Elliptic, Yangian-Invariant “Leading Singularity”

Bourjaily, Jacob L.; Kalyanapuram, Nikhil; Langer, Cameron; Patatoukos, Kokkimidis; Spradlin, Marcus

doi:10.1103/physrevlett.126.201601

Cited by 18 publications

(26 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the amplituhedron story naturally suggests the existence of alternate positive kinematic regions, Gr k (4, n), that are relevant for N k MHV amplitudes [47]. These positive spaces are much more non-trivial than Gr + (4, n) and could be tied to the appearance of more general functions beyond the MHV sector, such as elliptic polylogarithms [49,[138][139][140][141][142]. It seems highly plausible that some notion of critically positive coordinates does generalize to these positive kinematic regions.…”

Section: Jhep07(2021)049mentioning

confidence: 99%

Algebraic branch points at all loop orders from positive kinematics and wall crossing

Herderschee

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planar $$ \mathcal{N} $$ N = 4 SYM. A long-standing question has been precisely how algebraic branch points emerge from this picture. We use wall crossing and scattering diagrams to systematically study the boundary structure of the positive kinematic regions associated with MHV amplitudes. The notion of asymptotic chambers in the scattering diagram naturally explains the appearance of algebraic branch points. Furthermore, the scattering diagram construction also motivates a new coordinate system for kinematic space that rationalizes the relations between algebraic letters in the symbol alphabet. As a direct application, we conjecture a complete list of all algebraic letters that could appear in the symbol alphabet of the 8-point MHV amplitude.

show abstract

Section: Jhep07(2021)049mentioning

confidence: 99%

Algebraic branch points at all loop orders from positive kinematics and wall crossing

Herderschee

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…The coefficients of amplitudes in an appropriate prescriptive basis are then computable as 'on-shell functions' as defined in [297]. In [298], it was shown that the same approach can be extended to amplitudes involving elliptic curves, by generalizing the notion of leading singularities (traditionally used to refer to maximal-codimension residues) to any compact contour integral of maximal dimension. In particular, it was shown that on-shell functions defined for contours involving elliptic cycles enjoyed Yangian invariance in the case of planar maximally supersymmetric Yang-Mills theory.…”

Section: Iterated Integrals Involving Elliptic Curvesmentioning

confidence: 99%

“…Non-Polylogarithmic Leading Singularities Beyond Elliptic Curves -Although the definition of leading singularities introduced in [298] naturally extends to cases involving an arbitrary compact contour integral, those involving geometries that go beyond elliptic curves are stymied by a lack of clear computational methods for parameterizing such contours, or the existence of standard functions in terms of which these integrals can be expressed. It will be important to develop the technology for computing these higher-rigidity leading singularities over the coming years.…”

Section: Uniqueness Of Geometries -mentioning

confidence: 99%

Functions Beyond Multiple Polylogarithms for Precision Collider Physics

Bourjaily¹,

Broedel²,

Chaubey³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

Feynman diagrams constitute one of the essential ingredients for making precision predictions for collider experiments. Yet, while the simplest Feynman diagrams can be evaluated in terms of multiple polylogarithms-whose properties as special functions are well understood-more complex diagrams often involve integrals over complicated algebraic manifolds. Such diagrams already contribute at NNLO to the self-energy of the electron, t t production, γγ production, and Higgs decay, and appear at two loops in the planar limit of maximally supersymmetric Yang-Mills theory. This makes the study of these more complicated types of integrals of phenomenological as well as conceptual importance.In this white paper contribution to the Snowmass community planning exercise, we provide an overview of the state of research on Feynman diagrams that involve special functions beyond multiple polylogarithms, and highlight a number of research directions that constitute essential avenues for future investigation.

show abstract

“…On the support of each pair of solutions, we have LS ∝ 1 ∆ 9 , which is the generation of ∆ 9 (see appendix A for more details). Now we are interested in intersections produced by (EF ) i and (GH) i , especially on (67). A non-trivial fact is that, for each i = 1, 2 the intersection of (EF ) i with (GH) i precisely lies on (67) (see Fig.…”

Section: Mixed Algebraic Letters and The 9-point Double-box Integralmentioning

confidence: 99%

“…for each i, three lines (EF ) i , (GH) i and ( 67) are joint at the same point. we denote these two points as ǫ 1 = Z 6 + e 1 Z 7 and ǫ 2 = Z 6 + e 2 Z 7 on (67). Here e 1 and e 2 are two solutions of (A.5)= 0.…”

Section: Mixed Algebraic Letters and The 9-point Double-box Integralmentioning

confidence: 99%

Schubert Problems, Positivity and Symbol Letters

Yang

2022

Preprint

View full text Add to dashboard Cite

We propose a geometrical approach to generate symbol letters of amplitudes/integrals in planar N = 4 Super Yang-Mills theory, known as Schubert problems. Beginning with one-loop integrals, we find that intersections of lines in momentum twistor space are always ordered on a given line, once the external kinematics Z is in the positive region G + (4, n). Remarkably, cross-ratios of these ordered intersections on a line, which are guaranteed to be positive now, nicely coincide with symbol letters of corresponding Feynman integrals, whose positivity is then concluded directly from such geometrical configurations. In particular, we reproduce from this approach the 18 multiplicative independent algebraic letters for n = 8 amplitudes up to three loops. Finally, we generalize the discussion to two-loop Schubert problems and, again from ordered points on a line, generate a new kind of algebraic letters which mix two distinct square roots together. They have been found recently in the alphabet of two-loop double-box integral with n ≥ 9, and they are expected to appear in amplitudes at k + ℓ ≥ 4.

show abstract

Elliptic, Yangian-Invariant “Leading Singularity”

Cited by 18 publications

References 53 publications

Algebraic branch points at all loop orders from positive kinematics and wall crossing

Algebraic branch points at all loop orders from positive kinematics and wall crossing

Functions Beyond Multiple Polylogarithms for Precision Collider Physics

Schubert Problems, Positivity and Symbol Letters

Contact Info

Product

Resources

About