The analytic properties of the vertex functions for massless scalar and massless and massive spinor electrodynamics are investigated. First, a general tensor form for the vertex consistent with the Ward identities and free of kinematic singularities is constructed. All of the scalar functions that appear are then calculated to one-loop order in perturbation theory. It is found that in both massive and massless theories the infrared singularities appear in the longitudinal parts of the vertex. The massless theories have additional photon mass-shell singularities which appear in the transverse terms. Complete expressions for each vertex are obtained which contain only one nonelementary function.

The analytic properties of the three-gluon vertex function for quantum chromodynamics in covariant gauges are investigated. First, a general tensor form for the vertex consistent with the Ward identity and free of kinematic singularities is constructed. The vertex is then calculated to one-loop order in the Feynman gauge. The complete expression for the off-shell one-loop vertex is expressed in terms of elementary functions plus one nonelementary function, the dilogarithm. Various kinematic limits of the vertex are considered. The most interesting results are the following. (1) Gluon mass-shell singularities occur in the transverse terms as well as the longitudinal terms. (2) The leading IR singularity is in the longitudinal part of the vertex, as is the case for QED; however, it is a pole singularity rather than the usual logarithmic singularity.

We calculate pion vector and scalar form factors in two-flavor lattice QCD and study the chiral behavior of the vector and scalar radii $⟨r^2{⟩}_{V,S}$. Numerical simulations are carried out on a ${16}^3\times 32$ lattice at a lattice spacing of 0.12 fm with quark masses down to $\sim m_s/6$, where $m_s$ is the physical strange quark mass. Chiral symmetry, which is essential for a direct comparison with chiral perturbation theory (ChPT), is exactly preserved in our calculation at finite lattice spacing by employing the overlap quark action. We utilize the so-called all-to-all quark propagator in order to calculate the scalar form factor including the contributions of disconnected diagrams and to improve statistical accuracy of the form factors. A detailed comparison with ChPT reveals that the next-to-next-to-leading-order contributions to the radii are essential to describe their chiral behavior in the region of quark mass from $m_s/6$ to $m_s/2$. Chiral extrapolation based on two-loop ChPT yields $⟨r^2{⟩}_V=0.409(23)(37){\mathrm{fm}}^2$ and $⟨r^2{⟩}_S=0.617(79)(66){\mathrm{fm}}^2$, which are consistent with phenomenological analysis. We also present our estimates of relevant low-energy constants.

KAGRA is a second-generation interferometric gravitational-wave detector with 3 km arms constructed at Kamioka, Gifu, Japan. It is now in its final installation phase, which we call bKAGRA (baseline KAGRA), with scientific observations expected to begin in late 2019. One of the advantages of KAGRA is its underground location of at least 200 m below the ground surface, which reduces seismic motion at low frequencies and increases the stability of the detector. Another advantage is that it cools down the sapphire test mass mirrors to cryogenic temperatures to reduce thermal noise. In April–May 2018, we operated a 3 km Michelson interferometer with a cryogenic test mass for 10 d, which was the first time that km-scale interferometer was operated at cryogenic temperatures. In this article, we report the results of this ‘bKAGRA Phase 1’ operation. We have demonstrated the feasibility of 3 km interferometer alignment and control with cryogenic mirrors.