We study on-shell functions in the kinematic space for the Coulomb branch of  $$\mathcal{N}$$  = 4 SYM. We construct BCFW bridges that help us build bigger on-shell functions. As a consequence, we provide on-shell diagram formulations for BCFW shifts that correspond to various mass configurations. We will use this to calculate the quadruple cut for the one-loop amplitude on the Coulomb branch and maximal cuts for higher-loops. We make preliminary comments on finding the inequivalent set of on-shell functions for the Coulomb branch.

India

Md. Abhishek

Subramanya Hegde

Dileep Jatkar

Arnab Saha

Amit Suthar

On-shell functions on the Coulomb branch of  $$\mathcal{N}$$  = 4 SYM

We study four point planar loop amplitudes at an arbitrary point in the Coulomb branch of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super-Yang-Mills theory. We study two particle unitary cuts up to four loop order. We explicitly verify that bubble and triangle graphs do not contribute at one loop level and show that the results hold at higher loop level as well. We also write down an all loop recursion relation for two particle reducible graphs for four point amplitudes.

Loop amplitudes in the Coulomb branch of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super-Yang-Mills theory

We use on-shell Supersymmetry to constrain the three-point function of two massless particles and one massive particle in 3+1 dimensions. We use this information to write down the tree-level four-point function of massless particles for   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1, 2 and 4 theories. In particular, we derive the expressions for four-photon/gluon amplitudes with massive higher spin exchange in theories with   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 Supersymmetry in 3+1 dimensions.

Mahesh Balasubramanian

Kushal Chakraborty

Arnab Rudra

On-shell supersymmetry and higher-spin amplitudes

The formation and decay of metastable bound states can significantly decrease the thermal-relic dark matter density, particularly for dark matter masses around and above the TeV scale. Incorporating bound-state effects in the dark matter thermal decoupling requires in principle a set of coupled Boltzmann equations for the bound and unbound species. However, decaying bound states attain and remain in a quasi-steady state. Here we prove in generality that this reduces the coupled system into a single Boltzmann equation of the standard form, with an effective cross-section that describes the interplay among bound-state formation, ionisation, transitions and decays. We derive a closed-form expression for the effective cross-section for an arbitrary number of bound states, and show that bound-to-bound transitions can only increase it. Excited bound levels may thus decrease the dark matter density more significantly than otherwise estimated. Our results generalise the Saha ionisation equilibrium to metastable bound states, potentially with applications beyond the dark matter thermal decoupling.

Japan

Tobias Binder

Netherlands

Anastasiia Filimonova

France

Kalliopi Petraki

Graham White

Saha equilibrium for metastable bound states and dark matter freeze-out

Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured ℂℙ k − 1, are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster algebras. Recently connections between one-loop integrands for bi-adjoint cubic scalar theory and   <math> <msub> <mi>D</mi> <mi>n</mi> </msub> </math>  $$ {\mathcal{D}}_n $$  cluster polytope have been established. In this paper using the Gr (3, 6) cluster algebra, we relate the singularities of (3, 6) amplitude to four-point one-loop integrand in the bi-adjoint cubic scalar theory through the   <math> <msub> <mi>D</mi> <mn>4</mn> </msub> </math>  $$ {\mathcal{D}}_4 $$  cluster polytope. We also study factorisation properties of the (3, 6) amplitude at various boundaries in the worldsheet.

One-loop integrand from generalised scattering equations

Classical subleading soft graviton theorem in four space-time dimensions determines the gravitational wave-form at late and early retarded time, generated during a scattering or explosion, in terms of the four momenta of the ingoing and outgoing objects. This result was ‘derived’ earlier by taking the classical limit of the quantum soft graviton theorem, and making some assumptions about how to deal with the infrared divergences of the soft factor. In this paper we give a direct proof of this result by analyzing the classical equations of motion of gravity coupled to matter. We also extend the result to the electromagnetic wave-form generated during scattering of charged particles, and present a new conjecture on subsubleading corrections to the gravitational wave-form at early and late retarded time.

Biswajit Sahoo

Ashoke Sen

Proof of the classical soft graviton theorem in

In this paper we evaluate the modified celestial amplitude for gravitons and gluons, as defined in [4]. We find that the modified (tree) amplitude is finite for gravitons in Einstein gravity. The modified amplitude behaves like correlation function of operators inserted at various points of null-infinity in the Minkowski space-time. Therefore, unlike the standard celestial amplitudes, these are three dimensional objects. We also show that this amplitude admits conformal soft factorization recently studied in the literature.

Shamik Banerjee

Sudip Ghosh

Pranjal Pandey

Modified celestial amplitude in Einstein gravity

The production of light (anti-)(hyper-)nuclei in heavy-ion collisions at the LHC is considered in the framework of the Saha equation, making use of the analogy between the evolution of the early universe after the Big Bang and that of “Little Bangs” created in the lab. Assuming that disintegration and regeneration reactions involving light nuclei proceed in relative chemical equilibrium after the chemical freeze-out of hadrons, their abundances are determined through the famous cosmological Saha equation of primordial nucleosynthesis and show no exponential dependence on the temperature typical for the thermal model. A quantitative analysis, performed using the hadron resonance gas model in partial chemical equilibrium, shows agreement with experimental data of the ALICE collaboration on d, $^{3}$He, <math><mmultiscripts><mrow><mtext>H</mtext></mrow><mprescripts></mprescripts><mrow><mi>Λ</mi></mrow><mrow><mn>3</mn></mrow></mmultiscripts></math>, and $^{4}$He yields for a very broad range of temperatures at <math><mi>T</mi><mo>≲</mo><mn>155</mn></math> MeV. The presented picture is supported by the observed suppression of resonance yields in central Pb–Pb collisions at the LHC.

Germany

Volodymyr Vovchenko

Kai Gallmeister

Jürgen Schaffner-Bielich

Carsten Greiner

Nucleosynthesis in heavy-ion collisions at the LHC via the Saha equation

Following up on the recent work of Cachazo, He and Yuan [1], we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.