Motivated by the first LHCb searches for the rare $$ {\overline{B}}_{s,d}^0 $$ → $\textit{J}$/$\textit{ψμ}$ $\textit{μ}$ decays, we perform a detailed study of these processes within the QCD factorization formalism. Since the transverse size of the $\textit{J}$/$\textit{ψ}$ meson is small in the heavy quark mass limit, this formalism is generally expected to hold for these decays. We include both the leading- and next-to-leading-order QCD corrections to the hard-scattering kernels, which are convoluted with the light-cone distribution amplitudes (LCDAs) of the initial- and final-state hadrons. It is numerically found that, depending on the model parameters for the leading-twist $\textit{B}$-meson LCDA, the maximum branching ratios of $$ {\overline{B}}_s^0 $$ → $\textit{J}$/$\textit{ψμ}$ $\textit{μ}$ and $$ {\overline{B}}_d^0 $$ → $\textit{J}$/$\textit{ψμ}$ $\textit{μ}$ , integrated over the dimuon invariant mass squared $\textit{q}$ from 1 GeV to ( $$ {m}_{B_{s,d}} $$ − $\textit{m}$ ) , can reach up to 2.21 × 10 and 7.69 × 10 at the leading order in $\textit{α}$ , respectively. After incorporating the non-factorizable one-loop vertex corrections, these branching ratios are further reduced by about one order of magnitude, with $$ \mathcal{B}{\left.\left({\overline{B}}_s^0\to J/\psi {\mu}^{+}{\mu}^{-}\right)\right|}_{q^2\ge 1{\textrm{GeV}}^2} $$ = 2.88 × 10 and $$ \mathcal{B}{\left.\left({\overline{B}}_d^0\to J/\psi {\mu}^{+}{\mu}^{-}\right)\right|}_{q^2\ge 1{\textrm{GeV}}^2} $$ = 1.07 × 10 . In addition, we have presented the dimuon invariant mass distributions of the individual and total helicity amplitudes squared, as well as the differential and integrated longitudinal polarization fractions of the $\textit{J}$/$\textit{ψ}$ meson, which could be probed by the future LHCb and Belle II experiments with more accumulated data.

China

Xin-Qiang Li

Yan Shi

Ya-Dong Yang

Xing-Bo Yuan

Chun-Yang Zhao

$$ {\overline{B}}_{s,d}^0 $$ → $\textit{J}$/$\textit{ψμ}$ + $\textit{μ}$ − decays in QCD factorization

We consider planar codimension-one defects and interfaces in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills (SYM) theory, realized by the D3/D5-brane intersection. Working in the probe limit, where the number of D5-branes is small compared to the number of D3-branes, we obtain analytic results for the holographic entanglement entropy of a ball-shaped region centered on the defect. A defect renormalization group flow is triggered by giving the defect hypermultiplets a mass, which corresponds to separating the D3- and D5-branes. Along this flow the entanglement C-function decreases monotonically. We also allow the D5-branes to carry worldvolume flux corresponding to dissolved D3-branes, in which case the setup describes an interface between two copies of $$ \mathcal{N} $$ = 4 SYM theory with different gauge groups, where an RG flow is triggered by placing one side of the interface onto the Coulomb branch. Here we again find monotonic behavior of the entanglement C-function, although its interpretation as a measure of effective degrees of freedom is problematic. We investigate possible alternative measures of degrees of freedom.

Finland

Niko Jokela

Germany

Jani Kastikainen

Italy

José Penín

Sweden

Ronnie Rodgers

Helime Ruotsalainen

Entanglement C-functions of defects and interfaces in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

We have performed high-statistics lattice simulations using 4HEX improved staggered fermions on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>16</mn><mn>3</mn></msup><mo>×</mo><mn>8</mn></math> lattices. We calculated the Taylor expansion coefficients of the pressure with respect to the baryochemical potential to the tenth order at zero and the fourth order at purely imaginary chemical potentials. We used this data to construct rational function approximations of the free energy. We use a rational ansatz that explicitly satisfies the charge conjugation symmetry and the Roberge-Weiss periodicity, which are exact properties of the quantum chromodynamics free energy. We use this ansatz to estimate the position of Lee-Yang zeros in the complex chemical potential plane. The temperature dependence of the imaginary part of the Lee-Yang zeros is then fitted with ansätze motivated by the universal behavior of the free energy near a 3D Ising critical point. In principle, this allows one to estimate the temperature of the critical endpoint. We consider several sources of systematic errors. On this single lattice spacing, we find that with 84% probability the chiral critical endpoint is either below 103 MeV temperature or it does not exist. We also identify some caveats of the method, which do not disappear even with the extremely high statistics of this present study. We discuss to what extent these can be eliminated by future high statistics lattice analyses.

