arXiv subjects

Fei Teng

Publications and source records attributed to Fei Teng.

At least 181 records · Page 10Linked to original sources

arXiv2019

String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations

We further elaborate on the general construction proposed in arXiv:1812.03369, which connects, via tree-level double copy, massless string amplitudes with color-ordered QFT amplitudes that are given by Cachazo-He-Yuan formulas. The current paper serves as a detailed study of the integration-by-parts procedure for any tree-level massless string correlator outlined in the previous letter. We present two new results in the context of heterotic and (compactified) bosonic string theories. First, we find a new recursive expansion of any multitrace mixed correlator in these theories into a logarithmic part corresponding to the CHY integrand for Yang-Mills-scalar amplitudes, plus correlators with the total number of traces and gluons decreased. By iterating the expansion, we systematically reduce string correlators with any number of subcycles to linear combinations of Parke-Taylor factors and similarly for the case with gluons. Based on this, we then derive a CHY formula for the corresponding $(DF)^2 + {\rm YM} + ϕ^3$ amplitudes. It is the first closed-form result for such multitrace amplitudes and thus greatly extends our result for the single-trace case. As a byproduct, it gives a new CHY formula for all Yang-Mills-scalar amplitudes. We also study consistency checks of the formula such as factorizations on massless poles.

hep-th↗

arXiv2019

On the kinematic algebra for BCJ numerators beyond the MHV sector

The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggest the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. In this paper we introduce a framework that allows us to characterize the algebra beyond the MHV sector. This allows us to both constrain some of the ambiguities of the kinematic algebra, and better control the generalized gauge freedom that is associated with the BCJ numerators. Specifically, in this paper, we work in dimension-agnostic notation and determine the kinematic algebra valid up to certain ${\cal O}\big((\varepsilon_i \cdot \varepsilon_j)^2\big)$ terms that in four dimensions compute the next-to-MHV sector involving two scalars. The kinematic algebra in this sector is simple, given that we introduce tensor currents that generalize standard Yang-Mills vector currents. These tensor currents controls the generalized gauge freedom, allowing us to generate multiple different versions of BCJ numerators from the same kinematic algebra. The framework should generalize to other sectors in Yang-Mills theory.

hep-th↗

arXiv2019

String amplitudes from field-theory amplitudes and vice versa

We present an integration-by-parts reduction of any massless tree-level string correlator to an equivalence class of logarithmic functions, which can be used to define a field-theory amplitude via a Cachazo-He-Yuan (CHY) formula. The string amplitude is then shown to be the double copy of the field-theory one and a special disk/sphere integral. The construction is generic as it applies to any correlator that is a rational function of correct SL(2) weight. By applying the reduction to open bosonic/heterotic strings, we get a closed-form CHY integrand for the $(DF)^2+\text{YM}+ϕ^3$ theory.

hep-th↗

arXiv2019

Simultaneous Scheduling of Multiple Frequency Services in Stochastic Unit Commitment

The reduced level of system inertia in low-carbon power grids increases the need for alternative frequency services. However, simultaneously optimising the provision of these services in the scheduling process, subject to significant uncertainty, is a complex task given the challenge of linking the steady-state optimisation with frequency dynamics. This paper proposes a novel frequency-constrained Stochastic Unit Commitment (SUC) model which, for the first time, co-optimises energy production along with the provision of synchronised and synthetic inertia, Enhanced Frequency Response (EFR), Primary Frequency Response (PFR) and a dynamically-reduced largest power infeed. The contribution of load damping is modelled through a linear inner approximation. The effectiveness of the proposed model is demonstrated through several case studies for Great Britain's 2030 power system, which highlight the synergies and conflicts among alternative frequency services, as well as the significant economic savings and carbon reduction achieved by simultaneously optimising all these services.

