Related papers: One Spin Trace Formalism for $ B_K $
We present a general formalism for simplifying manipulations of spin indices of massless and massive spinors and vectors in Feynman diagrams. The formalism is based on covariantly reducing the number of field components in the action in…
A chiral-order parameter of spins in a crystal can not be inferred from measurements of Bragg reflections, although there are several claims in published literature to the contrary. Appropriate techniques use total scattering, of x-rays or…
Minimally doubled fermions realize one degenerate pair of Dirac fermions on the lattice. Similarities to staggered fermions exist, namely, spin and taste degrees of freedom become intertwined, and a remnant, non-singlet chiral symmetry and…
One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive,…
Recently, Grabowska and Kaplan constructed a four-dimensional lattice formulation of chiral gauge theories on the basis of the chiral overlap operator. At least in the tree-level approximation, the left-handed fermion is coupled only to the…
We study the correlation between the fermion composite system and quark spins by using the light-cone quark-diquark model. We do the calculations for $u$-quark and $d$-quark in the fermion system by considering the different polarization…
We perform the sewing of two (dual) Ramond reggeon vertices and derive an algorithm by means of which the so obtained four-Ramond reggeon vertex may be explicitly computed at arbitrary oscillator (mass) level. A closed form of the…
Lattice fermion actions are constructed with path integrals which are equivalent to the free one-flavour staggered fermion determinant. The Dirac operators used are local and have an identical spectrum of states to the staggered theory.…
We report on recent progress in the calculation of $B_K$ using HYP-smeared improved staggered fermions on the MILC asqtad lattices. We have added measurements on fine ($a\sim 0.09 $fm) and superfine ($a\sim 0.06 $fm) ensembles at different…
We derive a formalism to express the spin algebra $\mathfrak{su}(2)$ in a spin $s$ representation in terms of the algebra of $L$ fermionic operators that obey the Canonical Anti-commutation Relations. We also give the reverse direction of…
Tensor reduction is important for multi-loop amplitude calculation. And the projection method is one of the most popular approaches for tensor reduction. However, projection method could be problematic for amplitude with massive fermions…
Staggered fermions with smeared links can have greatly improved chiral properties. In a recent paper we introduced a simple and effective method to simulate four flavors of staggered smeared link fermions. In this work we extend the four…
We analyse four approaches to elimination of a fast variable, which are applicable to systems like passive Brownian particles: (i) moment formalism, (ii) corresponding cumulant formalism, (iii) Hermite function basis, (iv) formal…
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including…
Quark line disconnected matrix elements of an operator, such as the axial current, are difficult to compute on the lattice. The standard method uses a stochastic estimator of the operator, which is generally very noisy. We discuss and…
We provide new, mild conditions for strict stationarity and ergodicity of a class of BEKK processes. By exploiting that the processes can be represented as multivariate stochastic recurrence equations, we characterize the tail behavior of…
After a brief look at the well-known standard approaches to determine the angle gamma of the unitarity triangle, we focus on two kinds of strategies, employing $B\to\pi K$ modes, and U-spin-related B decays. Interesting "puzzles", which may…
We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As part of this formalism we define a modified variation operator which absorbs frame and spin dyad gauge…
We present preliminary results of weak matrix elements relevant to CP violation calculated using the HYP (II) staggered fermions. Since the complete set of matching coefficients at the one-loop level became available recently, we have…
Lattice matrix elements are briefly reviewed. In the quenched approximation $f_B$, $B_B$ and $B_K$ are now under good control. Experimental hints for $f^{\rm expt}_{D_S}> f^{\rm QQCD}_{D_S}$ are noted; precise determination of $f_{D_S}$…