Search results for " Regular"
showing 10 items of 197 documents
Can power corrections be reliably computed in models with extra dimensions?
2003
We critically revisit the issue of power-law running in models with extra dimensions. The analysis is carried out in the context of a higher-dimensional extension of QED, with the extra dimensions compactified on a torus. It is shown that a naive $\beta$ function, which simply counts the number of modes, depends crucially on the way the thresholds of the Kaluza-Klein modes are crossed. To solve these ambiguities we turn to the vacuum polarization, which, due to its special unitarity properties, guarantees the physical decoupling of the heavy modes. This latter quantity, calculated in the context of dimensional regularization, is used for connecting the low energy gauge coupling with the cou…
Pinch technique at two loops: The case of massless Yang-Mills theories
2000
The generalization of the pinch technique beyond one loop is presented. It is shown that the crucial physical principles of gauge-invariance, unitarity, and gauge-fixing-parameter independence single out at two loops exactly the same algorithm which has been used to define the pinch technique at one loop, without any additional assumptions. The two-loop construction of the pinch technique gluon self-energy, and quark-gluon vertex are carried out in detail for the case of mass-less Yang-Mills theories, such as perturbative QCD. We present two different but complementary derivations. First we carry out the construction by directly rearranging two-loop diagrams. The analysis reveals that, quit…
EXTRACTION OF INFRARED DIVERGENCES IN THE DIMENSIONAL REGULARIZED TWO-LOOP LADDER GRAPH
1994
We consider the evaluation of the fundamental scalar integral in the on-shell two-loop ladder graph with different external masses and arbitrary transfer momentum. A method for cleanly extracting the infrared divergences in the Feynman parameter integrals using dimensional regularization is presented, and we analyze one of the finite part contributions to this integral.
Calculation of theO(? s 2 ) parity-violating structure functions in $$e^ + e^ - \to q\bar qg$$
1986
We calculate the two nonvanishingO(αs2) parity-violating structure functions that contribute to\(e^ + e^ - \xrightarrow{{\gamma ,Z}}q\bar qg\). We discuss how these can be measured. We work with massless quarks and gluons and use dimensional regularization to regularize ultra-violet and infrared singularities. We carefully discuss how to deal withγ5 in the dimensional regularization scheme when infrared singularities are present.
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.
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.
Data analysis procedures for pulse ELDOR measurements of broad distance distributions
2004
The reliability of procedures for extracting the distance distribution between spins from the dipolar evolution function is studied with particular emphasis on broad distributions. A new numerically stable procedure for fitting distance distributions with polynomial interpolation between sampling points is introduced and compared to Tikhonov regularization in the dipolar frequency and distance domains and to approximate Pake transformation. Distance distributions with only narrow peaks are most reliably extracted by distance-domain Tikhonov regularization, while frequency-domain Tikhonov regularization is favorable for distributions with only broad peaks. For the quantification of distribut…