We numerically study the formation of the gauge-mediation type <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> balls in the logarithmic square potential on three-dimensional lattices. We obtain the broad charge distribution of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> ball of this type for the first time, to the best of our knowledge. The charge of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> ball at the peak of the distribution is smaller than what we estimated as the average of the largest tens of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> balls in the logarithmic potential for the same initial amplitude of the field at the onset of its oscillation. We also discuss some impacts of the broad distribution on cosmology and astrophysics. In the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> ball (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> being the baryon number) case, the broad distribution would lead to the coexistence of both stable and unstable <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> balls. We find that stable <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> balls can account for the dark matter of the Universe without affecting successful big bang nucleosynthesis by the decay of the unstable <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> balls, but the baryon number of the Universe cannot be explained by them. On the other hand, the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math> balls (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> being the lepton number) would be the dark matter as well while avoiding the constraints on the x- and/or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-rays from the decay of the smaller <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math> balls.

Japan

Shinta Kasuya

Masahiro Kawasaki

Charge distribution of the gauge-mediation type <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> ball

We show that, in the thin-wall regime, $\textit{Q}$-ball-anti-$\textit{Q}$-ball collisions reveal chaotic behaviour. This is explained by the resonant energy transfer mechanism triggered by the internal modes hosted by the $\textit{Q}$-balls and by the existence of $\textit{ephemeral}$ states, that is unstable, sometimes even short-lived, field configurations that appear as intermediate states. The most important examples of such states are the $\textit{bubble}$ of the false broken vacuum, which as intermediate states govern the $\textit{QQ}$ annihilation, and the $\textit{charged oscillons}$.

Spain

D. Canillas Martínez

United Kingdom

P. Dorey

Poland

T. Romańczukiewicz

Paul Saffin

K. Sławińska

A. Wereszczyński

Oscillons and bubbles in $\textit{Q}$-ball dynamics

We present a determination of the strong coupling $$\alpha _s(m_Z)$$ from a global dataset including both fixed-target and collider data from deep-inelastic scattering and a variety of hadronic processes, with a simultaneous determination of parton distribution functions (PDFs) based on the NNPDF4.0 methodology. This determination is performed at NNLO and approximate $${\textrm{N}}^3$$ LO ( $${\textrm{aN}}^3$$ LO) perturbative QCD accuracy, including QED corrections and a photon PDF up to NLO accuracy. We extract $$\alpha _s$$ using two independent methodologies, both of which take into account the cross-correlation between $$\alpha _s$$ and the PDFs. The two methodologies are validated by closure tests that allow us to detect and remove or correct for several sources of bias, and lead to mutually consistent results. We account for all correlated experimental uncertainties, as well as correlated theoretical uncertainties related to missing higher order perturbative corrections (MHOUs). We study the perturbative convergence of our results and the impact of QED corrections. We assess individual sources of uncertainty, specifically MHOUs and the value of the top quark mass. We provide a detailed appraisal of methodological choices, including the choice of input dataset, the form of solution of evolution equation, the treatment of the experimental covariance matrix, and the details of Monte Carlo data generation. We find $$\alpha _s(m_Z)=0.1194^{+0.0007}_{-0.0014}$$ at $${\textrm{aN}}^3$$ $${\textrm{LO}}_{\textrm{QCD}}\otimes {\textrm{NLO}}_{\textrm{QED}}$$ accuracy, consistent with the latest PDG average and with recent lattice results.

Richard Ball

Italy

Andrea Barontini

Switzerland

Juan Cruz-Martinez

Stefano Forte

Finland

Felix Hekhorn

Emanuele Nocera

Netherlands

Juan Rojo

Roy Stegeman

A determination of $$\alpha _s(m_Z)$$ at $${{\textrm{aN}}}^3{{\textrm{LO}}}_{{\textrm{QCD}}}\otimes {{\textrm{NLO}}}_{{\textrm{QED}}}$$ accuracy from a global PDF analysis

The principle of holography of information states that all information available in the bulk of asymptotically flat spacetime is also available near its boundary at spatial infinity. However, physical observers never have access to spatial infinity. Therefore, we ask the question: “Is information contained in a ball of finite radius also holographic in nature?”. Phrased differently, we ask whether correlation functions on the boundary of the ball capture all the information of all correlators in the bulk of the ball. In this work, we answer this question in the affirmative within the confines of linearised quantum gravity for generic low-energy (free Klein-Gordon) states in flat space created by the action of unitaries on the vacuum to leading order in a certain perturbative parameter. For an infinite sub-class of these states, our results are perturbatively exact and valid to all orders in this same parameter. Unlike at infinity, massive and massless fields can be captured within the same framework.

