All charmless <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> denotes the light pseudoscalar meson and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi></math> denotes the vector meson) decays have not been experimentally observed to date, but some of them might be measured in the near future. The charmless <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays with the axial-vector (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math>) resonance states, the tensor (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>) resonance states, and the excited vector (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>V</mi><mrow><mi>E</mi><mo>,</mo><mi>D</mi></mrow></msub></math>) resonance states are studied based on flavor SU(3) analysis in this work, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>V</mi><mi>E</mi></msub></math> contains <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><mi>ρ</mi><mo stretchy="false">(</mo><mn>1450</mn><mo stretchy="false">)</mo><mo>,</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>1410</mn><mo stretchy="false">)</mo><mo>,</mo><mi>ω</mi><mo stretchy="false">(</mo><mn>1420</mn><mo stretchy="false">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy="false">(</mo><mn>1680</mn><mo stretchy="false">)</mo><mo stretchy="false">}</mo></math> with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>n</mi><mrow><mn>2</mn><mi>S</mi><mo>+</mo><mn>1</mn></mrow></msup><msub><mi>L</mi><mi>J</mi></msub><mo>=</mo><msup><mn>2</mn><mn>3</mn></msup><msub><mi>S</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>V</mi><mi>D</mi></msub></math> contains <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><mi>ρ</mi><mo stretchy="false">(</mo><mn>1700</mn><mo stretchy="false">)</mo><mo>,</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>1680</mn><mo stretchy="false">)</mo><mo>,</mo><mi>ω</mi><mo stretchy="false">(</mo><mn>1650</mn><mo stretchy="false">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy="false">(</mo><mn>2170</mn><mo stretchy="false">)</mo><mo stretchy="false">}</mo></math> with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>n</mi><mrow><mn>2</mn><mi>S</mi><mo>+</mo><mn>1</mn></mrow></msup><msub><mi>L</mi><mi>J</mi></msub><mo>=</mo><msup><mn>1</mn><mn>3</mn></msup><msub><mi>D</mi><mn>1</mn></msub></math>. The hadronic amplitudes of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><mo>/</mo><mi>T</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays are related by the nonperturbative parameters, and the branching ratio predictions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><mo>/</mo><mi>T</mi><mo>/</mo><msub><mi>V</mi><mrow><mi>E</mi><mo>,</mo><mi>D</mi></mrow></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> are obtained, and then the branching ratios of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>T</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msub><mi>V</mi><mi>E</mi></msub><mo stretchy="false">(</mo><msub><mi>V</mi><mi>E</mi></msub><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msub><mi>V</mi><mi>D</mi></msub><mo stretchy="false">(</mo><msub><mi>V</mi><mi>D</mi></msub><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> are obtained by the narrow width approximation or further considering the width effects. We find that most branching ratios of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays and many branching ratios of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>A</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays are on the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mi>–</mi><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo stretchy="false">)</mo></math>, and all branching ratios with the tensor resonance states and the excited vector resonance states are small. Our results could be tested in the future Belle II and LHCb experiments.

China

Yi Qiao

Jin-Huan Sheng

Yuan-Guo Xu

Ru-Min Wang

Flavor SU(3) analysis of the charmless semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays

We perform a detailed computation of key quantities across the first-order deconfinement phase transition of the SU(3) Yang-Mills theory. Specifically, we calculate the entropy density, <math altimg='si1.svg'><mi>s</mi><mo stretchy='false'>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy='false'>)</mo><mo stretchy='false'>/</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow><mrow><mn>3</mn></mrow></msubsup></math>, on both sides of the transition and determine the latent heat <italic>h</italic>. The calculations are carried out in the lattice regularization with the Wilson action, employing shifted boundary conditions in the temporal direction. Our simulations are performed at five different values of the lattice spacing in order to extrapolate the results to the continuum limit. The latent heat can be measured also as the discontinuity in the trace anomaly of the energy-momentum tensor: our result using the entropy density is compatible with the one obtained from the trace anomaly, giving a combined estimate <math altimg='si2.svg'><mi>h</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1.175</mn><mo stretchy='false'>(</mo><mn>10</mn><mo stretchy='false'>)</mo></math>. Additionally, we determine the critical temperature <math altimg='si3.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math> in physical units with permille accuracy, yielding <math altimg='si4.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><msqrt><mrow><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msqrt><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0.24915</mn><mo stretchy='false'>(</mo><mn>29</mn><mo stretchy='false'>)</mo></math>. These results allow to connect with precision the confined and the deconfined phases and we present an improved computation of the Equation of State across the deconfinement transition for <italic>T</italic> between 0 and <math altimg='si5.svg'><mn>3.4</mn><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>.

