Search results for "Dimensional regularization"
showing 10 items of 36 documents
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.
Complete amplitude and cross section structure of one-loop contributions toe + e ??q $$\bar q$$ g
1985
We calculate theO(α 2 ) one-loop contributions to the seven (inn≠4) independent invariant amplitudes describinge + e −→q $$\bar q$$ g in massless QCD. After folding with theO(α 1/2 ) Born term contribution we obtain the nine independentO(α 2 ) structure functions that describe the parity-conserving and parity-violating contributions toe + e −→q $$\bar q$$ g. We use dimensional regularization to control infrared and ultraviolet divergencies.
Next-to-next-to-leading orderO(α2αs2)results for top quark pair production in photon-photon collisions: The one-loop squared contributions
2006
We calculate the one-loop squared contributions to the next-to-next-to-leading order ${\cal O}(\alpha^2\alpha_s^2)$ radiative QCD corrections for the production of heavy quark pairs in the collisions of unpolarized on--shell photons. In particular, we present analytical results for the squared matrix elements that correspond to the product of the one--loop amplitudes. All results of the perturbative calculation are given in the dimensional regularization scheme. These results represent the Abelian part of the corresponding gluon--induced next-to-next-to-leading order cross section for heavy quark pair hadroproduction.
Dimensionally regularized box and phase-space integrals involving gluons and massive quarks
1999
The basic box and phase space integrals needed to compute at second order the three-jet decay rate of the Z-boson into massive quarks are presented in this paper. Dimensional Regularization is used to regularize the infrared divergences that appear in intermediate steps. Finally, the cancellation of these divergences among the virtual and the real contributions is showed explicitly.