arXiv subjects

Masayasu Harada

Publications and source records attributed to Masayasu Harada.

152 records · Page 9Linked to original sources

arXiv1995

Solving the Homogeneous Bethe-Salpeter Equation

We study a method for solving the homogeneous Bethe-Salpeter equation. By introducing a `fictitious' eigenvalue $λ$ the homogeneous Bethe-Salpeter equation is interpreted as a linear eigenvalue equation, where the bound state mass is treated as an input parameter. Using the improved ladder approximation with the constant fermion mass, we extensively study the spectrum of the fictitious eigenvalue $λ$ for the vector bound states and find the discrete spectrum for vanishing bound state mass. We also evaluate the bound state masses by tuning appropriate eigenvalues $λ$ to be unity, and find massless vector bound states for specific values of the constant fermion masses.

hep-ph↗

arXiv1994

QCD S Parameter from Inhomogeneous Bethe-Salpeter Equation

We calculate the low-energy parameter S in QCD, which is also known as L_{10}, and the pion decay constant f_πusing inhomogeneous Bethe-Salpeter equation in improved ladder approximation. To extract these quantities we calculate the ``V-A'' two-point function, Π_{VV}(q^2) - Π_{AA}(q^2), in space-like region. We obtain S = 0.43 \sim 0.48, which is about 30% larger than the experimental value. The calculated f_πis well consistent with the result by solving the homogeneous Bethe-Salpeter equation for pion. We also evaluate $S$ parameter in SU(3) gauge theory with N_D doublets of fermions in connection with walking technicolor model, and find that the value of S/N_D hardly depends on N_D.

hep-ph↗

arXiv1993

External Gauge Invariance and Anomaly in BS Vertices and Boundstates

A systematic method is given for obtaining consistent approximations to the Schwinger-Dyson(SD) and Bethe-Salpeter(BS) equations which maintain the external gauge invariance. We show that for any order of approximation to the SD equation there is a corresponding approximation to the BS equations such that the solutions to those equations satisfy the Ward-Takahashi identities of the external gauge symmetry. This formulation also clarifies the way how we can calculate the Green functions of current operators in a consistent manner with the gauge invariance and the axial anomaly. We show which type of diagrams for the $π^0\rightarrowγγ$ amplitude using the pion BS amplitude give result consistent with the low-energy theorem. An interesting phenomenon is observed in the ladder approximation that the low energy theorem is saturated by the zeroth order terms in the external momenta of the pseudoscalar BS amplitude and the vector vertex functions.

hep-ph↗

arXiv1993

Axial Anomaly and Transition Form Factors

We investigate the properties of the amplitude induced by the anomaly. In a relatively high energy region those amplitudes are constructed by the vector meson poles and the anomaly terms, in which the anomaly terms can be essentially evaluated by the triangle quark graph. We pay our attention to the anomaly term and make intensive analysis of the existing experimental data, i.e., the electromagnetic $π^0$ and $ω$ transition form factors. Our result shows that it is essential to use the constituent quark mass instead of the current quark mass in evaluating the anomaly term from the triangle graph.

hep-ph↗

arXiv1993

Interpolating Axial Anomaly Induced Amplitudes

We propose an interpolating formula for the amplitude induced by the axial anomaly, concentrating on the $π^0γ^{\ast}γ^{\ast}$ transition form factor. The QCD corrections to this amplitude are generally described by two major contributions coming from the $q\bar{q}$ bound state and the background continuous spectrum, respectively. For the first contribution, we include the lowest vector bound state using the realization of the dynamical gauge boson of hidden local symmetry. The second contribution is included as the triangle quark loop in which a constituent mass is adopted as a internal quark mass and the amplitudes are smeared out around the threshold. Using the resulting form factor, we fit the experimental data for the $π^0γ$ and the $ωπ^0$ transition form factors and show that our result describes the experimental data well.

hep-ph↗

arXiv1993

Low Energy Theorems of Hidden Local Symmetries

We prove to all orders of the loop expansion the low energy theorems of hidden local symmetries in four-dimensional nonlinear sigma models based on the coset space $G/H$, with $G$ and $H$ being arbitrary compact groups. Although the models are non-renormalizable, the proof is done in an analogous manner to the renormalization proof of gauge theories and two-dimensional nonlinear sigma models by restricting ourselves to the operators with two derivatives (counting a hidden gauge boson field as one derivative), i.e., with dimension 2, which are the only operators relevant to the low energy limit. Through loop-wise mathematical induction based on the Ward-Takahashi identity for the BRS symmetry, we solve renormalization equation for the effective action up to dimension-2 terms plus terms with the relevant BRS sources. We then show that all the quantum corrections to the dimension-2 operators, including the finite parts as well as the divergent ones, can be entirely absorbed into a re-definition (renormalization) of the parameters and the fields in the dimension-2 part of the tree-level Lagrangian.

hep-ph↗

arXiv1993

Proving the Low Energy Theorem of Hidden Local Symmetry

Based on the Ward-Takahashi identity for the BRS symmetry, we prove to all orders of the loop expansion the low energy theorem of hidden local symmetry for the vector mesons (KSRF (I) relation) in the $U(N)_{\rm L}$ $\times$ $U(N)_{\rm R}$ / $U(N)_{\rm V}$ nonlinear chiral Lagrangian.

hep-ph↗

arXiv1992

Hidden Local Symmetry at One Loop

We show that one-loop corrections with the hidden gauge boson loop preserve in the low energy limit all the successful tree level predictions of the hidden local symmetry in the SU(2)${}_L$$\times$SU(2)${}_R$$/$SU(2)${}_V$ chiral Lagrangian. Most amazingly, the $ρ$ meson dominance of the pion electromagnetic form factor survives the one-loop corrections at any momentum, if and only if we take the parameter choice $a=2$. For the choice $a=1$ (``vector limit"), $a$ is not renormalized ($Z_a=1$) and no deviation from $a=1$ is induced by the loop effects of the hidden gauge bosons. Actually, $a=1$ is a nontrivial ultraviolet fixed point.

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