Related papers: Using Dimensional Reduction for Hadronic Collision…
One- and two-jet inclusive quantities in hadron collisions have already been calculated to next-to-leading order accuracy, using both the subtraction and the cone method. Since the one-loop corrections have recently been obtained for all…
We examine the singular behavior from the endpoint region x -> 1 in parton distributions unintegrated in both longitudinal and transverse momenta. We identify and regularize the singularities by using the subtraction method, and compare…
We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
It is proven by explicit construction that regularization by dimensional reduction can be formulated in a mathematically consistent way. In this formulation the quantum action principle is shown to hold. This provides an intuitive and…
We define the collinear factorization scheme, which absorbs only the collinear physics into the parton distribution functions. In order to isolate the collinear physics, we introduce a procedure to combine real and virtual corrections,…
We present a general subtraction method for computing radiative corrections to QCD jet cross sections at next-to-next-to-leading order accuracy. The steps needed to set up this subtraction scheme are the same as those used in…
We extend an implicit regularization scheme to be applicable in the $n$-dimensional space-time. Within this scheme divergences involving parity violating objects can be consistently treated without recoursing to dimensional continuation.…
High Energy collider experiments are moving to the highest precision frontier quickly. The predictions of observables are based on the factorization formula which helps to connect small to large distances. These predictions can be…
We describe the equivalence at one loop between constrained differential renormalization and regularization by dimensional reduction in the MS scheme. To illustrate it, we reexamine the calculation of supergravity corrections to (g-2)_l.
Factorization in gauge theories holds at the amplitude or amplitude-squared level for states of given soft or collinear momenta. When performing phase-space integrals over such states, one would generally like to avoid putting in explicit…
In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…
Zamolodchikov's famous analysis of the RG trajectory connecting successive minimal CFT models $M_p$ and $M_{p-1}$ for $p\gg 1$, is improved by including second order in coupling constant corrections. This allows to compute IR quantities…
An iteration-free method of domain decomposition is considered for approximate solving a boundary value problem for a second-order parabolic equation. A standard approach to constructing domain decomposition schemes is based on a partition…
Dimension reduction of multivariate data supervised by auxiliary information is considered. A series of basis for dimension reduction is obtained as minimizers of a novel criterion. The proposed method is akin to continuum regression, and…
The resummation of threshold logarithms for direct photon production cross sections in hadronic collisions is presented. The resummation is based on the factorization properties of the cross section and is formulated at next-to-leading…
We demonstrate a factorization formula for semi-inclusive deep-inelastic scattering with hadrons in the current fragmentation region detected at low transverse momentum. To facilitate the factorization, we introduce the transverse-momentum…
This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…
Dimensional regularization is applied to the Lippmann-Schwinger equation for a separable potential which gives rise to logarithmic singularities in the Born series. For this potential a subtraction at a fixed energy can be used to…
We calculate next to leading order QCD corrections to semi-inclusive polarized deep inelastic scattering and $e^+e^-$ annihilation cross sections for processes where the polarization of the identified final-state hadron can also be…