In a recent paper [<a href="http://dx.doi.org/10.1103/PhysRevLett.126.132001">Phys. Rev. Lett. 126, 132001 (2021)</a>], the LHCb data on the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production in proton-proton collisions were analyzed in a coupled-channel framework based on double-vector-charmonium channels. This investigation identified a robust pole near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> threshold, tagged <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>6200</mn><mo stretchy="false">)</mo></math>, suggesting it as a new state. The present work extends that investigation by incorporating recent di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production data from the CMS and ATLAS Collaborations and performing a combined analysis of all three datasets. This study confirms the existence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>6200</mn><mo stretchy="false">)</mo></math>, and its pole position is now determined with a higher precision than in the previous study, where only a single dataset was employed. The pole corresponding to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>6900</mn><mo stretchy="false">)</mo></math> is also extracted, though its actual position and residue depend on a particular coupled-channel model employed and deviate from values reported in the experimental investigations. Moreover, we demonstrate that the currently available data do not allow one to determine whether there is an additional pole in the studied mass range. The dielectron width of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>6200</mn><mo stretchy="false">)</mo></math> is estimated under different conjectures on its quantum numbers, and the number of such states that can be annually produced at the future Super <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math>-Charm Facility is estimated. The line shape in the complimentary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> channel is discussed, and a good agreement with the ATLAS data is found.

China

Yi-Lin Song

Yu Zhang

Germany

Vadim Baru

Feng-Kun Guo

Christoph Hanhart

Portugal

Alexey Nefediev

Toward a precision determination of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo stretchy="false">(</mo><mn>6200</mn><mo stretchy="false">)</mo></mrow></math> parameters from data

We analyze the latest LHCb data on 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> spectrum in the isospin-violating <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</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> decay, based on dispersion theory to deal with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> final state interactions. Additionally, the isospin breaking effects are properly introduced, allowing for a reliable and accurate extraction of the ratio, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mi>X</mi></msub></math>, between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> couplings to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ρ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ω</mi></math> channels from the data. We find very good agreement with the LHCb data for the whole range of 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> invariant mass, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mi>X</mi></msub></math> is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.26</mn><mo>±</mo><mn>0.03</mn></math>. Using this value, we make predictions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mo>−</mo></msup></math> mass distribution in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</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><mn>0</mn></msup><msup><mi>π</mi><mo>−</mo></msup></math> process, which is currently accessible by the BESIII Collaboration, and update a prediction for the pole positions of the isovector partner states of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>W</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math>, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></math>.

Brazil

Jorgivan Morais Dias

Teng Ji

Xiang-Kun Dong

Georgia

Ulf-G. Meißner

Zhen-Hua Zhang

Dispersive analysis of the isospin breaking in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo></mrow><mi>ψ</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo></mrow><mi>ψ</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> decays

We employ a chiral effective field theory-based approach to connect <math><mi>D</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> scattering observables at the physical and variable pion masses accessible in lattice QCD simulations. We incorporate all relevant scales associated with three-body DDπ dynamics and the left-hand cut induced by the one-pion exchange for pion masses higher than the physical one, as required by analyticity and unitarity. By adjusting the contact interactions to match experimental data at the physical pion mass and lattice finite-volume energy levels at <math><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>=</mo><mn>280</mn></math> MeV, we predict the trajectory of the <math><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> pole as a function of the pion mass, finding it consistent with the hadronic-molecule scenario. In particular, we find that the explicit treatment of the one-pion exchange has a pronounced effect on the pole trajectory for <math><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>≳</mo><mn>230</mn></math> MeV by pushing it into the complex energy plane.

