We present a joint analysis of the processes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> at center-of-mass energies from 4.13 to 4.36 GeV. The amplitudes are constructed using the Dalitz-plot decomposition formalism, with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> energy dependence encoded through the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4220</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4320</mn><mo stretchy="false">)</mo></math> resonant structures together with a nonresonant production mechanism. The scalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo>/</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> final-state interaction is treated dispersively using a coupled-channel Omnès representation. This allows us to describe the measured total cross sections and one-dimensional invariant-mass distributions with a single set of energy-independent parameters. We find that a purely resonant description of the BESIII data is insufficient, requiring a nonresonant term at the amplitude level which undergoes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo>/</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> rescattering. Within the present isobar model, we extract Breit-Wigner parameters for the <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>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4220</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4320</mn><mo stretchy="false">)</mo></math> states and determine the corresponding subprocess cross sections.

Germany

Viktoriia Ermolina

Igor Danilkin

Marc Vanderhaeghen

Simultaneous Dalitz-plot decomposition of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi mathvariant="normal">ψ</mi><mi>π</mi><mi>π</mi><mo stretchy="false">(</mo><mi>K</mi><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mo stretchy="false">)</mo></mrow></math> processes in the 4.13–4.36 GeV region using dispersive final-state interactions

We present a dispersive amplitude analysis of the low-energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> system in the radiative decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math>, using the mass-independent BESIII <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> intensities, the total spectrum, and the measured <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup><mo>−</mo><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup><mtext> </mtext><mtext> </mtext><mi>E</mi><mn>1</mn></math> phase difference. The isoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave is described by a coupled-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo>/</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> Muskhelishvili–Omnès representation, which implements the strong final-state interactions associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math>. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-wave is treated with a single-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> Muskhelishvili-Omnès representation, where we identify all kinematic constraints of helicity amplitudes before transforming them to the experimental <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi><mn>1</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mn>2</mn></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi><mn>3</mn></math> multipoles. Smooth short-distance production of a pseudoscalar-meson pair is encoded in subtraction polynomials, while left-hand-cut effects are estimated and found to be numerically subleading. We identify the negative solution of the BESIII <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup><mo>−</mo><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup><mtext> </mtext><mtext> </mtext><mi>E</mi><mn>1</mn></math> phase ambiguity, after using the modulo-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi></math> freedom of production amplitudes, as the phase solution compatible with unitarity constraints, showing that the measured phase information can be accommodated with the Omnès phase motion without requiring large additional phases. By normalizing the BESIII intensities with the extracted branching fraction, we fix the absolute scale of the fitted amplitudes, making them suitable as input for future dispersive studies of two-pion contributions to gravitational form factors.

Bai-Long Hoid

Italy

Anna Testa

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><mi>γ</mi><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> process

Experimental measurements of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> decays to octet baryon pairs reveal a negative-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mover accent="true"><mi mathvariant="normal">Σ</mi><mo stretchy="false">¯</mo></mover></math> puzzle in the angular distributions, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>α</mi><mi mathvariant="normal">Σ</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msubsup><mo>&lt;</mo><mn>0</mn></math>, whereas the other measured <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> octet channels and the corresponding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> channels have positive angular parameters. We show that an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math>-exact singlet description is strongly disfavored in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup></math> fit, giving <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup><mo>≃</mo><msup><mn>10</mn><mn>5</mn></msup></math>. By contrast, a reduced scenario in which a common final-state interaction mixes the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">S</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">D</mi></math>-wave amplitudes gives <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup><mo>=</mo><mn>4.21</mn></math> for the 22 isospin-reduced inputs and two nominal degrees of freedom. We find that the negative-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mover accent="true"><mi mathvariant="normal">Σ</mi><mo stretchy="false">¯</mo></mover></math> puzzle can be reproduced with direct-production <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math> breaking at the 40% level. This is larger than the conventional quark-mass expectation of about 30%, but numerically smaller than the order-one channel variation suggested by the experimental data. The sizable observable effect is amplified by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math>-breaking rescattering paths involving S–D mixing. These paths feed the much larger D-wave source into the final <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math>-breaking S-wave amplitude. The largest remaining pull comes from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">→</mo><mi>N</mi><mover accent="true"><mi>N</mi><mo stretchy="false">¯</mo></mover></math> angular input, motivating a renewed experimental check of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">→</mo><mi>n</mi><mover accent="true"><mi>n</mi><mo stretchy="false">¯</mo></mover></math>.

