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

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 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

Iteration Complexity of Randomized Primal-Dual Methods for Convex-Concave Saddle Point Problems

In this paper we propose a class of randomized primal-dual methods to contend with large-scale saddle point problems defined by a convex-concave function $\mathcal{L}(\mathbf{x},y)\triangleq\sum_{i=1}^m f_i(x_i)+\Phi(\mathbf{x},y)-h(y)$. We analyze the convergence rate of the proposed method under the settings of mere convexity and strong convexity in $\mathbf{x}$-variable. In particular, assuming $\nabla_y\Phi(\cdot,\cdot)$ is Lipschitz and $\nabla_\mathbf{x}\Phi(\cdot,y)$ is coordinate-wise Lipschitz for any fixed $y$, the ergodic sequence generated by the algorithm achieves the convergence rate of $\mathcal{O}(m/k)$ in a suitable error metric where $m$ denotes the number of coordinates for the primal variable. Furthermore, assuming that $\mathcal{L}(\cdot,y)$ is uniformly strongly convex for any $y$, and that $\Phi(\cdot,y)$ is linear in $y$, the scheme displays convergence rate of $\mathcal{O}(m/k^2)$. We implemented the proposed algorithmic framework to solve kernel matrix learning problem, and tested it against other state-of-the-art solvers

Wilson Lines off the Light-cone in TMD PDFs

Transverse Momentum Dependent (TMD) parton distribution functions (PDFs) also take into account the transverse momentum ($p_T$) of the partons. The $p_T$-integrated analogues can be linked directly to quark and gluon matrix elements using the operator product expansion in QCD, involving operators of definite twist. TMDs also involve operators of higher twist, which are not suppressed by powers of the hard scale, however. Taking into account gauge links that no longer are along the light-cone, one finds that new distribution functions arise. They appear at leading order in the description of azimuthal asymmetries in high-energy scattering processes. In analogy to the collinear operator expansion, we define a universal set of TMDs of definite rank and point out the importance for phenomenology.Comment: 12 pages, presented by the first author at the Light-Cone Conference 2013, May 20-24, 2013, Skiathos, Greece. To be published in Few Body System

An Asynchronous Distributed Proximal Gradient Method for Composite Convex Optimization

Abstract We propose a distributed first-order augmented Lagrangian (DFAL) algorithm to minimize the sum of composite convex functions, where each term in the sum is a private cost function belonging to a node, and only nodes connected by an edge can directly communicate with each other. This optimization model abstracts a number of applications in distributed sensing and machine learning. We show that any limit point of DFAL iterates is optimal; and for any ǫ > 0, an ǫ-optimal and ǫ-feasible solution can be computed within O(log(ǫ −1 )) DFAL iterations, which require O( ψ 1.5 max dmin ǫ −1 ) proximal gradient computations and communications per node in total, where ψ max denotes the largest eigenvalue of the graph Laplacian, and d min is the minimum degree of the graph. We also propose an asynchronous version of DFAL by incorporating randomized block coordinate descent methods; and demonstrate the efficiency of DFAL on large scale sparse-group LASSO problems