1,183 research outputs found
Analytic Continuation of Massless Two-Loop Four-Point Functions
We describe the analytic continuation of two-loop four-point functions with
one off-shell external leg and internal massless propagators from the Euclidean
region of space-like decay to Minkowskian regions relevant to all
and reactions with one space-like or time-like off-shell
external leg. Our results can be used to derive two-loop master integrals and
unrenormalized matrix elements for hadronic vector-boson-plus-jet production
and deep inelastic two-plus-one-jet production, from results previously
obtained for three-jet production in electron--positron annihilation.Comment: 26 pages, LaTe
The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
The class of the two-loop massless crossed boxes, with light-like external
legs, is the final unresolved issue in the program of computing the scattering
amplitudes of 2 --> 2 massless particles at next-to-next-to-leading order.
In this paper, we describe an algorithm for the tensor reduction of such
diagrams. After connecting tensor integrals to scalar ones with arbitrary
powers of propagators in higher dimensions, we derive recurrence relations from
integration-by-parts and Lorentz-invariance identities, that allow us to write
the scalar integrals as a combination of two master crossed boxes plus
simpler-topology diagrams.
We derive the system of differential equations that the two master integrals
satisfy using two different methods, and we use one of these equations to
express the second master integral as a function of the first one, already
known in the literature. We then give the analytic expansion of the second
master integral as a function of epsilon=(4-D)/2, where D is the space-time
dimension, up to order O(epsilon^0).Comment: 30 pages, 5 figure
NNLO phase space master integrals for two-to-one inclusive cross sections in dimensional regularization
We evaluate all phase space master integrals which are required for the total
cross section of generic 2 -> 1 processes at NNLO as a series expansion in the
dimensional regulator epsilon. Away from the limit of threshold production, our
expansion includes one order higher than what has been available in the
literature. At threshold, we provide expressions which are valid to all orders
in terms of Gamma functions and hypergeometric functions. These results are a
necessary ingredient for the renormalization and mass factorization of
singularities in 2 -> 1 inclusive cross sections at NNNLO in QCD.Comment: 37 pages, plus 3 ancillary files containing analytic expressions in
Maple forma
The fully differential hadronic production of a Higgs boson via bottom quark fusion at NNLO
The fully differential computation of the hadronic production cross section
of a Higgs boson via bottom quarks is presented at NNLO in QCD. Several
differential distributions with their corresponding scale uncertainties are
presented for the 8 TeV LHC. This is the first application of the method of
non-linear mappings for NNLO differential calculations at hadron colliders.Comment: 27 pages, 13 figures, 1 lego plo
Subtraction at NNLO
We propose a framework for the implementation of a subtraction formalism at
NNLO in QCD, based on an observable- and process-independent cancellation of
infrared singularities. As a first simple application, we present the
calculation of the contribution to the e+e- dijet cross section proportional to
C_F T_RComment: 42 pages Latex; 7 figures included. Modifications to the text, and
references added; the results are unchange
Two-Loop Master Integrals for Jets: The non-planar topologies
The calculation of the two-loop corrections to the three-jet production rate
and to event shapes in electron--positron annihilation requires the computation
of a number of two-loop four-point master integrals with one off-shell and
three on-shell legs. Up to now, only those master integrals corresponding to
planar topologies were known. In this paper, we compute the yet outstanding
non-planar master integrals by solving differential equations in the external
invariants which are fulfilled by these master integrals. We obtain the master
integrals as expansions in \e=(4-d)/2, where is the space-time dimension.
The fully analytic results are expressed in terms of the two-dimensional
harmonic polylogarithms already introduced in the evaluation of the planar
topologies.Comment: 22 pages, LaTeX, version to be published, Note added on numerical
checks of the results, typos correcte
Fresh and hardened properties of cement mortars using marble sludge fines and cement sludge fines
The construction sector could provide solutions for the safe utilization of industrial by-products as construction materials, if proper characterization and control of the materials properties is undertaken. Under this consideration, fines produced from marble cutting and fines produced from concrete truck washing were investigated as fine material for use in cement mortars. Both these by-products are produced in large amounts in the form of sludge. Marble Sludge Fines (MSF) and Cement Sludge Fines (CSF) were characterized in terms of fineness, density, chemical analysis and suitability for use with cement. Mortars with variable rate (10%, 20% and 30%) of cement substitution with MSF or CSF were tested and compared to a reference cement mortar in respect to their fresh and hardened properties. Packing ability and viscosity were measured in fresh mortars, while strength development, water absorption and porosity were measured in hardened mortars. The results confirm the suitability of both as filler material; although MSF performed better regarding fresh mortar properties and CSF showed better results regarding strength development
Hepta-Cuts of Two-Loop Scattering Amplitudes
We present a method for the computation of hepta-cuts of two loop scattering
amplitudes. Four dimensional unitarity cuts are used to factorise the integrand
onto the product of six tree-level amplitudes evaluated at complex momentum
values. Using Gram matrix constraints we derive a general parameterisation of
the integrand which can be computed using polynomial fitting techniques. The
resulting expression is further reduced to master integrals using conventional
integration by parts methods. We consider both planar and non-planar topologies
for 2 to 2 scattering processes and apply the method to compute hepta-cut
contributions to gluon-gluon scattering in Yang-Mills theory with adjoint
fermions and scalars.Comment: 37 pages, 6 figures. version 2 : minor updates, published versio
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