China

Chao-Qiang Geng

Xiang-Nan Jin

Chia-Wei Liu

Negative-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mover accent="true"><mi mathvariant="normal">Σ</mi><mo stretchy="false">¯</mo></mover></math> angular-parameter puzzle in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> decays

Within the QCD sum-rule framework, we investigate hidden-heavy tetraquark channels with the exotic quantum number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>J</mi></mrow><mrow><mi>PC</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mo>−</mo></mrow></msup></mrow></math> using four representative local color-octet–octet interpolating currents. The currents include both vector-axialvector and scalar-pseudoscalar Dirac structures. The operator product expansion is carried out up to dimension-eight condensates. The four diagonal sum rules yield mutually consistent mass estimates in the range 10.8–11.1 GeV for the hidden-bottom sector and around 4.3–4.6 GeV for the corresponding hidden-charm sector, with the bottom sector exhibiting the clearest Borel stability. Since local tetraquark currents with the same quantum numbers are related by Fierz rearrangements, the current-dependent results do not by themselves imply four distinct states or uniquely defined internal color structures. We also discuss quantum-number-allowed decay channels and emphasize the absence of the lowest pseudoscalar-pseudoscalar heavy-meson modes for a neutral <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> state. The results provide theoretical guidance for future experimental searches at Belle II, LHCb, and BESIII.

Bing-Dong Wan

Jun-Hao Zhang

Yan Zhang

Ming-Yang Yuan

Spectroscopy of hidden-heavy tetraquark states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>J</mi></mrow><mrow><mi>PC</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mo>−</mo></mrow></msup></mrow></math> in a color-octet configuration

We perform a systematic QCD sum rule study of light tetraquark states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> in the diquark-antidiquark picture. A complete set of local interpolating currents is constructed and projected onto six flavor-isospin configurations (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mo>=</mo><mi>u</mi><mo>/</mo><mi>d</mi></math>): the isoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> sectors, the isovector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> sectors, and the isotensor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> sector. From the nonderivative currents studied in the present work, the extracted masses of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> configurations lie in the ranges 1.53–2.37 GeV, 1.86–2.51 GeV, and 2.46–2.60 GeV, respectively. For the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> vector sector, we also quote the previous derivative-current result <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>2.34</mn><mrow><mo>−</mo><mn>0.30</mn></mrow><mrow><mo>+</mo><mn>0.23</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> as a complementary benchmark. We further compare the present <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> tetraquark spectrum with previous QCD sum rule results for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> tetraquark and hybrid states [N. Su, E.-L. Cui, Y.-W. Jiang, and H.-X. Chen, <a href="http://dx.doi.org/10.1140/epjc/s10052-026-15939-y">Eur. Phys. J. C 86, 724 (2026)</a>.], aiming to provide useful information for distinguishing tetraquark and hybrid configurations in the light hadron spectrum. As an additional improvement, we complete the previously missing isotensor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> tetraquark entry and obtain its lowest mass to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mo>=</mo><mn>2.1</mn><msubsup><mn>9</mn><mrow><mo>−</mo><mn>0.24</mn></mrow><mrow><mo>+</mo><mn>0.26</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, which is included in the spectral comparison.

Yi-Wei Jiang

Hua-Xing Chen

Er-Liang Cui

Ding-Kun Lian

Wen-Ying Liu

Niu Su

Light tetraquark states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> from QCD sum rules

