Aneesh V. Manohar

Effective field theories

These lectures introduce some of the basic ideas of effective field theories. The topics discussed include: relevant and irrelevant operators and scaling, renormalization in effective field theories, decoupling of heavy particles, power counting, and naive dimensional analysis. Effective Lagrangians are used to study the ΔS=2 weak interactions and chiral perturbation theory.

Renormalons in effective field theories

We investigate the high-order behavior of perturbative matching conditions in effective field theories. These series are typically badly divergent, and are not Borel summable due to infrared and ultraviolet renormalons which introduce ambiguities in defining the sum of the series. We argue that, when treated consistently, there is no physical significance to these ambiguities. Although nonperturbative matrix elements and matching conditions are in general ambiguous, the ambiguity in any physical observable is always higher order in 1/{ital M} than the theory has been defined. We discuss the implications for the recently noticed infrared renormalon in the pole mass of a heavy quark. We show that a ratio of form factors in exclusive {Lambda}{sub {ital b}} decays (which is related to the pole mass) is free from renormalon ambiguities regardless of the mass used as the expansion parameter of heavy quark effective theory. The renormalon ambiguities also cancel in inclusive heavy hadron decays. Finally, we demonstrate the cancellation of renormalons in a four-Fermi effective theory obtained by integrating out a heavy colored scalar.

Semiclassical meson-baryon dynamics from large-Nc QCD☆

Abstract The large- N c limit of the meson-baryon effective Lagrangian is shown to reduce to a semiclassical field theory. A chiral bag structure emerges naturally in the N c → ∞ limit. A possible connection between the chiral bag picture and the Skyrme model is discussed. The classical meson-baryon theory is used to reproduce the M π 3 non-analytic correction to the baryon mass obtained previously as a loop correction in chiral perturbation theory.

Electroweak logarithms in inclusive cross sections

A bstractWe develop the framework to perform all-orders resummation of electroweak logarithms of Q/M for inclusive scattering processes at energies Q much above the electroweak scale M. We calculate all ingredients needed at next-to-leading logarithmic (NLL) order and provide an explicit recipe to implement this for 2 → 2 processes. PDF evolution including electroweak corrections, which lead to Sudakov double logarithms, is computed. If only the invariant mass of the final state is measured, all electroweak logarithms can be resummed by the PDF evolution, at least to LL. However, simply identifying a lepton in the final state requires the corresponding fragmentation function and introduces angular dependence through the exchange of soft gauge bosons. Furthermore, we show the importance of polarization effects for gauge bosons, due to the chiral nature of SU(2) — even the gluon distribution in an unpolarized proton becomes polarized at high scales due to electroweak effects. We justify our approach with a factorization analysis, finding that the objects entering the factorization theorem do not need to be SU(2) × U(1) gauge singlets, even though we perform the factorization and resummation in the symmetric phase. We also discuss a range of extensions, including jets and how to calculate the EW logarithms when you are fully exclusive in the central (detector) region and fully inclusive in the forward (beam) regions.