21 research outputs found
The one-loop gluon amplitude for heavy-quark production at NNLO
We compute the one-loop QCD amplitude for the process gg-->Q\bar{Q} in
dimensional regularization through order \epsilon^2 in the dimensional
regulator and for arbitrary quark mass values. This result is an ingredient of
the NNLO cross-section for heavy quark production at hadron colliders. The
calculation is performed in conventional dimensional regularization, using well
known reduction techniques as well as a method based on recent ideas for the
functional form of one-loop integrands in four dimensions.Comment: 27 pages, 3 figure
The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
The resummation of soft gluon exchange for QCD hard scattering requires a
matrix of anomalous dimensions. We compute this matrix directly for arbitrary 2
to n massless processes for the first time at two loops. Using color generator
notation, we show that it is proportional to the one-loop matrix. This result
reproduces all pole terms in dimensional regularization of the explicit
calculations of massless 2 to 2 amplitudes in the literature, and it predicts
all poles at next-to-next-to-leading order in any 2 to n process that has been
computed at next-to-leading order. The proportionality of the one- and two-loop
matrices makes possible the resummation in closed form of the
next-to-next-to-leading logarithms and poles in dimensional regularization for
the 2 to n processes.Comment: 5 pages, 1 figure, revte
Calculation of TMD Evolution for Transverse Single Spin Asymmetry Measurements
The Sivers transverse single spin asymmetry (TSSA) is calculated and compared
at different scales using the TMD evolution equations applied to previously
existing extractions. We apply the Collins-Soper-Sterman (CSS) formalism, using
the version recently developed by Collins. Our calculations rely on the
universality properties of TMD-functions that follow from the TMD-factorization
theorem. Accordingly, the non-perturbative input is fixed by earlier
experimental measurements, including both polarized semi-inclusive deep
inelastic scattering (SIDIS) and unpolarized Drell-Yan (DY) scattering. It is
shown that recent COMPASS measurements are consistent with the suppression
prescribed by TMD evolution.Comment: 4 pages, 2 figures. Version published in Physical Review Letter
The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
We extend the resummation of dimensionally-regulated amplitudes to next-to-next-to-leading poles. This requires the calculation of two-loop anomalous dimension matrices for color mixing through soft gluon exchange. Remarkably, we find that they are proportional to the corresponding one-loop matrices. Using the color generator notation, we reproduce the two-loop single-pole quantities H{sup (2)} introduced by Catani for quark and gluon elastic scattering. Our results also make possible threshold and a variety of other resummations at next-to-next-to leading logarithm. All of these considerations apply to 2 {yields} n processes with massless external lines
Stability of Scalar Fields in Warped Extra Dimensions
This work sets up a general theoretical framework to study stability of
models with a warped extra dimension where N scalar fields couple minimally to
gravity. Our analysis encompasses Randall-Sundrum models with branes and bulk
scalars, and general domain-wall models. We derive the Schrodinger equation
governing the spin-0 spectrum of perturbations of such a system. This result is
specialized to potentials generated using fake supergravity, and we show that
models without branes are free of tachyonic modes. Turning to the existence of
zero modes, we prove a criterion which relates the number of normalizable zero
modes to the parities of the scalar fields. Constructions with definite parity
and only odd scalars are shown to be free of zero modes and are hence
perturbatively stable. We give two explicit examples of domain-wall models with
a soft wall, one which admits a zero mode and one which does not. The latter is
an example of a model that stabilizes a compact extra dimension using only bulk
scalars and does not require dynamical branes.Comment: 25 pages, 2 figures; v2: minor changes to text, references added,
matches published versio
Transverse momentum dependent parton distribution and fragmentation functions with QCD evolution
