We propose a novel approach for extracting symmetry breaking effects from symmetry conserving three-body decays. The method is based on mapping the Dalitz plot to a unit disk, and the difference of the disk distributions of two related decays isolates purely symmetry breaking effects. We demonstrate this method by extracting the fundamental parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>, an isospin breaking ratio of light quark masses defined as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup><mo>≡</mo><mo stretchy="false">(</mo><msubsup><mi>m</mi><mi>s</mi><mn>2</mn></msubsup><mo>−</mo><msup><mover accent="true"><mi>m</mi><mo stretchy="false">^</mo></mover><mn>2</mn></msup><mo stretchy="false">)</mo><mo>/</mo><mo stretchy="false">(</mo><msubsup><mi>m</mi><mi>d</mi><mn>2</mn></msubsup><mo>−</mo><msubsup><mi>m</mi><mi>u</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>m</mi><mo stretchy="false">^</mo></mover></math> the average of up and down quark masses, from the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup><mo stretchy="false">→</mo><mi>η</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup><mo stretchy="false">→</mo><mi>η</mi><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math>. With the Dalitz plot distributions for these two decays reported by BESIII, we illustrate the method and obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mo>=</mo><mn>22.5</mn><mo>±</mo><mn>1.0</mn></math>, which is consistent with previous determinations and has a comparable uncertainty. With the full BESIII dataset, which is eight times larger than the one used here, a more precise determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> should become possible. This promising and novel method can be generalized to other three-body decays to extract symmetry breaking effects.

China

Mexico

Adolfo Guevara

Feng-Kun Guo

Hao-Jie Jing

Novel method for determining the light quark mass ratio using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup><mo stretchy="false">→</mo><mi>η</mi><mi>π</mi><mi>π</mi></math> decays

A model-independent parametrization of the low-energy scattering amplitude that incorporates the left-hand cut from one-particle exchange, an extension of the conventional effective range expansion (ERE), was recently proposed and successfully applied to the low-energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> system [, Effective-range expansion with a long-range force, <a href="http://dx.doi.org/10.1103/cwdt-dj6z">Phys. Rev. Lett. 135, 011903 (2025)</a>]. While the original formulation is based on a nonrelativistic approximation and is thus limited to a [1, 1] approximant for self-consistency, we extend the framework by explicitly including the higher order terms up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>k</mi><mn>6</mn></msup><mo stretchy="false">)</mo></math>. We systematically investigate the reliability and robustness of the generalized ERE by incorporating relativistic kinematic effects. In addition, we develop a relativistic version of the ERE that accounts for the left-hand cut contributions. These results affirm the generalized ERE as a robust and systematically improvable framework for near-threshold scattering processes, providing both analytical and numerical reliability for applications in two-body scattering problems with a particle exchange.

Wen-Jia Wang

Bing Wu

Meng-Lin Du

Effective range expansion with the left-hand cut: Higher order improvements

We investigate the discovery potential of the $T_{bc}$ state with $J^P = 0^+$ in proton-proton ( $pp$ ) collisions at LHCb at a center-of-mass energy of $\sqrt{s} = 13~{\rm{TeV}}$ . The study focuses on the decay channel $T_{bc} \to B^- D^+$ . A phenomenological approach is employed to construct the background model based on the associated production of $\textit{B}$ and $\textit{D}$ mesons, incorporating previously published LHCb results. Background processes are simulated using ${\mathtt{MadGraph5\_aMC@NLO}}$ and ${\mathtt{Pythia8.3}}$ . We explore the parameter space of the $T_{bc}$ mass, width, production cross section, and the effective double-parton scattering cross section ( $\sigma_{{\rm{eff}}}$ ) relevant for the $B D$ meson background. The integrated luminosity required for a $5\sigma$ discovery at LHCb is evaluated under various assumptions. In particular, we consider three representative $T_{bc}$ production cross section scenarios: an optimistic estimate of $103~{\rm{nb}}$ , an intermediate value of $18~{\rm{nb}}$ obtained by scaling from the $T_{cc}^+$ production cross section, and a conservative lower bound of $0.3~{\rm{nb}}$ . We find that a $5\sigma$ observation is achievable for a production cross section of $103~{\rm{nb}}$ , which is expected to be within reach during Run4. In contrast, the more realistic cross section estimate of $18~{\rm{nb}}$ requires the full Run5 dataset ( $300~{\rm{fb}}^{-1}$ ) under the most favorable parameter choices. For the conservative scenario, no significant signal would be observable even with $300~{\rm{fb}}^{-1}$ . In addition, we estimate the minimum observable $\sigma(T_{bc}) \times {\cal{B}}(T_{bc} \to $ $ B^- D^+)$ for a $5\sigma$ discovery under different luminosity scenarios, providing guidance for future experimental searches at LHCb.

