An $\textit{SU}$(3) flavor projection operator technique is implemented to construct the baryon-meson scattering amplitude within the framework of the $1/N_c$ expansion of quantum chromodynamics (QCD), where $N_c$ represents the number of color charges. The operator technique is implemented to evaluate not only the lowest-order scattering amplitude but also effects from the first-order perturbative $\textit{SU}$(3) flavor symmetry breaking and strong isospin breaking. The most general expression is obtained by explicitly accounting for the effects of the decuplet-octet baryon mass difference. At order ${\cal{O}}(1/N_c^2)$ , a large number of unknown operator coefficients appear, and therefore, there is little additional predictive power unless leading and subleading terms are retained. Although the resultant expression is sufficiently general that it can be applied to any incoming and outgoing baryons and pseudo scalar mesons, provided that the Gell-Mann--Nishijima scheme is respected, results for $N\pi\to N\pi$ scattering processes are explicitly considered.

Víctor Miguel Banda Guzmán

Rubén Flores-Mendieta

Johann Hernández

Use of $\textit{SU}$(3) flavor projection operators to construct baryon-meson scattering amplitudes in the 1/ N$_{c}$ expansion * The authors are grateful to Consejo Nacional de Humanidades, Ciencias y Tecnologías (Mexico) for support through the $\textit{Ciencia de Frontera}$ project CF-2023-I-162

Semi-holography provides a formulation of dynamics in gauge theories involving both weakly self-interacting (perturbative) and strongly self-interacting (non-perturbative) degrees of freedom. These two subsectors interact via their effective metrics and sources, while the full local energy-momentum tensor is conserved in the physical background metric. In the large $\textit{N}$ limit, the subsectors have their individual entropy currents, and so the full system can reach a pseudo-equilibrium state in which each subsector has a different physical temperature.

Germany

Toshali Mitra

India

Sukrut Mondkar

Chile

Ayan Mukhopadhyay

Slovenia

Alexander Soloviev

Hybrid thermalization in the large $\textit{N}$ limit

We formulate a general fusion procedure for open $$\mathfrak{g}\mathfrak{l}(N)$$ spin chains. We construct the fused boundary reflection matrices and the corresponding fused reflection equations. By using the intertwining relation between the fused reflection matrices and the fusion operator, we identify the invariant subspace of the fused reflection matrices carrying the irreducible representations of $$\mathfrak{g}\mathfrak{l}(N)$$ . We also construct the fused transfer matrix and evaluate it explicitly in the total tensor product space and the invariant subspaces. Finally, we demonstrate that the ABJM spin chain model originates from such fusion procedure and derive three classes of boundary reflection matrices solutions on the anti-fundamental representation space of $$\mathfrak{s}\mathfrak{u}(4)$$ .

China

Nan Bai

A general fusion procedure for open $$\mathfrak{g}\mathfrak{l}(N)$$ spin chains: application to the ABJM spin chain

Using the Monte Carlo <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>HYDJET</mi><mo>+</mo><mo>+</mo></mrow></math> model, we investigate the transverse momentum (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>) spectra of heavy-flavor hadrons, namely <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup><mo>,</mo><mo> </mo><msup><mover><mi>D</mi><mo>¯</mo></mover><mn>0</mn></msup><mo>,</mo><mo> </mo><msup><mi>D</mi><mo>+</mo></msup><mo>,</mo><mo> </mo><msup><mi>D</mi><mo>−</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math>, along with the nuclear modification factors of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mo>±</mo></msup></math> in Au <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math> Au collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV RHIC energy across various centrality bins. This work extends the earlier study by relaxing the assumption of identical chemical and thermal freezeout and by exploring the effect of a higher chemical freezeout temperature relative to thermal freezeout. The study also explores the centrality and mass dependence of the charm enhancement factor (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>γ</mi><mi>c</mi></msub></math>). Furthermore, we investigate medium-induced energy loss, particle-antiparticle asymmetry, and the role of fragmentation in the hadronization process. The <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>HYDJET</mi><mo>+</mo><mo>+</mo></mrow></math> model, with its default parameters, is unable to reproduce heavy hadron yields due to their early thermal freezeout and initial state production of heavy quarks. Therefore, a systematic tuning of model parameters is performed to improve the overall agreement with experimental data. Additionally, to assess the performance of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>HYDJET</mi><mo>+</mo><mo>+</mo></mrow></math> model relative to other theoretical approaches, its results are compared with the TAMU, SUBATECH, Torino, and Duke models, for which corresponding simulation data are available. This study shows a decreasing trend in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>γ</mi><mi>c</mi></msub></math> from central to peripheral collisions. Moreover, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>γ</mi><mi>c</mi></msub></math> increases with increasing charm-hadron mass. The model approximately reproduces the experimental data of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math> spectra at low and intermediate <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>. However, it overestimates the data at high <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>, indicating a need for improvements in modeling the energy loss of heavy quarks. The nuclear modification factors (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math>) for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math> mesons exhibit significant suppression at high <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>. At low <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub><mo>,</mo><mo> </mo><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> results show deviations from the data, reflecting limitations in the model where coalescence becomes important. The antiparticle-to-particle ratios are consistent with experimental data, whereas mixed-particle ratios are underestimated, revealing the model's limitation in estimating the baryon-to-meson enhancement.