Michael Abolnikov

Evgeny Epelbaum

Arseniy A. Filin

Lu Meng

Internal structure of the (3875) From its Light-quark Mass Dependence

Using chiral effective field theory, we predict that there must be isovector charmonium-like <math> <mi>D</mi> <msup> <mover> <mi>D</mi> <mo>¯</mo> </mover> <mo>∗</mo> </msup> </math> $$ D{\overline{D}}^{\ast } $$ hadronic molecules with J PC = 1++ denoted as W c1. The inputs are the properties of the X(3872), including its mass and the ratio of its branching fractions of decays into J/ψρ 0 and J/ψω. The predicted states are virtual state poles of the scattering matrix, pointing at a molecular nature of the X(3872) as well as its spin partners. They should show up as either a mild cusp or dip at the <math> <mi>D</mi> <msup> <mover> <mi>D</mi> <mo>¯</mo> </mover> <mo>∗</mo> </msup> </math> $$ D{\overline{D}}^{\ast } $$ thresholds, explaining why they are elusive in experiments. The so far negative observation also indicates that the X(3872) is either a bound state with non-vanishing binding energy or a virtual state, only in these cases the X(3872) signal dominates over that from the <math> <msubsup> <mi>W</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> <mn>0</mn> </msubsup> </math> $$ {W}_{c1}^0 $$ . The pole positions are <math> <msubsup> <mn>3881.2</mn> <mrow> <mo>−</mo> <mn>0.0</mn> </mrow> <mrow> <mo>+</mo> <mn>0.8</mn> </mrow> </msubsup> </math> $$ {3881.2}_{-0.0}^{+0.8} $$ − <math> <mi>i</mi> <msubsup> <mn>1.6</mn> <mrow> <mo>−</mo> <mn>0.9</mn> </mrow> <mrow> <mo>+</mo> <mn>0.7</mn> </mrow> </msubsup> </math> $$ i{1.6}_{-0.9}^{+0.7} $$ MeV for <math> <msubsup> <mi>W</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> <mn>0</mn> </msubsup> </math> $$ {W}_{c1}^0 $$ on the fourth Riemann sheet of the <math> <msup> <mi>D</mi> <mn>0</mn> </msup> <msup> <mover> <mi>D</mi> <mo>¯</mo> </mover> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </math> $$ {D}^0{\overline{D}}^{\ast 0} $$ -D + D ∗− coupled-channel system, and <math> <msubsup> <mn>3866.9</mn> <mrow> <mo>−</mo> <mn>7.7</mn> </mrow> <mrow> <mo>+</mo> <mn>4.6</mn> </mrow> </msubsup> </math> $$ {3866.9}_{-7.7}^{+4.6} $$ − i(0.07 ± 0.01) MeV for <math> <msubsup> <mi>W</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> <mo>±</mo> </msubsup> </math> $$ {W}_{c1}^{\pm } $$ on the second Riemann sheet of the <math> <msup> <mfenced> <mrow> <mi>D</mi> <msup> <mover> <mi>D</mi> <mo>¯</mo> </mover> <mo>∗</mo> </msup> </mrow> </mfenced> <mo>±</mo> </msup> </math> $$ {\left(D{\overline{D}}^{\ast}\right)}^{\pm } $$ single-channel system. The findings imply that the peak in the J/ψπ + π − invariant mass distribution is not purely from the X(3872) but contains contributions from <math> <msubsup> <mi>W</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> <mn>0</mn> </msubsup> </math> $$ {W}_{c1}^0 $$ predicted here. The states should have isovector heavy quark spin partners with J PC = 0++, 2++ and 1+−, with the last one corresponding to Z c . We suggest to search for the charged 0++, 1++ and 2++ states in J/ψπ ± π 0.

Akaki Rusetsky

Predicting isovector charmonium-like states from X(3872) properties

We demonstrate that the dip observed near the total energy of 3872 MeV in the recent cross section data from the BESIII Collaboration for <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> admits a natural explanation as a coupled-channel effect: it is a consequence of unitarity and a strong <math><mi>S</mi></math>-wave <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> attraction that generates the state <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>. We anticipate the appearance of a similar dip in the <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> final state near the <math><msup><mi>D</mi><mo>*</mo></msup><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> threshold driven by the same general mechanism, then to be interpreted as a signature of the predicted spin-2 partner of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>.

Slovenia

How does the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> show up in <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collisions: Dip versus peak

In recent years many vector charmonium(like) states were reported by different electron-positron collider experiments above 4.2 GeV. However, so far, there not only exists sizable tension in the parameters of those states, but there is also no consensus on the number of the vector states in this energy range. To some extend, this might be caused by the fact that the experimental data were typically analyzed in single channel analyses employing overlapping Breit-Wigner functions, in particular ignoring the effect of opening thresholds. In this study, we focus on the mass range between 4.2 GeV and 4.35 GeV, conducting a comprehensive analysis of eight different final states in <math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> annihilation. Our findings demonstrate that, within this mass range, a single vector charmoniumlike state, exhibiting properties consistent with a <math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> molecular structure and characterized by a pole location <math><mrow><msqrt><mrow><msubsup><mrow><mi>s</mi></mrow><mrow><mi>pole</mi></mrow><mrow><mi>Y</mi><mo>(</mo><mn>4230</mn><mo>)</mo></mrow></msubsup></mrow></msqrt><mo>=</mo><mrow><mo>(</mo><mn>4227</mn><mo>±</mo><mn>4</mn><mo>−</mo><mfrac><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>(</mo><msubsup><mrow><mn>50</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow><mrow><mo>+</mo><mn>8</mn></mrow></msubsup><mo>)</mo><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></mrow></math>, can effectively describe all the collected data. This is made possible by allowing for an interference with the well-established vector charmonium <math><mi>ψ</mi><mo>(</mo><mn>4160</mn><mo>)</mo></math> along with the inclusion of the <math><msub><mi>D</mi><mn>1</mn></msub><mover><mi>D</mi><mo>¯</mo></mover></math> threshold effect. Moreover, in contrast to experimental analyses, our study reveals that the highly asymmetric total cross sections for <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi><mi>π</mi></math> and <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>K</mi><mover><mi>K</mi><mo>¯</mo></mover></math> around 4230 MeV stem from the same physics, rooted in the approximate SU(3) flavor symmetry of QCD.

