3,391 research outputs found
The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions
We consider the application of the DRA method to the case of several master
integrals in a given sector. We establish a connection between the homogeneous
part of dimensional recurrence and maximal unitarity cuts of the corresponding
integrals: a maximally cut master integral appears to be a solution of the
homogeneous part of the dimensional recurrence relation. This observation
allows us to make a necessary step of the DRA method, the construction of the
general solution of the homogeneous equation, which, in this case, is a coupled
system of difference equations.Comment: 17 pages, 2 figure
Analytic Results for Massless Three-Loop Form Factors
We evaluate, exactly in d, the master integrals contributing to massless
three-loop QCD form factors. The calculation is based on a combination of a
method recently suggested by one of the authors (R.L.) with other techniques:
sector decomposition implemented in FIESTA, the method of Mellin--Barnes
representation, and the PSLQ algorithm. Using our results for the master
integrals we obtain analytical expressions for two missing constants in the
ep-expansion of the two most complicated master integrals and present the form
factors in a completely analytic form.Comment: minor revisions, to appear in JHE
The R*-operation for Feynman graphs with generic numerators
Abstract The R *-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional external momenta. It can be used to compute the divergent parts of such Feynman graphs from products of simpler Feynman graphs of lower loops. In this paper we extend the R *-operation to Feynman graphs with arbitrary numerators, including tensors. We also provide a novel way of defining infrared counterterms which closely resembles the definition of its ultraviolet counterpart. We further express both infrared and ultraviolet counterterms in terms of scaleless vacuum graphs with a logarithmic degree of divergence. By exploiting symmetries, integrand and integral relations, which the counterterms of scaleless vacuum graphs satisfy, we can vastly reduce their number and complexity. A FORM implementation of this method was used to compute the five loop beta function in QCD for a general gauge group. To illustrate the procedure, we compute the poles in the dimensional regulator of all top-level propagator graphs at five loops in four dimensional ϕ 3 theory
On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
We propose a first implementation of the integrand-reduction method for
two-loop scattering amplitudes. We show that the residues of the amplitudes on
multi-particle cuts are polynomials in the irreducible scalar products
involving the loop momenta, and that the reduction of the amplitudes in terms
of master integrals can be realized through polynomial fitting of the
integrand, without any apriori knowledge of the integral basis. We discuss how
the polynomial shapes of the residues determine the basis of master integrals
appearing in the final result. We present a four-dimensional constructive
algorithm that we apply to planar and non-planar contributions to the 4- and
5-point MHV amplitudes in N=4 SYM. The technique hereby discussed extends the
well-established analogous method holding for one-loop amplitudes, and can be
considered a preliminary study towards the systematic reduction at the
integrand-level of two-loop amplitudes in any gauge theory, suitable for their
automated semianalytic evaluation.Comment: 26 pages, 11 figure
Mesozoic fossils (>145 Mya) suggest the antiquity of the subgenera of Daphnia and their coevolution with chaoborid predators
<p>Abstract</p> <p>Background</p> <p>The timescale of the origins of <it>Daphnia </it>O. F. Mueller (Crustacea: Cladocera) remains controversial. The origin of the two main subgenera has been associated with the breakup of the supercontinent Pangaea. This vicariance hypothesis is supported by reciprocal monophyly, present day associations with the former Gondwanaland and Laurasia regions, and mitochondrial DNA divergence estimates. However, previous multilocus nuclear DNA sequence divergence estimates at < 10 Million years are inconsistent with the breakup of Pangaea. We examined new and existing cladoceran fossils from a Mesozoic Mongolian site, in hopes of gaining insights into the timescale of the evolution of <it>Daphnia</it>.</p> <p>Results</p> <p>We describe new fossils of ephippia from the Khotont site in Mongolia associated with the Jurassic-Cretaceous boundary (about 145 MYA) that are morphologically similar to several modern genera of the family Daphniidae, including the two major subgenera of <it>Daphnia</it>, i.e., <it>Daphnia </it>s. str. and <it>Ctenodaphnia</it>. The daphniid fossils co-occurred with fossils of the predaceous phantom midge (Chaoboridae).</p> <p>Conclusions</p> <p>Our findings indicate that the main subgenera of <it>Daphnia </it>are likely much older than previously known from fossils (at least 100 MY older) or from nuclear DNA estimates of divergence. The results showing co-occurrence of the main subgenera far from the presumed Laurasia/Gondwanaland dispersal barrier shortly after formation suggests that vicariance from the breakup of Pangaea is an unlikely explanation for the origin of the main subgenera. The fossil impressions also reveal that the coevolution of a dipteran predator (Chaoboridae) with the subgenus <it>Daphnia </it>is much older than previously known -- since the Mesozoic.</p
Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory
We study light-like polygonal Wilson loops in three-dimensional Chern-Simons
and ABJM theory to two-loop order. For both theories we demonstrate that the
one-loop contribution to these correlators cancels. For pure Chern-Simons, we
find that specific UV divergences arise from diagrams involving two cusps,
implying the loss of finiteness and topological invariance at two-loop order.
