arXiv subjects

Bo Feng

Publications and source records attributed to Bo Feng.

At least 91 records · Page 5Linked to original sources

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.

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arXiv2017

Expansion of Einstein-Yang-Mills Amplitude

In this paper, we provide a thorough study on the expansion of single trace Einstein-Yang-Mills amplitudes into linear combination of color-ordered Yang-Mills amplitudes, from various different perspectives. Using the gauge invariance principle, we propose a recursive construction, where EYM amplitude with any number of gravitons could be expanded into EYM amplitudes with less number of gravitons. Through this construction, we can write down the complete expansion of EYM amplitude in the basis of color-ordered Yang-Mills amplitudes. As a byproduct, we are able to write down the polynomial form of BCJ numerator, i.e., numerators satisfying the color-kinematic duality, for Yang-Mills amplitude. After the discussion of gauge invariance, we move to the BCFW on-shell recursion relation and discuss how the expansion can be understood from the on-shell picture. Finally, we show how to interpret the expansion from the aspect of KLT relation and the way of evaluating the expansion coefficients efficiently.

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arXiv2017

Derivation of Feynman Rules for Higher Order Poles Using Cross-ratio Identities in CHY Construction

In order to generalize the integration rules to general CHY integrands which include higher order poles, algorithms are proposed in two directions. One is to conjecture new rules, and the other is to use the cross-ratio identity method. In this paper,we use the cross-ratio identity approach to re-derive the conjectured integration rules involving higher order poles for several special cases: the single double pole, single triple pole and duplex-double pole. The equivalence between the present formulas and the previously conjectured ones is discussed for the first two situations.

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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.

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arXiv2017

Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism

For a physical field theory, the tree-level amplitudes should possess only single poles. However, when computing amplitudes with Cachazo-He-Yuan (CHY) formulation, individual terms in the intermediate steps will contribute higher-order poles. In this paper, we investigate the cancelation of higher-order poles in CHY formula with Pfaffian as the building block. We develop a diagrammatic rule for expanding the reduced Pfaffian. Then by organizing diagrams in appropriate groups and applying the cross-ratio identities, we show that all potential contributions to higher-order poles in the reduced Pfaffian are canceled out, i.e., only single poles survive in Yang-Mills theory and gravity. Furthermore, we show the cancelations of higher-order poles in other field theories by introducing appropriate truncations, based on the single pole structure of Pfaffian.

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arXiv2017

Chiral Magnetic Effect in a Lattice Model

We study analytically the one-loop contribution to the Chiral Magnetic Effect(CME) using lattice regularization with a Wilson fermion field. In the continuum limit, we find that the chiral magnetic current vanishes at nonzero temperature but emerges at zero temperature consistent with that found by Pauli-Villas regularization. For finite lattice size, however, the chiral magnetic current is nonvanishing at nonzero temperature. But the numerical vaule of the coefficient of CME current is very small compared with that extracted from the full QCD simulation for the same lattice parameters. The possibility of higher order corrections from QCD dynamics is also assessed.

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arXiv2016

Analytic Representations of Yang-Mills Amplitudes

Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space---fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Mobius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.

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arXiv2016

Note on recursion relations for the $\mathcal{Q}$-cut representation

In this note, we study the $\mathcal{Q}$-cut representation by combining it with BCFW deformation. As a consequence, the one-loop integrand is expressed in terms of a recursion relation, i.e., $n$-point one-loop integrand is constructed using tree-level amplitudes and $m$-point one-loop integrands with $m\leq n-1$. By giving explicit examples, we show that the integrand from the recursion relation is equivalent to that from Feynman diagrams or the original $\mathcal{Q}$-cut construction, up to scale free terms.

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arXiv2016

Manifesting Color-Kinematics Duality in the Scattering Equation Formalism

We prove that the scattering equation formalism for Yang-Mills amplitudes can be used to make manifest the theory's color-kinematics duality. This is achieved through a concrete reduction algorithm which renders this duality manifest term-by-term. The reduction follows from the recently derived set of identities for amplitudes expressed in the scattering equation formalism that are analogous to monodromy relations in string theory. A byproduct of our algorithm is a generalization of the identities among gravity and Yang-Mills amplitudes.

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arXiv2016

Cross-ratio Identities and Higher-order Poles of CHY-integrand

The evaluation of generic Cachazo-He-Yuan(CHY)-integrands is a big challenge and efficient computational methods are in demand for practical evaluation. In this paper, we propose a systematic decomposition algorithm by using cross-ratio identities, which provides an analytic and easy to implement method for the evaluation of any CHY-integrand. This algorithm aims to decompose a given CHY-integrand containing higher-order poles as a linear combination of CHY-integrands with only simple poles in a finite number of steps, which ultimately can be trivially evaluated by integration rules of simple poles. To make the method even more efficient for CHY-integrands with large number of particles and complicated higher-order pole structures, we combine the $Λ$-algorithm and the cross-ratio identities, and as a by-product it provides us a way to deal with CHY-integrands where the $Λ$-algorithm was not applicable in its original formulation.