Sunidhi Saxena

Rajiv Gupta

Gauri Devi

Ajay Kumar

Heavy hadron production in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Au</mi><mo>+</mo><mi>Au</mi></math> collisions at a center-of-mass energy of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV

We propose a novel strategy to derive explicit and uniform upper bounds on the particle spectrum of six-dimensional gravitational theories with minimal supersymmetry, focusing initially on the tensor sector. The strategy is motivated by considerations of F-theory compactifications on elliptic Calabi-Yau threefolds. However, it admits a clear bottom-up interpretation and is, thus, applicable to general supergravity theories modulo certain physical conjectures. At the heart of the strategy are two key structures, most natural in birational geometry: One concerns the singularity of the natural pairs on the base manifolds, and the other the fibration generically exhibited by the bases. Put physically, the former structure keeps the effective theories from decompactifying, and the latter ensures the (generic) presence of a heterotic string. We sketch our bounding strategy and present, for an illustration, the explicit bounds thereby derived on the tensor spectrum, with the technical details relegated to a companion paper [C. Birkar and S. J. Lee, <a href="http://arXiv.org/abs/2507.06317">arXiv:2507.06317</a>].

Caucher Birkar

South Korea

Seung-Joo Lee

Explicit bounds on the spectrum of 6D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></math> supergravity

Are perturbative superstring amplitudes for massless external states just an $\textit{α}$ dressing of super-Yang-Mills/supergravity? This is the case at tree level, where the worldsheet correlators at $\textit{n}$ points can be written in a natural worldsheet basis, such that the kinematic coefficients are BCJ numerators of super-Yang-Mills/supergravity amplitudes, with the non-trivial $\textit{α}$ dependence carried only by the Koba-Nielsen factor. Motivated by this construction, we present for the first time a complete worldsheet basis of one-loop superstring correlators at $\textit{n}$ points. All the kinematic coefficients associated to non-cusp basis elements are identified with pieces of one-loop BCJ numerators of super-Yang-Mills/supergravity. This determines the superstring correlators up to 15 points in terms of field theory. Starting at 16 points (modular weight 12), the worldsheet basis may include cusp forms, which vanish in the field-theory degeneration, such that the associated coefficients cannot be fixed in this manner. Therefore, the one-loop answer to our initial question is determined, at high multiplicity, by whether the coefficients of cusp basis elements vanish or not. As a by-product of our construction, we present new constraints on the field-theory limit that result from string modularity. These are expressed as additional relations among one-loop BCJ numerators in maximal super-Yang-Mills/supergravity starting at 6 points.

United Kingdom

Ricardo Monteiro

Lecheng Ren

Superstring amplitudes from the field-theory limit: an $\textit{n}$-point map at one loop

We show that the lattice glueball masses <italic>M<inf>G</inf></italic> versus <italic>N</italic> in SU( <italic>N</italic>) and Sp(2 <italic>N</italic>) Yang-Mills theories scale as <math altimg='si38.svg'><mrow><mfrac><msub><mi>M</mi><mi>G</mi></msub><msqrt><mi>&#963;</mi></msqrt></mfrac><mo>&#8764;</mo><msqrt><mfrac><mrow><msub><mi>C</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>a</mi><mi>d</mi><mi>j</mi><mo>)</mo></mrow></mrow><mrow><msub><mi>C</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow></mrow></mfrac></msqrt></mrow></math>, with <italic>&#963;</italic> the fundamental string tension and <italic>C</italic> <inf>2</inf>( <italic>adj</italic>) and <italic>C</italic> <inf>2</inf>( <italic>f</italic>) the quadratic Casimir of the gauge algebra in the adjoint and fundamental representations. This scaling behaviour is followed by the great majority of available lattice glueball states, and may set constraints on <italic>SU</italic>(3) models by imposing a specific behaviour at <italic>N</italic>&#8239;&#8800;&#8239;3. The observed scaling is compatible with two assumptions: (1) The glueball masses are proportional to the square root of the adjoint string tension, <math altimg='si39.svg'><mrow><msub><mi>M</mi><mi>G</mi></msub><mo>&#8764;</mo><msub><msqrt><mi>&#963;</mi></msqrt><mrow><mi>a</mi><mi>d</mi><mi>j</mi></mrow></msub></mrow></math>; (2) The string tension follows the Casimir scaling, i.e. <math altimg='si40.svg'><mrow><msub><mi>&#963;</mi><mrow><mi>a</mi><mi>d</mi><mi>j</mi></mrow></msub><mo linebreak='goodbreak'>=</mo><mfrac><mrow><msub><mi>C</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>a</mi><mi>d</mi><mi>j</mi><mo>)</mo></mrow></mrow><mrow><msub><mi>C</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow></mrow></mfrac><mi>&#963;</mi></mrow></math>. In a constituent gluon picture, our results suggest a low-lying glueball spectrum made of two transverse constituent gluons bound by an adjoint string, completed by three transverse constituent gluons bound by a Y-junction of adjoint strings rather than a <math altimg='si41.svg'><mrow><mstyle mathvariant='normal'><mi>&#916;</mi></mstyle><mo linebreak='goodbreak'>&#8722;</mo></mrow></math>shaped junction of fundamental strings.