Alexander Adam

Szabolcs Borsányi

United States

Hungary

Zoltán Fodor

Jana N. Guenther

Piyush Kumar

Paolo Parotto

Attila Pásztor

Chik Him Wong

High-precision baryon number cumulants from lattice QCD in a finite box: Cumulant ratios, Lee-Yang zeros, and critical endpoint predictions

A first-order, confinement/deconfinement phase transition appears in the finite temperature behavior of many non-Abelian gauge theories. These theories play an important role in proposals for completion of the Standard Model of particle physics, hence the phase transition might have occurred in the early stages of evolution of our Universe, leaving behind a detectable relic stochastic background of gravitational waves. Lattice field theory studies implementing the density of states method have the potential to provide detailed information about the phase transition, and measure the parameters determining the gravitational-wave power spectrum, by overcoming some of the challenges faced by importance-sampling methods. We assess this potential for a representative choice of Yang-Mills theory with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>p</mi><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo></math> gauge group. We characterize its finite-temperature, first-order phase transition, in the thermodynamic (infinite volume) limit, for two different choices of number of sites in the compact time direction, hence taking the first steps toward the continuum limit extrapolation. We demonstrate the persistence of nonperturbative phenomena associated to the first-order phase transition: coexistence of states, metastability, latent heat, surface tension. We find consistency between several different strategies for the extraction of the volume-dependent critical coupling, hence assessing the size of systematic effects. We also determine the minimum choice of ratio between spatial and time extent of the lattice that allows one to identify the contribution of the surface tension to the free energy. We observe that this ratio scales nontrivially with the time extent of the lattice, and comment on the implications for future high-precision numerical studies.

United Kingdom

Ed Bennett

Biagio Lucini

David Mason

Maurizio Piai

Japan

Enrico Rinaldi

Davide Vadacchino

Fabian Zierler

Finite-temperature Yang-Mills theories with the density of states method: Toward the continuum limit

We extend the celestial Roiban-Spradlin-Volovich-Witten (RSVW) formalism developed in our previous work to minitwistor superspace. Using the Drummond-Henn formula for all tree-level amplitudes in <math altimg='si37.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> supersymmetric Yang-Mills (SYM) theory, we construct tree-level N <italic>k</italic>-MHV celestial leaf amplitudes and show that their minitwistor-Fourier transforms are given by integrals over moduli spaces of families of minitwistor lines. We also adapt the Korchemsky-Sokatchev twistor-transform techniques for gluon amplitudes to the minitwistor-Fourier transforms of leaf amplitudes. We then describe two dynamical formulations of these celestial amplitudes. First, we show that semiclassical correlators of Wilson operators supported on algebraic cycles in minitwistor superspace act as generating functionals for tree-level N <italic>k</italic>-MHV leaf-gluon amplitudes. Second, we analyse a semiclassical minitwistor sigma model, identify its vertex operators, and construct from them celestial gluon operators that close on the <italic>S</italic>-algebra in the semiclassical approximation; their leading-trace semiclassical correlators again reproduce the tree-level N <italic>k</italic>-MHV leaf amplitudes. A companion paper extends this construction beyond tree level, in particular to one-loop amplitudes via a celestial version of the Brandhuber-Spence-Travaglini formalism.

Brazil

Igor Mol

A celestial description of planar super-Yang-Mills theory

We compute three-loop corrections to the three-point form factor of the operator <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>tr</mi><mo stretchy="false">(</mo><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> supersymmetric Yang-Mills theory. In particular, our result is valid beyond the leading-color limit and will consequently be an important input towards extending the amplitude-bootstrap program beyond the leading-color approximation. We find that our analytic formulae are strikingly compact expressions in terms of integer linear combinations of generalized polylogarithms of weight six.