We show that fixed-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>j</mi></math> holographic double deeply virtual Compton scattering (DDVCS) and its DVCS limit give a fixed-scale structural match to the singlet conformal-operator product expansion Wilson-kernel family of QCD in the leading-twist unpolarized singlet vector channel. The open-string <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mi>δ</mi><mo>,</mo><mi>ϑ</mi><mo stretchy="false">)</mo></math> hypergeometric kernel was derived by Nishio-Watari; the new closed-string result is that the Brower-Polchinski-Strassler-Tan (BPST) upper Witten vertex gives the same family with a different near-boundary power count, because <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Δ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mi>j</mi><mo stretchy="false">)</mo></math> is fixed by the BPST trajectory rather than by open-Regge data. The Mellin exponent is therefore derived as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mi>j</mi><mo stretchy="false">)</mo><mo>=</mo><mi>j</mi><mo>+</mo><msub><mi mathvariant="normal">Δ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mi>j</mi><mo stretchy="false">)</mo><mo>−</mo><mn>2</mn><mo>=</mo><mn>2</mn><mi>j</mi><mo>+</mo><msub><mi>γ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mi>j</mi><mo stretchy="false">)</mo></math> rather than inserted by hand. The even open branch gives the parallel unprotected counterpart in the projected singlet vector amplitude. At <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mo>=</mo><mi>μ</mi><mo>=</mo><msub><mi>μ</mi><mn>0</mn></msub><mo>=</mo><msub><mi>μ</mi><mo>*</mo></msub></math>, the point is not merely that equal-endpoint evolution is trivial; it is that the ultraviolet Witten vertex has already produced the fixed-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>j</mi></math> conformal kernel before the lower conformal moment is matched. In the conformal partial-wave/conformal subtraction representation, beta-proportional conformal-anomaly terms and scheme transformations are coefficient/evolution bookkeeping away from the matching point, not replacements for the projected fixed-scale hypergeometric <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>/</mo><mi>ξ</mi></math> Wilson-kernel family. The protected/unprotected <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>j</mi><mo>=</mo><mn>2</mn></math> split identifies the protected closed branch with the (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>−</mo></mrow></math>) conformal partial wave and the even open branch with the unprotected (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>+</mo></mrow></math>) counterpart; these are mixed singlet eigenchannels, not literal unmixed quark/gluon operators at finite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math>. The comparison therefore gives a direct conformal-basis interpretation of the fixed-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>j</mi></math> holographic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel Witten diagram: the ultraviolet vertex generates the universal Wilson-kernel family, while the lower vertex supplies the channel-dependent nonperturbative conformal moment.

United States

Kiminad A. Mamo

Holographic open-closed exchange in double deeply virtual Compton scattering: Fixed-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>j</mi></math> structural matching to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>±</mo></math>-basis Wilson kernels

We point out several algebraic and dimensional inconsistencies in the derivation of the teleparallel double-wall dynamics and of the axial torsion coupling bound published in this Journal [Eur. Phys. J. C (2026) 86: 785]. Recomputing the torsion two-forms from the tetrads with vanishing spin connection, we obtain expressions that differ from those used in the paper. Consequently, the equations for the wall separation function do not lead to the reported solution, and the approximation $$h^2\ll z^2$$ does not restore the polynomial form adopted there. We also show that the proposed wave equation for the wall separation and the corresponding gravitational-wave interpretation require rederivation. In the fermionic sector, the zero-mode solutions and the scalar Dirac bilinear must be distinguished from the positive density $$\varPsi ^\dagger \varPsi $$ . With the corrected solutions, the effective coefficient $$A=eB+g_T S$$ determines a localization length $$\ell _{\textrm{loc}}\sim |A|^{-1/2}$$ , so that estimating $$g_T$$ requires specifying an additional physical scale rather than imposing $$A=0$$ . Hence the claimed constant condensate and the bound $$g_T\sim 10^{-4}$$ are not established by the calculations presented.

Brazil

Luis Castro

Comment on “Einstein–Cartan fermion condensates trapped in double walls induce axial torsion coupling bounds [Eur. Phys. J. C (2026) 86: 785]”

We present the first measurements of the Dalitz plot for ortho-positronium annihilation to three photons. Our measurements, accurate to about 3% statistical and 2-3% systematic uncertainty in angular representation over almost the entire available phase space, were performed using the Jagiellonian Positron Emission Tomograph (J-PET) based on organic scintillator strips. Until now, the Dalitz plot for the three-body positronium decay has been poorly explored. The new measurements presented here are consistent with the leading-order QED prediction for the Dalitz plot.

Poland

Magdalena Skurzok

Austria

Steven D. Bass

Kamila Kasperska

Ermias Beyene

Neha Chug

Catalina Curceanu

Eryk Czerwiński

Manish Das

Marek Gorgol

Sharareh Jalali

Bożena Jasińska

Krzysztof Kacprzak

Tevfik Kaplanoglu

Łukasz Kapłon

Aleksander Khreptak

Tomasz Kozik

Karol Kubat

Deepak Kumar

Sumit Kumar Kundu

Edward Lisowski

Filip Lisowski

Bartłomiej Łach

Justyna Mędrala-Sowa

Simbarashe Moyo

Wiktor Mryka

Szymon Niedźwiecki

Anand Pandey

Piyush Pandey

Chile

Alessio Porcelli

Bartłomiej Rachwał

Martin Rädler

Sushil Sharma

Ewa Stępień

Tomasz Szumlak

Pooja Tanty

Keyvan Tayefi Ardebili

Satyam Tiwari

Kavya Valsan Eliyan

Anoop K. Venadan

Paweł Moskal

Experimental determination of the Dalitz plot for positronium decay using the J-PET detection system

