Search results for " Regular"
showing 10 items of 197 documents
A practicableγ 5-scheme in dimensional regularization
1992
We present a new simpleγ5 regularization scheme. We discuss its use in the standard radiative correction calculations including the anomaly contributions. The new scheme features an anticommutingγ5 which leads to great simplifications in practical calculations. We carefully discuss the underlying mathematics of ourγ5-scheme which is formulated in terms of simple projection operations.
Regularized Euler-alpha motion of an infinite array of vortex sheets
2016
We consider the Euler- $$\alpha $$ regularization of the Birkhoff–Rott equation and compare its solutions with the dynamics of the non regularized vortex-sheet. For a flow induced by an infinite array of planar vortex-sheets we analyze the complex singularities of the solutions.Through the singularity tracking method we show that the regularized solution has several complex singularities that approach the real axis. We relate their presence to the formation of two high-curvature points in the vortex sheet during the roll-up phenomenon.
The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
2018
We compute systematically for the planar double box Feynman integral relevant to top pair production with a closed top loop the Laurent expansion in the dimensional regularisation parameter $\varepsilon$. This is done by transforming the system of differential equations for this integral and all its sub-topologies to a form linear in $\varepsilon$, where the $\varepsilon^0$-part is strictly lower triangular. This system is easily solved order by order in the dimensional regularisation parameter $\varepsilon$. This is an example of an elliptic multi-scale integral involving several elliptic sub-topologies. Our methods are applicable to similar problems.
Analytic result for a two-loop five-particle amplitude
2019
We compute the symbol of the full-color two-loop five-particle amplitude in $\mathcal{N}=4$ super Yang-Mills, including all non-planar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function. We study the multi-Regge limit of the non-planar terms, analyze its subleading power corrections, and present analytically the leading logarithmic terms.
Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
2018
Integration-by-parts identities between loop integrals arise from the vanishing integration of total derivatives in dimensional regularization. Generic choices of total derivatives in the Baikov or parametric representations lead to identities which involve dimension shifts. These dimension shifts can be avoided by imposing a certain constraint on the total derivatives. The solutions of this constraint turn out to be a specific type of syzygies which correspond to logarithmic vector fields along the Gram determinant formed of the independent external and loop momenta. We present an explicit generating set of solutions in Baikov representation, valid for any number of loops and external mome…
Running gravitational couplings, decoupling, and curved spacetime renormalization
2020
We propose to slightly generalize the DeWitt-Schwinger adiabatic renormalization subtractions in curved space to include an arbitrary renormalization mass scale $\mu$. The new predicted running for the gravitational couplings are fully consistent with decoupling of heavy massive fields. This is a somewhat improvement with respect to the more standard treatment of minimal (DeWitt-Schwinger) subtractions via dimensional regularization. We also show how the vacuum metamorphosis model emerges from the running couplings.
All Master Integrals for Three-Jet Production at Next-to-Next-to-Leading Order
2019
We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integrals with constant leading singularities, in D space-time dimensions. These integrals evaluate to Q-linear combinations of multiple polylogarithms of uniform weight at each order in the expansion in the dimensional regularization parameter and are in agreement with previous conjectures for nonplanar pentagon functions. Our results provide the complete set of two-loop Feynman integrals for any massless 2→3 scattering process, thereby opening up a ne…
Deconvolution of the spectral line profiles for the plasma temperature estimation
2010
Abstract The Hg 253.7 nm spectral line profiles, emitted from the mercury–argon high-frequency electrodeless discharge lamps (HFEDL) have been measured by means of a high-resolution scanning Fabry–Perrot interferometer at the mercury cold spot temperature value at 20 °C, different discharge current and buffer gas values. The deconvolution procedure by means of the Tikhonov's regularization method was performed to obtain the real spectral line shape. The influence of the instrumental function and absorption, real width of the Hg 253.7 nm resonance line and temperature of the radiating atoms are obtained. The results were compared with the results of the nonlinear multiparameter mathematical …
Renormalization of the 1S0 One-Pion-Exchange NN Interaction in Presence of Derivative Contact Interactions
2003
We use standard distorted wave theory techniques and dimensional regularization to find out solutions of the nucleon-nucleon Lippman--Schwinger equation with a kernel determined by the Weinberg's next-to-leading potential, which consists of one--pion exchange and additional contact terms with derivatives. Though for simplicity, we restrict the discussion to the $^1S_0$ channel and to contact terms containing up to two derivatives, the generalization to higher waves and/or number of derivatives is straightforward. The undetermined low energy constants emerging out of the renormalization procedure are fitted to data.
S-waveKK*interactions in a finite volume and thef1(1285)
2015
Lattice QCD simulations provide a promising way to disentangle different interpretations of hadronic resonances, which might be of particular relevance to understand the nature of the so-called XY Z particles. Recent studies have shown that in addition to the well-established naive quark model picture, the axial-vector meson f1(1285) can also be understood as a dynamically generated state built upon the KK ∗ interaction. In this work, we calculate the energy levels of the KK ∗ system in the f1(1285) channel in finite volume using the chiral unitary approach. We propose to calculate the loop function in the dimensional regularization scheme, which is equivalent to the hybrid approach adopted…