Precision theoretical predictions for high multiplicity scattering rely on the evaluation of increasingly complicated scattering amplitudes which come with an extremely high CPU cost. For state-of-the-art processes this can cause technical bottlenecks in the production of fully differential distributions. In this article we explore the possibility of using neural networks to approximate multi-variable scattering amplitudes and provide efficient inputs for Monte Carlo integration. We focus on QCD corrections to $e^+e^-\to$ jets up to one-loop and up to five jets. We demonstrate reliable interpolation when a series of networks are trained to amplitudes that have been divided into sectors defined by their infrared singularity structure. Complete simulations for one-loop distributions show speed improvements of at least an order of magnitude over a standard approach.
Phenomenological Parametrization of the Charged Particle Multiplicity Distributions in Restricted Rapidity Intervals in e+e- Annihilation into Hadrons and e+p Scattering at HERA
Pushing the reach of NNLO QCD predictions to $2\to3$ production processes is one of the pillars of precision phenomenology program at the LHC. In this talk we will overview recent results and developments in the calculation of two-loop five-point amplitudes contributing towards achieving this goal. We will discuss challenges encountered in advancing the state-of-the-art beyond the class of massless five-point scattering. We will then present a basis set of transcendental functions sufficient to express any planar two-loop five-particle scattering amplitude with one external massive leg. This b…
We explore the on-shell recursion for tree-level scattering amplitudes with massive spinning particles. Based on the factorization structure encoded in the same way by two different recursion relations, we conjecture an all-multiplicity formula for two gauged massive particles of arbitrary spin and any number of identical-helicity gluons. Specializing to quantum chromodynamics (QCD), we solve the on-shell recursion relations in the presence of two pairs of massive quarks and an arbitrary number of identical-helicity gluons. We find closed-form expressions for the two distinct families of color…
We study the proposal by Kharzeev-Levin to determine entanglement entropy in Deep Inelastic Scattering (DIS) from parton distribution functions (PDFs) and to relate the former to the entropy of final state hadrons. We find several uncertainties in the current comparison to data, in particular the overall normalization, the relation between charged versus total hadron multiplicity in the comparison to experimental results as well as different methods to determine the number of partons in Deep Inelastic Scattering. We further provide a comparison to data based on leading order HERA PDF as well a…
Calculations of high multiplicity Higgs amplitudes exhibit a rapid growth that may signal an end of perturbative behavior or even the need for new physics phenomena. As a step towards this problem we consider the quantum mechanical equivalent of $1 \to n$ scattering amplitudes in a spontaneously broken $ϕ^4$-theory by extending our previous results on the quartic oscillator with a single minimum to transitions $\langle n \lvert \hat{x} \rvert 0 \rangle$ in the symmetric double-well potential with quartic coupling $λ$. Using recursive techniques to high order in perturbation theory, we argue th…
We generalized our model for the description of hard processes, and calculate the value of the azimuthal angle correlations ( Fourier harmonics $v_n$ ), for proton-proton scattering.The energy and multiplicity independence, as well as the value of $v_n$, turn out the be in accord with the experimental data, or slightly larger. Therefore, before making extreme assumptions on proton-proton collisions, such as the production of quark-gluon plasma in the large multiplicity events, we need to explain how these effect theBose-Einstein correlations which are so large, that have to be taken into accou…
One of the remarkable features of high-multiplicity hadronic events in proton-proton collisions at the LHC is the fact that the produced particles appear as two "ridges", opposite in azimuthal angle $ϕ$, with approximately flat rapidity distributions. This phenomena can be identified with the inelastic collision of gluonic flux tubes associated with the QCD interactions responsible for quark confinement in hadrons. In this paper we analyze the ridge phenomena when the collision involves a flux tube connecting the quark and antiquark of a high energy real or virtual photon. We discuss gluonic t…
Calculations of $1\to N$ amplitudes in scalar field theories at very high multiplicities exhibit an extremely rapid growth with the number $N$ of final state particles. This either indicates an end of perturbative behaviour, or possibly even a breakdown of the theory itself. It has recently been proposed that in the Standard Model this could even lead to a solution of the hierarchy problem in the form of a "Higgsplosion". To shed light on this question we consider the quantum mechanical analogue of the scattering amplitude for $N$ particle production in $ϕ^4$ scalar quantum field theory, which…