India

Nava Gaddam

Ashik H

Holography of information in a ball of finite radius

We present a novel family of analytical and numerical classical solitonic solutions to the nonlinear equations governing the dynamics of the bosonic part of a supermembrane (M2-brane) mass operator formulated on a flat spacetime toroidally compactified with worldvolume fluxes. The dynamics of membrane excitations is associated with sectors of the supermembrane theory that exhibit a discrete spectrum at the supersymmetric level, which is an expected property of any well-defined sector of the M-theory. Contrary to expectations, the presence of worldvolume fluxes facilitates the acquisition of novel solutions while preserving the theory’s nonlinear character even in the absence of bosonic scalar potential. The theory remains nonlinear due to the coupling of the scalars with the fluxes and with a symplectic gauge field that arises in the theory. It is noteworthy that the theory also permits the existence of quasiharmonic solutions to the nonlinear equations. We then focus on the M2 brane theory realization of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-ball-like solitons. In order to ascertain the behavior of these solutions, we examine the existence of M2-brane solitonic nondispersive solutions, their composition rules, their dynamics, and the existence of localized solutions along the worldvolume. We also establish a relation between the worldvolume fluxes and the nontopological <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-ball charges.

Venezuela

P. Garcia

M.P. Garcia del Moral

Chile

J.M. Peña

R. Prado-Fuentes

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-ball-like solitons on the M2-brane with worldvolume fluxes

We analyze in detail the interactions between the nontopological soliton (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-ball) and its perturbations. We extend the previous literature by carefully identifying the domain of applicability of linear analysis as well as discussing Friedberg, Lee, and Sirlin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-balls. Applications to early Universe physics are briefly commented.

Aleksandr Azatov

Quoc Trung Ho

Mohamed Mahdi Khalil

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-ball perturbations with more details: Linear analysis vs lattice

We show that in the complex <math altimg='si1.svg'><msup><mrow><mi>&#981;</mi></mrow><mrow><mn>6</mn></mrow></msup></math> theory the oscillon, together with its spectral structure and the amplitude modulation, arises from the excited Q-ball carrying the bound and the quasi-normal modes.

Czechia

F. Blaschke

T. Romanczukiewicz

K. Slawinska

A. Wereszczynski

Q-ball polarization - A smooth path to oscillons

In this paper, we study solutions of a static spherically symmetric system, which is composed of the coupling with the Bardeen action and two Dirac fields. For the case where only the Bardeen action is present, the magnetic charge can be infinite, then when the magnetic charge is greater than a certain value $$q_b$$ , there exists a black hole solution, which is called the Bardeen black hole (BBH). However, if the Dirac field is introduced, we find that the magnetic charge can only be smaller than the critical value $$q_b$$ , in which there is no black hole solution. Moreover, in the region $$q<q_b$$ , we find that if the magnetic charge exceeds another critical value $$q_c$$ (i.e., $$q_c<q<q_b$$ ), the frequency of the Dirac field can approach zero, and the solution where a critical horizon appears is similar to an extremal black hole outside the critical horizon but has a nonsingular interior. The Dirac fields are also almost concentrated within it. In fact, this is a frozen star solution, we call such solutions frozen Bardeen-Dirac stars (FBDSs). We analyze the light rings of FBDSs and find that there exists a “true” light ring outside the critical horizon, but inside it, the velocity of photons is very close to zero, which leads to the formation of a “light ball” inside the critical horizon.

China

Long-Xing Huang

Shi-Xian Sun

Yong-Qiang Wang

Frozen Bardeen-Dirac stars and light ball

Puzzles are still preventing people from further understanding and manipulating the Casimir interaction in spherical systems. Here we investigate the behaviors of Casimir stresses in the system consisting of a ball immersed in the background, emphasizing the roles of spherical geometry and inhomogeneity. Spherical modes are employed to evaluate Green’s dyadic and thus the Casimir stresses. The inhomogeneity of the media essentially modifies the wave form of the spherical mode, leading to significant impacts on the Casimir stresses, especially when far away from the surface of the ball. As the surface approached, the divergence (surface divergence) in Casimir stresses is seen. For both homogeneous and inhomogeneous cases, the leading behaviors (zero for the radial component, and inverse quantic order of distance for the transverse components) of Casimir stresses are exactly the same as those for the corresponding planar homogeneous wall, involving only properties of media at the surface and reflecting no information about the spherical geometry and the inhomogeneity, which implies the local nature. The other surface divergences are influenced by the spherical geometry and for the transverse component always weaker than the planar contribution. The general impacts from the inhomogeneity of media to the surface divergences are also shown. The inhomogeneity will further soften the surface divergence. For two touching media with permittivities and permeabilities equal up to a high enough order of their expansion over the distance to the surface, surface divergences may disappear together with the interaction Casimir stresses. Other factors, such as the refractivity and anisotropy, are also included, which may raise considerable complexities, but typically not related to divergences. Perspectives on the renormalization of the surface divergence are briefly outlined.

Yang Li

Casimir stresses of the dielectric ball: Inhomogeneity and divergences

Sydney Coleman’s Q-ball remains a compelling instance of the formation of localized objects within classical field theory, independently of the quantum evolution. The theoretical possibility of such objects forming and colliding in the early Universe from models such as Affleck-Dine fragmentation, or from a number of mechanisms where they are produced copiously with various sizes and charges to constitute dark matter in the Universe, makes it important to study in detail Q-ball collision phenomenology. In this work, we present certain results from the study of Q-ball collisions and their generation of gravitational waves, using a new general code package for scalar fields coupled to gravity. We then comment on the possibility of future gravitational wave detectors searching for signals of Q-ball collisions.

South Korea

Deog Ki Hong

Stephen J. Lonsdale

<math><mi>Q</mi></math>-ball collisions and their gravitational waves