Neutron electric dipole moment with external electric field method in lattice QCD

We discuss a possibility that the Neutron Electric Dipole Moment (NEDM) can be calculated in lattice QCD simulations in the presence of the CP violating $\theta$ term. In this paper we measure the energy difference between spin-up and spin-down states of the neutron in the presence of an uniform and static external electric field. We first test this method in quenched QCD with the RG improved gauge action on a $16^3\times 32$ lattice at $a^{-1}\simeq$ 2 GeV, employing two different lattice fermion formulations, the domain-wall fermion and the clover fermion for quarks, at relatively heavy quark mass $(m_{PS}/m_V \simeq 0.85)$. We obtain non-zero values of NEDM from calculations with both fermion formulations. We next consider some systematic uncertainties of our method for NEDM, using $24^3\times 32$ lattice at the same lattice spacing only with the clover fermion. We finally investigate the quark mass dependence of NEDM and observe a non-vanishing behavior of NEDM toward the chiral limit. We interpret this behavior as a manifestation of the pathology in the quenched approximation.Comment: LaTeX2e, 51 pages, 43 figures, uses revtex4 and graphicx, References and comments added, typos corrected, accepted by PR

Electromagnetic and spin polarisabilities in lattice QCD

We discuss the extraction of the electromagnetic and spin polarisabilities of nucleons from lattice QCD. We show that the external field method can be used to measure all the electromagnetic and spin polarisabilities including those of charged particles. We then turn to the extrapolations required to connect such calculations to experiment in the context of finite volume chiral perturbation theory. We derive results relevant for lattice simulations of QCD, partially-quenched QCD and quenched QCD. Our results for the polarisabilities show a strong dependence on the lattice volume and quark masses, typically differing from the infinite volume limit by ~10% for current lattice volumes and quark masses.Comment: Minor change

Metaplectic Ice

Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika formula this fact is related to Tokuyama's deformation of the Weyl character formula. It is shown that various properties of these Whittaker functions may be expressed in terms of the commutativity of row transfer matrices for the system. Potentially these properties (which are already proved by other methods, but very nontrivial) are amenable to proof by the Yang-Baxter equation

A lecture on the Liouville vertex operators

We reconsider the construction of exponential fields in the quantized Liouville theory. It is based on a free-field construction of a continuous family or chiral vertex operators. We derive the fusion and braid relations of the chiral vertex operators. This allows us to simplify the verification of locality and crossing symmetry of the exponential fields considerably. The calculation of the matrix elements of the exponential fields leads to a constructive derivation of the formula proposed by Dorn/Otto and the brothers Zamolodchikov.Comment: Contribution to the proceedings of the 6th International Conference on CFTs and Integrable Models, Chernogolovka, Russia, 2002 v2: Remarks added, typos correcte

Neutron electric dipole moment from lattice QCD

We carry out a feasibility study for the lattice QCD calculation of the neutron electric dipole moment (NEDM) in the presence of the $\theta$ term. We develop the strategy to obtain the nucleon EDM from the CP-odd electromagnetic form factor $F_3$ at small $\theta$, in which NEDM is given by $\lim_{q^2\to 0}\theta F_3(q^2)/(2m_N)$ where $q$ is the momentum transfer and $m_N$ is the nucleon mass. We first derive a formula which relates $F_3$, a matrix element of the electromagnetic current between nucleon states, with vacuum expectation values of nucleons and/or the current. In the expansion of $\theta$, the parity-odd part of the nucleon-current-nucleon three-point function contains contributions not only from the parity-odd form factors but also from the parity-even form factors multiplied by the parity-odd part of the nucleon two-point function, and therefore the latter contribution must be subtracted to extract $F_3$. We then perform an explicit lattice calculation employing the domain-wall quark action with the RG improved gauge action in quenched QCD at $a^{-1}\simeq 2$ GeV on a $16^3\times 32\times 16$ lattice. At the quark mass $m_f a =0.03$, corresponding to $m_\pi/m_\rho \simeq 0.63$, we accumulate 730 configurations, which allow us to extract the parity-odd part in both two- and three-point functions. Employing two different Dirac $\gamma$ matrix projections, we show that a consistent value for $F_3$ cannot be obtained without the subtraction described above. We obtain $F_3(q^2\simeq 0.58 \textrm{GeV}^2)/(2m_N) =$ $-$0.024(5) $e\cdot$fm for the neutron and $F_3(q^2\simeq 0.58 \textrm{GeV}^2)/(2m_N) =$ 0.021(6) $e\cdot$fm for the proton.Comment: LaTeX2e, 43 pages, 42 eps figures, uses revtex4 and graphicx, comments added and typos corrected, final version to appear in Phys. Rev.

Initial nucleon structure results with chiral quarks at the physical point

We report initial nucleon structure results computed on lattices with 2+1 dynamical M\"obius domain wall fermions at the physical point generated by the RBC and UKQCD collaborations. At this stage, we evaluate only connected quark contributions. In particular, we discuss the nucleon vector and axial-vector form factors, nucleon axial charge and the isovector quark momentum fraction. From currently available statistics, we estimate the stochastic accuracy of the determination of $g_A$ and $_{u-d}$ to be around 10%, and we expect to reduce that to 5% within the next year. To reduce the computational cost of our calculations, we extensively use acceleration techniques such as low-eigenmode deflation and all-mode-averaging (AMA). We present a method for choosing optimal AMA parameters.Comment: 7 pages, 11 figures; talk presented at the 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Columbia University, New York, US