Mingjie Feng

Yiming Li

France

Hua-Sheng Shao

Prospects for discovering strongly decaying doubly heavy T$_{bc}$ tetraquark states at LHCb * Mingjie Feng and Yiming Li is Supported by the National Natural Science Foundation of China (NSFC) (2175245, 12188102, W2443008). Hua-Sheng Shao is Supported by the European Research Council (101041109, 'BOSON') and the French National Research Agency (grant ANR-20-CE31-0015, 'PrecisOnium')

We evaluate discovery prospects for photophobic axion-like particles (ALPs) in the $\textit{WWjj}$ final state at the High-Luminosity LHC (HL-LHC; $\sqrt{s}=14\ {\rm{TeV}}$ , ${\cal{L}}=3\ {\rm{ab}}^{-1}$ ). In the photophobic limit ( $g_{a\gamma\gamma}=0$ ), ALPs couple to electroweak gauge bosons and are produced in association with two jets ( $ pp\to jj\ a $ ) via both $\textit{s}$-channel electroweak exchange and vector boson fusion (VBF)–like topologies, followed by $a\to W^+W^-$ decay. We target the different-flavour dilepton mode $W^+W^- \to e^\pm\mu^\mp\nu \bar{\nu}$ with two jets and moderate missing transverse momentum. The analysis employs a two-step strategy: initial preselection that defines the signal-like final state, followed by a multivariate analysis (MVA) trained on dijet and dileptonic-$\textit{WW}$ kinematics from both the $\textit{s}$-channel and VBF-like production mechanisms to separate signal from background; the MVA threshold is optimized independently at each $m_a$ . We present 2$\textit{σ}$ and 5$\textit{σ}$ discovery sensitivities for the ALP–$\textit{W}$ coupling $g_{aWW}$ across the 170–4000 GeV mass range. For $260\ {\rm{GeV}}\le m_a\le1500\ {\rm{GeV}}$ , the 2$\textit{σ}$ (5$\textit{σ}$) sensitivity is approximately flat around $ 0.61(0.76)\ {\rm{TeV}}^{-1}$ . At large masses/couplings, the mapping between an experimental rate and a single EFT parameter $g_{aWW}$ can become UV sensitive, and we treat the extreme high-mass/high-coupling corner as an extrapolation; therefore, we also report model-independent discovery thresholds for the fiducial quantity $ \sigma(pp\to jj\ a)\times\rm{Br}(a\to W^+W^-) $ over the same mass range to enable reinterpretation for other models. These results indicate that the $WWjj$ topology offers competitive and complementary sensitivity to heavy photophobic ALPs at the HL-LHC.

Jiaojiao Feng

Ying-nan Mao

Kechen Wang

Discovery prospects for photophobic axion-like particles in the $\textit{WWjj}$ final state at the High-Luminosity LHC * Jiaojiao Feng and Kechen Wang are supported by the National Natural Science Foundation of China (11905162), the Excellent Young Talents Program of the Wuhan University of Technology (40122102, 40122103) and the research program of the Wuhan University of Technology (2020IB024, 104972025KFYjc0101). Ying-nan Mao is supported by the National Natural Science Foundation of China (12205227). The simulation and analysis work of this article was completed with the computational cluster provided by the Theoretical Physics Group at the Department of Physics, School of Physics and Mechanics, Wuhan University of Technology

Motivated by the discrepancies noted recently between the theoretical predictions of the electromagnetic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>γ</mi><mo>*</mo></msup></math> transition form factor and the BESIII data, we reanalyze this transition form factor using the dispersive Khuri-Treiman equations, with final-state interactions in both the direct channel and the crossed channels properly considered. This improved framework incorporates <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>–</mi><mi>ω</mi></math> mixing effects. The effect of four-pion states is evaluated through a dispersively improved vector-meson-dominance model. From this information, we propose a two-parameter fit that provides an excellent description of the BESIII data over the broad energy range from 0 to 2.8 GeV. We demonstrate that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><msup><mi>π</mi><mn>0</mn></msup></math> decay mode of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> is dominated by strong interaction, while the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><msup><mi>π</mi><mn>0</mn></msup></math> mode is dominated by one-photon exchange. From this, we extract the relative phase between the strong and the one-virtual-photon (electromagnetic) modes in hadronic decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>62</mn><mo>±</mo><mn>21</mn><mo stretchy="false">)</mo><mo>°</mo></math>. This could provide useful information in understanding the long-standing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>π</mi></math> puzzle in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decays.

Xiong-Hui Cao

Germany

Christoph Hanhart

Bastian Kubis

Dispersive analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>γ</mi><mo>*</mo></msup></math> transition form factor with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo>–</mo><mi>ω</mi></math> mixing effects

We study the radiative decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>D</mi><mn>0</mn></msup><msup><mi>K</mi><mo>+</mo></msup><mo>/</mo><mi>γ</mi><msup><mi>D</mi><mo>+</mo></msup><msup><mi>K</mi><mn>0</mn></msup></math> and argue them to constitute a paradigmatic case of reactions sensitive to the short-range component of the decaying meson wave function that can, in principle, be quantified in a model-independent way employing experimental data. We demonstrate how a simultaneous measurement of the above radiative decay widths, or at least a constraint on the ratio of the corresponding branching fractions, can allow one to probe the nature of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math> mesons.

