov ghost term for the SU(2) Yang-Mills theory, which leaves the global U(1) gauge symmetry intact (i.e., the most general Maximal Abelian gauge). We show that the most general form involves eleven independent gauge parameters. Then we require various symmetries which help to reduce the number of independent parameters for obtaining the simpler form. In the simplest case, the off-diagonal part of the gauge fixing term obtained in this way is identical to the modified maximal Abelian gauge term with two gauge parameters which was proposed in the previous paper from the viewpoint of renormalizability. In this case, moreover, we calculate the beta function, anomalous dimensions of all fields and renormalization group functions of all gauge parameters in perturbation theory to one-loop order. We also discuss the implication of these results to obtain information on low-energy physics of QCD.

hep-th↗
arXiv2002

Renormalizing a BRST-invariant composite operator of mass dimension 2 in Yang-Mills theory

We discuss the renormalization of a BRST and anti-BRST invariant composite operator of mass dimension 2 in Yang-Mills theory with the general BRST and anti-BRST invariant gauge fixing term of the Lorentz type. The interest of this study stems from a recent claim that the non-vanishing vacuum condensate of the composite operator in question can be an origin of mass gap and quark confinement in any manifestly covariant gauge, as proposed by one of the authors. First, we obtain the renormalization group flow of the Yang-Mills theory. Next, we show the multiplicative renormalizability of the composite operator and that the BRST and anti-BRST invariance of the bare composite operator is preserved under the renormalization. Third, we perform the operator product expansion of the gluon and ghost propagators and obtain the Wilson coefficient corresponding to the vacuum condensate of mass dimension 2. Finally, we discuss the connection of this work with the previous works and argue the physical implications of the obtained results.

hep-th↗
arXiv2001

Renormalizable Abelian-projected effective gauge theory derived from Quantum Chromodynamics

We show that an effective Abelian gauge theory can be obtained as a renormalizable theory from QCD in the maximal Abelian gauge. The derivation improves in a systematic manner the previous version that was obtained by one of the authors and was referred to as the Abelian-projected effective gauge theory. This result supports the view that we can construct an effective Abelian gauge theory from QCD without losing characteristic features of the original non-Abelian gauge theory. In fact, it is shown that the effective coupling constant in the resulting renormalizable theory has a renormalization-scale dependence governed by the $β$-function that is exactly the same as that of the original Yang-Mills theory, irrespective of the choice of gauge fixing parameters of the maximal Abelian gauge and the parameters used for identifying the dual variables. Moreover, we evaluate the anomalous dimensions of the fields and parameters in the resultant theory. By choosing the renormalized parameters appropriately, we can switch the theory into an electric or a magnetic theory.

hep-th↗
arXiv2000

Abelian dominance in low-energy Gluodynamics due to dynamical mass generation

We show that off-diagonal gluons and off-diagonal ghosts acquire their masses dynamically in QCD if the maximal Abelian gauge is adopted. This result strongly supports the Abelian dominance in low-energy region of QCD. The mass generation is shown to occur due to ghost-anti-ghost condensation caused by attractive quartic ghost interactions within the Abelian projected effective gauge theory (derived by one of the authors). In fact, the quartic ghost interaction is indispensable for the renormalizability due to nonlinearity of the maximal Abelian gauge. The ghost-anti-ghost condensation is associated with the spontaneous breaking of global SL(2,R) symmetry recently found by Schaden at least for SU(2) case. Moreover we write down a new extended BRS algebra in the maximal Abelian gauge which should be compared with that of Nakanishi-Ojima for the Lorentz gauge. Finally, we argue that the mass generation may be related to the spontaneous breaking of a supersymmetry $OSp(4|2)$ hidden in the maximal Abelian gauge.

hep-th↗
arXiv1998

Single and Double Universal Seesaw Mechanisms with Universal Strength for Yukawa Couplings

Single and double universal seesaw mechanisms and the hypothesis of universal strength for Yukawa couplings are applied to formulate a unified theory of fermion mass spectrum in a model based on an extended Pati-Salam symmetry. Five kinds of Higgs fields are postulated to mediate scalar interactions among electroweak doublets of light fermions and electroweak singlets of heavy exotic fermions with relative Yukawa coupling constants of exponential form. At the first-order seesaw approximation, quasi-democratic mass matrices with equal diagonal elements are derived for all charged fermion sectors and a diagonal mass matrix is obtained for the neutrino sector under an additional ansatz. Assuming the vacuum neutrino oscillation, the problems of solar and atmospheric neutrino anomalies are investigated.

hep-ph↗
arXiv1998

Approximate Sum Rules of CKM Matrix Elements from Quasi-Democratic Mass Matrices

To extract sum rules of CKM matrix elements, eigenvalue problems for quasi-democratic mass matrices are solved in the first order perturbation approximation with respect to small deviations from the democratic limit. Mass spectra of up and down quark sectors and the CKM matrix are shown to have clear and distinctive hierarchical structures. Numerical analysis shows that the absolute values of calculated CKM matrix elements fit the experimental data quite well. The order of the magnitude of the Jarlskog parameter is estimated by the relation $|J| \approx \sqrt{2}(m_c/m_t + m_s/m_b)|V_{us}|^2|V_{cb}|/4$.

hep-ph↗