scholarly journals Open associahedra and scattering forms

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Aidan Herderschee ◽  
Fei Teng
Keyword(s):  
Scattering Amplitudes ◽  
Canonical Form ◽  
Recursion Relations ◽  
Fiber Product ◽  
New Phenomena

Abstract We continue the study of open associahedra associated with bi-color scattering amplitudes initiated in ref. [1]. We focus on the facet geometries of the open associahedra, uncovering many new phenomena such as fiber-product geometries. We then provide novel recursion procedures for calculating the canonical form of open associahedra, generalizing recursion relations for bounded polytopes to unbounded polytopes.

scholarly journals ANALYTIC SCATTERING AMPLITUDES FOR QCD

2008 ◽  
Vol 23 (12) ◽  
pp. 847-856 ◽  
Author(s):  
DIANA VAMAN ◽  
YORK-PENG YAO
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Invariance ◽  
Recursion Relations

By analytically continuing QCD scattering amplitudes through specific complexified momenta, one can study and learn about the nature and the consequences of factorization and unitarity. In some cases, when coupled with the largest time equation and gauge invariance requirement, this approach leads to recursion relations, which greatly simplify the construction of multi-gluon scattering amplitudes. The setting for this discussion is in the space-cone gauge.

scholarly journals QUANTUM RINGS AND RECURSION RELATIONS IN 2D QUANTUM GRAVITY

1992 ◽  
Vol 07 (16) ◽  
pp. 1419-1425 ◽  
Author(s):  
SHAMIT KACHRU
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Quantum Gravity ◽  
Matrix Model ◽  
Ring Structure ◽  
Two Dimensional ◽  
Recursion Relations ◽  
Quantum Rings ◽  
Bulk Scattering

I study tachyon condensate perturbations to the action of the two-dimensional string theory corresponding to the c=1 matrix model. These are shown to deform the action of the ground ring on the tachyon modules, confirming a conjecture of Witten. The ground ring structure is used to derive recursion relations which relate (N+1) and N tachyon bulk scattering amplitudes. These recursion relations allow one to compute all bulk amplitudes.

scholarly journals Yangian and SUSY symmetry of high spin parton splitting amplitudes in generalised Yang–Mills theory

2017 ◽  
Vol 32 (23) ◽  
pp. 1750121 ◽  
Author(s):  
Roland Kirschner ◽  
George Savvidy
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Field ◽  
High Spin ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Recursion Relations ◽  
Yang Mills ◽  
Underlying Theory ◽  
Half Integer ◽  
Yangian Symmetry

We have calculated the high spin parton splitting amplitudes postulating the Yangian symmetry of the scattering amplitudes for tensor gluons. The resulting splitting amplitudes coincide with the earlier calculations, which were based on the BCFW recursion relations. The resulting formula unifies all known splitting probabilities found earlier in gauge field theories. It describes splitting probabilities for integer and half-integer spin particles. We also checked that the splitting probabilities fulfil the generalised Kounnas–Ross [Formula: see text] = 1 supersymmetry relations hinting to the fact that the underlying theory can be formulated in an explicit supersymmetric manner.

scholarly journals Plahte diagrams for string scattering amplitudes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Pongwit Srisangyingcharoen ◽  
Paul Mansfield
Keyword(s):  
Scattering Amplitudes ◽  
Analytic Continuation ◽  
Complex Plane ◽  
Open String ◽  
Tree Level ◽  
Recursion Relations ◽  
Sign Changes ◽  
String Amplitudes

Abstract Plahte identities are monodromy relations between open string scattering amplitudes at tree level derived from the Koba-Nielsen formula. We represent these identities by polygons in the complex plane. These diagrams make manifest the appearance of sign changes and singularities in the analytic continuation of amplitudes. They provide a geometric expression of the KLT relations between closed and open string amplitudes. We also connect the diagrams to the BCFW on-shell recursion relations and generalise them to complex momenta resulting in a relation between the complex phases of partial amplitudes.

scholarly journals Weights, recursion relations and projective triangulations for positive geometry of scalar theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Renjan Rajan John ◽  
Ryota Kojima ◽  
Sujoy Mahato
Keyword(s):  
Scattering Amplitudes ◽  
Detailed Analysis ◽  
Tree Level ◽  
Massless Scalar ◽  
Weighted Sum ◽  
Canonical Forms ◽  
Factorization Property ◽  
Scalar Theory ◽  
Recursion Relations ◽  
Scalar Theories

