arXiv subjects

Qingjun Jin

Publications and source records attributed to Qingjun Jin.

29 records · Page 2Linked to original sources

arXiv2019

Hidden Analytic Structure of Higgs Amplitudes and Maximal Transcendentality Principle

We present the computation of two-loop Higgs plus three-parton amplitudes with dimension-seven operators in Higgs effective field theory. The computation is based on the combination of unitarity cut and integration by parts methods in an unconventional way. The analytic results take remarkably simple form. In particular, the results show that the QCD and N=4 SYM results share the same leading transcendental parts. This generalizes the so-call maximal transcendentality principle to the Higgs amplitudes with high dimension operators and also with fundamental external quark states. Further simplicity also exists in lower transcendental parts, suggesting hidden structures beyond maximal transcendentality.

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arXiv2019

Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory

We present analytic forms of three-loop four-gluon planar amplitudes in pure Yang-Mills theory in this letter. Gauge invariant bases and a set of proper master integrals are chosen such that the amplitudes are explicitly invariant under cyclic permutations of external particles. The $D$-dimensional unitarity method and integration-by-parts reductions with cut conditions are performed to determine the coefficients of the master integrals. Helicity amplitudes in the conventional dimension regularization scheme are obtained by setting gauge invariant bases to helicity configurations. After renormalizing the ultraviolet divergences, remaining divergences of the amplitudes agree with known infrared divergence structures exactly. Our results provide an essential piece of three-loop amplitudes required for the ${\rm N^3LO}$ order corrections to the production of two jets at hadron colliders.

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arXiv2018

Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle

We obtain for the first time the two-loop amplitudes for Higgs plus three gluons in Higgs effective field theory including dimension-seven operators. This provides the S-matrix elements for the top mass corrections for Higgs plus a jet production at LHC. The computation is based on the on-shell unitarity method combined with integration by parts reduction. We work in conventional dimensional regularization and obtain analytic expressions renormalized in the MS-bar scheme. The two-loop anomalous dimensions present operator mixing behavior. The infrared divergences agree with that predicted by Catani and the finite remainders take remarkably simple forms, where the maximally transcendental parts are identical to the corresponding results in N=4 super-Yang-Mills theory. The parts of lower transcendentality turn out to be also largely determined by the N=4 results.

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arXiv2018

Efficient integrand reduction for particles with spin

Scattering amplitudes with spinning particles are shown to decompose into multiple copies of simple building blocks to all loop orders, which can be used to efficiently reduce these amplitudes to sums over scalar integrals. Absence of unphysical kinematic singularities cleanly exposed by the method uncover novel consistency relations among master integrals and their coefficients. Analytic results are obtained for the five gluon, two loop, and four gluon, three loop planar scattering amplitudes in pure Yang-Mills theory as well as for leading singularities to even higher orders.

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arXiv2016

Emergent Supersymmetry in the Marginal Deformations of N=4 SYM

We study the one loop renormalization group flow of the marginal deformations of N=4 SYM theory using the a-function. We found that in the planar limit some non-supersymmetric deformations flow to the supersymmetric infrared fixed points described by the Leigh-Strassler theory. This means supersymmetry emerges as a result of renormalization group flow.

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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

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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arXiv2015

Recursion Relation for Boundary Contribution

It is well known that under a BCFW-deformation, there is a boundary contribution when the amplitude scales as O(1) or worse. We show that boundary contributions have a similar recursion relation as scattering amplitude. Just like the BCFW recursion relation, where scattering amplitudes are expressed as the products of two on-shell sub-amplitudes (plus possible boundary contributions), our new recursion relation expresses boundary contributions as products of sub-amplitudes and boundary contributions with less legs, plus yet another possible boundary contribution. In other words, the complete scattering amplitude, including boundary contributions, can be obtained by multiple steps of recursions, unless the boundary contributions are still non-zero when all possible deformations are exploited. We demonstrate this algorithm by several examples. Especially, we show that for standard model like renormalizable theory in 4D, i.e., the theory including only gauge boson, fermions and scalars, the complete amplitude can always be computed by at most four recursive steps using our algorithm.

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arXiv2014

Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory

To explore color/kinematics duality for general representations of the gauge group we formulate the duality for general abelian orbifolds of the SU(N), N=4 super Yang-Mills theory in four dimensions, which have fields in the bi-fundamental representation, and use it to construct explicitly complete four-vector and four-scalar amplitudes at one loop. For fixed number of supercharges, graph-organized L-loop n-point integrands of all orbifold theories are given in terms of a fixed set of polynomials labeled by L representations of the orbifold group. In contrast to the standard duality-satisfying presentation of amplitudes of the N=4 super Yang-Mills theory, each graph may appear several times with different internal states. The color and R-charge flow provide a way to deform the amplitudes of orbifold theories to those of more general quiver gauge theories which do not necessarily exhibit color/kinematics duality on their own. Based on the organization of amplitudes required by the duality between color and kinematics in orbifold theories we show how the amplitudes of certain non-factorized matter-coupled supergravity theories can be found through a double-copy construction. We also carry out a comprehensive search for theories with fields solely in the adjoint representation of the gauge group and amplitudes exhibiting color/kinematics duality for all external states and find an interesting relation between supersymmetry and existence of the duality.

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arXiv2013

The Emergence of Supersymmetry in $γ_i$-deformed ${\cal N}=4$ super-Yang-Mills theory

The $γ_i$-deformed $\mathcal{N}=4$ super-Yang-Mills theory is a non-supersymmetric deformation of the maximally-supersymmetric gauge theory in four dimensions which is conformally-invariant at the planar level. At the non-planar level non-trivial renormalization of marginal double-trace operators appears to break conformal invariance. At non-planar level, however, the behavior of this theory is less well understood. We study the one loop renormalization of the theory and the resulting flow of Yukawa and scalar coupling at the order ${\cal O}(\fracλ{N^2})$, and find $γ_i$ parameters receive nontrivial quantum corrections. We show that, at low energies, the $γ_i$ parameters flow to a common value and $γ_i$-deformed theory reaches an $\mathcal{N}=1$-supersymmetric fixed point described by the $β$-deformed $\mathcal{N}=4$ super Yang-Mills theory.

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