arXiv subjects

Atsushi Yamada

Publications and source records attributed to Atsushi Yamada.

27 records · Page 2Linked to original sources

arXiv1999

A comment on the index of the lattice Dirac operator and the Ginsparg-Wilson relation

We pursue Ginsparg and Wilsons' block spin approach in the derivation of the Ginsparg-Wilson relation and study the correspondence of the eigenmodes of the Dirac operators in the continuum and lattice theories. After introducing a suitable cut-off in the continuum theory, we identify unphysical modes of the lattice Dirac operator which do not correspond to any physical modes of the regulated continuum Dirac operator. We also consider zero modes in the continuum and lattice theories. Our studies give a physical interpretation of the expression of the index defined on a lattice and a formal argument on the relation of the indices between the continuum and lattice theories.

hep-lat↗

arXiv1998

A note on the exact lattice chiral symmetry in the overlap formalism

Using the grassman-number-integral representation of the vacuum overlap formula, it is shown that the symmetry of the auxiliary quantum fermion system in the overlap formalism induces exact chiral symmetry of the action of the type given by Luscher under the chiral transformation $δψ_n = γ_5(1-a D)ψ_n$ and $ δ\bar ψ_n = \bar ψ_n γ_5$. With this relation, we consider the connection between the covariant form of the anomaly discussed in the context of the overlap formula and the axial anomaly associated to the exact chiral symmetry in the action formalism. The covariant gauge current in the overlap formalism is translated to the action formalism and its explicit expression is obtained.

hep-lat↗

arXiv1998

Axial vector current of exact chiral symmetry on the lattice

We discuss the exact chiral symmetry and its spontaneous breakdown in lattice QCD with the Dirac operators satisfying the Ginsparg-Wilson relation. The axial vector current, which turns out to be related to the vector current simply by the insertion of the operator γ_5 (1-aD), is explicitly constructed in the case of the Neuberger-Dirac operator. We also consider an Euclidean proof of the Nambu-Goldstone theorem using the Ward-Takahashi identity of this symmetry.

hep-lat↗

arXiv1998

Lattice perturbation theory in the overlap formulation for the Yukawa and gauge interactions

Lattice perturbation theory is discussed in the overlap formulation for the Yukawa and gauge interactions. One and two point functions are studied for fermion, scalar and gauge fields, taking the Standard Model as an example. The formulae for the self-energies are given from which their divergent and finite parts can be computed at the one loop level.

hep-lat↗

arXiv1997

Weak coupling expansion of a chiral gauge theory on a lattice in the overlap formulation

Weak coupling expansion of a chiral gauge theory on a lattice is discussed in the overlap formulation. We analyze the fermion propagator and the fermion-fermion-gauge boson vertex in the one loop level. The chiral properties of the propagator and vertex are correctly preserved without tuning the parameters involved even after the one-loop renormalization, and the ultraviolet divergent parts agree with the continuum theory. Our analysis, together with the existing studies on the vacuum polarization and the gauge boson n-point functions, completes the proof of the renormalizability of this formulation to the one loop level.

hep-lat↗

arXiv1997

Renormalizability of a lattice chiral fermion in the overlap formulation

Renormalizability of a lattice chiral fermion is studied at one loop level in the overlap formulation in four dimensions. The fermion chirality is examined including the self-energy corrections due to gauge interactions. Divergent terms breaking the chiral symmetry do not appear and the chiral fermion is renormalized, preserving the correct chiral properties without adding new counter-terms or tuning the parameters involved. The divergent part of the wave function renormalization factor agrees with that of the continuum theory. The overlap formulation of a lattice chiral fermion has passed the important test, the renormalizability, at one loop level.

hep-lat↗

arXiv1995

A Decisive Test of Superstring-Inspired E(6) Models

We point out that in a large class of superstring--inspired $E(6)$ models, either an e+e- collider operating at a center--of--mass energy $\rs= 1.5$ TeV or higher must detect the pair production of charged or neutral exotic leptons, or an e+e- collider with $\rs \geq 300$ GeV must discover at least one light neutral Higgs boson with invisible branching ratio exceeding 50\%. If neither of these two signals is seen, the lightest neutral exotic lepton would overclose the universe, and the model could be completely excluded, independent of the values of the numerous free parameters. Future Higgs searches might lower the energy of the e+e- collider needed to test these models decisively. The only assumptions we have to make are that $R-$parity is exact, so that the lightest exotic lepton is stable if it is lighter than the lightest neutralino, and that no $SO(10)$ singlet scalar gets a vacuum expectation of order $10^{10}$ GeV or higher. If the second condition is violated, the model effectively reduces to an $SO(10)$ model as far as collider experiments are concerned.

hep-ph↗

arXiv1995

A new method of determining $|V_{ub}|$ by the processes $\bar{B} \to ρl \barν$ and $\bar{B} \to K^* l \lbar$

The differential decay width of the process $\bar{B} \rightarrow ρl \barν$ is related to that of the process $\bar{B} \rightarrow K^* l \lbar$ by using $SU(3)$-flavor symmetry and the heavy quark symmetry. The ratio of the Kobayashi-Maskawa matrix elements is obtained in the zero recoil limit of $ρ$ and $K^*$, allowing a determination of $|V_{ub}|$.

hep-ph↗

arXiv1993

Constraints on left-right symmetric models from the process $b \rightarrow s γ$

In left-right symmetric models, large contributions to the decay amplitude $b \rightarrow s+ γ$ can arise from the mixing of the $W_L$ and $W_R$ gauge bosons as well as from the charged Higgs boson. These amplitudes are enhanced by the factor $\mt/\mb$ compared to the contributions in the standard model. We use the recent CLEO results on the radiative $B$ decay to place constraints on the $W_L-W_R$ mixing angle $ζ$ and the mass of the charged Higgs boson $m_{H^\pm}$. Significant departures from the standard model predictions occur when $|ζ| > 0.003$ and/or when $m_{H^\pm} < $ a few TeV.

hep-ph↗