We assess the current phenomenological status of transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FFs) and study the effect of consistently including perturbative QCD (pQCD) evolution. Our goal is to initiate the process of establishing reliable, QCD-evolved parametrizations for the TMD PDFs and TMD FFs that can be used both to test TMD factorization and to search for evidence of the breakdown of TMD factorization that is expected for certain processes. In this article, we focus on spin-independent processes because they provide the simplest illustration of the basic steps and can already be used in direct tests of TMD factorization. Our calculations are based on the Collins-Soper-Sterman (CSS) formalism, supplemented by recent theoretical developments which have clarified the precise definitions of the TMD PDFs and TMD FFs needed for a valid TMD-factorization theorem. Starting with these definitions, we numerically generate evolved TMD PDFs and TMD FFs using as input existing parametrizations for the collinear PDFs, collinear FFs, nonperturbative factors in the CSS factorization formalism, and recent fixed-scale fits. We confirm that evolution has important consequences, both qualitatively and quantitatively, and argue that it should be included in future phenomenological studies of TMD functions. Our analysis is also suggestive of extensions to processes that involve spin-dependent functions such as the Boer-Mulders, Sivers, or Collins functions, which we intend to pursue in future publications. At our website, we have made available the tables and calculations needed to obtain the TMD parametrizations presented herein. © 2011 American Physical Society
Model Independent Evolution of Transverse Momentum Dependent Distribution Functions (TMDs) at NNLL
We discuss the evolution of the eight leading twist transverse momentum
dependent parton distribution functions, which turns out to be universal and
spin independent. By using the highest order perturbatively calculable
ingredients at our disposal, we perform the resummation of the large logarithms
that appear in the evolution kernel of transverse momentum distributions up to
next-to-next-to-leading logarithms (NNLL), thus obtaining an expression for the
kernel with highly reduced model dependence. Our results can also be obtained
using the standard CSS approach when a particular choice of the
prescription is used. In this sense, and while restricted to the perturbative
domain of applicability, we consider our results as a "prediction" of the
correct value of which is very close to . We
explore under which kinematical conditions the effects of the non-perturbative
region are negligible, and hence the evolution of transverse momentum
distributions can be applied in a model independent way. The application of the
kernel is illustrated by considering the unpolarized transverse momentum
dependent parton distribution function and the Sivers function.Comment: To appear in EPJC. 17 pages, 7 figure
Flavour Physics in the Soft Wall Model
We extend the description of flavour that exists in the Randall-Sundrum (RS)
model to the soft wall (SW) model in which the IR brane is removed and the
Higgs is free to propagate in the bulk. It is demonstrated that, like the RS
model, one can generate the hierarchy of fermion masses by localising the
fermions at different locations throughout the space. However, there are two
significant differences. Firstly the possible fermion masses scale down, from
the electroweak scale, less steeply than in the RS model and secondly there now
exists a minimum fermion mass for fermions sitting towards the UV brane. With a
quadratic Higgs VEV, this minimum mass is about fifteen orders of magnitude
lower than the electroweak scale. We derive the gauge propagator and despite
the KK masses scaling as , it is demonstrated that the
coefficients of four fermion operators are not divergent at tree level. FCNC's
amongst kaons and leptons are considered and compared to calculations in the RS
model, with a brane localised Higgs and equivalent levels of tuning. It is
found that since the gauge fermion couplings are slightly more universal and
the SM fermions typically sit slightly further towards the UV brane, the
contributions to observables such as and , from the
exchange of KK gauge fields, are significantly reduced.Comment: 33 pages, 15 figures, 5 tables; v2: references added; v3:
modifications to figures 4,5 and 6. version to appear in JHE
The Effective Lagrangian for Bulk Fermions in Models with Extra Dimensions
We compute the dimension 6 effective Lagrangian arising from the tree level
integration of an arbitrary number of bulk fermions in models with warped extra
dimensions. The coefficients of the effective operators are written in terms of
simple integrals of the metric and are valid for arbitrary warp factors, with
or without an infrared brane, and for a general Higgs profile. All relevant
tree level fermion effects in electroweak and flavor observables can be
computed using this effective Lagrangian.Comment: 22 pages. V2: typos corrected, matches published versio