Bulk Fermions in Soft Wall Models

We discuss the implementation of bulk fermions in soft wall models. The introduction of a position dependent bulk mass allows for a well defined Kaluza-Klein expansion for bulk fermions. The realization of flavor and the contribution to electroweak precision observables are shown to be very similar to the hard wall case. The bounds from electroweak precision test are however milder with gauge boson Kaluza-Klein modes as light as $\sim 1.5$ TeV compatible with current experimental bounds.Comment: Based on seminars given by the authors. To appear in the SUSY 09 proceeding

Universality and Evolution of TMDs

In this talk, we summarize how QCD evolution can be exploited to improve the treatment of transverse momentum dependent (TMD) parton distribution and fragmentation functions. The methods allow existing non-perturbative fits to be turned into fully evolved TMDs that are consistent with a complete TMD-factorization formalism over the full range of kT. We argue that evolution is essential to the predictive power of calculations that utilize TMD parton distribution and fragmentation functions, especially TMD observables that are sensitive to transverse spin.Comment: To appear in the proceedings of the Third International Workshop on Transverse Polarization Phenomena in Hard Scattering (Transversity 2011), in Veli Losinj, Croatia, 29 August - 2 September 2011. 5 pages, 1 figur

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

Bulk Fermions in Warped Models with a Soft Wall

We study bulk fermions in models with warped extra dimensions in the presence of a soft wall. Fermions can acquire a position dependent bulk Dirac mass that shields them from the deep infrared, allowing for a systematic expansion in which electroweak symmetry breaking effects are treated perturbatively. Using this expansion, we analyze properties of bulk fermions in the soft wall background. These properties include the realization of non-trivial boundary conditions that simulate the ones commonly used in hard wall models, the analysis of the flavor structure of the model and the implications of a heavy top. We implement a soft wall model of electroweak symmetry breaking with custodial symmetry and fermions propagating in the bulk. We find a lower bound on the masses of the first bosonic resonances, after including the effects of the top sector on electroweak precision observables for the first time, of m_{KK} \gtrsim 1-3 TeV at the 95% C.L., depending on the details of the Higgs, and discuss the implications of our results for LHC phenomenology.Comment: 34 pages, 8 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 $b^*$ 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 $b_{\rm max}$ which is very close to $1.5 {\rm GeV}^{-1}$. 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