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.
14406149
Multi-field inflation with a random potential
Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian-like motion with a drift in the D-dimensional field space, allowing entropic perturbation modes to continuously and randomly feed into the adiabatic mode. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario where the stochastic scatterings are frequent but mild, the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, in which the coarse-grained motion of the inflaton is significantly slowed down by the scatterings, leads to rich phenomenologies. The power spectrum exhibits primordial fluctuations on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and have been smoothed out by binning of data points. With more data coming in the future, we expect these features can be detected or falsified. On the other hand the tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced by the large ratio of the Brownian-like motion speed over the drift speed. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, and is negligible in the weakly random scenario. However, non-Gaussianity can possibly be enhanced by resonant effects in the strongly random scenario or arise from the entropic perturbations during the onset of (p)reheating if the background inflaton trajectory exhibits particular properties. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.
119230697
Elliptic functions and maximal unitarity
Modern perturbative scattering amplitudes in gauge theories such as QCD are calculated from general principles of analyticity and unitarity without inspecting Feynman diagrams. By virtue of analyticity, amplitudes are reconstructed from their singularity structure, while unitarity ensures that residues factorize onto simpler objects. Starting from complex internal momenta and three-point amplitudes whose form is entirely xed by eld theory arguments, all trees are generated recursively
18535552
Massive nonplanar two-loop maximal unitarity
A bstractWe explore maximal unitarity for nonplanar two-loop integrals with up to four massive external legs. In this framework, the amplitude is reduced to a basis of master integrals whose coefficients are extracted from maximal cuts. The hepta-cut of the nonplanar double box defines a nodal algebraic curve associated with a multiply pinched genus-3 Riemann surface. All possible configurations of external masses are covered by two distinct topological pictures in which the curve decomposes into either six or eight Riemann spheres. The procedure relies on consistency equations based on vanishing of integrals of total derivatives and Levi-Civita contractions. Our analysis indicates that these constraints are governed by the global structure of the maximal cut. Lastly, we present an algorithm for computing generalized cuts of massive integrals with higher powers of propagators based on the Bezoutian matrix method.
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.
657952
Coleman-De Luccia Tunneling and The Gibbons-Hawking Temperature
We study Coleman–de Luccia tunneling in some detail. We show that, for a single scalar field potential with a true and a false vacuum, there are four types of tunneling, depending on the properties of the potential. A general tunneling process involves a combination of thermal (Gibbons–Hawking temperature) fluctuation part way up the barrier followed by quantum tunneling. The thin-wall approximation is a special limit of the case (of only quantum tunneling) where inside the nucleation bubble is the true vacuum while the outside reaches the false vacuum. Hawking–Moss tunneling is the (only thermal fluctuation) limit of the case where the inside of the bubble does not reach the true vacuum at the moment of its creation, and the outside is cut off by the de Sitter horizon before it reaches the false vacuum. A typical tunneling process is a combination of thermal and quantum tunnelings. We estimate the tunneling rate for this case and find that the corrections to the Hawking–Moss formula can be large. In all cases, we see that the Euclidean action of the bounce decreases rapidly as the vacuum energy density increases, signaling that the tunneling is not exponentially suppressed. This phenomenon may be interpreted as a finite temperature effect due to the Gibbons–Hawking temperature of the de Sitter space. As an application, we discuss the implication of this tunneling property to the cosmic landscape.
119978808
AFFINE (TWO-LOOP) WZNW MODEL, REDUCTION AND SPONTANEOUS BREAKDOWN OF CONFORMAL SYMMETRY
A large theory—the affine (two-loop) WZNW theory, which is universal in the sense that (at least classically) conformal and integrable models may be considered as its various reductions, has been proposed in our recent papers with Bonora and Martellini. In this letter we study a different Hamiltonian reduction (named as type III reduction in the text) of the affine (two-loop) WZNW model and discuss the integrability property of the reduced model. By a BRST analysis, we elaborate on a previously introduced idea regarding integrable systems as spontaneously conformal-symmetry-broken versions of CFTs.
122482555
Exact solutions of the schrodinger equation with spherically symmetric octic potential
We present exact solutions of the Schrodinger equation with spherically symmetric octic potential. We give closed-form expressions for the energies and the wave functions as well as the allowed values of the potential parameters in terms of a set of algebraic equations.
118387796
Majorana neutrino mass matrices with three texture zeros and the sterile neutrino
As a consequence of the LSND anomaly and other hints of an eV scale sterile neutrino from particle physics and cosmology, the neutrino sector of the standard model of particle physics has to be extended and the smallest extension is the (3+1) model, i.e. three active neutrinos plus one sterile one. In this work we study the neutrino mass matrix $M_\nu$ with three texture zeros in the (3+1) model, assuming all the neutrino states are of Majorana type. With the mass hierarchy between the active and sterile neutrinos as well as the smallness of the reactor neutrino mixing and active-sterile mixing, the analytical expressions can be greatly simplified. We systematically examine all the 120 texture zeros, via both analytical and numerical analysis, and find that the 100 textures with zeros in the fourth column and row of $M_\nu$ can hardly be compatible with experiments whereas 19 of the other 20 are feasible. We can foresee that the active neutrino masses are required to be around 0.01 eV and the next generation neutrinoless double beta decay experiments are promising to test these textures. Many other phenomenologically meaningful predictions are also obtained. All the CP conserving (3+1) textures with three zeros are excluded by experiments.
14103118
Integrable electron model with correlated hopping and quantum supersymmetry
Abstract We give the q -deformed analogue of a recently introduced electron model which generalizes the Hubbard model with additional correlated hopping terms and electron pair hopping. The model contains two independent parameters and is invariant with respect to the quantum superalgebra U q ( gl (2|1)). It is shown to be integrable in one dimension by means of the quantum inverse scattering method.
9959506
TWISTED QUANTUM AFFINE ALGEBRAS AND SOLUTIONS TO THE YANG-BAXTER EQUATION
We construct spectral-parameter-dependent R matrices for the quantized enveloping algebras of twisted affine Lie algebras. These give new solutions to the spectral-parameter-dependent quantum Yang-Baxter equation.