Hadronic electromagnetic form factors and radiative decay properties offer a crucial window into the nonperturbative dynamics of quantum chromodynamics (QCD). In this work, we employ the light-cone sum rules (LCSR) method to systematically investigate the M1 radiative decay of vector mesons. Our study covers processes including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mrow><mo>*</mo><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>−</mo></msup><mi>γ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mi>D</mi><mi>γ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mi>B</mi><mi>γ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mi>γ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><msub><mi>B</mi><mi>s</mi></msub><mi>γ</mi></math>, and further extends to the excited charmonium state <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>. Our calculations yield decay widths for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></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> that are in excellent agreement with experimental data. For the charm and bottom meson decays, where precise measurements are lacking, we provide theoretical predictions and compare them with other theoretical approaches. Most notably, our analysis reveals a universal linear dependence of the decay width on a function A(x) in the logarithmic coordinate system, which originates from the two-body decay dynamics and the ratio of the initial and final state decay constants. This relationship holds for the ground state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo stretchy="false">→</mo><mi>P</mi><mi>γ</mi></math> processes here and suggests a broader applicability to radiative decays of ground-state vector mesons.

China

Zhi Jun Wang

Russia

Di Gao

Kai Kai Zhang

Yuan Yuan Ma

Yan Jun Sun

Radiative decays of vector mesons with light-cone sum rules

In the Cachazo-He-Yuan (CHY) representation, many tree-level scattering amplitudes are written as integrals localized by the scattering equations, where the CHY integrand encodes the theory and must reproduce the physical factorization pattern of Mandelstam singularities. The inverse CHY problem therefore asks for a rational integrand whose physical poles match a prescribed set of factorization channels, a task that becomes rapidly combinatorial at higher multiplicity. We present an algorithmic approach that makes the subset structure of pole data explicit by assigning each particle subset <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math> a generalized pole degree <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow></math>, realized as a signed internal-edge count in a colored integrand graph. Additivity under integrand multiplication and an elementary face recursion on the subset lattice imply that all higher-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></math> are linear functions of the two-particle integers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><mi>K</mi><mo stretchy="false">(</mo><msub><mi>s</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">}</mo></math>, so the inverse step becomes a mixed-integer linear feasibility problem. The same subset lattice provides a fixed computation graph for exact constraint satisfaction: pole requirements and recursion identities are treated as hard constraints, updates are restricted to those that preserve feasibility, and whenever a proposed change would enter a fixed node its constraint residual is rerouted and redistributed through unfixed degrees of freedom so that all constraints remain satisfied throughout. After a factorial rescaling, every local propagation update is purely integral, keeping the entire procedure exact in integer arithmetic and avoiding a posteriori reconstruction from numerical evaluations. Since physical tree-level amplitudes must contain only simple factorization poles as dictated by unitarity and locality, we further organize generalized integrands by an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math>-regular grading under multiplication, where degree-zero factors act as Möbius-invariant insertions admitting a decomposition into products of four-point cross ratios, which guides efficient higher-order pole reduction. We illustrate the construction at six and eight points, including pole selection and higher-order pole reduction.

Simeng Li

Yaobo Zhang

Inverse Cachazo-He-Yuan integrand construction from factorization channels with exact integer constraint propagation

Motivated by the observation of the doubly charmed tetraquark $ T_{cc}(3875)^+ $ , we present a systematic study of doubly heavy tetraquarks ( $ T_{QQ'\bar{q}\bar{q}'} $ ) using heavy antiquark-diquark symmetry (HADS) within a constituent quark model. By calibrating model parameters to known hadron spectra and incorporating the effective mass formula, we predict the masses for 38 ground-state tetraquarks with $ cc $ , $ bb $ , and $ bc $ heavy quark pairs, including the non-strange, single-strange, and double-strange configurations with quantum numbers $ J^P = 0^+, 1^+ $ and $ 2^+ $ . Notably, we identify several stable states below the relevant meson-meson thresholds, particularly in the $ bb\bar{q}\bar{q}' $ sector. The explicit connection between the doubly heavy tetraquark and the heavy baryon spectra through HADS reduces model dependence and reveals the fundamental systematics in the heavy-quark hadron landscape.

