A
bstract
A scheme is proposed for the subtraction of soft and collinear divergences present in massless final state real emission phase space integrals. The scheme is based on a local slicing ...procedure which utilises the soft and collinear factorisation properties of amplitudes to produce universal counter-terms whose analytic integration is relatively simple. As a first application the scheme is applied to establish a general pole formula for final state real radiation at NLO and NNLO in Yang Mills theory for arbitrary multiplicities. All required counter-terms are evaluated to all orders in the dimensional regulator in terms of Γ — and
p
F
q
hypergeometric — functions. As a proof of principle the poles in the dimensional regulator of the
H
→
gggg
double real emission contribution to the
H
→
gg
decay rate are reproduced.
We review Zimmermann's forest formula, which solves Bogoliubov's recursive R-operation for the subtraction of ultraviolet divergences in perturbative Quantum Field Theory. We further discuss a ...generalisation of the R-operation which subtracts besides ultraviolet also Euclidean infrared divergences. This generalisation, which goes under the name of the R⁎-operation, can be used efficiently to compute renormalisation constants. We will discuss several results obtained by this method with focus on the QCD beta function at five loops as well as the application to hadronic Higgs boson decay rates at N4LO. This article summarizes a talk given at the Wolfhart Zimmermann Memorial Symposium.
A
bstract
We provide the all-loop structure of gauge-variant operators required for the renormalisation of Green’s functions with insertions of twist-two operators in Yang-Mills theory. Using this ...structure we work out an explicit basis valid up to 4-loop order for an arbitrary compact simple gauge group. To achieve this we employ a generalised gauge symmetry, originally proposed by Dixon and Taylor, which arises after adding to the Yang-Mills Lagrangian also operators proportional to its equation of motion. Promoting this symmetry to a generalised BRST symmetry allows to generate the ghost operator from a single exact operator in the BRST-generalised sense. We show that our construction complies with the theorems by Joglekar and Lee. We further establish the existence of a generalised anti-BRST symmetry which we employ to derive non-trivial relations among the anomalous dimension matrices of ghost and equation-of-motion operators. For the purpose of demonstration we employ the formalism to compute the
N
= 2
,
4 Mellin moments of the gluonic splitting function up to 4 loops and its
N
= 6 Mellin moment up to 3 loops, where we also take advantage of additional simplifications of the background field formalism.
A
bstract
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.
A
bstract
We present the most precise value for the Higgs boson cross-section in the gluon-fusion production mode at the LHC. Our result is based on a perturbative expansion through N
3
LO in QCD, in ...an effective theory where the top-quark is assumed to be infinitely heavy, while all other Standard Model quarks are massless. We combine this result with QCD corrections to the cross-section where all finite quark-mass effects are included exactly through NLO. In addition, electroweak corrections and the first corrections in the inverse mass of the top-quark are incorporated at three loops. We also investigate the effects of threshold resummation, both in the traditional QCD framework and following a SCET approach, which resums a class of π
2
contributions to all orders. We assess the uncertainty of the cross-section from missing higher-order corrections due to both perturbative QCD effects beyond N
3
LO and unknown mixed QCD-electroweak effects. In addition, we determine the sensitivity of the cross-section to the choice of parton distribution function (PDF) sets and to the parametric uncertainty in the strong coupling constant and quark masses. For a Higgs mass of
m
H
= 125 GeV and an LHC center-of-mass energy of 13 TeV, our best prediction for the gluon fusion cross-section is
σ
=
48.58
p
b
−
3.27
p
b
+
2.22
p
b
theory
±
1.56
p
b
3.20
%
P
D
F
+
α
s
.
