Related papers: Connecting Scalar Amplitudes using The Positive Tr…
We apply on-shell methods to the bottom-up construction of electroweak amplitudes, allowing for both renormalizable and non-renormalizable interactions. We use the little-group covariant massive-spinor formalism, and flesh out some of its…
Scattering and production amplitudes involving scalar resonances are known, according to Watson's theorem, to share the same phase $\delta(s)$. We show that, at low energies, the production amplitude is fully determined by the combination…
The concept of phase space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more…
We study a quartic matrix model with partition function $Z=\int d\ M\exp{\rm Tr}\ (-\Delta M^2-\frac{\lambda}{4}M^4)$. The integral is over the space of Hermitian $(\Lambda+1)\times(\Lambda+1)$ matrices, the matrix $\Delta$, which is not a…
Dai and Pennington have performed a comprehensive analysis of essentially all pion and kaon pair production data from two-photon collisions below 1.5 GeV, including all high statistics results from Belle, as well as the older data from Mark…
I review some recent work on the problem of multiparticle production in a phi^4-theory with an O(N) symmetry. Threshold amplitudes with fixed number of produced particles are exactly calculated at large-N to all loops and vanish on mass…
The amplitudes of the non-linear sigma model can be obtained from those of Tr($\Phi^3$) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr($\Phi^3$)…
The scalar field exchange diagram for the correlation function of four scalar operators is evaluated in anti-de Sitter space, $AdS_{d+1}$. The conformal dimensions $\Delta_i$, $i=1,...,4$ of the scalar operators and the dimension $\Delta$…
In truncated partial-wave analysis, one fits observables that are bilinear in the amplitudes rather than the amplitudes themselves. Truncation is therefore not merely a restriction of the amplitude basis, but of the bilinear interference…
In these notes we use the recently found relation between facets of tropical Grassmannians and generalizations of Feynman diagrams to compute all "biadjoint amplitudes" for $n=7$ and $k=3$. We also study scattering equations on $X(3,7)$,…
We extend our model for the pion, which we used previously to calculate its diagonal structure function, to the off-forward case. The imaginary part of the off-forward gamma* pi -> gamma* pi scattering amplitude is evaluated in the chiral…
We present a complete set of 4-point amplitudes in the constructive Standard Model at tree level. Any 4-point amplitude can be obtained from the results presented here by a suitable choice of masses, a permutation of the particles (by…
We present a dispersive representation of the $\gamma N\rightarrow \pi N$ partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for $\pi N$ final-state-interaction…
We consider certain elliptic modular graph functions that arise in the asymptotic expansion around the non--separating node of genus two string invariants that appear in the integrand of the $D^8 R^4$ interaction in the low momentum…
Scaffolds are the one-dimensional skeleta of high-dimensional flag simplicial complexes of nonpositive curvature. They generalize the phylogenetic trees of Trop G(2,n) to arbitrary $k$, drawing together SL(k)-web bases, affine buildings,…
We present full analytic results for the four-point one-loop amplitude of a conformally coupled scalar in four-dimensional Anti-de-Sitter space dual to a primary operator with scaling dimension 1. The computation is based on an intriguing…
In this paper we study the renormalization of the Schwinger-Dyson equations that arise in the auxiliary field formulation of the O(N) $\phi^4$ field theory. The auxiliary field formulation allows a simple interpretation of the large-N…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…
We define a Mellin amplitude for CFT$_1$ four-point functions. Its analytical properties are inferred from physical requirements on the correlator. We discuss the analytic continuation that is necessary for a fully nonperturbative…
Motivated by our previous work on hypergeometric functions and the parbelos constant, we perform a deeper investigation on the interplay among generalized complete elliptic integrals, Fourier-Legendre (FL) series expansions, and ${}_p F_q$…