Search results for "Loop integral"
showing 6 items of 16 documents
Discussion on triangle singularities in the Λb→J/ψK−p reaction
2016
We have analyzed the singularities of a triangle loop integral in detail and derived a formula for an easy evaluation of the triangle singularity on the physical boundary. It is applied to the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{\ensuremath{-}}p$ process via ${\mathrm{\ensuremath{\Lambda}}}^{*}$-charmonium-proton intermediate states. Although the evaluation of absolute rates is not possible, we identify the ${\ensuremath{\chi}}_{c1}$ and the $\ensuremath{\psi}(2S)$ as the relatively most relevant states among all possible charmonia up to the $\ensuremath{\psi}(2S)$. The $\mathrm{\ensuremath{\Lambda}}(1890){\ensuremath{\chi}}_{c1}p$ loop is ver…
Feynman graph polynomials
2010
The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.
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…
Foundations of the Quantum Chromodynamics
2015
Quantum chromodynamics (QCD) is a theory to describe the strong interaction in hadrons. It was developed in the history of understanding the structure of the hadrons. In the 1950s, a large number of hadrons were discovered in experiments.
The real–virtual antenna functions forS→QQ¯Xat NNLO QCD
2014
Abstract We determine, in the antenna subtraction framework for handling infrared divergences in higher order QCD calculations, the real–virtual antenna functions for processes involving the production of a pair of massive quarks by an uncolored initial state at NNLO QCD. The integrated leading and subleading color real–virtual antenna functions are computed analytically in terms of (cyclotomic) harmonic polylogarithms. As a by-product and check we compute R Q = σ ( e + e − → γ ⁎ → Q Q ¯ X ) / σ ( e + e − → γ ⁎ → μ + μ − ) and compare with existing results. Our result for R Q is exact to order α s 2 .
One-loop corrections to light cone wave functions: the dipole picture DIS cross section
2018
We develop methods needed to perform loop calculations in light cone perturbation theory using a helicity basis, refining the method introduced in our earlier work. In particular this includes implementing a consistent way to contract the four-dimensional tensor structures from the helicity vectors with d-dimensional tensors arising from loop integrals, in a way that can be fully automatized. We demonstrate this explicitly by calculating the one-loop correction to the virtual photon to quark-antiquark dipole light cone wave function. This allows us to calculate the deep inelastic scattering cross section in the dipole formalism to next-to-leading order accuracy. Our results, obtained using …