Search results for "amplitud"
showing 10 items of 1171 documents
Testing Rate Dependent corrections on timing mode EPIC-pn spectra of the accreting Neutron Star GX 13+1
2014
When the EPIC-pn instrument on board XMM-Newton is operated in Timing mode, high count rates (>100 cts/s) of bright sources may affect the calibration of the energy scale, resulting in a modification of the real spectral shape. The corrections related to this effect are then strongly important in the study of the spectral properties. Tests of these calibrations are more suitable in sources which spectra are characterised by a large number of discrete features. Therefore, in this work, we carried out a spectral analysis of the accreting Neutron Star GX 13+1, which is a dipping source with several narrow absorption lines and a broad emission line in its spectrum. We tested two different co…
To d , or not to d : recent developments and comparisons of regularization schemes
2017
We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them.
Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD
2015
Virtual two-loop corrections to scattering amplitudes are a key ingredient to precision physics at collider experiments. We compute the full set of planar master integrals relevant to five-point functions in massless QCD, and use these to derive an analytical expression for the two-loop five-gluon all-plus-helicity amplitude. After subtracting terms that are related to the universal infrared and ultraviolet pole structure, we obtain a remarkably simple and compact finite remainder function, consisting only of dilogarithms.
Matter Dependence of the Four-Loop Cusp Anomalous Dimension
2019
We compute analytically the matter-dependent contributions to the quartic Casimir term of the four-loop light-like cusp anomalous dimension in QCD, with $n_f$ fermion and $n_s$ scalar flavours. The result is extracted from the double pole of a scalar form factor. We adopt a new strategy for the choice of master integrals with simple analytic and infrared properties, which significantly simplifies our calculation. To this end we first identify a set of integrals whose integrands have a dlog form, and are hence expected to have uniform transcendental weight. We then perform a systematic analysis of the soft and collinear regions of loop integration and build linear combinations of integrals w…
Enhanced local-type inflationary trispectrum from a non-vacuum initial state
2011
We compute the primordial trispectrum for curvature perturbations produced during cosmic inflation in models with standard kinetic terms, when the initial quantum state is not necessarily the vacuum state. The presence of initial perturbations enhances the trispectrum amplitude for configuration in which one of the momenta, say $k_3$, is much smaller than the others, $k_3 \ll k_{1,2,4}$. For those squeezed configurations the trispectrum acquires the so-called local form, with a scale dependent amplitude that can get values of order $ \epsilon ({k_1}/{k_3})^2$. This amplitude can be larger than the prediction of the so-called Maldacena consistency relation by a factor $10^6$, and can reach t…
Massless positivity in graviton exchange
2021
We formulate Positivity Bounds for scattering amplitudes including exchange of massless particles. We generalize the standard construction through dispersion relations to include the presence of a branch cut along the real axis in the complex plane for the Maldestam variable $s$. In general, validity of these bounds require the cancellation of divergences in the forward limit of the amplitude, proportional to $t^{-1}$ and $\log(t)$. We show that this is possible in the case of gravitons if one assumes a Regge behavior of the amplitude at high energies below the Planck scale, as previously suggested in the literature, and that the concrete UV behaviour of the amplitude is uniquely determined…
Space-like (vs. time-like) collinear limits in QCD: Is factorization violated?
2012
We consider the singular behaviour of QCD scattering amplitudes in kinematical configurations where two or more momenta of the external partons become collinear. At the tree level, this behaviour is known to be controlled by factorization formulae in which the singular collinear factor is universal (process independent). We show that this strict (process-independent) factorization is not valid at one-loop and higher-loop orders in the case of the collinear limit in space-like regions (e.g., collinear radiation from initial-state partons). We introduce a generalized version of all-order collinear factorization, in which the space-like singular factors retain some dependence on the momentum a…
Double collinear splitting amplitudes at next-to-leading order
2013
We compute the next-to-leading order (NLO) QCD corrections to the $1 \to 2$ splitting amplitudes in different dimensional regularization (DREG) schemes. Besides recovering previously known results, we explore new DREG schemes and analyze their consistency by comparing the divergent structure with the expected behavior predicted by Catani's formula. Through the introduction of scalar-gluons, we show the relation among splittings matrices computed using different schemes. Also, we extended this analysis to cover the double collinear limit of scattering amplitudes in the context of QCD+QED.
Triple collinear splitting functions at NLO for scattering processes with photons
2014
We present splitting functions in the triple collinear limit at next-to-leading order. The computation was performed in the context of massless QCD+QED, considering only processes which include at least one photon. Through the comparison of the IR divergent structure of splitting amplitudes with the expected known behavior, we were able to check our results. Besides that we implemented some consistency checks based on symmetry arguments and cross-checked the results among them. Studying photon-started processes, we obtained very compact results.
Analytic result for the nonplanar hexa-box integrals.
2019
In this paper, we analytically compute all master integrals for one of the two non-planar integral families for five-particle massless scattering at two loops. We first derive an integral basis of 73 integrals with constant leading singularities. We then construct the system of differential equations satisfied by them, and find that it is in canonical form. The solution space is in agreement with a recent conjecture for the non-planar pentagon alphabet. We fix the boundary constants of the differential equations by exploiting constraints from the absence of unphysical singularities. The solution of the differential equations in the Euclidean region is expressed in terms of iterated integral…