Hai-Long Fu

Alexey Nefediev

What can we learn from the radiative decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math> meson?

The <italic>f</italic> <inf>0</inf>(980) is a light scalar meson whose internal structure remains under debate and investigation. Assuming that the <italic>f</italic> <inf>0</inf>(980) is a <math altimg='si4.svg'><mrow><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> molecule that can only survive at the kinetic freeze-out of the evolving bulk matter, we implement the coalescence model to study its transverse momentum ( <italic>p<inf>T</inf></italic>) spectra and elliptic flow ( <italic>v</italic> <inf>2</inf>) in high-multiplicity p-Pb collisions at <math altimg='si5.svg'><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo linebreak='goodbreak'>=</mo><mn>5.02</mn></mrow></math> TeV. Using the well-tuned kaon phase-space distributions from the Hydro-Coal-Frag model, our <math altimg='si4.svg'><mrow><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> coalescence calculations with reasonable values for the <italic>f</italic> <inf>0</inf>(980) radius successfully reproduce the elliptic flow measured by CMS over the range 0&#8239;&lt;&#8239; <italic>p<inf>T</inf></italic>&#8239;&lt;&#8239;12 GeV and also agree with the <italic>p<inf>T</inf></italic>-spectra from ALICE. These results in heavy ion collisions are compatible with the <math altimg='si4.svg'><mrow><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> molecular picture of the <italic>f</italic> <inf>0</inf>(980) with effective root-mean-square (RMS) radius. We also find that the number-of-constituent scaling of <italic>v</italic> <inf>2</inf> for the <italic>f</italic> <inf>0</inf>(980) is violated in p-Pb collisions at the LHC because most <italic>f</italic> <inf>0</inf>(980) are produced from the coalescence of kaons that have different momenta. Our study demonstrates the necessity of realistic coalescence model calculations and also explains why the CMS interpretation of the <italic>f</italic> <inf>0</inf>(980) as an ordinary <math altimg='si6.svg'><mrow><mi>q</mi><mover accent='true'><mi>q</mi><mo>&#175;</mo></mover></mrow></math> meson is no longer valid by interpreting the measured <italic>v</italic> <inf>2</inf> with a simple scaling formula based on the assumption of equal momentum coalescence. The investigation also provides a novel way to explore the internal structure of light exotic hadrons that can be abundantly produced in relativistic heavy and/or light ion collisions.

Yili Wang

Wenbin Zhao

United States

Che Ming Ko

Ju-Jun Xie

Huichao Song

Probing the structure of <italic>f</italic> <inf>0</inf>(980) from the elliptic flow in p-Pb collisions at the LHC

We generalize chiral perturbation theory with spinless matter fields in the fundamental representation of SU($\textit{N}$) to curved spacetime in the presence of an external gravitational field. This work is motivated by recent interest in investigating energy-momentum tensor matrix elements of matter fields. The complete chiral Lagrangian is constructed, including both minimal extensions from flat spacetime and new curvature-induced terms, up to the next-to-next-to-leading order in the chiral expansion, $$ \mathcal{O}\left({p}^3\right) $$ . We perform a systematic one-loop renormalization of the generating functional using the background field method combined with the heat-kernel technique, and explicitly compute the resulting ultraviolet divergences.

Cheng-Cheng Li

Renormalization of chiral perturbation theory with spinless matter field in curved spacetime

In light of recent high-precision data taken by the BESIII Collaboration, we reconsider the dipion transition <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>. The strong pion-pion final-state interactions are taken into account model independently by using dispersion theory. We find that we can reproduce the substructure near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> threshold observed experimentally without introducing an extra resonance state. While a helicity-flip amplitude plays an important role for the formation of the dip in the invariant-mass distribution, the virtual exchange of the charmoniumlike exotic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> state improves the fit quality only slightly.

Yun-Hua Chen

Xiang-Kun Dong

Decoding the structure near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> mass threshold in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> decays

We propose a novel method to identify the two-pole structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math>. The two poles owe their origin to different quark flavor irreducible representations in the meson-baryon coupled-channel interactions, thus they should be individually manifested in reactions that provide good flavor eigenstate sources. Hadronic decays of charmonia into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi mathvariant="normal">Σ</mi><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">(</mo><mn>1520</mn><mo stretchy="false">)</mo><mi mathvariant="normal">Σ</mi><mi>π</mi></math> are such reactions, and the flavor octet and singlet poles can be approximately singled out in these two decay modes. This SU(3) flavor filter works even considering the flavor symmetry breaking. With the huge charmonium data sets collected, it is therefore promising to solve the long-standing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math> puzzle employing the proposed flavor filter.

Ying-Bo He

Xiao-Hai Liu

Li-Sheng Geng

Identifying the two-pole structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></mrow></math> using an SU(3) flavor filter