Search results for "Mathematica"
showing 10 items of 7971 documents
BK from the lattice with Wilson quarks
2004
We report our results for the bag-parameter BK obtained from the quenched simulations on the lattice with Wilson fermions at three values of the lattice spacing. We implemented the method by which no subtraction of the mixing with other four-fermion dS=2 operators is needed. Our final result, in terms of the renormalisation group invariant bag-parameter, is BK = 0.96 +/- 0.10.
Nonperturbative renormalization and O(a) -improvement of the nonsinglet vector current with Nf=2+1 Wilson fermions and tree-level Symanzik improved g…
2019
In calculating hadronic contributions to precision observables for tests of the Standard Model in lattice QCD, the electromagnetic current plays a central role. Using a Wilson action with $\mathrm{O}(a)$ improvement in QCD with ${N}_{\mathrm{f}}$ flavors, a counterterm must be added to the vector current in order for its on-shell matrix elements to be $\mathrm{O}(a)$ improved. In addition, the local vector current, which has support on one lattice site, must be renormalized. At $\mathrm{O}(a)$, the breaking of the $\mathrm{SU}({N}_{\mathrm{f}})$ symmetry by the quark mass matrix leads to a mixing between the local currents of different quark flavors. We present a nonperturbative calculation…
Quark Contraction Tool -- QCT
2016
We present a Mathematica package for the calculation of Wick contractions in quantum field theories - QCT. Furthermore the package aims at automatically generating code for the calculation of physical matrix elements, suitable for numerical evaluation in a C++ program. To that end commonly used algebraic manipulations for the calculation of matrix elements in lattice QCD are implemented.
Probing the chiral weak Hamiltonian at finite volumes
2006
Non-leptonic kaon decays are often described through an effective chiral weak Hamiltonian, whose couplings ("low-energy constants") encode all non-perturbative QCD physics. It has recently been suggested that these low-energy constants could be determined at finite volumes by matching the non-perturbatively measured three-point correlation functions between the weak Hamiltonian and two left-handed flavour currents, to analytic predictions following from chiral perturbation theory. Here we complete the analytic side in two respects: by inspecting how small ("epsilon-regime") and intermediate or large ("p-regime") quark masses connect to each other, and by including in the discussion the two …
Abelian dominance and the dual Meissner effect in local unitary gauges in SU(2) gluodynamics
2007
Performing highly precise Monte-Carlo simulations of SU(2) gluodynamics, we observe for the first time Abelian dominance in the confining part of the static potential in local unitary gauges such as the F12 gauge. We also study the flux-tube profile between the quark and antiquark in these local unitary gauges and find a clear signal of the dual Meissner effect. The Abelian electric field is found to be squeezed into a flux tube by the monopole supercurrent. This feature is the same as that observed in the non-local maximally Abelian gauge. These results suggest that the Abelian confinement scenario is gauge independent. Observing the important role of space-like monopoles in the Polyakov g…
Color decomposition of multi-quark one-loop QCD amplitudes
2014
In this talk we discuss the color decomposition of tree-level and one-loop QCD amplitudes with arbitrary numbers of quarks and gluons. We present a method for the decomposition of partial amplitudes into primitive amplitudes, which is based on shuffle relations and is purely combinatorial. Closed formulae are derived, which do not require the inversion of a system of linear equations.
Scalar diagrammatic rules for Born amplitudes in QCD
2005
We show that all Born amplitudes in QCD can be calculated from scalar propagators and a set of three- and four-valent vertices. In particular, our approach includes amplitudes with any number of quark pairs. The quarks may be massless or massive. The proof of the formalism is given entirely within quantum field theory.
On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
2009
A closed formula is obtained for the infrared singularities of dimensionally regularized, massless gauge-theory scattering amplitudes with an arbitrary number of legs and loops. It follows from an all-order conjecture for the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory. We show that the form of this anomalous dimension is severely constrained by soft-collinear factorization, non-abelian exponentiation, and the behavior of amplitudes in collinear limits. Using a diagrammatic analysis, we demonstrate that these constraints imply that to three-loop order the anomalous dimension involves only two-parton correlations, with the possible exception of a single c…
Laurent series expansion of a class of massive scalar one-loop integrals toO(ε2)
2005
We use dimensional regularization to calculate the O({epsilon}{sup 2}) expansion of all scalar one-loop one-, two-, three-, and four-point integrals that are needed in the calculation of hadronic heavy quark production. The Laurent series up to O({epsilon}{sup 2}) is needed as input to that part of the next-to-next-to-leading order corrections to heavy flavor production at hadron colliders where the one-loop integrals appear in the loop-by-loop contributions. The four-point integrals are the most complicated. The O({epsilon}{sup 2}) expansion of the three- and four-point integrals contains in general polylogarithms up to Li{sub 4} and functions related to multiple polylogarithms of maximal …
Renormalization of the effective theory for heavy quarks at small velocity
1995
The slope of the Isgur-Wise function at the normalization point, $\xi^{(1)}(1)$,is one of the basic parameters for the extraction of the $CKM$ matrix element $V_{cb}$ from exclusive semileptonic decay data. A method for measuring this parameter on the lattice is the effective theory for heavy quarks at small velocity $v$. This theory is a variant of the heavy quark effective theory in which the motion of the quark is treated as a perturbation. In this work we study the lattice renormalization of the slow heavy quark effective theory. We show that the renormalization of $\xi^{(1)}(1)$ is not affected by ultraviolet power divergences, implying no need of difficult non-perturbative subtraction…