Italy

Leonardo Giusti

Mitsuaki Hirasawa

Michele Pepe

Luca Virzì

A precise study of the thermodynamic properties of the SU(3) Yang-Mills theory across the deconfinement transition

The structure of center vortices is studied in SU(4) Yang-Mills theory for the first time to illuminate the interplay between elementary (center charge <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>±</mo><mn>1</mn></math>) and doubly charged vortices. Unlike in SU(3), where charge <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>+</mo><mn>2</mn></math> vortices are simply elementary vortices with reversed orientations in spacetime, these possibilities are physically distinct in SU(4). Visualizations of the vortex structure in three-dimensional slices reveal the various ways in which doubly charged objects manifest, as the convergence and matching of elementary vortices or as isolated doubly charged loops. An algorithm is described to classify every doubly charged chain as one of these three types. A collection of vortex statistics is considered to quantify the vortex structure. Many of these pertain to the novel doubly charged objects, including their relative proportions and chain lengths, which are analyzed to highlight the differences between each chain type. Three different lattice spacings are employed to investigate the approach to the continuum limit. Vortex matching chains are found to be shorter on average but also more prevalent than vortex convergences, ascribed to their interpretation as extended center monopoles. In addition, the lengths of both vortex convergences and vortex matchings are observed to follow an exponential distribution, allowing the introduction of a constant probability for a doubly charged chain to split into two elementary vortices as it propagates. Combined, these findings provide a characterization of the vortices that comprise center-vortex structures in SU(4) Yang-Mills theory.

Australia

Jackson A. Mickley

Derek B. Leinweber

Brazil

Luis E. Oxman

Structure of center-vortex matter in SU(4) Yang-Mills theory

We study the charmed baryon two-body decays of → $\textit{M}$ under the SU(3) flavor symmetry, where refers to anti-triplet singly charmed baryons, and and $\textit{M}$ denote decuplet baryons and pseudoscalar mesons, respectively. We consider the released energy dependence of both partial waves and phase space for the SU(3) symmetry breaking effects. With 4 real parameters in total and 8 experimental data points, we achieve a minimal $\textit{χ}$ /d.o.f. value of 0$\textit{.}$81, providing a satisfactory explanation to the experiment results. We evaluate the branching ratios and decay asymmetries with unusual positive decay asymmetry in → $\textit{M}$, indicating the nontrivial SU(3) -breaking effects. The results of the large SU(3) -breaking effects can be verified in the further research by the experiments at BESIII, Belle II and LHCb.

Chao-Qiang Geng

Chia-Wei Liu

Sheng-Lin Liu

Two-body charmed baryon nonleptonic weak decays with decuplet baryon involving SU(3)

We study the scattering of the gluon-dressed physical quarks, defined as the eigenstates of the vacuum QCD Hamiltonian, off a colored medium. We solve the wave function of the physical quark state by diagonalizing the QCD Hamiltonian in vacuum in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>q</mi><mo stretchy="false">⟩</mo><mo>+</mo><mo stretchy="false">|</mo><mrow><mi>q</mi><mi>g</mi></mrow><mo stretchy="false">⟩</mo></math> Fock space, with implementing the sector-dependent mass renormalization scheme. We then perform numerical simulations of the real-time quantum state evolution of the initially dressed quark state at various medium densities. The results are compared with those of an initially bare or off-shell quark states. With the obtained light-front wave function of the evolved state, we extract the quark jet transverse momentum broadening, the quenching parameter, the cross section, the gluon emission rate, and the evolution of the invariant mass. The scenario considered is relevant for high energy scattering processes, where the quark originates from far outside the color field describing the scattering target. This investigation on dressed quarks complements our earlier studies of the single quark scattering in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>q</mi><mo stretchy="false">⟩</mo></math> Fock space, and of the bare quark scattering in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>q</mi><mo stretchy="false">⟩</mo><mo>+</mo><mo stretchy="false">|</mo><mrow><mi>q</mi><mi>g</mi></mrow><mo stretchy="false">⟩</mo></math> Fock space, providing a novel systematic description of quark scattering process using a nonperturbative formalism.

Spain

Meijian Li

Finland

Tuomas Lappi

Xingbo Zhao

Carlos A. Salgado

Scattering and gluon emission of physical quarks in a SU(3) colored field

Higher order calculations in chiral gauge theories such as the Electroweak Standard Model require a sound treatment of the notoriously problematic $\textit{γ}$ -matrix in Dimensional Regularization (DReg). In the all-order consistent BMHV scheme anticommutativity has to be sacrificed, resulting in spurious breakings of BRST invariance, the restoration of which necessitates finite, symmetry-restoring counterterms. Following recent advances in successfully applying this scheme to multi-loop calculations for Abelian models, we shall here present the first complete non-Abelian two-loop result for the case of SU(2), which is of particular interest to the Standard Model. We provide the complete list of finite, two-loop symmetry-restoring counterterms and discuss intricacies of the non-Abelian implementation. Except for one novel term, the finite counterterm action exhibits the same structure as at one-loop order.

Germany

Paul Kühler

Dominik Stöckinger

Two-loop renormalization of a chiral SU(2) gauge theory in dimensional regularization with non-anticommuting $\textit{γ}$

We investigate the phase diagram of the three-dimensional SU(3) spin model with finite chemical potential, which is an effective Polyakov loop model for finite density QCD, using the tensor renormalization group method. We successfully determine the location of the critical endpoints being free from the complex action problem in the standard Monte Carlo approach. The critical values of the parameters show the consistency with previous ones obtained by other analytic and numerical methods.