Leon von Detten

Qian Wang

Daniel Winney

Qiang Zhao

How many vector charmoniumlike states lie in the mass range 4.2–4.35 GeV?

We study the inclusive and exclusive cross sections of $$e^+e^-\rightarrow \text {hadrons}$$ <math> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>-</mo> </msup> <mo>→</mo> <mtext>hadrons</mtext> </mrow> </math> for center-of-mass energies between 3.70 and $$3.83\,\,\textrm{GeV} $$ <math> <mrow> <mn>3.83</mn> <mspace width="0.166667em"></mspace> <mspace width="0.166667em"></mspace> <mtext>GeV</mtext> </mrow> </math> to infer the mass, width, and couplings of the $$\psi (3770)$$ <math> <mrow> <mi>ψ</mi> <mo>(</mo> <mn>3770</mn> <mo>)</mo> </mrow> </math> resonance. By using a coupled-channel K-matrix approach, we setup our analysis to respect unitarity and the analyticity properties of the underlying scattering amplitudes. We fit several models to the full dataset and identify our nominal results through a statistical model comparison. We find that, accounting for the interplay between the $$\psi (2S)$$ <math> <mrow> <mi>ψ</mi> <mo>(</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </math> and the $$\psi (3770)$$ <math> <mrow> <mi>ψ</mi> <mo>(</mo> <mn>3770</mn> <mo>)</mo> </mrow> </math> , no further pole is required to describe the $$\psi (3770)$$ <math> <mrow> <mi>ψ</mi> <mo>(</mo> <mn>3770</mn> <mo>)</mo> </mrow> </math> line shape. In particular we derive from the pole location $$M_{\psi (3770)}~=~3778.8~\pm ~0.3~\,\textrm{MeV} $$ <math> <mrow> <msub> <mi>M</mi> <mrow> <mi>ψ</mi> <mo>(</mo> <mn>3770</mn> <mo>)</mo> </mrow> </msub> <mspace width="3.33333pt"></mspace> <mo>=</mo> <mspace width="3.33333pt"></mspace> <mn>3778.8</mn> <mspace width="3.33333pt"></mspace> <mo>±</mo> <mspace width="3.33333pt"></mspace> <mn>0.3</mn> <mspace width="3.33333pt"></mspace> <mspace width="0.166667em"></mspace> <mtext>MeV</mtext> </mrow> </math> and $$\varGamma _{\psi (3770)}~=~25.0~\pm ~0.5~\,\textrm{MeV} $$ <math> <mrow> <msub> <mi>Γ</mi> <mrow> <mi>ψ</mi> <mo>(</mo> <mn>3770</mn> <mo>)</mo> </mrow> </msub> <mspace width="3.33333pt"></mspace> <mo>=</mo> <mspace width="3.33333pt"></mspace> <mn>25.0</mn> <mspace width="3.33333pt"></mspace> <mo>±</mo> <mspace width="3.33333pt"></mspace> <mn>0.5</mn> <mspace width="3.33333pt"></mspace> <mspace width="0.166667em"></mspace> <mtext>MeV</mtext> </mrow> </math> . Moreover, we find the decay to $$D^+D^-$$ <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> </mrow> </math> and $$D^0\bar{D}^0$$ <math> <mrow> <msup> <mi>D</mi> <mn>0</mn> </msup> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> </mrow> </math> to be consistent with isospin symmetry and derive an upper bound on the branching ratio $${\mathcal {B}}(\psi (3770) \rightarrow \text {non-}D\bar{D}) &lt; 6\%$$ <math> <mrow> <mi>B</mi> <mo>(</mo> <mi>ψ</mi> <mo>(</mo> <mn>3770</mn> <mo>)</mo> <mo>→</mo> <mtext>non-</mtext> <mi>D</mi> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>)</mo> <mo>&lt;</mo> <mn>6</mn> <mo>%</mo> </mrow> </math> at $$90\%$$ <math> <mrow> <mn>90</mn> <mo>%</mo> </mrow> </math> probability.

