Bordes, J., Dominguez, C. A., Moodley, P., Peñarrocha, J., & Schilcher, K. (2010). Chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes-Renner relation. J. High Energy Phys., 05(5), 064–16pp.
Abstract: The next to leading order chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes- Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order Perturbation Theory, Contour Improved Perturbation Theory, and a fixed renormalization scale scheme. We obtain for the corrections to the GMOR relation, delta(pi), the value delta(pi) = (6.2 +/- 1.6)%. This result is substantially more accurate than previous determinations based on QCD sum rules; it is also more reliable as it is basically free of systematic uncertainties. It implies a light quark condensate < 0 vertical bar(u) over baru vertical bar 0 > similar or equal to < 0 vertical bar(d) over bard vertical bar 0 > < 0 vertical bar(q) over barq vertical bar 0 >vertical bar(2GeV) = (-267 +/- 5MeV)(3). As a byproduct, the chiral perturbation theory (unphysical) low energy constant H-2(r) is predicted to be H-2(r)(nu(X) = M-p) = -(5.1 +/- 1.8) x10(-3), or H-2(r) (nu(X) = M-eta) = -(5.7 +/- 2.0) x10(-3).
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Kleiss, R. H. P., Malamos, I., Papadopoulos, C. G., & Verheyen, R. (2012). Counting to one: reducibility of one- and two-loop amplitudes at the integrand level. J. High Energy Phys., 12(12), 038–24pp.
Abstract: Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction methods proved to be very helpful, lowering the number of integrals that need to be actually calculated. Especially reduction at the integrand level improves the speed and set-up of these calculations. In this article we demonstrate, by counting the numbers of tensor structures and independent coefficients, how to write such relations at the integrand level for one-and two-loop amplitudes. We clarify their connection to the so-called spurious terms at one loop and discuss their structure in the two-loop case. This method is also applicable to higher loops, and the results obtained apply to both planar and non-planar diagrams.
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Deak, M. (2013). Estimation of saturation and coherence effects in the KGBJS equation – a non-linear CCFM equation. J. High Energy Phys., 07(7), 087–18pp.
Abstract: We solve the modified non-linear extension of the CCFM equation – KGBJS equation – numerically for certain initial conditions and compare the resulting dipole amplitudes with those obtained front solving the original CCFM equation and the BFKL and BK equations for the same initial conditions. We improve the low transversal momentum behaviour of the KGBJS equation by a small modification.
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Buchta, S., Chachamis, G., Draggiotis, P., Malamos, I., & Rodrigo, G. (2014). On the singular behaviour of scattering amplitudes in quantum field theory. J. High Energy Phys., 11(11), 014–13pp.
Abstract: We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop-tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.
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Deak, M., & Kutak, K. (2015). Kinematical constraint effects in the evolution equations based on angular ordering. J. High Energy Phys., 05(5), 068–13pp.
Abstract: We study effects of imposing various forms of the kinematical constraint on the full form of the CCFM equation and its non-linear extension. We find, that imposing the constraint in its complete form modifies significantly the shape of gluon density as compared to forms of the constraint used in numerical calculations and phenomenological applications. In particular the resulting gluon density is suppressed for large values of the hard scale related parameter and k(T) of gluon. This result might be important in description of jet correlations at Large Hadron Collider within the CCFM approach.
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Chachamis, G., Deak, M., Hentschinski, M., Rodrigo, G., & Sabio Vera, A. (2015). Single bottom quark production in kT-factorisation. J. High Energy Phys., 09(9), 123–17pp.
Abstract: We present a study within the k(T)-factorisation scheme on single bottom quark production at the LHC. In particular, we calculate the rapidity and transverse momentum differential distributions for single bottom quark/anti-quark production. In our setup, the unintegrated gluon density is obtained from the NLx BFKL Green function whereas we included mass effects to the Lx heavy quark jet vertex. We compare our results to the corresponding distributions predicted by the usual collinear factorisation scheme. The latter were produced with Pythia 8.1.
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de Florian, D., Sborlini, G. F. R., & Rodrigo, G. (2016). Two-loop QED corrections to the Altarelli-Parisi splitting functions. J. High Energy Phys., 10(10), 056–16pp.
Abstract: We compute the two-loop QED corrections to the Altarelli-Parisi (AP) splitting functions by using a deconstructive algorithmic Abelianization of the well-known NLO QCD corrections. We present explicit results for the full set of splitting kernels in a basis that includes the leptonic distribution functions that, starting from this order in the QED coupling, couple to the partonic densities. Finally, we perform a phenomenological analysis of the impact of these corrections in the splitting functions.
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Ayala, C., Cvetic, G., & Kogerler, R. (2017). Lattice-motivated holomorphic nearly perturbative QCD. J. Phys. G, 44(7), 075001–30pp.
Abstract: Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite non-zero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of quantum field theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with small higher-twist effects. Subsequent application of the Borel sum rules to the V + A spectral functions of tau lepton decays, as measured by OPAL Collaboration, determines the values of the gluon condensate and of the V + A six-dimensional condensate, and reproduces the data to a significantly higher precision than the usual (MS) over bar running coupling.
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Llanes Jurado, J., Rodrigo, G., & Torres Bobadilla, W. J. (2017). From Jacobi off-shell currents to integral relations. J. High Energy Phys., 12(12), 122–22pp.
Abstract: In this paper, we study off-shell currents built from the Jacobi identity of the kinematic numerators of gg -> X with X = ss, q (q) over bar, gg. We find that these currents can be schematically written in terms of three-point interaction Feynman rules. This representation allows for a straightforward understanding of the Colour-Kinematics duality as well as for the construction of the building blocks for the generation of higher-multiplicity tree-level and multi-loop numerators. We also provide one-loop integral relations through the Loop-Tree duality formalism with potential applications and advantages for the computation of relevant physical processes at the Large Hadron Collider. We illustrate these integral relations with the explicit examples of QCD one-loop numerators of gg -> ss.
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Bierenbaum, I., Buchta, S., Draggiotis, P., Malamos, I., & Rodrigo, G. (2013). Tree-loop duality relation beyond single poles. J. High Energy Phys., 03(3), 025–24pp.
Abstract: We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multi-loop integrals derived in previous publications. We prove a generalization of the formula for single poles to multiple poles and we develop a strategy for dealing with higher-order pole integrals by reducing them to single pole integrals using Integration By Parts.
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