21 research outputs found
Locally Causal Dynamical Triangulations in Two Dimensions
We analyze the universal properties of a new two-dimensional quantum gravity
model defined in terms of Locally Causal Dynamical Triangulations (LCDT).
Measuring the Hausdorff and spectral dimensions of the dynamical geometrical
ensemble, we find numerical evidence that the continuum limit of the model lies
in a new universality class of two-dimensional quantum gravity theories,
inequivalent to both Euclidean and Causal Dynamical Triangulations
The diamond rule for multi-loop Feynman diagrams
An important aspect of improving perturbative predictions in high energy
physics is efficiently reducing dimensionally regularised Feynman integrals
through integration by parts (IBP) relations. The well-known triangle rule has
been used to achieve simple reduction schemes. In this work we introduce an
extensible, multi-loop version of the triangle rule, which we refer to as the
diamond rule. Such a structure appears frequently in higher-loop calculations.
We derive an explicit solution for the recursion, which prevents spurious poles
in intermediate steps of the computations. Applications for massless propagator
type diagrams at three, four, and five loops are discussed
Numerical Loop-Tree Duality: contour deformation and subtraction
We introduce a novel construction of a contour deformation within the
framework of Loop-Tree Duality for the numerical computation of loop integrals
featuring threshold singularities in momentum space. The functional form of our
contour deformation automatically satisfies all constraints without the need
for fine-tuning. We demonstrate that our construction is systematic and
efficient by applying it to more than 100 examples of finite scalar integrals
featuring up to six loops. We also showcase a first step towards handling
non-integrable singularities by applying our work to one-loop infrared
divergent scalar integrals and to the one-loop amplitude for the ordered
production of two and three photons. This requires the combination of our
contour deformation with local counterterms that regulate soft, collinear and
ultraviolet divergences. This work is an important step towards computing
higher-order corrections to relevant scattering cross-sections in a fully
numerical fashion.Comment: 87 page
Loop Tree Duality for multi-loop numerical integration
Loop Tree Duality (LTD) offers a promising avenue to numerically integrate
multi-loop integrals directly in momentum space. It is well-established at one
loop, but there have been only sparse numerical results at two loops. We
provide a formal derivation for a novel multi-loop LTD expression and study its
threshold singularity structure. We apply our findings numerically to a diverse
set of up to four-loop finite topologies with kinematics for which no contour
deformation is needed. We also lay down the ground work for constructing such a
deformation. Our results serve as an important stepping stone towards a
generalised and efficient numerical implementation of LTD, applicable to the
computation of virtual corrections.Comment: 13 page
Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order
We propose a novel representation of differential scattering cross-sections
that locally realises the direct cancellation of infrared singularities
exhibited by its so-called real-emission and virtual degrees of freedom. We
take advantage of the Loop-Tree Duality representation of each individual
forward-scattering diagram and we prove that the ensuing expression is locally
free of infrared divergences, applies at any perturbative order and for any
process without initial-state collinear singularities. Divergences for loop
momenta with large magnitudes are regulated using local ultraviolet
counterterms that reproduce the usual Lagrangian renormalisation procedure of
quantum field theories. Our representation is especially suited for a numerical
implementation and we demonstrate its practical potential by computing fully
numerically and without any IR counterterm the next-to-leading order accurate
differential cross-section for the process . We
also show first results beyond next-to-leading order by computing interference
terms part of the N4LO-accurate inclusive cross-section of a
scalar scattering process.Comment: 88 page
Two- and three-loop anomalous dimensions of Weinberg's dimension-six CP-odd gluonic operator
We apply a fully automated extension of the -operation capable of
calculating higher-loop anomalous dimensions of n-point Green's functions of
arbitrary, possibly non-renormalisable, local Quantum Field Theories. We focus
on the case of the CP-violating Weinberg operator of the Standard Model
Effective Field Theory whose anomalous dimension is so far known only at one
loop. We calculate the two-loop anomalous dimension in full QCD and the
three-loop anomalous dimensions in the limit of pure Yang-Mills theory. We find
sizeable two-loop and large three-loop corrections, due to the appearance of a
new quartic group invariant. We discuss phenomenological implications for
electric dipole moments and future applications of the method.Comment: New results included: two-loop anomalous dimension in full QCD,
constraint on the Wilson coefficient with nEDM bounds. Included new section
explaining the computational metho