Karol Kampf

Effective Field Theories from Soft Limits of Scattering Amplitudes

We derive scalar effective field theories-Lagrangians, symmetries, and all-from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.

On-Shell Recursion Relations for Effective Field Theories.

We derive the first ever on-shell recursion relations applicable to effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in the nonlinear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible.

A Periodic Table of Effective Field Theories

A bstractWe systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d < 6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.

Tree-level amplitudes in the nonlinear sigma model

A bstractWe study in detail the general structure and further properties of the tree-level amplitudes in the SU(N) nonlinear sigma model. We construct the flavor-ordered Feynman rules for various parameterizations of the SU(N) fields U (x), write down the Berends-Giele relations for the semi-on-shell currents and discuss their efficiency for the amplitude calculation in comparison with those of renormalizable theories. We also present an explicit form of the partial amplitudes up to ten external particles. It is well known that the standard BCFW recursive relations cannot be used for reconstruction of the the on-shell amplitudes of effective theories like the SU(N) nonlinear sigma model because of the inappropriate behavior of the deformed on-shell amplitudes at infinity. We discuss possible generalization of the BCFW approach introducing “BCFW formula with subtractions” and with help of Berends-Giele relations we prove particular scaling properties of the semi-on-shell amplitudes of the SU(N) nonlinear sigma model under specific shifts of the external momenta. These results allow us to define alternative deformation of the semi-on-shell amplitudes and derive BCFW-like recursion relations. These provide a systematic and effective tool for calculation of Goldstone bosons scattering amplitudes and it also shows the possible applicability of on-shell methods to effective field theories. We also use these BCFW-like relations for the investigation of the Adler zeroes and double soft limit of the semi-on-shell amplitudes.

Analytical dispersive construction of eta -> 3 pi amplitude: First order in isospin breaking

Because of their small electromagnetic corrections, the isospin-breaking decays n -> 3 pi seem to be good candidates for extracting isospin-breaking parameters similar to(m(d) - m(u)). This task is unfortunately complicated by large chiral corrections and the discrepancy between the experimentally measured values of the Dalitz parameters describing the energy dependence of the amplitudes of these decays and those predicted from chiral perturbation theory. We present two methods based on an analytic dispersive representation that use the information from the NNLO chiral result and the one from the measurement of the charged n -> 3 pi decay by KLOE together in a harmonized way in order to determine the value of the quark mass ratio R. Our final result is R = 37.7 +/- 2.2. This value supplemented by values of m(s)/(m) over cap or even (m) over cap and m(s) from other methods (as sum-rules or lattice) enables us to obtain further quark mass characteristics. For instance the recent lattice value for m(s)/(m) over cap similar to 27: 5 leads to Q = 23.1 +/- 0.7. We also quote the corresponding values of the current masses m(u) and m(d). (Less)

Chiral expansions of the pi0 lifetime

The corrections induced by light quark masses to the current algebra result for the

The Dalitz decay π0 → e+e– γ revisited

{\ensuremath{\pi}}^{0}

Tests of the naturalness of the coupling constants in ChPT at order p6

lifetime are reexamined. We consider next-to-next-to-leading order corrections and we compute all the one-loop and the two-loop diagrams which contribute to the decay amplitude at this order in the two-flavor chiral expansion. We show that the result is renormalizable, as Weinberg consistency conditions are satisfied. We find that chiral logarithms are present at this order unlike the case at next-to-leading order. The result could be used in conjunction with lattice QCD simulations, the feasibility of which was recently demonstrated. We discuss the matching between the two-flavor and the three-flavor chiral expansions in the anomalous sector at order one-loop and derive the relations between the coupling constants. A modified chiral counting is proposed, in which

Unification of Galileon dualities

{m}_{s}

Recursion relations for tree-level amplitudes in the

counts as