118631762
Multivariate residues and maximal unitarity
A bstractWe extend the maximal unitarity method to amplitude contributions whose cuts define multidimensional algebraic varieties. The technique is valid to all orders and is explicitly demonstrated at three loops in gauge theories with any number of fermions and scalars in the adjoint representation. Deca-cuts realized by replacement of real slice integration contours by higher-dimensional tori encircling the global poles are used to factorize the planar triple box onto a product of trees. We apply computational algebraic geometry and multivariate complex analysis to derive unique projectors for all master integral coefficients and obtain compact analytic formulae in terms of tree-level data.
54593568
On genera of curves from high-loop generalized unitarity cuts
A bstractGeneralized unitarity cut of a Feynman diagram generates an algebraic system of polynomial equations. At high-loop levels, these equations may define a complex curve or a (hyper-)surface with complicated topology. We study the curve cases, i.e., a 4-dimensional L-loop diagram with (4L−1) cuts. The topology of a complex curve is classified by its genus. Hence in this paper, we use computational algebraic geometry to calculate the genera of curves from two and three-loop unitarity cuts. The global structure of degenerate on-shell equations under some specific kinematic configurations is also sketched. The genus information can also be used to judge if a unitary cut solution could be rationally parameterized.
117774008
Remarks on the Identities of Gluon Tree Amplitudes
Recently, Bjerrum-Bohr, Damgaard, Feng, and Sondergaard derived a set of new interesting quadratic identities of the Yang-Mills (YM) tree scattering amplitudes, besides Bern-Carrasco-Johansson (BCJ) identities. Here we comment that these quadratic identities of YM amplitudes actually follow directly from the KLT (Kawai-Lewellen-Tye) relation for graviton-dilaton-axion scattering amplitudes (in four-dimensional spacetime). This clarifies their physical origin and also provides a simpler version of the new identities. We also comment that the recently discovered BCJ identities of YM helicity amplitudes, at least for the maximal helicity-violating case, can be verified by using (repeatedly) the Schouten identity. We also point out additional quadratic identities that can be written down from the KLT relations.
118419441
Multi-loop integrand reduction techniques
We review recent progress in D-dimensional integrand reduction algorithms for two loop amplitudes and give examples of their application to non-planar maximal cuts of the five-point all-plus helicity amplitude in QCD.
118592385
The complete KLT-map between gravity and gauge theories
A bstractWe present the complete map of any pair of super Yang-Mills theories to supergravity theories as dictated by the KLT relations in four dimensions. Symmetries and the full set of associated vanishing identities are derived. A graphical method is introduced which simplifies counting of states, and helps in identifying the relevant set of symmetries.
119221055
An integrand reconstruction method for three-loop amplitudes
A bstractWe consider the maximal cut of a three-loop four point function with massless kinematics. By applying Gröbner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an arbitrary triple-box configuration via generalized unitarity cuts. As an example we present analytic results for the three loop triple-box contribution to gluon-gluon scattering in Yang-Mills with adjoint fermions and scalars in terms of three master integrals.
119165682
Electroweak cogenesis
A bstractWe propose a simple renormalizable model of baryogenesis and asymmetric dark matter generation at the electroweak phase transition. Our setup utilizes the two Higgs doublet model plus two complex gauge singlets, the lighter of which is stable dark matter. The dark matter is charged under a global symmetry that is broken in the early universe but restored during the electroweak phase transition. Because the ratio of baryon and dark matter asymmetries is controlled by model parameters, the dark matter need not be light. Thus, new force carriers are unnecessary and the symmetric dark matter abundance can be eliminated via Higgs portal interactions alone. Our model places a rough upper bound on the dark matter mass, and has implications for direct detection experiments and particle colliders.
119272201
Angular momentum in non-relativistic QED and photon contribution to spin of hydrogen atom
Abstract We study angular momentum in non-relativistic quantum electrodynamics (NRQED). We construct the effective total angular momentum operator by applying Noether's theorem to the NRQED lagrangian. We calculate the NRQED matching for the individual components of the QED angular momentum up to one loop. We illustrate an application of our results by the first calculation of the angular momentum of the ground state hydrogen atom carried in radiative photons, α em 3 / 18 π , which might be measurable in future atomic experiments.
118409577
Proton Sea Quark Flavour Asymmetry and Roper Resonance
We study the proton and the Roper resonance together with the meson cloud model, by constructing a Hamiltonian matrix and solving the eigenvalue equation. The proton sea quark flavour asymmetry and some properties of the Roper resonance are thus reproduced in one scheme.
2107479
Local Quasitriangular Hopf Algebras
We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.
119129530
Exact polynomial solutions of second order differential equations and their applications
We find all polynomials Z(z) such that the differential equation where X(z), Y(z), Z(z) are polynomials of degree at most 4, 3, 2, respectively, has polynomial solutions S(z) = ?ni = 1(z ? zi) of degree n with distinct roots zi. We derive a set of n algebraic equations which determine these roots. We also find all polynomials Z(z) which give polynomial solutions to the differential equation when the coefficients of X(z) and Y(z) are algebraically dependent. As applications to our general results, we obtain the exact (closed-form) solutions of the Schr?dinger-type differential equations describing: (1) two Coulombically repelling electrons on a sphere; (2) Schr?dinger equation from the kink stability analysis of ?6-type field theory; (3) static perturbations for the non-extremal Reissner?Nordstr?m solution; (4) planar Dirac electron in Coulomb and magnetic fields; and (5) O(N) invariant decatic anharmonic oscillator.