Sinya Aoki

Fermions in the hypercharge sector of the standard lattice electroweak theory. Global limit

Abstract We study the global limit of the hypercharge U(1) Y sector of the standard lattice electroweak theory. We show that for fermions with both Y R =0 and Y R ≠0 the doubler modes can be removed in the continuum limit while the physical fermion masses can be tuned to agree with physical values.

Properties of the hypercharge sector of the standard model on the lattice

Abstract Using a hopping parameter expansion, we demonstrate the decoupling of fermion doubler modes in the hypercharge U(1)Y lattice gauge theory. We also show analytically that it is possible to tune the bare Yukawa coupling to a value such that the fundamental physical fermion amf=0 (as is necessary in order to obtain a finite physical mass mf in the continuum limit), and we calculate this value. The appropriate special case of these results is compared with numerical simulations of the frozen-gauge limit of the U(1)Y theory, and good agreement is found. The role of the Yukawa coupling in a chiral lattice gauge theory is contrasted with that in a nonchiral Yukawa model.

Study of nonperturbative continuum limits in a lattice Yukawa model

Abstract Using analytic methods and dynamical fermion simulations, we study the properties of two nonperturbative continuum limits of a lattice Yukawa model with a real scalar field, at the (a) ferromagnetic-ferrimagnetic and (b) ferrimagnetic-antiferromagnetic phase boundaries. This work makes use of a new analytic result that the fermion mass vanishes identically in the antiferromagnetic phase.

More on parity and Wilson fermions. Quenched simulations in finite temperature QCD

Abstract We study the properties of Wilson fermions under space reflection (parity) in quenched, finite temperature lattice QCD. The spontaneous breaking of parity at the critical hopping parameter observed at zero temperature is shown to be absent at high temperatures. The splitting of hadrons differing only in their parity assignment is much reduced over the zero temperature case but a finite gap remains. We interpret this as the effect of chiral symmetry breaking terms that remain a finite gauge coupling but vanish with the lattice spacing.

Studies of a U(1) × U(1) Yukawa model with staggered fermions☆

Abstract A U(1)×U(1) Yukawa model with staggered fermions is investigated in the broken phase. Spontaneous symmetry breaking on finite lattices is studied in two ways. In the first approach, which is similar to what is done in lattice QCD studies, we work with nonzero bare-fermion masses and try to extrapolate to the massless limit. In the second method, which to date has been the more common approach in Higgs-Yukawa models, we simulate directly the zero-bare-fermion-mass theory and carry out a global rotation on the fields before taking measurements. In the m f ≠0 calculations Ward identities are monitored to asses the quality of the simulations and both fermion-antifermion and purely bosonic operators are used in Goldstone boson correlation-functions. We point out differences between the fermion-antifermion channel in the current model and analogous calculations of the pion correlation-function in lattice QCD. We show that noisy estimates of the fundamental fermion propagator can also be used very effectively for meson correlations, where the fermion and antifermion annihilate into pure bosonic matter (the so called annihilation channel). Estimates for renormalized Yukawa and λφ 4 couplings obtained via the two methods, m f = 0 and m f ≠ 0, are also presented. Renormalized Yukawa-couplings are never much larger than the value obtained from the tree-level j = 0 partial wave unitarity bound for fermion-antifermion elastic scattering in a continuum theory with the appropriate number of flavors.

Strong CP violation and the neutron electric dipole moment revisited

The relation between the CP violating operator {theta}F{tilde F} and its effective version L{sub CP}{sup eff} is reconsidered on the basis of the anomalous Ward-Takahashi (WT) identity. The consistency of the previous phenomenological calculations of the neutron electric dipole moment (NEDM) with the WT identity is critically examined. A consistent evaluation of an O(N{sub c}{sup o}) contribution to NEDM is given and the result is compared with the leading term in the chiral expansion which is O(N{sub c}{sup {minus}1}).

Fermion propagator in lattice chiral gauge theories: Analytic results

Abstract Using a hopping parameter expansion, we demonstrate the decoupling of fermion doubler modes in lattice chiral gauge theories, where both the right-handed and left-handed fermions may be non-singlets. The decoupling of the doublers for the case of a single right-handed fermion was previously first shown by Aoki, Lee, and Xue. We also show analytically that it is possible to tune the bare Yukawa coupling to a value such that the fundamental physical fermion mass is zero in lattice units.

Charged fermion correlation functions in a lattice scalar-fermion model with global chiral U(1) symmetry

Abstract We construct a charged vectorial field in the global limit of a U(1) chiral lattice gauge theory and, using the hopping parameter expansion, calculate its propagator. We show that the doubler modes are removed and that it is possible to tune a bare Yukawa-like coupling to obtain a finite mass for this field in the continuum limit. Related results are given for the propagators of chiral fermions.

Sanity check for NN bound states in lattice QCD with Lüscher’s finite volume formula – Disclosing Symptoms of Fake Plateaux –

The sanity check is to rule out certain classes of obviously false results, not to catch every possible error. After reviewing such a sanity check for NN bound states with the Luscher’s finite volume formula [1–3], we give further evidences for the operator dependence of plateaux, a symptom of the fake plateau problem, against the claim [4]. We then present our critical comments on [5] by NPLQCD: (i) Operator dependences of plateaux in NPL2013 [6, 7] exist with the P value of 4–5%. (ii) The volume independence of plateaux in NPL2013 does not prove their correctness. (iii) Effective range expansions (EREs) in NPL2013 violate the physical pole condition. (iv) Their comment is partly based on new data and analysis different from the original ones. (v) Their new ERE does not satisfy the Luscher’s finite volume formula.

Phase shifts in

We compare two approaches used for computing scattering phase shifts and other low-energy observables in lattice QCD: the finite size method invented by Luscher as well as the recently introduced HAL QCD method which is based on the extraction of multi body potentials from Nambu-Bethe-Salpeter wave functions. We perform quenched QCD simulations featuring lattices with spatial extents of 1.8fm to 5.5fm, a lattice spacing of 0.115fm and a pion mass of 940MeV. We compute phase shifts and scattering length of ππ scattering in the I=2 channel for either method and compare the results.