Search results for "Regular"
showing 10 items of 855 documents
Non-Perturbative Renormalization of Lattice Four-Fermion Operators without Power Subtractions
1999
A general non-perturbative analysis of the renormalization properties of $\Delta I=3/2$ four-fermion operators in the framework of lattice regularization with Wilson fermions is presented. We discuss the non-perturbative determination of the operator renormalization constants in the lattice Regularization Independent (RI or MOM) scheme. We also discuss the determination of the finite lattice subtraction coefficients from Ward Identities. We prove that, at large external virtualities, the determination of the lattice mixing coefficients, obtained using the RI renormalization scheme, is equivalent to that based on Ward Identities, in the continuum and chiral limits. As a feasibility study of …
N3LOHiggs boson and Drell-Yan production at threshold: The one-loop two-emission contribution
2014
In this paper, we study phenomenologically interesting soft radiation distributions in massless QCD. Specifically, we consider the emission of two soft partons off of a pair of lightlike Wilson lines, in either the fundamental or the adjoint representation, at next-to-leading order. Our results are an essential component of the next-to-next-to-next-to-leading order threshold corrections to both Higgs boson production in the gluon fusion channel and Drell-Yan lepton production. Our calculations are consistent with the recently published results for Higgs boson production. As a nontrivial cross-check on our analysis, we rederive a recent prediction for the Drell-Yan threshold cross section us…
Use of helicity methods in evaluating loop integrals: A QCD example
1991
We discuss the use of helicity methods in evaluating loop diagrams by analyzing a specific example: the one-loop contribution to e+e- → qqg in massless QCD. By using covariant helicity representations for the spinor and vector wave functions we obtain the helicity amplitudes directly from the Feynman loop diagrams by covariant contraction. The necessary loop integrations are considerably simplified since one encounters only scalar loop integrals after contraction. We discuss crossing relations that allow one to obtain the corresponding one-loop helicity amplitudes for the crossed processes as e.g. qq → (W, Z, γ∗) + g including the real photon cases. As we treat the spin degrees of freedom i…
Heavy quark pair production in gluon fusion at next-to-next-to-leadingO(αs4)order: One-loop squared contributions
2008
We calculate the next-to-next-to-leading-order $\mathcal{O}({\ensuremath{\alpha}}_{s}^{4})$ one-loop squared corrections to the production of heavy-quark pairs in the gluon-gluon fusion process. Together with the previously derived results on the $q\overline{q}$ production channel, the results of this paper complete the calculation of the one-loop squared contributions of the next-to-next-to-leading-order $\mathcal{O}({\ensuremath{\alpha}}_{s}^{4})$ radiative QCD corrections to the hadroproduction of heavy flavors. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in dimensional regularization.
One-loop amplitudes for four-point functions with two external massive quarks and two external massless partons up toO(ε2)
2006
We present complete analytical O({epsilon}{sup 2}) results on the one-loop amplitudes relevant for the next-to-next-to-leading order (NNLO) quark-parton model description of the hadroproduction of heavy quarks as given by the so-called loop-by-loop contributions. All results of the perturbative calculation are given in the dimensional regularization scheme. These one-loop amplitudes can also be used as input in the determination of the corresponding NNLO cross sections for heavy flavor photoproduction, and in photon-photon reactions.
ON FRACTIONAL RELAXATION
2002
Generalized fractional relaxation equations based on generalized Riemann-Liouville derivatives are combined with a simple short time regularization and solved exactly. The solution involves generalized Mittag-Leer functions. The associated frequency dependent susceptibilities are related to symmetrically broadened ColeCole susceptibilities occurring as Johari Goldstein -relaxation in many glass formers. The generalized susceptibilities exhibit a high frequency wing and strong minimum enhancement.
On the regularity of critical and minimal sets of a free interface problem
2015
We study a free interface problem of finding the optimal energy configuration for mixtures of two conducting materials with an additional perimeter penalization of the interface. We employ the regularity theory of linear elliptic equations to study the possible opening angles of Taylor cones and to give a different proof of a partial regularity result by Fan Hua Lin [Calc Var. Partial Differential Equations, 1993].
A 3D Meshless Approach for Transient Electromagnetic PDEs
2012
A full wave three dimensional meshless approach for electromagnetic transient simulations is presented. The smoothed particle hydrodynamic (SPH) method is used by considering the particles as interpolation points, arbitrarily placed in the computational domain. Maxwell’s equations in time domain with the assigned boundary and initial conditions are numerically solved by means of the proposed method. The computational tool is assessed and, for the first time, a 3D test problem is simulated in order to validate the proposed approach.
Dimensional Regularization. Ultraviolet and Infrared Divergences
2015
The cornerstone of Quantum Field Theory is renormalization. We shall speak more about in the next chapters. Before, it is necessary to discuss the method. The best and most simple is, of course, dimensional regularization (doesn’t break the symmetries, doesn’t violate the Ward Identities, preserves Lorentz invariance, etc.). When explained consistently, it becomes very simple and clear. Here, we shortly discuss ultraviolet (UV) and infrared (IR) divergences with a few examples. However, in Chap. 8, we shall extensively treat one-loop two and three-point functions and analyse many more examples of IR and UV divergences.
Note on the pragmatic mode-sum regularization method: Translational-splitting in a cosmological background
2021
The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that when the background metric possesses an isometry, like stationary or spherically symmetric black holes, the method can be upgraded into a pragmatic procedure of renormalization that produces efficient numerical calculations. In this note we show that when the background enjoys three-dimensional spatial symmetries, like homogeneous expanding universes, the above pragmatic regularization technique reduces to the well established adiabatic regularization metho…