Studying those UV divergences we derive anomalous conformal Ward identities for
n-cusped Wilson loops which restrict the finite part of the latter to
conformally invariant functions. We also compute the four-cusp Wilson loop in
ABJM theory to two-loop order and find that the result is remarkably similar to
that of the corresponding Wilson loop in N=4 SYM. Finally, we speculate about
the existence of a Wilson loop/scattering amplitude relation in ABJM theory.Comment: 37 pages, many figures; v2: references added, minor changes; v3:
references added, sign error fixed and note adde
Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
In this paper we continue the investigation of aspects of integrability of
the type IIA AdS(3) x S(3) x S(3) x S(1) and AdS(3) x S(3) x T(4) superstrings.
By constructing a one parameter family of flat connections we prove that the
Green-Schwarz string is classically integrable, at least to quadratic order in
fermions, without fixing the kappa-symmetry. We then compare the quantum
dispersion relation, fixed by integrability up to an unknown interpolating
function h(lambda), to explicit one-loop calculations on the string worldsheet.
For AdS(3) x S(3) x S(3) x S(1) the spectrum contains heavy, as well as light
and massless modes, and we find that the one-loop contribution differs
depending on how we treat these modes showing that similar regularization
ambiguities as appeared in AdS(4)/CFT(3) occur also here.Comment: 29 pages; v2: updated references and acknowledgmen
Simultaneous decoupling of bottom and charm quarks
We compute the decoupling relations for the strong coupling, the light quark
masses, the gauge-fixing parameter, and the light fields in QCD with heavy
charm and bottom quarks to three-loop accuracy taking into account the exact
dependence on . The application of a low-energy theorem allows the
extraction of the three-loop effective Higgs-gluon coupling valid for
extensions of the Standard Model with additional heavy quarks from the
decoupling constant of .Comment: 30 page
Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory
In this paper we study the one- and two-loop corrections to the four-point
amplitude of N=6 Chern-Simons matter theory. Using generalized unitarity
methods we express the one- and two-loop amplitudes in terms of dual-conformal
integrals. Explicit integration by using dimensional reduction gives vanishing
one-loop result as expected, while the two-loop result is non-vanishing and
matches with the Wilson loop computation. Furthermore, the two-loop correction
takes the same form as the one-loop correction to the four-point amplitude of
N=4 super Yang-Mills. We discuss possible higher loop extensions of this
correspondence between the two theories. As a side result, we extend the method
of dimensional reduction for three dimensions to five dimensions where dual
conformal symmetry is most manifest, demonstrating significant simplification
to the computation of integrals.Comment: 32 pages and 6 figures. v2: minus sign corrections, ref updated v3:
Published versio
Five-loop renormalisation of QCD in covariant gauges
We present the complete set of vertex, wave function and charge
renormalisation constants in QCD in a general simple gauge group and with the
complete dependence on the covariant gauge parameter in the minimal
subtraction scheme of conventional dimensional regularisation. Our results
confirm all already known results, which were obtained in the Feynman gauge,
and allow the extraction of other useful gauges such as the Landau gauge. We
use these results to extract the Landau gauge five-loop anomalous dimensions of
the composite operator as well as the Landau gauge scheme independent
gluon, ghost and fermion propagators at five loops.Comment: 17 pages; FORM and Mathematica result files available with the
source; corrected minor typos, added references, journal ref, 1 remark, 1
note and 1 additional result fil
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