math.OC↗

arXiv2019

Dual-Timescale Spectrum Management in Small-Cell Wireless Networks

To attain the targeted data rates of next generation cellular networks requires dense deployment of small cells in addition to macro cells which provide wide coverage. Dynamic radio resource management is crucial to the success of such heterogeneous networks due to much more pronounced traffic and interference variations in small cells. This work proposes a framework for spectrum management organized according to two timescales, which include 1) centralized optimization on a moderate timescale corresponding to typical duration of user sessions (several seconds to minutes in today's networks), and 2) distributed spectrum allocation on a fast timescale corresponding to typical latency requirements (a few milliseconds). An optimization problem is formulated to allocate resources on the slower timescale with consideration of (distributed) opportunistic scheduling on the faster timescale. Both fixed and fully flexible user association schemes are considered. Iterative algorithms are developed to solve these optimization problems efficiently for a cluster of cells with guaranteed convergence. Simulation results demonstrate advantages of the proposed framework and algorithms.

cs.IT↗

arXiv2018

Unraveling conformal gravity amplitudes

Conformal supergravity amplitudes are obtained from the double-copy construction using gauge-theory amplitudes, and compared to direct calculations starting from conformal supergravity Lagrangians. We consider several different theories: minimal ${\cal N}=4$ conformal supergravity, non-minimal ${\cal N}=4$ Berkovits-Witten conformal supergravity, mass-deformed versions of these theories, as well as supersymmetry truncations thereof. Coupling the theories to a Yang-Mills sector is also considered. For all cases we give the gravity Lagrangians that the double copy implicitly generates. The two main results are: we determine a Lagrangian for the non-minimal Berkovits-Witten theory, and we uncover the double-copy prescription for the minimal ${\cal N}=4$ conformal supergravity.

hep-th↗

arXiv2018

On the Prospects for Detecting a Net Photon Circular Polarization Produced by Decaying Dark Matter

If dark matter interactions with Standard Model particles are $CP$-violating, then dark matter annihilation/decay can produce photons with a net circular polarization. We consider the prospects for experimentally detecting evidence for such a circular polarization. We identify optimal models for dark matter interactions with the Standard Model, from the point of view of detectability of the net polarization, for the case of either symmetric or asymmetric dark matter. We find that, for symmetric dark matter, evidence for net polarization could be found by a search of the Galactic Center by an instrument sensitive to circular polarization with an efficiency-weighted exposure of at least $50000~\text{cm}^2~\text{yr}$, provided the systematic detector uncertainties are constrained at the $1\%$ level. Better sensitivity can be obtained in the case of asymmetric dark matter. We discuss the prospects for achieving the needed level of performance using possible detector technologies.

astro-ph.CO↗

arXiv2018

Permutation in the CHY-Formulation

The CHY-integrand of bi-adjoint cubic scalar theory is a product of two PT-factors. This pair of PT-factors can be interpreted as defining a permutation. We introduce the cycle representation of permutation in this paper for the understanding of cubic scalar amplitude. We show that, given a permutation related to the pair of PT-factors, the pole and vertex information of Feynman diagrams of corresponding CHY-integrand is completely characterized by the cycle representation of permutation. Inversely, we also show that, given a set of Feynman diagrams, the cycle representation of corresponding PT-factor can be recursively constructed. In this sense, there exists a deep connection between cycles of a permutation and amplitude. Based on these results, we have investigated the relations among different independent pairs of PT-factors in the context of cycle representation as well as the multiplication of cross-ratio factors.

hep-th↗

arXiv2017

Expansion of All Multitrace Tree Level EYM Amplitudes

In this paper, we investigate the expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes. First, we propose two types of recursive expansions of tree level EYM amplitudes with an arbitrary number of gluons, gravitons and traces by those amplitudes with fewer traces or/and gravitons. Then we give many support evidence, including proofs using the Cachazo-He-Yuan (CHY) formula and Britto-Cachazo-Feng-Witten (BCFW) recursive relation. As a byproduct, two types of generalized BCJ relations for multitrace EYM are further proposed, which will be useful in the BCFW proof. After one applies the recursive expansions repeatedly, any multitrace EYM amplitudes can be given in the Kleiss-Kuijf (KK) basis of tree level color ordered Yang-Mills (YM) amplitudes. Thus the Bern-Carrasco-Johansson (BCJ) numerators, as the expansion coefficients, for all multitrace EYM amplitudes are naturally constructed.

