ACCOUNTING FOR PHASE CANCELLATIONS IN NON-NEGATIVE MATRIX FACTORIZATION USING WEIGHTED DISTANCES

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Renormalization group coefficients and the S-matrix

We show how to use on-shell unitarity methods to calculate renormalization group coefficients such as beta functions and anomalous dimensions. The central objects are the form factors of composite operators. Their discontinuities can be calculated via phase-space integrals and are related to corresponding anomalous dimensions. In particular, we find that the dilatation operator, which measures the anomalous dimensions, is given by minus the phase of the S-matrix divided by pi. We illustrate our method using several examples from Yang-Mills theory, perturbative QCD and Yukawa theory at one-loop level and beyond.Comment: 25 pages, 4 figures; v2: explanations improved, references added, matches journal versio

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We compute the decay rates and $H$-energy distributions of $B$ mesons into the final state $H+X$, where $H$ can be any one of the $S$-wave or $P$-wave charmonia, at next-to-leading order in the strong coupling. We find that a significant fraction of the observed $J/\psi$, $\psi'$ and $\chi_c$ must be produced through $c\bar{c}$ pairs in a colour octet state and should therefore be accompanied by more than one light hadron. At the same time we obtain stringent constraints on some of the long-distance parameters for colour octet production.Comment: 40 pages, RevTeX, 4 figure

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The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to the equation in planar N = 4 super Yang-Mills theory. Our method exploits a recently established equivalence with the physics of soft wide-angle radiation, so-called non-global logarithms, and thus yields at the same time the three-loop evolution equation for non-global logarithms. As a by-product of our analysis, we develop a Lorentz-covariant method to subtract infrared and collinear divergences in cross-section calculations in the planar limit. We compare our result in the linear regime with a recent prediction for the so-called Pomeron trajectory, and compare its collinear limit with predictions from the spectrum of twist-two operators.Peer reviewe

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A certain pattern of divergence of perturbative expansions in quantum field theories, related to their small and large momentum behaviour, is known as renormalons. We review formal and phenomenological aspects of renormalon divergence. We first summarize what is known about ultraviolet and infrared renormalons from an analysis of Feynman diagrams. Because infrared renormalons probe large distances, they are closely connected with non-perturbative power corrections in asymptotically free theories such as QCD. We discuss this aspect of the renormalon phenomenon in various contexts, and in particular the successes and failures of renormalon-inspired models of power corrections to hard processes in QCD.Comment: 168 pages, LaTeX, 23 figures, rmpbib.sty file required and included. v2: minor rearrangements, bibliographical style change

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This is the summary and introduction to the proceedings contributions for the Les Houches 2009 "Tools and Monte Carlo" working group.Comment: 144 Pages. Workshop site http://wwwlapp.in2p3.fr/conferences/LesHouches/Houches2009/ . Conveners were Butterworth, Maltoni, Moortgat, Richardson, Schumann and Skand

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We provide a rigorous basis for factorization for a large class of non-leptonic two-body $B$-meson decays in the heavy-quark limit. The factorization formula incorporates elements of the naive factorization approach and the hard-scattering approach, but allows us to compute systematically radiative (``non-factorizable'') corrections to naive factorization for decays such as $B\to D\pi$ and $B\to \pi \pi$. We discuss the factorization formula for a general final state from a general point of view. We then consider factorization for decays into heavy-light final states (such as $B\to D\pi$) in more detail, including a proof of the factorization formula at two-loop order. Explicit results for the leading QCD corrections to factorization are presented and compared to existing measurements of branching fractions and final-state interaction phases

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