The dependence of the inelasticity in terms of the center of mass energy is studied in the eikonal formalism, which provides connection between elastic and inelastic channels. Due to the absence of inelasticity experimental datasets, the present analysis is based on experimental information available on the full phase space multiplicity distribution covering a large range of energy, namely 30 $<$ $\sqrt{s}$ $\leq$ 1800 GeV. Our results indicate that the decrease of inelasticity is consequence of minijets production from semihard interactions arising from the scattering of gluons carrying only …
Oscillations in modified combinants ($C_j$s) have been of interest to multiparticle production mechanisms since the 1990s. Recently, there has been a discussion on how these oscillations can be reproduced by compounding a binomial distribution with a negative binomial distribution. In this work, we explore a stochastic branching model based on a simple interaction term $λ\overlineψϕψ$ for partons and propose a hadronization scheme to arrive at the final multiplicity distribution. We study the effects that compounding our model with a binomial distribution has on $C_j$s and explore its physical…
Analysis of the charged multiplicity in proton-proton inelastic interactions at the LHC energies in the setting of Dual Parton Model is presented. Data from the CMS experiment and the data simulated at different energies in various pseudo-rapidity windows using the event generator PYTHIA8are analysed and compared with the calculations from the model. Each inelastic scattering is assumed to follow the Poisson distribution. The theoretical Koba-Nielsen-Olesen (KNO) scaling of the multiplicity distributions is studied and compared with previously published experimental results at $\sqrt{s}$ = 0.9…
Elastic $pp$ scattering at LHC energies is treated in Additive Quark Model together with Pomeron exchange theory. The obtained results are compared with the new experimental data on the ratio of real to imaginary part of the scattering amplitude at the small transverse momenta
Scenario for restoration of the real part of the elastic scattering amplitude has been proposed for the unitarity saturation case. Dependence of the real part of the elastic scattering amplitude on the transferred momentum $-t$ at the asymptotical energies has been restored from the corresponding imaginary part on the basis of derivative analyticity relations (analytization procedure).
We prove the general theorem that the real part of the forward two-body scattering amplitude is positive at sufficiently high energies if, above a certain energy, the total cross section increases monotonically to infinity at infinite energy.
The dependence of the production of the $X(3872)$ meson on the hadron multiplicity in $pp$ collisions has been used as evidence against $X$ being a charm-meson molecule. The argument is based in part on the incorrect assumption that the cross section for the breakup of $X$ by scattering with comovers can be approximated by a geometric cross section inversely proportional to the binding energy of $X$. The breakup cross section should instead be approximated by the probability-weighted sum of the cross sections for the scattering of comoving pions from the charm-meson constituents of $X$, which …
We construct an irreducible s- and t-channel tensor basis for Bhabha scattering like amplitudes based on the properties of the underlying Lorentz symmetry in four space-time dimensions. In the given basis the calculation of amplitude contractions like the amplitude square reduces to the contraction of their corresponding coefficient tensors. Further the basis retains the full amplitude information and thus can be applied in off-shell cases. The general Fierz transformations which relate the s- and t-channel basis with each other are obtained. As an example for application we use the basis to c…
The factorization of multi-leg gauge theory amplitudes in the soft and collinear limits provides strong constraints on the structure of amplitudes, and enables efficient calculations of multi-jet observables at the LHC. There is significant interest in extending this understanding to include subleading powers in the soft and collinear limits. While this has been achieved for low point amplitudes, for higher point functions there is a proliferation of variables and more complicated phase space, making the analysis more challenging. By combining the subleading power expansion of spinor-helicity …
In this paper we discuss the inclusive $J/ψ$ production in proton-proton collisions from fusion of three pomerons. We demonstrate that this mechanism gets dominant contribution from the region which can be theoretically described by CGC/Saturation approach. Numerically, it gives a substantial contribution to the $J/ψ$ production, and is able to describe the experimentally observable shapes of the rapidity, momenta and multiplicity distributions. The latter fact provides a natural explanation of the experimentally observed enhancement of multiplicity distribution in $J/ψ$ production.
