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.
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.
119263398
Multi-loop Integrand Reduction with Computational Algebraic Geometry
We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general parameterisation of any multi-loop integrand in a renormalizable gauge theory. The method relies on computational algebraic geometry techniques such as Grobner bases and primary decomposition of ideals. We present some results for two and three loop amplitudes obtained with the help of the MACAULAY2 computer algebra system and the Mathematica package BASISDET.
118465032
Integration-by-parts identities from the viewpoint of differential geometry
We present a new method to construct integration-by-part (IBP) identities from the viewpoint of differential geometry. Vectors for generating IBP identities are reformulated as differential forms, via Poincar\'{e} duality. Using the tools of differential geometry and commutative algebra, we can efficiently find differential forms which generate on-shell IBP relation without doubled propagator. Various $D=4$ two-loop examples are presented.
118432235
Dual identities inside the gluon and the graviton scattering amplitudes
Recently, Bern, Carrasco and Johansson conjectured dual identities inside the gluon tree scattering amplitudes. In this paper, we use the properties of the heterotic string and open string tree scattering amplitudes to refine and derive these dual identities. These identities can be carried over to loop amplitudes using the unitarity method. Furthermore, given the M-gluon (as well as gluon-gluino) tree amplitudes, M-graviton (as well as graviton-gravitino) tree scattering amplitudes can be written down immediately, avoiding the derivation of Feynman rules and the evaluation of Feynman diagrams for graviton scattering amplitudes.
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.
55981517
Hawking-Moss instanton in nonlinear massive gravity
As a first step toward understanding a lanscape of vacua in a theory of non-linear massive gravity, we consider a landscape of a single scalar field and study tunneling between a pair of adjacent vacua. We study the Hawking-Moss (HM) instanton that sits at a local maximum of the potential, and evaluate the dependence of the tunneling rate on the parameters of the theory. It is found that provided with the same physical HM Hubble parameter HHM, depending on the values of parameters ?3 and ?4 in the action (2.2), the corresponding tunneling rate can be either enhanced or suppressed when compared to the one in the context of General Relativity (GR). Furthermore, we find the constraint on the ratio of the physical Hubble parameter to the fiducial one, which constrains the form of potential. This result is in sharp contrast to GR where there is no bound on the minimum value of the potential.
7757733
Stable bound states of asymmetric dark matter
The simplest renormalizable effective field theories with asymmetric dark matter bound states contain 
two additional gauge singlet fields, one being the dark matter and the other a mediator particle that the dark 
matter annihilates into. We examine the physics of one such model with a Dirac fermion as the dark matter 
and a real scalar mediator. For a range of parameters the Yukawa coupling of the dark matter to the mediator 
gives rise to stable asymmetric dark matter bound states. We derive properties of the bound states including 
nuggets formed from N ≫ 1 dark matter particles. We also consider the formation of bound states in the 
early Universe and direct detection of dark matter bound states. Many of our results also hold for symmetric 
dark matter.
119077959
Probing natural SUSY from stop pair production at the LHC
A bstractWe consider the natural supersymmetry scenario in the framework of the R-parity conserving minimal supersymmetric standard model (called natural MSSM) and examine the observability of stop pair production at the LHC. We first scan the parameters of this scenario under various experimental constraints, including the SM-like Higgs boson mass, the indirect limits from precision electroweak data and B-decays. Then in the allowed parameter space we study the stop pair production at the LHC followed by the stop decay into a top quark plus a lightest neutralino or into a bottom quark plus a chargino. From detailed Monte Carlo simulations of the signals and backgrounds, we find the two decay modes are complementary to each other in probing the stop pair production, and the LHC with $ \sqrt{s}=14 $ TeV and 100 fb−1 luminosity is capable of discovering the stop predicted in natural MSSM up to 450 GeV. If no excess events were observed at the LHC, the 95% C.L. exclusion limits of the stop masses can reach around 537 GeV.
27700488
Long-lived Light Mediator to Dark Matter and Primordial Small Scale Spectrum
We calculate the early universe evolution of perturbations in the dark matter energy density in the context of simple dark sector models containing a GeV scale light mediator. We consider the case that the mediator is long-lived, with lifetime up to a second, and before decaying it temporarily dominates the energy density of the universe. We show that for primordial perturbations that enter the horizon around this period, the interplay between linear growth during matter domination and collisional damping can generically lead to a sharp peak in the spectrum of dark matter density perturbation. As a result, the population of the smallest DM halos gets enhanced. Possible implications of this scenario are discussed.
119698561
Exact solutions to relativistic singular fractional power potentials
We present (exact) solutions of the Dirac equation with equally mixed interactions for a single fermion bounded by the family of fractional power singular potentials. Closed-form expressions as well as numerical values for the energies were obtained. The wave functions and the allowed values of the potential parameters for the first two members of the family are obtained in terms of a set of algebraic equations. The non-relativistic limit is also discussed and using the Hellmann–Feynmann theorem, some useful expectation values are obtained.