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

Soft gluons and superleading logarithms in QCD

After a brief introduction to the physics of soft gluons in QCD we present a surprising prediction. Dijet production in hadron-hadron collisions provides the paradigm, i.e. h_1 +h_2 \to jj+X. In particular, we look at the case where there is a restriction placed on the emission of any further jets in the region in between the primary (highest p_T) dijets. Logarithms in the ratio of the jet scale to the veto scale can be summed to all orders in the strong coupling. Surprisingly, factorization of collinear emissions fails at scales above the veto scale and triggers the appearance of double logarithms in the hard sub-process. The effect appears first at fourth order relative to the leading order prediction and is subleading in the number of colours.Comment: Talk presented at the workshop "New Trends in HERA Physics", Ringberg Castle, Tegernsee, 5-10 October 200

High Probability and Risk-Averse Guarantees for a Stochastic Accelerated Primal-Dual Method

We consider stochastic strongly-convex-strongly-concave (SCSC) saddle point (SP) problems which frequently arise in applications ranging from distributionally robust learning to game theory and fairness in machine learning. We focus on the recently developed stochastic accelerated primal-dual algorithm (SAPD), which admits optimal complexity in several settings as an accelerated algorithm. We provide high probability guarantees for convergence to a neighborhood of the saddle point that reflects accelerated convergence behavior. We also provide an analytical formula for the limiting covariance matrix of the iterates for a class of stochastic SCSC quadratic problems where the gradient noise is additive and Gaussian. This allows us to develop lower bounds for this class of quadratic problems which show that our analysis is tight in terms of the high probability bound dependency to the parameters. We also provide a risk-averse convergence analysis characterizing the ``Conditional Value at Risk'', the ``Entropic Value at Risk'', and the $\chi^2$-divergence of the distance to the saddle point, highlighting the trade-offs between the bias and the risk associated with an approximate solution obtained by terminating the algorithm at any iteration

Robust Accelerated Primal-Dual Methods for Computing Saddle Points

We consider strongly convex/strongly concave saddle point problems assuming we have access to unbiased stochastic estimates of the gradients. We propose a stochastic accelerated primal-dual (SAPD) algorithm and show that SAPD iterate sequence, generated using constant primal-dual step sizes, linearly converges to a neighborhood of the unique saddle point, where the size of the neighborhood is determined by the asymptotic variance of the iterates. Interpreting the asymptotic variance as a measure of robustness to gradient noise, we obtain explicit characterizations of robustness in terms of SAPD parameters and problem constants. Based on these characterizations, we develop computationally tractable techniques for optimizing the SAPD parameters, i.e., the primal and dual step sizes, and the momentum parameter, to achieve a desired trade-off between the convergence rate and robustness on the Pareto curve. This allows SAPD to enjoy fast convergence properties while being robust to noise as an accelerated method. We also show that SAPD admits convergence guarantees for the gap metric with a variance term optimal up to a logarithmic factor --which can be removed by employing a restarting strategy. Furthermore, to our knowledge, our work is the first one showing an iteration complexity result for the gap function on smooth SCSC problems without the bounded domain assumption. Finally, we illustrate the efficiency of our approach on distributionally robust logistic regression problems