We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large-z behaviour. This work is a generalization of the recursion relations recently obtained by Cheung et al for amplitudes in scalar effective field theories with enhanced vanishing soft behaviours, which can be regarded as a special case of those with non-vanishing soft limits. We apply the recursion relations to tree-level amplitudes in various theories, including amplitudes in the Akulov-Volkov theory, amplitudes containing dilatons of spontaneously-broken conformal symmetry.Comment: 21 pages, typos and some statements modified, references adde

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.

BCJ relation reveals a dual between color structures and kinematic structure and can be used to reduce the number of independent color-ordered amplitudes at tree level. Refer to the loop-level in Yang-Mills theory, we investigate the similar BCJ relation in this paper. Four-point 1-loop example in N = 4 SYM can hint about the relation of integrands. Five-point example implies that the general formula can be proven by unitary-cut method. We will then prove a 'general' BCJ relation for 1-loop integrands by D-dimension unitary cut, which can be regarded as a non-trivial generalization of the (fundamental)BCJ relation given by Boels and Isermann in [13,14].

Abstract:Tree and loop level scattering amplitudes which involve physical massless bosons are derived directly from physical constraints such as locality, symmetry and unitarity, bypassing path integral constructions. Amplitudes can be projected onto a minimal basis of kinematic factors through linear algebra, by employing four dimensional spinor helicity methods or at its most general using projection techniques. The linear algebra analysis is closely related to amplitude relations, especially the Bern-Carrasco-Johansson relations for gluon amplitudes and the Kawai-Lewellen-Tye relations between gluons and graviton amplitudes. Projection techniques are known to reduce the computation of loop amplitudes with spinning particles to scalar integrals. Unitarity, locality and integrationby-parts identities can then be used to fix complete tree and loop amplitudes efficiently. The loop amplitudes follow algorithmically from the trees. A number of proof-of-concept examples are presented. These include the planar four point two-loop amplitude in pure Yang-Mills theory as well as a range of one loop amplitudes with internal and external scalars, gluons and gravitons. Several interesting features of the results are highlighted, such as the vanishing of certain basis coefficients for gluon and graviton amplitudes. Effective field theories are naturally and efficiently included into the framework. Dimensional regularisation is employed throughout; different regularisation schemes are worked out explicitly. The presented methods appear most powerful in non-supersymmetric theories in cases with relatively few legs, but with potentially many loops. For instance, in the introduced approach iterated unitarity cuts of four point amplitudes for non-supersymmetric gauge and gravity theories can be computed by matrix multiplication, generalising the socalled rung-rule of maximally supersymmetric theories. The philosophy of the approach to kinematics also leads to a technique to control colour quantum numbers of scattering amplitudes with matter, especially efficient in the adjoint and fundamental representations.

Abstract:In this paper, we study the single and double soft behaviors of tree level offshell currents and on-shell amplitudes in nonlinear sigma model (NLSM). We first propose and prove the leading soft behavior of the tree level currents with a single soft particle. In the on-shell limit, this single soft emission becomes the Adler's zero. Then we establish the leading and subleading soft behaviors of tree level currents with two adjacent soft particles. With a careful analysis of the on-shell limit, we obtain the double soft behaviors of on-shell amplitudes where the two soft particles are adjacent to each other. By applying KleissKuijf (KK) relation, we further obtain the leading and subleading behaviors of amplitudes with two nonadjacent soft particles.

Determination of γ and −2β s from charmless two-body decays of beauty mesons .LHCb Collaboration a r t i c l e i n f o a b s t r a c tUsing the latest LHCb measurements of time-dependent CP violation in the B 0 s → K + K − decay, a U-spin relation between the decay amplitudes of B 0 s → K + K − and B 0 → π + π − decay processes allows constraints to be placed on the angle γ of the unitarity triangle and on the B 0 s mixing phase −2β s .Results from an extended approach, which uses additional inputs on B 0 → π 0 π 0 and B + → π + π 0 decays from other experiments and exploits isospin symmetry, are also presented. The dependence of the results on the maximum allowed amount of U-spin breaking is studied. At 68% probability, the value γ = (63.5 +7.2 −6.7 ) • modulo 180 • is determined. In an alternative analysis, the value −2β s = −0.12 +0.14 −0.16 rad is found. In both measurements, the uncertainties due to U-spin breaking effects up to 50% are included. decays are related by the U-spin symmetry of strong interactions. This symmetry, related to the exchange of d and s quarks in the decay diagrams, can be exploited to determine the unknown hadronic factors. A more sophisticated analysis has also been proposed [13], where it is suggested to combine the U-spin analysis of B 0 → π + π − and B 0 s → K + K − decays with the isospin analysis of B 0 → π + π − , B 0 → π 0 π 0 and B + → π + π 0 decays [14], in order to achieve a more robust determination of γ with respect to U-spin breaking effects. The B 0, can also be determined with either analysis approach. An analysis based on Bayesian statistics, aimed at determining probability density functions (PDFs) for γ and −2β s , is presented in this Letter. This uses the latest LHCb measurements of time-dependent CP violation in the B 0 s → K + K − decay, exploiting U-spin symmetry with the B 0 → π + π − decay. An extended analysis, including measurements on B 0 → π 0 π 0 and B + → π + π 0 decays from other experiments, is also performed. The Letter is organized as follows. First, the theoretical formalism needed to describe CP violation is introduced in Section 2, including the SM parameterization of the decay amplitudes of the various decays.

Jet identification is one of the fields in high energy physics that machine learning has begun to make an impact. More often than not, convolutional neural networks are used to classify jet images with the benefit that essentially no physics input is required. Inspired by a recent work by Datta and Larkoski, we study the classification of quark/gluon-initiated jets based on fully-connected neural networks (FNNs), where expertdesigned physical variables are taken as input. FNNs are applied in two ways: trained separately on various narrow jet transverse momentum p T J bins; trained on a wide region of p T J ∈ [200, 1000] GeV. We find their performances are almost the same. The performance is better when the p T J is larger. Jet discrimination with FNN is studied on both particle and detector level data. The results based on particle level data are comparable with those from deep convolutional neural networks, while the significance improvement characteristic (SIC) from detector level data would at most decrease by 15%. We also test the performance of FNNs with full set or subsets of jet observables as input features. The FNN with one subset consisting of fourteen observables shows nearly no degradation of performance. This indicates that these fourteen expert-designed observables could have captured the most necessary information for separating quark and gluon jets.

This paper starts with a self-contained discussion of the so-called Akulov-Volkov action S AV , which is traditionally taken to be the leading-order action of Goldstino field. Explicit expressions for S AV and its chiral version S ch AV are presented. We then turn to the issue on how these actions are related to the leading-order action S NL proposed in the newly proposed constrained superfield formalism. We show that S NL may yield S AV /S ch AV or a totally different action S KS , depending on how the auxiliary field in the former is integrated out. However, S KS and S AV /S ch AV always yield the same S-matrix elements, as one would have expected from general considerations in quantum field theory.