Search results for "Dimensional regularization"
showing 10 items of 36 documents
The one loop gluon emission light cone wave function
2017
Light cone perturbation theory has become an essential tool to calculate cross sections for various small-$x$ dilute-dense processes such as deep inelastic scattering and forward proton-proton and proton-nucleus collisions. Here we set out to do one loop calculations in an explicit helicity basis in the four dimensional helicity scheme. As a first process we calculate light cone wave function for one gluon emission to one-loop order in Hamiltonian perturbation theory on the light front. We regulate ultraviolet divergences with transverse dimensional regularization and soft divergences with using a cut-off on longitudinal momentum. We show that when all the renormalization constants are comb…
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.
Transcendental numbers and the topology of three-loop bubbles
1999
We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.
Gluon mass generation without seagull divergences
2009
Dynamical gluon mass generation has been traditionally plagued with seagull divergences, and all regularization procedures proposed over the years yield finite but scheme-dependent gluon masses. In this work we show how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. The ability to trigger the aforementioned identity hinges crucially on the particular Ansatz employed for the three-gluon vertex entering into the Schwinger-Dyson equation governing the gluon propagator. The use of the appropriate three-gluon vertex brings about an additional advantage: one obtains two separate (but coupled) integral equations, one for t…
Gluon mass generation in the PT-BFM scheme
2006
In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search …
Threshold expansion of the sunset diagram
1999
By use of the threshold expansion we develop an algorithm for analytical evaluation, within dimensional regularization, of arbitrary terms in the expansion of the (two-loop) sunset diagram with general masses m_1, m_2 and m_3 near its threshold, i.e. in any given order in the difference between the external momentum squared and its threshold value, (m_1+m_2+m_3)^2. In particular, this algorithm includes an explicit recurrence procedure to analytically calculate sunset diagrams with arbitrary integer powers of propagators at the threshold.
Polarized triple-collinear splitting functions at NLO for processes with photons
2014
We compute the polarized splitting functions in the triple collinear limit at next-to-leading order accuracy (NLO) in the strong coupling $\alpha_{\rm S}$, for the splitting processes $\gamma \to q \bar{q} \gamma$, $\gamma \to q \bar{q} g$ and $g \to q \bar{q} \gamma$. The divergent structure of each splitting function was compared to the predicted behaviour according to Catani's formula. The results obtained in this paper are compatible with the unpolarized splitting functions computed in a previous article. Explicit results for NLO corrections are presented in the context of conventional dimensional regularization (CDR).
Dimensional interpolation and the Selberg integral
2019
Abstract We show that a version of dimensional interpolation for the Riemann–Roch–Hirzebruch formalism in the case of a grassmannian leads to an expression for the Euler characteristic of line bundles in terms of a Selberg integral. We propose a way to interpolate higher Bessel equations, their wedge powers, and monodromies thereof to non–integer orders, and link the result with the dimensional interpolation of the RRH formalism in the spirit of the gamma conjectures.
A quasi-finite basis for multi-loop Feynman integrals
2014
We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and ultraviolet divergences, and allow for an immediate and trivial expansion in the parameter of dimensional regularization. Our approach avoids the introduction of spurious structures and thereby leaves integrals particularly accessible to direct analytical integration techniques. Alternatively, the resulting convergent Feynman parameter integrals may be evaluated numerically. Our approach is guided by previous work by the second author but overcomes practical …
Running couplings from adiabatic regularization
2019
We extend the adiabatic regularization method by introducing an arbitrary mass scale $\mu$ in the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding $\mu$-invariance of the effective semiclassical (Maxwell-Einstein) equations. In particular, we get the running of the electric charge of perturbative quantum electrodynamics. Furthermore, the method brings about a renormalization of the cosmological constant and the Newtonian gravitational constant. The running obtained for these dimensionful coupling constants has new relevant (non-logarithmic) contributions, not predicted by dimensional regularization.