Belgium

Fabien Buisseret

Cyrille Chevalier

Spain

Vincent Mathieu

Claude Semay

Casimir scaling in glueballs in SU( <italic>N</italic>) and Sp(2 <italic>N</italic>) gauge theories: Hints from constituent approaches

I present a large-$\textit{N}$ determination of the topological susceptibility $\textit{χ}$ of SU($\textit{N}$) Yang-Mills theories using non-perturbative numerical Monte Carlo simulations of the lattice-discretized theory for 3 ≤ $\textit{N}$ ≤ 6, and adopting the Parallel Tempering on Boundary Conditions (PTBC) algorithm to bypass topological freezing for $\textit{N >}$ 3. Thanks to this algorithm I am able to explore a uniform range of lattice spacings across all values of $\textit{N}$, and to precisely determine $\textit{χ}$ for finer lattice spacings compared to previous studies with periodic or open boundary conditions. By taking the continuum limit at fixed smoothing radius in physical units, I am also able to show the independence of the continuum limit of $\textit{χ}$ from this choice. I conclude providing a comprehensive comparison of my new PTBC results with previous determinations of the topological susceptibility in the literature, both at finite $\textit{N}$ and in the large-$\textit{N}$ limit.

Claudio Bonanno

The large-$\textit{N}$ limit of the topological susceptibility of SU($\textit{N}$) Yang-Mills theories via Parallel Tempering on Boundary Conditions

This work implements the combined baryon chiral perturbation theory (BChPT) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub></math> expansions for pion-nucleon elastic scattering. The effective theory is based on the baryon sector dynamical spin-flavor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo></math> symmetry emergent in the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> limit, whose breaking is controlled by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub></math> expansion. The noncommutativity of the chiral and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub></math> expansions in unitarity corrections (loops) requires a linking of both expansions. As it was shown in the case of baryon masses and currents, the natural linking is the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ξ</mi></math> expansion, in which <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mrow><mn>1</mn><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub></mrow><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo stretchy="false">)</mo></math>. The spin-flavor symmetry requires that the ground state baryons span an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo></math> symmetric irreducible representation which implies that in particular <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi></math> are active degrees of freedom in the effective theory. The scattering amplitude is expanded to the next-to-next-to leading order in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ξ</mi></math> expansion, corresponding to the one-loop contributions with the leading-order Lagrangian. The results are given for generic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> in order to demonstrate the consistency of the framework. The spin-flavor symmetry plays a central role in maintaining the consistency of the effective theory with respect to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub></math> expansion. This consistency manifests itself in an improvement in the convergence of the low energy expansion with respect to the case of the ordinary BChPT without an explicit dynamical <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi></math>, which is known to be inconsistent with the constraints of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> scaling. Fits to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>N</mi><mo stretchy="false">→</mo><mi>π</mi><mi>N</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> partial wave amplitudes from the SAID data base are finally used to test the framework and to determine the energy range of its applicability.

United States

D. Jayakodige

J.L. Goity

Pion-nucleon scattering in baryon chiral perturbation theory combined with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub></math> expansion

By fitting the two-point correlation functions of topological charge density operators calculated on two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>+</mo><mn>1</mn></math>-flavor gauge ensembles with physical pion mass, we determine both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> masses and also the mixing angle to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>η</mi></msub><mo>=</mo><mn>0.505</mn><mo stretchy="false">(</mo><mn>72</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>75</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><msup><mi>η</mi><mo>′</mo></msup></msub><mo>=</mo><mn>0.952</mn><mo stretchy="false">(</mo><mn>47</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>40</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>θ</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>8.9</mn><mo stretchy="false">(</mo><mn>2.1</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>1.8</mn><mo stretchy="false">)</mo><mo>°</mo></math>, respectively, where the first error is the statistical uncertainty and the second one is the systematic uncertainty. This is the first extraction of both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>/</mo><msup><mi>η</mi><mo>′</mo></msup></math> masses and the mixing angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>θ</mi><mn>1</mn></msub></math> using topological charge operators. Compared with previous studies using quark bilinear operators, the error of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> mass is relatively large, but the mixing angle has comparable precision. This demonstrates that the topological charge operators are well suited to study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> mesons.

Yue Su

Nan Wang

Long-cheng Gui

Jun Hua

Jian Liang

Jun Shi

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>η</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> mesons from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math> lattice QCD at the physical point using topological charge operators