The identification of crosslinks by mass spectrometry has recently been established as an integral part of the hybrid structural analysis of protein complexes and networks. The crosslinking analysis ...determines distance restraints between two covalently linked amino acids which are typically summarized in a table format that precludes the immediate and comprehensive interpretation of the topological data. xVis displays crosslinks in clear schematic representations in form of a circular, bar or network diagram. The interactive graphs indicate the linkage sites and identification scores, depict the spatial proximity of structurally and functionally annotated protein regions and the evolutionary conservation of amino acids and facilitate clustering of proteins into subcomplexes according to the crosslink density. Furthermore, xVis offers two options for the qualitative assessment of the crosslink identifications by filtering crosslinks according to identification scores or false discovery rates and by displaying the corresponding fragment ion spectrum of each crosslink for the manual validation of the mass spectrometric data. Our web server provides an easy-to-use tool for the fast topological and functional interpretation of distance information on protein complex architectures and for the evaluation of crosslink fragment ion spectra. xVis is available under a Creative Commons Attribution-ShareAlike 4.0 International license at http://xvis.genzentrum.lmu.de/.
A
bstract
We compute the three-loop correction to the universal single-soft emission current for the case of scattering amplitudes with two additional color-charged partons. We present results valid ...for QCD and
N
= 4 super-symmetric Yang-Mills theory. To achieve our results we develop a new integrand expansion technique for scattering amplitudes in the presence of soft emissions. Furthermore, we obtain contributions from single final-state parton matrix elements to the Higgs boson and Drell-Yan production cross section at next-to-next-to-next-to-next-to leading order (N
4
LO) in perturbative QCD in the threshold limit.
The Hopf algebra structure of the R∗-operation Beekveldt, Robert; Borinsky, Michael; Herzog, Franz
The journal of high energy physics,
07/2020, Letnik:
2020, Številka:
7
Journal Article
Recenzirano
Odprti dostop
A
bstract
We give a Hopf-algebraic formulation of the
R
∗
-operation, which is a canonical way to render UV and IR divergent Euclidean Feynman diagrams finite. Our analysis uncovers a close ...connection to Brown’s Hopf algebra of motic graphs. Using this connection we are able to provide a verbose proof of the long observed ‘commutativity’ of UV and IR subtractions. We also give a new duality between UV and IR counterterms, which, entirely algebraic in nature, is formulated as an inverse relation on the group of characters of the Hopf algebra of log-divergent scaleless Feynman graphs. Many explicit examples of calculations with applications to infrared rearrangement are given.
A
bstract
We study the application of the method of regions to Feynman integrals with massless propagators contributing to off-shell Green’s functions in Minkowski spacetime (with non-exceptional ...momenta) around vanishing external masses,
p
i
2
→
0
. This
on-shell expansion
allows us to identify all infrared-sensitive regions at any power, in terms of infrared subgraphs in which a subset of the propagators become collinear to external lightlike momenta and others become soft. We show that each such region can be viewed as a solution to the Landau equations, or equivalently, as a facet in the Newton polytope constructed from the Symanzik graph polynomials. This identification allows us to study the properties of the graph polynomials associated with infrared regions, as well as to construct a graph-finding algorithm for the on-shell expansion, which identifies all regions using exclusively graph-theoretical conditions. We also use the results to investigate the analytic structure of integrals associated with regions in which every connected soft subgraph connects to just two jets. For such regions we prove that multiple on-shell expansions commute. This applies in particular to all regions in Sudakov form-factor diagrams as well as in any planar diagram.
The identification of proximate amino acids by chemical cross-linking and mass spectrometry (XL-MS) facilitates the structural analysis of homogeneous protein complexes. We gained distance restraints ...on a modular interaction network of protein complexes affinity-purified from human cells by applying an adapted XL-MS protocol. Systematic analysis of human protein phosphatase 2A (PP2A) complexes identified 176 interprotein and 570 intraprotein cross-links that link specific trimeric PP2A complexes to a multitude of adaptor proteins that control their cellular functions. Spatial restraints guided molecular modeling of the binding interface between immunoglobulin binding protein 1 (IGBP1) and PP2A and revealed the topology of TCP1 ring complex (TRiC) chaperonin interacting with the PP2A regulatory subunit 2ABG. This study establishes XL-MS as an integral part of hybrid structural biology approaches for the analysis of endogenous protein complexes.
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