On Baryogenesis and nn-Oscillations

We study a simple model where color sextet scalars violate baryon number at tree level but do not give rise to proton decay. In particular, we include one light and two heavy sextets with ΔB=2 baryon number violating interactions that induce neutron anti-neutron oscillations. This setup also suggests an intimate connection to the generation of the observed baryon asymmetry in the Universe via the out of equilibrium decay of the heavy sextet scalars at around 10^(14) GeV. The large SU(3)-color charges of the scalar fields involved in generating the baryon asymmetry motivate us to study potentially significant washout effects. We numerically solve a set of Boltzmann evolution equations and find restrictions on the available model parameters imposed by successful high scale baryogenesis. Combining our new numerical results for baryogenesis with nn-oscillation predictions and collider limits on the light sextet, we identify parameter regions where this model can be probed by current and future experiments

Amplitudes at Infinity

We investigate the asymptotically large loop-momentum behavior of multi-loop amplitudes in maximally supersymmetric quantum field theories in four dimensions. We check residue-theorem identities among color-dressed leading singularities in $\mathcal{N}=4$ supersymmetric Yang-Mills theory to demonstrate the absence of poles at infinity of all MHV amplitudes through three loops. Considering the same test for $\mathcal{N}=8$ supergravity leads us to discover that this theory does support non-vanishing residues at infinity starting at two loops, and the degree of these poles grow arbitrarily with multiplicity. This causes a tension between simultaneously manifesting ultraviolet finiteness---which would be automatic in a representation obtained by color-kinematic duality---and gauge invariance---which would follow from unitarity-based methods.Comment: 4+1+1 pages; 15 figures; details provided in ancillary Mathematica file

Bootstrapping two-loop Feynman integrals for planar N=4 sYM

We derive analytic results for the symbol of certain two-loop Feynman integrals relevant for seven- and eight-point two-loop scattering amplitudes in planar $\mathcal{N}=4$ super-Yang--Mills theory. We use a bootstrap inspired strategy, combined with a set of second-order partial differential equations that provide powerful constraints on the symbol ansatz. When the complete symbol alphabet is not available, we adopt a hybrid approach. Instead of the full function, we bootstrap a certain discontinuity for which the alphabet is known. Then we write a one-fold dispersion integral to recover the complete result. At six and seven points, we find that the individual Feynman integrals live in the same space of functions as the amplitude, which is described by the 9- and 42-letter cluster alphabets respectively. Starting at eight points however, the symbol alphabet of the MHV amplitude is insufficient for individual integrals. In particular, some of the integrals require algebraic letters involving four-mass box square-root singularities. We point out that these algebraic letters are relevant at the amplitude level directly starting with N$^2$MHV amplitudes even at one loop.Comment: 49 page

Gravity On-shell Diagrams

We study on-shell diagrams for gravity theories with any number of super-symmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only d log-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for =8N=8 supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinity are present, in complete agreement with the conjecture presented in [1]

The planar two-loop four-point form factor in maximally supersymmetric Yang-Mills theory

We derive the four-dimensional integrand of the maximal-helicity-violating four-particle form factor for the chiral part of the stress-tensor supermultiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory at two loops. In our integrand construction, we adopt a special integrand basis with triangle powercounting where each basis element has unit leading singularities on all co-dimension eight residues. This basis was first constructed in the context of two-loop $n$-point scattering amplitudes in $\mathcal{N}=4$ beyond the planar limit and we describe here, how to directly utilize it for the form factor computation. Our result sets the stage for an independent confirmation of the symbol level bootstrap results of Dixon et al.~via direct evaluation. The imminent availability of all relevant two-loop five-point, one-mass master integrals will permit further investigations of a set of marvelous (self-)dualities between form factors and scattering amplitudes in planar $\mathcal{N}=4$ in the near future.Comment: 27 pages+references, 1 figure, 1 tabl

Prescriptive Unitarity

We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in the case of planar, maximally supersymmetric Yang-Mills theory (SYM), where we construct closed-form representations of all (n-point N^kMHV) scattering amplitudes through three loops. The prescriptive approach contrasts with the ordinary description of unitarity-based methods by avoiding any need for linear algebra to determine integrand coefficients. We describe this approach in general terms as it should have applications to many quantum field theories, including those without planarity, supersymmetry, or massless spectra defined in any number of dimensions