Abstract
We investigate the dispersion relation of Möbius domain-wall fermions in free field theory at finite Ls. We find that there are Ls - 1 extra poles of Möbius domain-wall fermions in addition to the pole which realizes the physical mode in the continuum limit. The unphysical contribution of these extra poles could be significant when we introduce heavy quarks. We show in this report the fundamental properties of these unphysical poles and discuss the optimal choice of Möbius parameters to minimize their contribution to four-dimensional physics.
Highlights
Lattice calculation including the charm quark as well as the lighter quarks is desired to give accurate prediction of the Standard Model, which could play a key role in probing for new physics beyond the Standard Model
That work explained that the hermitian operator involves unphysical modes as well as the physical modes and that the eigenvalues of unphysical modes are largely independent of the input quark mass, while those of physical modes are roughly proportional to the input mass
Since the number of these oscillations is proportional to Ls, the number of unphysical poles increases as Ls increases and we find Ls − 1 unphysical poles in our analysis
Summary
Lattice calculation including the charm quark as well as the lighter quarks is desired to give accurate prediction of the Standard Model, which could play a key role in probing for new physics beyond the Standard Model. Domain-wall fermions with large input masses are known to have some special difficulties as well as the naïve O(a) discretization errors Such difficulties were originally suggested [1, 2] by analyzing the eigenvalues of the hermitian version of the domain-wall operator, the five-dimensional Dirac operator multiplied by the chirality operator γ5 and the five-dimensional reflection operator. A few years later, [3] observed the oscillatory behavior of correlation functions, which is known as a particular issue of domain-wall fermions and is observed at large values of the domain-wall height such as M5 = 1.7 This oscillatory behavior was described as the result of negative eigenvalues of the transfer matrix [4], which were found to exist at large values of M5, M5 > 1 in the case of free field theory.
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