Higher-Order Gravitational Lensing Reconstruction using Feynman Diagrams

We develop a method for calculating the correlation structure of the Cosmic Microwave Background (CMB) using Feynman diagrams, when the CMB has been modified by gravitational lensing, Faraday rotation, patchy reionization, or other distorting effects. This method is used to calculate the bias of the Hu-Okamoto quadratic estimator in reconstructing the lensing power spectrum up to O(\phi^4) in the lensing potential $\phi$. We consider both the diagonal noise TTTT, EBEB, etc. and, for the first time, the off-diagonal noise TTTE, TBEB, etc. The previously noted large O(\phi^4) term in the second order noise is identified to come from a particular class of diagrams. It can be significantly reduced by a reorganization of the $\phi$ expansion. These improved estimators have almost no bias for the off-diagonal case involving only one $B$ component of the CMB, such as EEEB.Comment: 17 pages, 17 figure

Gravitational Lensing of the CMB: a Feynman Diagram Approach

We develop a Feynman diagram approach to calculating correlations of the Cosmic Microwave Background (CMB) in the presence of distortions. As one application, we focus on CMB distortions due to gravitational lensing by Large Scale Structure (LSS). We study the Hu-Okamoto quadratic estimator for extracting lensing from the CMB and derive the noise of the estimator up to ${\mathcal O}(\phi^4)$ in the lensing potential $\phi$. The previously noted large ${\mathcal O}(\phi^4)$ term can be significantly reduced by a reorganization of the $\phi$ expansion. Our approach makes it simple to obtain expressions for quadratic estimators based on any CMB channel. We briefly discuss other applications to cosmology of this diagrammatic approach, such as distortions of the CMB due to patchy reionization, or due to Faraday rotation from primordial axion fields.Comment: 5 pages, 8 figures, v2: journal versio

Factorization and resummation for generic hierarchies between Jets

Jets are an important probe to identify the hard interaction of interest at the LHC. They are routinely used in Standard Model precision measurements as well as in searches for new heavy particles, including jet substructure methods. In processes with several jets, one typically encounters hierarchies in the jet transverse momenta and/or dijet invariant masses. Large logarithms of the ratios of these kinematic jet scales in the cross section are at present primarily described by parton showers. We present a general factorization framework called SCET$_+$, which is an extension of Soft-Collinear Effective Theory (SCET) and allows for a systematic higher-order resummation of such kinematic logarithms for generic jet hierarchies. In SCET$_+$ additional intermediate soft/collinear modes are used to resolve jets arising from additional soft and/or collinear QCD emissions. The resulting factorized cross sections utilize collinear splitting amplitudes and soft gluon currents and fully capture spin and color correlations. We discuss how to systematically combine the different kinematic regimes to obtain a complete description of the jet phase space. To present its application in a simple context, we use the case of $e^+e^- \to$3 jets. We then discuss in detail the application to N-jet processes at hadron colliders, considering representative classes of hierarchies from which the general case can be built. This includes in particular multiple hierarchies that are either strongly ordered in angle or energy or not.Comment: 63 pages, 6 figures, v2: minor typos fixed, Ref. added, v3: journal versio