Liu-Yu Zhang

Tian-Wei Wu

Yong-Liang Ma

Bridging doubly heavy tetraquark mass spectrum with heavy baryons utilizing heavy antiquark-diquark symmetry * The work of Tian-Wei Wu is supported by the National Natural Science Foundation of China (12405108). Yong-Liang Ma is supported in part by the National Science Foundation of China (NSFC) (12347103) and Gusu Talent Innovation Program (ZXL2024363)

We extend on-shell bootstrap methods from spacetime amplitudes to the world sheet objects of the Cachazo-He-Yuan formalism. We observe that the integrands corresponding to tree-level nonlinear sigma model, Yang-Mills and <math><mo>(</mo><mi>D</mi><mi>F</mi><msup><mo>)</mo><mn>2</mn></msup></math> theory are determined by demanding enhanced UV scaling under Britto-Cachazo-Feng-Witten shifts. Back in spacetime, we also find that <math><mo>(</mo><mi>D</mi><mi>F</mi><msup><mo>)</mo><mn>2</mn></msup></math> theory is fixed by gauge invariance/UV scaling and simple locality assumptions.

France

Laurentiu Rodina

UV consistency conditions for Cachazo-He-Yuan integrands

The Cachazo-He-Yuan formula was originally proposed to describe on-shell scattering of particles from a single massless field. We present a method to modify it to include several interacting scalar fields, all possessing different masses and possibly off-shell momenta. The method is applied to Yukawa interactions between a number of scalar nucleons and pions, and to the <math><msub><mi>ϕ</mi><mn>1</mn></msub><msub><mi>ϕ</mi><mn>2</mn></msub><msub><mi>ϕ</mi><mn>3</mn></msub></math> coupling of three different scalar fields. Composite models constructed from existing theories can be used to broaden the scope of the method. The modification is applied to describe Compton scattering from a massive particle and to photon bremsstrahlung. It is also employed to generalize the disk function <math><mi>Z</mi></math> and the sphere function <math><mi>J</mi></math>.

Canada

C. S. Lam

Cachazo-He-Yuan theory for several fields

Möbius invariance is used to construct gluon tree amplitudes in the Cachazo, He, and Yuan (CHY) formalism. If it is equally effective in steering the construction of off-shell tree amplitudes, then the S-matrix CHY theory can be used to replace the Lagrangian Yang-Mills theory. Unfortunately that is not possible. We find that the CHY formula can indeed be modified to obtain a Möbius-invariant off-shell amplitude <math><msub><mi>M</mi><mi>P</mi></msub></math>, but this modified amplitude lacks local gauge invariance, which can be restored to give the correct Yang-Mills amplitude only by the addition of a complementary amplitude <math><msub><mi>M</mi><mi>Q</mi></msub></math>. Although neither <math><msub><mi>M</mi><mi>P</mi></msub></math> nor <math><msub><mi>M</mi><mi>Q</mi></msub></math> is fully gauge invariant, both are partially gauge invariant in a sense to be explained.

Off-shell Yang-Mills amplitude in the Cachazo-He-Yuan formalism

We show that the use of Sudakov variables greatly simplifies the study of the solutions to the scattering equations in the Cachazo-He-Yuan formalism. We work in the center-of-mass frame for the two incoming particles, which partially fixes the SL(2, ℂ) redundancy in the integrand defining the scattering amplitudes, the remaining freedom translates into a global shift in the azimuthal angle of the outgoing particles. Studying four- and five-particle amplitudes, we see how an appropriate choice of this phase allows for algebraic simplifications when finding solutions to the scattering equations, as well as in the expression of the scattering amplitudes in terms of the locations of the punctures in the sphere. These punctures themselves are remarkably simple functions of the Sudakov parameters.

Spain

Grigorios Chachamis

Diego Jiménez

Agustín Vera

Miguel Vázquez-Mozo

Sudakov representation of the Cachazo-He-Yuan scattering equations formalism

The last few years have been witness to a proliferation of new results concerning heavy exotic hadrons. Experimentally, many new signals have been discovered that could be pointing towards the existence of tetraquarks, pentaquarks, and other exotic configurations of quarks and gluons. Theoretically, advances in lattice field theory techniques place us at the cusp of understanding complex coupled-channel phenomena, modelling grows more sophisticated, and effective field theories are being applied to an ever greater range of situations. It is thus an opportune time to evaluate the status of the field. In the following, a series of high priority experimental and theoretical issues concerning heavy exotic hadrons is presented.