Based on $ (10087\pm44)\times10^{6} $ $ J/\psi $ events collected with the BESIII detector, the $ J/\psi\rightarrow \gamma K^{0}_{S}K^{0}_{S}\pi^{0} $ and $ J/\psi\rightarrow \gamma \pi^{0}\pi^{0}\eta $ processes are studied. The $ X(2370) $ is observed in both the $ K^{0}_{S}K^{0}_{S}\pi^{0} $ and $ \pi^{0}\pi^{0}\eta $ invariant mass spectra, with statistical significances greater than $ 14\sigma $ and $ 20\sigma $ , respectively. By combining measurements from these processes with those from the previously reported $ J/\psi\rightarrow \gamma K^{0}_{S}K^{0}_{S}\eta^{\prime} $ process, the mass and width of the $ X(2370) $ are determined to be $ 2359^{+13}_{-14}\; \text{MeV}/c^{2} $ and $ 170^{+44}_{-29}\; \text{MeV} $ , respectively. In addition, the decay $ X(2370)\to a_{0}(980)^{0}\pi^{0} $ with $ a_{0}(980)^{0}\to \pi^{0}\eta $ is observed with a statistical significance exceeding $ 9\sigma $ . The properties of the $ X(2370) $ —decay pattern similarities to that of $ \eta_{c} $ , are consistent with those of a pseudoscalar glueball.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

C.S. Akondi

R. Aliberti

A. Amoroso

Q. An

Y.H. An

M.S. Anderson

Y. Bai

O. Bakina

H.R. Bao

X.L. Bao

M. Barbagiovanni

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R. Briere

A. Brueggemann

D. Cabiati

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. Chang

G.R. Che

Y.Z. Che

C.H. Chen

C. Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.M. Chen

T. Chen

W. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J. Cheng

L.N. Cheng

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

X.C. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denisenko

M. Destefanis

F. De Mori

E. Di Fiore

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

Z.J. Dong

M.C. Du

S.X. Du

X.L. Du

Y.Q. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

Observation of the ${\boldsymbol X(2370)}$ in ${{\boldsymbol J}/\boldsymbol\psi\rightarrow\gamma K^{0}_{S}K^{0}_{S}\pi^{0}}$ and ${J/\psi\rightarrow\gamma \pi^{0}\pi^{0}\eta}$ * This work is supported in part by the National Key R&D Program of China under Contracts Nos. 2025YFA1613900, 2023YFA1606000, 2023YFA1606704; National Natural Science Foundation of China (NSFC) under Contracts Nos. 11635010, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12342502, 12361141819, 12535005; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the Strategic Priority Research Program of Chinese Academy of Sciences under Contract No. XDA0480600; CAS under Contract No. YSBR-101; 100 Talents Program of CAS; China Postdoctoral Science Foundation under Contracts Nos. GZC20252256, 2025M773423; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile under Contract No. ANID CCTVal CIA250027; ERC under Contract No. 758462; German Research Foundation DFG under Contract No. FOR5327; Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation under Contracts Nos. 2021.0174, 2021.0299, 2023.0315; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Research Foundation of Korea under Contract No. NRF-2022R1A2C1092335; National Science and Technology fund of Mongolia; Polish National Science Centre under Contract No. 2024/53/B/ST2/00975; STFC (United Kingdom); Swedish Research Council under Contract No. 2019.04595; U. S. Department of Energy under Contract No. DE-FG02-05ER41374

In this work, we compute the next-to-next-to-leading-order (NNLO) QCD corrections to the process $\textit{e}$ $\textit{e}$ → $\textit{J}$/$\textit{ψ}$ + $\textit{χ}$ at B factories within the NRQCD factorization framework. The helicity amplitudes are obtained via asymptotic expansions around $\textit{r}$ = 0 and $\textit{r}$ = 1, with $$r=16{m}_{c}^{2}/s$$ . Our asymptotic expressions reproduce the exact numerical results with high accuracy across the kinematic range 0 ≤ $\textit{r}$ ≤ 1, achieving a relative error below 10 , which is sufficient for phenomenological applications. Notably, the large logarithmic terms are obtained analytically, and the explicit expressions established in this work provide a useful basis for further theoretical investigations.

Hao-Yang Liu

Cong Li

Wen-Long Sang

Semi-analytical two-loop QCD corrections to $\textit{e}$ + $\textit{e}$ − → $\textit{J}$/$\textit{ψ}$ + $\textit{χ}$ $\textit{cJ}$ at B factories