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arXiv2016

Note on Identities Inspired by New Soft Theorems

The new soft theorems, for both gravity and gauge amplitudes, have inspired a number of works, including the discovery of new identities related to amplitudes. In this note, we present the proof and discussion for two sets of identities. The first set includes an identity involving the half-soft function which had been used in the soft theorem for one-loop rational gravity amplitudes, and another simpler identity as its byproduct. The second set includes two identities involving the KLT momentum kernel, as the consistency conditions of the KLT relation plus soft theorems for both gravity and gauge amplitudes. We use the CHY formulation to prove the first identity, and transform the second one into a convenient form for future discussion.

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arXiv2016

The Q-cut Representation of One-loop Integrands and Unitarity Cut Method

Recently, a new construction for complete loop integrands of massless field theories has been proposed, with on-shell tree-level amplitudes delicately incorporated into its algorithm. This new approach reinterprets integrands in a novel form, namely the Q-cut representation. In this paper, by deriving one-loop integrands as examples, we elaborate in details the technique of this new representation, e.g., the summation over all possible Q-cuts as well as helicity states for the non-scalar internal particle in the loop. Moreover, we show that the integrand in the Q-cut representation naturally reduces to the integrand in the traditional unitarity cut method for each given cut channel, providing a cross-check for the new approach.

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arXiv2016

Feynman Rules of Higher-order Poles in CHY Construction

In this paper, we generalize the integration rules for scattering equations to situations where higher-order poles are present. We describe the strategy to deduce the Feynman rules of higher-order poles from known analytic results of simple CHY-integrands, and propose the Feynman rules for single double pole and triple pole as well as duplex-double pole and triplex-double pole structures. We demonstrate the validation and strength of these rules by ample non-trivial examples.

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arXiv2016

Boundary Operators of BCFW Recursion Relation

We show that boundary contributions of BCFW recursions can be interpreted as the form factors of some composite operators which we call 'boundary operators'. The boundary operators can be extracted from the operator product expansion of deformed fields. We also present an algorithm to compute the boundary operators using path integral.

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arXiv2016

Form Factor and Boundary Contribution of Amplitude

The boundary contribution of an amplitude in the BCFW recursion relation can be considered as a form factor involving boundary operator and unshifted particles. At the tree-level, we show that by suitable construction of Lagrangian, one can relate the leading order term of boundary operators to some composite operators of N=4 super-Yang-Mills theory, then the computation of form factors is translated to the computation of amplitudes. We compute the form factors of these composite operators through the computation of corresponding double trace amplitudes.

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arXiv2016

Bose-Einstein Condensation of Bound Pairs of Relativistic Fermions in a Magnetic Field

The Bose-Einstein condensation of bound pairs made of equally and oppositely charged fermions in a magnetic field is investigated using a relativistic model. The Gaussian fluctuations have been taken into account in order to study the spectrum of bound pairs in the strong coupling region. We found, in weak coupling reagion, the condensation temperature increases with an increasing magnetic field displaying the magnetic catalysis effect. In strong coupling region, the inverse magnetic catalysis appears when the magnetic field is low and is replaced by the usual magnetic catalysis effect when magnetic field is sufficiently high, in contrast to the nonrelativistic case where the inverse magnetic catalysis prevails in strong coupling region regardless of the strength of the magnetic field. The resulting response to the magnetic field is the consequence of the competition between the dimensional reduction by Landau orbitals in pairing dynamics and the anisotropy of the kinetic spectrum of the bound pairs. We thus conclude that dimensional reduction dominates in weak domain and strong coupling one except the small magnetic field region, where the enhanced fluctuations dominates.

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arXiv2016

CHY-construction of Planar Loop Integrands of Cubic Scalar Theory

In this paper, by treating massive loop momenta to massless momenta in higher dimension, we are able to treat all-loop scattering equations as tree ones. As an application of the new aspect, we consider the CHY-construction of bi-adjoint phi_3 theory. We present the explicit formula for two-loop planar integrands. We discuss carefully how to subtract various forward singularities in the construction. We count the number of terms obtained by our formula and by direct Feynman diagram calculation and find the perfect match, thus provide a strong support for our results.

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arXiv2015

An Algebraic Approach to the Scattering Equations

We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.

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