hep-th↗

arXiv2017

Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame

Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of tree level single trace Einstein-Yang-Mills (EYM) amplitudes with arbitrary number of gluons and gravitons, which is valid for general spacetime dimensions and any helicity configurations. The recursion is written in terms of fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be further carried out until we reach an expansion in terms of pure YM amplitudes in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning tree structure rooted on gluons whose vertices are gravitons. We further propose a set of graph theoretical rules based on spanning trees that evaluate directly the pure YM expansion coefficients.

hep-th↗

arXiv2017

BCJ numerators from reduced Pfaffian

By expanding the reduced Pfaffian in the tree level Cachazo-He-Yuan (CHY) integrands for Yang-Mills (YM) and nonlinear sigma model (NLSM), we can get the Bern-Carrasco-Johansson (BCJ) numerators in Del Duca-Dixon-Maltoni (DDM) form for arbitrary number of particles in any spacetime dimensions. In this work, we give a set of very straightforward graphic rules based on spanning trees for a direct evaluation of the BCJ numerators for YM and NLSM. Such rules can be derived from the Laplace expansion of the corresponding reduced Pfaffian. For YM, the each one of the $(n-2)!$ DDM form BCJ numerators contains exactly $(n-1)!$ terms, corresponding to the increasing trees with respect to the color order. For NLSM, the number of nonzero numerators is at most $(n-2)!-(n-3)!$, less than those of several previous constructions.

hep-th↗

arXiv2017

Sharing of Unlicensed Spectrum by Strategic Operators

Facing the challenge of meeting ever-increasing demand for wireless data, the industry is striving to exploit large swaths of spectrum which anyone can use for free without having to obtain a license. Major standards bodies are currently considering a proposal to retool and deploy Long Term Evolution (LTE) technologies in unlicensed bands below 6 GHz. This paper studies the fundamental questions of whether and how the unlicensed spectrum can be shared by intrinsically strategic operators without suffering from the tragedy of the commons. A class of general utility functions is considered. The spectrum sharing problem is formulated as a repeated game over a sequence of time slots. It is first shown that a simple static sharing scheme allows a given set of operators to reach a subgame perfect Nash equilibrium for mutually beneficial sharing. The question of how many operators will choose to enter the market is also addressed by studying an entry game. A sharing scheme which allows dynamic spectrum borrowing and lending between operators is then proposed to address time-varying traffic and proved to achieve perfect Bayesian equilibrium. Numerical results show that the proposed dynamic sharing scheme outperforms static sharing, which in turn achieves much higher revenue than uncoordinated full-spectrum sharing. Implications of the results to the standardization and deployment of LTE in unlicensed bands (LTE-U) are also discussed.

cs.IT↗

arXiv2016

Gamma-ray signal from Dark Matter Annihilation mediated by mixing scalar mediators

We present here a study of the direct and indirect detection prospects of a generic dark matter simplified model, in which the Majorana dark matter interacts only with a Standard Model lepton and a pair of uncolored mixing scalar mediators. We first show that the mixing angle significantly changes the feature of internal bremsstrahlung, as well as the flux ratio of $γγ$ and $γZ$ line signals. The $CP$-violation phase will introduce an polarization asymmetry in the $γγ$ final state. Then we study the direct detection prospect and discuss the complimentarity of these two search strategies.

hep-ph↗

arXiv2016

Characterizing the solutions to scattering equations that support tree-level $\text{N}^{k}\text{MHV}$ gauge/gravity amplitudes

In this paper we define, independent of theories, two discriminant matrices involving a solution to the scattering equations in four dimensions, the ranks of which are used to divide the solution set into a disjoint union of subsets. We further demonstrate, {entirely within the Cachazo-He-Yuan formalism,} that each subset of solutions gives nonzero contribution to tree-level $\text{N}^{k}\text{MHV}$ gauge/gravity amplitudes only for a specific value of $k$. Thus the solutions can be characterized by the rank of their discriminant matrices, which in turn determines the value of $k$ of the $\text{N}^{k} \text{MHV}$ amplitudes a solution can support. As another application of the technique developed, we show analytically that in Einstein-Yang-Mills theory, if all gluons have the same helicity, the tree-level single-trace amplitudes must vanish.

hep-th↗

arXiv2016

Correspondence between Solutions of Scattering Equations and Scattering Amplitudes in Four Dimensions