Abstract The story of positive geometry of massless scalar theories was pioneered in [1] in the context of bi-adjoint ϕ3 theories. Further study proposed that the positive geometry for a generic massless scalar theory with polynomial interaction is a class of polytopes called accordiohedra [2]. Tree-level planar scattering amplitudes of the theory can be obtained from a weighted sum of the canonical forms of the accordiohedra. In this paper, using results of the recent work [3], we show that in theories with polynomial interactions all the weights can be determined from the factorization property of the accordiohedron. We also extend the projective recursion relations introduced in [4, 5] to these theories. We then give a detailed analysis of how the recursion relations in ϕp theories and theories with polynomial interaction correspond to projective triangulations of accordiohedra. Following the very recent development [6] we also extend our analysis to one-loop integrands in the quartic theory.

scholarly journals Gravity loop integrands from the ultraviolet

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Alex Edison ◽  
Enrico Herrmann ◽  
Julio Parra-Martinez ◽  
Jaroslav Trnka
Keyword(s):  
Scattering Amplitudes ◽  
Momentum Space ◽  
Indirect Evidence ◽  
Tree Level ◽  
Large Momentum ◽  
Recursion Relations ◽  
Yang Mills ◽  
The One ◽  
Geometric Picture ◽  
Super Yang Mills Theory

We demonstrate that loop integrands of (super-)gravity scattering amplitudes possess surprising properties in the ultraviolet (UV) region. In particular, we study the scaling of multi-particle unitarity cuts for asymptotically large momenta and expose an improved UV behavior of four-dimensional cuts through seven loops as compared to standard expectations. For N=8 supergravity, we show that the improved large momentum scaling combined with the behavior of the integrand under BCFW deformations of external kinematics uniquely fixes the loop integrands in a number of non-trivial cases. In the integrand construction, all scaling conditions are homogeneous. Therefore, the only required information about the amplitude is its vanishing at particular points in momentum space. This homogeneous construction gives indirect evidence for a new geometric picture for graviton amplitudes similar to the one found for planar N=4 super Yang-Mills theory. We also show how the behavior at infinity is related to the scaling of tree-level amplitudes under certain multi-line chiral shifts which can be used to construct new recursion relations.

scholarly journals Soft matters, or the recursions with massive spinors

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Adam Falkowski ◽  
Camila S. Machado
Keyword(s):  
Scattering Amplitudes ◽  
Compton Scattering ◽  
Scattering Amplitude ◽  
Massless Particle ◽  
Technical Innovation ◽  
Recursion Relations ◽  
Soft Limit ◽  
Soft Matters ◽  
Two Parameter ◽  
Soft Factors

Abstract We discuss recursion relations for scattering amplitudes with massive particles of any spin. They are derived via a two-parameter shift of momenta, combining a BCFW-type spinor shift with the soft limit of a massless particle involved in the process. The technical innovation is that spinors corresponding to massive momenta are also shifted. Our recursions lead to a reformulation of the soft theorems. The well-known Weinberg’s soft factors are recovered and, in addition, the subleading factors appear reshaped such that they are directly applicable to massive amplitudes in the modern on-shell language. Moreover, we obtain new results in the context of non-minimal interactions of massive matter with photons and gravitons. These soft theorems are employed for practical calculations of Compton and higher-point scattering. As a by-product, we introduce a convenient representation of the Compton scattering amplitude for any mass and spin.

scholarly journals Constraining the weights of Stokes polytopes using BCFW recursions for ϕ4

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Ishan Srivastava
Keyword(s):  
Scattering Amplitudes ◽  
Great Depth ◽  
Tree Level ◽  
Recursion Relations ◽  
3 Dimensional ◽  
Loop Level ◽  
Boundary Terms ◽  
Geometric Objects ◽  
The Relationship ◽  
Geometric Formulation

Abstract The relationship between certain geometric objects called polytopes and scattering amplitudes has revealed deep structures in QFTs. It has been developed in great depth at the tree- and loop-level amplitudes in $$ \mathcal{N} $$ N = 4 SYM theory and has been extended to the scalar ϕ3 and ϕ4 theories at tree-level. In this paper, we use the generalized BCFW recursion relations for massless planar ϕ4 theory to constrain the weights of a class of geometric objects called Stokes polytopes, which manifest in the geometric formulation of ϕ4 amplitudes. We see that the weights of the Stokes polytopes are intricately tied to the boundary terms in ϕ4 theories. We compute the weights of N = 1, 2, and 3 dimensional Stokes polytopes corresponding to six-, eight- and ten-point amplitudes respectively. We generalize our results to higher-point amplitudes and show that the generalized BCFW recursions uniquely fix the weights for an n-point amplitude.

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