Xin Guan

Bernhard Mistlberger

Michael Ruf

Subleading Color Corrections at Three Loops to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>tr</mi><mo stretchy="false">(</mo><msup><mi>ϕ</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> Three-Point Form Factor in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> Supersymmetric Yang-Mills Theory

We investigate the (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math>-deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><msub><mo stretchy="false">)</mo><mi>k</mi></msub></math> Yang-Mills theory in the lattice Hamiltonian formalism, which is characterized by three parameters: the number of colors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, the coupling constant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>, and the level <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi></math>. By treating these as tunable parameters, we explore how key properties of the theory, such as confinement and topological order, emerge in different regimes. Employing a variational mean-field analysis that interpolates between the strong- and weak-coupling regimes, we determine the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> phase structure in terms of the ’t Hooft coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mi>tH</mi></msub><mo>=</mo><msup><mi>g</mi><mn>2</mn></msup><mi>N</mi></math> and the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi><mo>/</mo><mi>N</mi></math>. We find that the topologically ordered phase remains robust at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> under appropriate scalings of these parameters. This result indicates that the continuum limit of large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> gauge theory may be more intricate than naively expected, and it motivates studies beyond the mean-field theory, both to achieve a further understanding of confinement in gauge theories and to guide quantum simulations of large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> gauge theories.

Tomoya Hayata

Yoshimasa Hidaka

Hiromasa Watanabe

Phases of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math>-deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> Yang-Mills theory at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>

We investigate the QCD phase diagram and the associated Lee–Yang edge singularities using the two-flavor nonlocal Nambu–Jona-Lasinio model extended to complex chemical potential. We show explicitly there exists a strong correlation between the chiral phase transition and the patterns in the effective potential in the complex plane of order parameter, serving as a criterion to differentiate crossover from first-order transitions. Typically, the Lee–Yang edge singularities can be understood as a generalization of the critical end point (CEP) separating the crossover and the first-order transition, where the positive Nambu phase and the Wigner phase coalesce. We further analyze the scaling behavior near the CEP by extracting the critical exponent associated with the Lee–Yang singularities. Additionally, we confirm that the extrapolation of the Lee–Yang edge singularity trajectories provides an efficient method of determining the CEP location, even at a small real chemical potential. This provides a viable method for exploring regions of the QCD phase diagram that remain inaccessible to lattice QCD.

Zong-shuai Zhang

Yi Lu

Yu-xin Liu

Lee-Yang edge singularities in a nonlocal Nambu–Jona-Lasinio model

We propose a SymTFT for 4d U($\textit{N}$) Yang-Mills theory and its variants. We show that the SymTFT reproduces the structure of the global one-form symmetry in these theories. We consider the holographic embedding of this SymTFT, and observe that SymTFT’s containing continuous symmetries are not always obtained as a near boundary limit of the supergravity action.

Israel

Oren Bergman

Eduardo Garcia-Valdecasas

Spain

Francesco Mignosa

Diego Rodriguez-Gomez

The SymTFT of $\textit{u}$($\textit{N}$) Yang-Mills Theory and holography

It is known that Yang-Mills theories, especially in the large-$\textit{N}$ limit, exhibit a $\textit{θ}$-vacuum structure with a multi-branched vacuum energy. In this work, we demonstrate that this multi-branch structure can play a crucial role in axion cosmology when the axion acquires its mass from the Yang-Mills sector, even when that sector is never reheated by the inflaton. The key observation is that the axion potential is directly tied to the tunneling rate between adjacent branches. We find qualitatively new phenomena, including a new class of first-order phase transitions, bouncing bubbles, and nested “bubbles-within-bubbles”. When the axion has a decay constant around the Planck scale, as motivated by the string Axiverse, the axion can be driven near the hilltop by inflationary dynamics, allowing the phase transition to be triggered. The associated energy release can be large enough to generate a significant stochastic gravitational-wave background, produce primordial black holes, or populate the Yang-Mills sector with particles. These phenomena represent novel predictions of the Axiverse and should be taken into account when assessing the cosmological impact of axions or axion-like particles. To recover conventional axion cosmology, one must suppress or avoid the dynamics discussed in this work.

Tsubasa Sugeno

Wen Yin

Axion cosmology with multi-branch Yang-Mills