In this talk, we review our recent work on direct evaluation of tree-level MHV amplitudes by Cachazo-He-Yuan (CHY) formula. We also investigate the correspondence between solutions to scattering equations and amplitudes in four dimensions along this line. By substituting the MHV solution of scattering equations into the integrated CHY formula, we explicitly calculate the tree-level MHV amplitudes for four dimensional Yang-Mills theory and gravity. These results naturally reproduce the Parke-Taylor and Hodges formulas. In addition, we derive a new compact formula for tree-level single-trace MHV amplitudes in Einstein-Yang-Mills theory, which is equivalent to the known Selivanov-Bern-De Freitas-Wong (SBDW) formula. Other solutions do not contribute to the MHV amplitudes in Yang-Mills theory, gravity and Einstein-Yang-Mills theory. We further investigate the correspondence between solutions of scattering equation and helicity configurations beyond MHV and proposed a method for characterizing solutions of scattering equations.

hep-th↗

arXiv2016

Simplified Dark Matter Models with Charged Mediators: Prospects for Direct Detection

We consider direct detection prospects for a class of simplified models of fermionic dark matter (DM) coupled to left and right-handed Standard Model fermions via two charged scalar mediators with arbitrary mixing angle $α$. DM interactions with the nucleus are mediated by higher electromagnetic moments, which, for Majorana DM, is the anapole moment. After giving a full analytic calculation of the anapole moment, including its $α$ dependence, and matching with limits in the literature, we compute the DM-nucleon scattering cross-section and show the LUX and future LZ constraints on the parameter space of these models. We then compare these results with constraints coming from $Fermi$-LAT continuum and line searches. Results in the supersymmetric limit of these simplified models are provided in all cases. We find that future direct detection experiments will be able to probe most of the parameter space of these models for $\mathcal{O}(100-200)$ GeV DM and lightest mediator mass $\lesssim \mathcal{O}(5\%)$ larger than the DM mass. The direct detection prospects dwindle for larger DM mass and larger mass gap between the DM and the lightest mediator mass, although appreciable regions are still probed for $\mathcal{O}(200)$ GeV DM and lightest mediator mass $\lesssim \mathcal{O}(20\%)$ larger than the DM mass. The direct detection bounds are also attenuated near certain "blind spots" in the parameter space, where the anapole moment is severely suppressed due to cancellation of different terms. We carefully study these blind spots and the associated $Fermi$-LAT signals in these regions.

hep-ph↗

arXiv2016

Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism

In this paper we extend our techniques, developed in a previous paper (Du, etc, JHEP 05(2016)086) for direct evaluation of arbitrary $n$-point tree-level MHV amplitudes in 4d Yang-Mills and gravity theory using the Cachazo-He-Yuan (CHY) formalism, to the 4d Einstein-Yang-Mills (EYM) theory. Any single-trace color-ordered $n$-point tree-level MHV amplitude in EYM theory, obtained by a direct evaluation of the CHY formula, is of an elegant factorized form of a Parke-Taylor factor and a Hodges determinant, much simpler and more compact than the existing formulas in the literature. We prove that our new expression is equivalent to the conjectured Selivanov-Bern-De Freitas-Wong (SBDW) formula, with the help of a new theorem showing that the SBDW generating function has a graph theory interpretation. Together with Ref. (Du, etc, JHEP 05(2016)086), we provide strong analytic evidence for hidden simplicity in quantum field theory.

hep-th↗

arXiv2016

Gamma-ray Signals from Dark Matter Annihilation Via Charged Mediators

We consider a simplified model in which Majorana fermion dark matter annihilates to charged fermions through exchange of charged mediators. We consider the gamma-ray signals arising from the processes $XX \rightarrow \bar f f γ$, $γγ$, and $γZ$ in the most general case, including non-trivial fermion mass and non-trivial left-right mixing and $CP$-violating phase for the charged mediators. In particular, we find the most general spectrum for internal bremsstrahlung, which interpolates between the regimes dominated by virtual internal bremsstrahlung and by final state radiation. We also examine the variation in the ratio $σ(γγ) / σ(γZ)$ and the helicity asymmetry in the $XX \rightarrow γγ$ process, each as a function of mixing angle and $CP$-violating phase. As an application, we apply these results to searches for a class of MSSM models.

hep-ph↗