A proof of factorization for B -> D pi

We prove that the matrix elements of four fermion operators mediating the decay B^0 -> D^+ \pi^- and B^- -> D^0 \pi^- factor into the product of a form factor describing the B -> D transition and a convolution of a short distance coefficient with the nonperturbative pion light-cone wave function. This is shown to all orders in alpha_s, up to corrections suppressed by factors of 1/mb, 1/mc, and 1/E_pi. It is not necessary to assume that the pion state is dominated by the q-qbar Fock state.Comment: 4 pages, 3 figs, PRL versio

Power Counting in the Soft-Collinear Effective Theory

We describe in some detail the derivation of a power counting formula for the soft-collinear effective theory (SCET). This formula constrains which operators are required to correctly describe the infrared at any order in the Lambda_QCD/Q expansion (lambda expansion). The result assigns a unique lambda-dimension to graphs in SCET solely from vertices, is gauge independent, and can be applied independent of the process. For processes with an OPE the lambda-dimension has a correspondence with dynamical twist.Comment: 12 pages, 1 fig, journal versio

Factorization for generic jet production

Factorization is the central ingredient in any theoretical prediction for collider experiments. We introduce a factorization formalism that can be applied to any desired observable, like event shapes or jet observables, for any number of jets and a wide range of jet algorithms in leptonic or hadronic collisions. This is achieved by using soft-collinear effective theory to prove the formal factorization of a generic fully-differential cross section in terms of a hard coefficient, and generic jet and soft functions. In this formalism, whether a given observable factorizes in the usual sense, depends on whether it is inclusive enough, so the jet functions can be calculated perturbatively. The factorization formula for any such observable immediately follows from our general result, including the precise definition of the jet and soft functions appropriate for the observable in question. As examples of our formalism, we work out several results in two-jet production for both e+e- and pp collisions. For the latter, we also comment on how our formalism allows one to treat underlying events and beam remnants.Comment: 33 pages, v2: minor typos corrected, journal versio

Enhanced nonperturbative effects in jet distributions

We consider the triple differential distribution d\Gamma/(dE_J)(dm_J^2)(d\Omega_J) for two-jet events at center of mass energy M, smeared over the endpoint region m_J^2 << M^2, |2 E_J -M| ~ \Delta, \lqcd << \Delta << M. The leading nonperturbative correction, suppressed by \lqcd/\Delta, is given by the matrix element of a single operator. A similar analysis is performed for three jet events, and the generalization to any number of jets is discussed. At order \lqcd/\Delta, non-perturbative effects in four or more jet events are completely determined in terms of two matrix elements which can be measured in two and three jet events.Comment: Significant changes made. The first moment does not vanish--the paper has been modified to reflect this. Relations between different numbers of jets still hol

CFD study of oil-jet gear interaction flow phenomena in spur gears

Oil-jet lubrication and cooling of high-speed gears is frequently employed in aeronautical systems, such as novel high-bypass civil aero engines based on the geared turbofan technology. Using such oil-jet system, practitioners aim to achieve high cooling rates on the flanks of the highly thermally loaded gears with minimum oil usage. Thus, for an optimal design, detailed knowledge about the flow processes is desired. These involve the oil exiting the nozzle, the oil impacting on the gear teeth, the oil spreading on the flanks, the subsequent oil fling-off, as well as the effect of the design parameters on the oil flow. Better understanding of these processes will improve the nozzle design phase, e.g. regarding the nozzle positioning and orientation, as well as the nozzle sizing and operation. Most related studies focus on the impingement depth to characterize the two-phase flow. However, the level of information of this scalar value is rather low for a complete description of the highly dynamic three-dimensional flow. Motivated by the advancements in numerical methods and the computational resources available nowadays, the investigation of the oil-jet gear interaction by means of computational fluid dynamics (CFD) has come into focus lately. In this work, a numerical setup based on the volume-of-fluid method is presented and employed to investigate the two-phase flow phenomena occurring in the vicinity of the gear teeth. The setup consists of a single oil-jet impinging on a single rotating spur gear. By introducing new metrics for characterizing the flow phenomena, extensive use of the possibilities of modern CFD is made, allowing a detailed transient and spatially resolved flow analysis. Thus, not only the impingement depth, but also the temporal and spatial evolution of wetted areas on the gear flanks, as well as the evolution of the oil volume in contact with the gear flanks are extracted from the simulation data and compared in a CFD study. The study consists of 21 different simulation cases, whereby the effect of varying the jet velocity, the jet inclination angle, the jet diameter, and the gear speed are examined. Consistent results compared to a simplified analytical approach for the impinging depth are obtained and the results for the newly introduced metrics are presented

Soft-Collinear Factorization in Effective Field Theory

The factorization of soft and ultrasoft gluons from collinear particles is shown at the level of operators in an effective field theory. Exclusive hadronic factorization and inclusive partonic factorization follow as special cases. The leading order Lagrangian is derived using power counting and gauge invariance in the effective theory. Several species of gluons are required, and softer gluons appear as background fields to gluons with harder momenta. Two examples are given: the factorization of soft gluons in B->D pi, and the soft-collinear convolution for the B->Xs gamma spectrum.Comment: 32 pages, 11 figs, journal versio

On Glauber modes in Soft-Collinear Effective Theory

Gluon interactions involving spectator partons in collisions at hadronic machines are investigated. We find a class of examples in which a mode, called Glauber gluons, must be introduced to the effective theory for consistency.Comment: 19 pages, three figures. Uses JHEP3.cl