Japan

Xiao Luo

Yoshinobu Kuramashi

Critical endpoints of three-dimensional finite density SU(3) spin model with tensor renormalization group

We revisit the doublet–triplet splitting problem within the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo></math> gauge group framework to advocate a viable regime with the light scalar leptoquark of the doublet–triplet splitting notoriety that is compatible with the current experimental bounds on partial proton decay lifetimes. We explicitly demonstrate, through a consistent use of higher-dimensional operators, how to implement suppression of baryon number violating interactions of the aforementioned color triplet. Our study thus offers an alternative approach to the doublet-triplet splitting problem as it removes a need for an extreme mass hierarchy between the partners residing in the same representation. We furthermore pursue two different extensions of two distinct symmetry breaking scenarios of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo></math>, one with a 24-dimensional representation and the other one with a 75-dimensional representation, to produce comparative study of novel consequences for the gauge coupling unification and the one-loop level neutrino mass generation. Our results point toward qualitatively novel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo></math> scenarios, where the light scalar leptoquarks, responsible for the neutrino mass generation, might be even accessible at colliders and thus serve as an accelerator accessible portal to the high-scale physics.

Croatia

Slovenia

Ilja Doršner

Mijo Matković

Shaikh Saad

Nonrenormalizable SU(5) GUTs: Leptoquark-induced neutrino masses

This article investigates the thermodynamic properties of the SU(2) Nambu–Jona–Lasinio (NJL) model under the chiral chemical potential $$ \mu _5 $$ , employing Tsallis non-extensive statistics. The introduction of the parameter $$ q $$ , which characterizes the non-extensivity of the system through Tsallis statistics, offers a novel perspective for studying the behavior of strongly interacting matter under extreme conditions. By calculating thermodynamic quantities such as quark mass, critical temperature, chiral density, pressure, entropy, and speed of sound, we systematically analyze the effects of $$ \mu _5 $$ and $$ q $$ on these quantities. It is observed that both $$ \mu _5 $$ and $$ q $$ exhibit an inverse relationship with the critical temperature $$ T_\textrm{pc} $$ , while showing a positive correlation with the chiral density $$\left\langle n_{5}\right\rangle $$ .

Xiang-Qiong Liu

The QCD phase diagram of the SU(2) NJL model with chiral chemical potential under a non-extensive framework

An <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi></mrow><mo stretchy="false">(</mo><mn>8</mn><mo stretchy="false">)</mo></math> theory was previously found to be the minimal simple gauge group where all three-generational Standard Model (SM) fermions can be nontrivially embedded. It is maximally broken into a subgroup of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi></mrow><mo stretchy="false">(</mo><mn>8</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mi mathvariant="script">G</mi><mn>441</mn></msub><mo>≡</mo><mrow><mi>SU</mi></mrow><mo stretchy="false">(</mo><mn>4</mn><msub><mo stretchy="false">)</mo><mi>s</mi></msub><mo stretchy="false">⊗</mo><mrow><mi>SU</mi></mrow><mo stretchy="false">(</mo><mn>4</mn><msub><mo stretchy="false">)</mo><mi>W</mi></msub><mo stretchy="false">⊗</mo><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><msub><mi>X</mi><mn>0</mn></msub></msub></math> at the grand unified theory scale by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi></mrow><mo stretchy="false">(</mo><mn>8</mn><mo stretchy="false">)</mo></math> adjoint Higgs field of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn mathvariant="bold">6</mn><msub><mn mathvariant="bold">3</mn><mi mathvariant="bold">H</mi></msub></mrow></math>. Gauge symmetries in the strong and the weak sectors are extended by one and two ranks, respectively. The sequential strong-weak-weak (SWW) symmetry breaking stages were found to generate the observed hierarchical SM quark/lepton masses as well as the Cabibbo-Kobayashi-Maskawa mixing pattern with the precise flavor identifications [The global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">B</mi><mo stretchy="false">−</mo></mrow></math> L symmetry in the flavor-unified SU(N) theories, <a href="http://dx.doi.org/10.1007/JHEP04(2024)046">J. High Energy Phys. 04 (2024) 046</a>. and The standard model quark/lepton masses and the Cabibbo-Kobayashi-Maskawa mixing in an SU(8) theory, <a href="http://dx.doi.org/10.1007/JHEP12(2024)137">J. High Energy Phys. 12 (2024) 137</a>.]. We further study the possible weak-strong-weak and weak-weak-strong symmetry breaking patterns and compare with the results that we have obtained by following the SWW sequence. The two-loop renormalization group equations following both patterns are analyzed, where we cannot achieve the gauge coupling unification in the field theory framework. Through these analyses, we suggest the gauge coupling unification to be interpreted in the context of the affine Lie algebra.

Ning Chen

Zhiyuan Chen

Zhanpeng Hou

Zhaolong Teng

Bin Wang

Further study of the maximally symmetry breaking patterns in an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi></mrow><mo stretchy="false">(</mo><mn>8</mn><mo stretchy="false">)</mo></math> theory