United States

R.A. Briceño

T.D. Cohen

S. Coito

J.J. Dudek

E. Eichten

Germany

C.S. Fischer

M. Fritsch

W. Gradl

A. Jackura

M. Kornicer

Brazil

G. Krein

R. F. Lebed

F. A. Machado

R. E. Mitchell

C.J. Morningstar

Ireland

M. Peardon

M. R. Pennington

K. Peters

J. M. Richard

C. P. Shen

M.R. Shepherd

T. Skwarnicki

E. S. Swanson

A. P. Szczepaniak

C. Z. Yuan

Issues and Opportunities in Exotic HadronsSupported by U.S. Department of Energy (Cohen); the Institute of Modern Physics and Chinese Academy of Sciences under contract Y104160YQ0 and agreement No. 2015-BH-02 (Coito); the U.S. Department of Energy, for grant DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, manages and operates Jefferson Laboratory and DE-SC0006765, Early Career award (Dudek); Fermilab, operated by the Fermi Research Alliance under contract number DEAC02-07CH11359 with the U.S. Department of Energy (Eichten); BMBF, under contract No. 06GI7121, and the DAAD under contract No. 56889822 and by the Helmholtz International Center for FAIR within the LOEWE program of the State of Hesse (Fischer); the German Research Foundation DFG under contract number Collaborative Research Centre CRC-1044 (Gradl); the Conselho Nacional de Desenvolvimento CientÃ­fico e TecnolÃ³gico - CNPq, Grant No. 305894/2009-9 and FundaÃ§Ã£o de Amparo Ã Pesquisa do Estado de SÃ£o Paulo - FAPESP, Grant No. 2013/01907-0 (Krein); U.S. National Science Foundation, under grants PHY-1068286 and PHY-1403891 (Lebed); the Brazilian National Council for Scientific and Technological Development under grant CNPq/CAPES-208188/2014-2 (Machado); U.S. Department of Energy under grant DE-FG02-05ER41374 (Mitchell); U.S. National Science Foundation under grant PHY-1306805 (Morningstar); U.S. Department of Energy, supported by Jefferson Science Associates, LLC under contract No. DE-AC05-06OR23177 (Pennington); the National Natural Science Foundation of China (NSFC) under contract No. 11575017, the Ministry of Science and Technology of China under Contract No. 2015CB856701 (Shen); U.S. Department of Energy, under grant DE-FG02-05ER41374 (Shepherd); U.S. National Science Foundation under grant PHY-1507572 (Skwarnicki); U.S. Department of Energy, under contract DE-AC05-06OR23177 and grant DE-FG0287ER40365 (Szczepaniak); the National Natural Science Foundation of China (NSFC) under contract numbers 11235011 and 11475187 (Yuan).

We consider right-handed neutrino dark matter N1 in local U(1)LÎ¼âLÏ -extended Ma model. With the light U(1)Î¼âÏ gauge boson ( mZâ²â¼O(100)Â MeV ) and small U(1)Î¼âÏ gauge coupling ( gZâ²â¼10â4â10â3 ) which can accommodate the muon (gâ2) anomaly and is still allowed by other experimental constraints, we show that we can get correct relic density of dark matter for wide range of dark matter mass ( M1â¼10â200Â GeV ), although the gauge coupling constant gZâ² is small. This is due to the fact that the annihilation cross section of dark matter pair is enhanced by M14/mZâ²4 in the processes N1N1âZâ²Zâ² or N1N1âZâ²H2 . We also consider the constraints from direct detection, collider searches.

South Korea

Seungwon Baek

Dark matter and muon ( g − 2) in local U(1)Lμ−Lτ -extended Ma model

A proof is given of the formula, recently proposed by Cachazo, He and Yuan (CHY) for gluon tree amplitudes in pure Yang-Mills theory in arbitrary dimension. The approach is to first establish the corresponding result for massless ϕ 3 theory using the BCFW recurrence relation and then to extend this to the gauge theory case. Additionally, it is shown that the scattering equations introduced by CHY can be generalized to massive particles, enabling the description of tree amplitudes for massive ϕ 3 theory.

Louise Dolan

Peter Goddard

Proof of the formula of Cachazo, He and Yuan for Yang-Mills tree amplitudes in arbitrary dimension