Gravitational Radiation from Color-Kinematics Duality

We perturbatively calculate classical radiation in Yang-Mills theory and dilaton gravity, to next-to-leading order in couplings. The radiation is sourced by the scattering of two relativistic massive scalar sources with the dynamical effect taken into account, corresponding to the post-Minkowskian regime in gravity. We show how to arrange the Yang-Mills radiation such that the duality between colors and kinematics is manifest, including the three-term Jacobi identity. The search for duality-satisfying expressions exploits an auxiliary bi-adjoint scalar theory as a guide for locality. The double copy is obtained by replacing the color factors in Yang-Mills with kinematic counterparts, following Bern-Carrasco-Johansson construction in S- matrix. On the gravity side, the radiation is directly computed at the third post-Minkowskian order with massive sources. We find perfect agreement between observables in dilaton gravity and the Yang-Mills double copy. This non-trivially generalizes the leading-order rules by Goldberger and Ridgway. For the first time, the kinematic Jacobi identity appears beyond field-theory S-matrix, suggesting that the color-kinematics duality holds more generally. Our results offer a path for simplifying analytical calculations in post-Minkowskian regime.Comment: 3 figures, 3 tables, and 7 ancillary files; comments are welcomed; v2: references added, typos fixed, one more figure is include

Non-renormalization Theorems without Supersymmetry

We derive a new class of one-loop non-renormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and anti-holomorphic weights, $(w,\overline w) =(n - h,n+h)$, where $n$ and $h$ are the number and sum over helicities of the particles created by that operator. We argue that an operator ${\cal O}_i$ can only be renormalized by an operator ${\cal O}_j$ if $w_i \geq w_j$ and $\overline w_i \geq \overline w_j$, absent non-holomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally.Comment: 6 pages, 2 figures, and 2 table

Symmetry and Action for Flavor-Kinematics Duality

We propose a new representation of the nonlinear sigma model that exhibits a manifest duality between flavor and kinematics. The fields couple exclusively through cubic Feynman vertices which also serve as the structure constants of an underlying kinematic algebra. The action is invariant under a combination of internal and spacetime symmetries whose conservation equations imply flavor-kinematics duality, ensuring that all Feynman diagrams satisfy kinematic Jacobi identities. Substituting flavor for kinematics, we derive a new cubic action for the special Galileon theory. In this picture, the vanishing soft behavior of amplitudes is a byproduct of the Weinberg soft theorem.Comment: 5 pages+refs; matched to published versio

Simple Recursion Relations for General Field Theories

On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. Our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.Comment: 27 pages and 2 figures; v2: typos corrected to match journal versio

Hidden Conformal Invariance of Scalar Effective Field Theories

We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension $D=0$. For the case of a quartic ${\cal O}(p^6)$ vertex, classical conformal invariance constrains the theory to be the special Galileon in $D=-2$ dimensions. We also verify the conformal invariance of these theories by showing that their amplitudes are uniquely fixed by the conformal Ward identities. In these theories, conformal invariance is a much more stringent constraint than scale invariance.Comment: 7 page

Leading Effect of CP Violation with Four Generations

In the Standard Model with a fourth generation of quarks, we study the relation between the Jarlskog invariants and the triangle areas in the 4-by-4 CKM matrix. To identify the leading effects that may probe the CP violation in processes involving quarks, we invoke small mass and small angle expansions, and show that these leading effects are enhanced considerably compared to the three generation case by the large masses of fourth generation quarks. We discuss the leading effect in several cases, in particular the possibility of large CP violation in $b \to s$ processes, which echoes the heightened recent interest because of experimental hints.Comment: 12 pages, no figur

Aspects of Effective Field Theories from Scattering Amplitudes

On-shell methods offer an alternative definition of quantum field theory at tree-level. We first determine the space of constructible theories solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory in four dimensions are constructible, but only a subset of amplitudes is constructible in non-renormalizable theories. The obstructions to effective field theories (EFTs) are then lifted for the non-linear sigma model, Dirac-Born-Infeld theory, and the Galileon, using the enhanced soft limits of their amplitudes. We then systematically explore the space of scalar EFTs based on the soft lim- its and power counting of amplitudes. We prove that EFTs with arbitrarily soft behavior are forbidden by on-shell momentum shifts and recursion relations. The 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. 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. Next, a new representation of the nonlinear sigma model is proposed to manifest the duality between flavor and kinematics. The action consists of only cubic interactions, which define the structure constants of an underlying kinematic algebra. The action is invariant under a combination of internal and spacetime symmetries whose conservation equations imply flavor-kinematics duality, ensuring that all Feynman diagrams satisfy kinematic Jacobi identities. Substituting flavor for kinematics, we derive a new cubic action for the special Galileon. The vanishing soft behavior of amplitudes is shown as a byproduct of the Weinberg soft theorem. Finally, we derive a class of one-loop non-renormalization theorems that strongly constrain the running of higher dimension operators in four-dimensional quantum field theory. Our derivation combines unitarity and helicity selection rules at tree level. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model.</p

On-Shell Recursion Relations for Effective Field Theories

We derive the first ever on-shell recursion relations for amplitudes in 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 theories like the non- linear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible.Comment: 5 page

Symmetry for Flavor-Kinematics Duality from an Action

We propose a new representation of the nonlinear sigma model that exhibits a manifest duality between flavor and kinematics. The fields couple exclusively through cubic Feynman vertices which define the structure constants of an underlying kinematic algebra. The action is invariant under a combination of internal and spacetime symmetries whose conservation equations imply flavor-kinematics duality, ensuring that all Feynman diagrams satisfy kinematic Jacobi identities. Substituting flavor for kinematics, we derive a new cubic action for the special Galileon theory. In this picture, the vanishing soft behavior of amplitudes is a by-product of the Weinberg soft theorem