Stephan Kürten

Méril Reboud

United Kingdom

Danny Dyk

Analysis of the $${\psi (3770)}$$ <math> <mrow> <mi>ψ</mi> <mo>(</mo> <mn>3770</mn> <mo>)</mo> </mrow> </math> resonance in line with unitarity and analyticity constraints

We discuss recent lattice data for the <math><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>(</mo><mn>3875</mn><msup><mo>)</mo><mo>+</mo></msup></math> state to stress, for the first time, a potentially strong impact of left-hand cuts from the one-pion exchange on the pole extraction for near-threshold exotic states. In particular, if the left-hand cut is located close to the two-particle threshold, which happens naturally in the <math><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> system for the pion mass exceeding its physical value, the effective-range expansion is valid only in a very limited energy range up to the cut and as such is of little use to reliably extract the poles. Then, an accurate extraction of the pole locations requires the one-pion exchange to be implemented explicitly into the scattering amplitudes. Our findings are general and potentially relevant for a wide class of hadronic near-threshold states.

Meng-Lin Du

Arseniy Filin

Spain

Juan Nieves

Role of Left-Hand Cut Contributions on Pole Extractions from Lattice Data: Case Study for <math><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>(</mo><mn>3875</mn><msup><mo>)</mo><mo>+</mo></msup></math>

It was demonstrated in a series of papers employing unitarized chiral perturbation theory that the phenomenology of the scalar open-charm state, the $$D_0^*(2300)$$ <math> <mrow> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mrow> <mo>(</mo> <mn>2300</mn> <mo>)</mo> </mrow> </mrow> </math> , can be understood as the interplay of two poles, corresponding to two scalar-isospin doublet states with different SU(3) flavor content. Within this formalism the lightest open charm positive parity states emerge as being dynamically generated from the scattering of the Goldstone-boson octet off D mesons, a picture that at the same time solves various problems that the experimental observations posed. However, in recent lattice studies of $$D\pi $$ <math> <mrow> <mi>D</mi> <mi>π</mi> </mrow> </math> scattering at different pion masses only one pole was reported in the $$D_0^*$$ <math> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> </math> channel, while it was not possible to extract reliable parameters of a second pole from the lattice data. In this paper we demonstrate how this seeming contradiction can be understood and that imposing SU(3) constraints on the fitting amplitudes allows one to extract information on the second pole from the lattice data with minimal bias. The results may also be regarded as a showcase how approximate symmetries can be imposed in the K-matrix formalism to reduce the number of parameters.

Anuvind Asokan

Meng-Na Tang

Yuki Kamiya

Can the two-pole structure of the $$D_{0}^{*}(2300)$$ <math> <mrow> <msubsup> <mi>D</mi> <mrow> <mn>0</mn> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mn>2300</mn> <mo>)</mo> </mrow> </mrow> </math> be understood from recent lattice data?

In this addendum to Ref. [1] we show that the mismatch between the $$\rho $$ <math> <mi>ρ</mi> </math> – $$\omega $$ <math> <mi>ω</mi> </math> mixing parameter $$\epsilon _{\rho \omega }$$ <math> <msub> <mi>ϵ</mi> <mrow> <mi>ρ</mi> <mi>ω</mi> </mrow> </msub> </math> as extracted from $$\eta '\rightarrow \pi ^+\pi ^-\gamma $$ <math> <mrow> <msup> <mi>η</mi> <mo>′</mo> </msup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <msup> <mi>π</mi> <mo>-</mo> </msup> <mi>γ</mi> </mrow> </math> and $$e^+e^-\rightarrow \pi ^+\pi ^-$$ <math> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>-</mo> </msup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <msup> <mi>π</mi> <mo>-</mo> </msup> </mrow> </math> can be resolved by including higher orders in the expansion in $$e^2$$ <math> <msup> <mi>e</mi> <mn>2</mn> </msup> </math> in the description of the $$\eta '\rightarrow \pi ^+\pi ^-\gamma $$ <math> <mrow> <msup> <mi>η</mi> <mo>′</mo> </msup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <msup> <mi>π</mi> <mo>-</mo> </msup> <mi>γ</mi> </mrow> </math> decay. We repeat the analysis in this extended framework and update the numerical results accordingly.

Switzerland

Simon Holz

Martin Hoferichter

Bastian Kubis

Addendum: A dispersive analysis of $$\varvec{\eta '\rightarrow \pi ^+\pi ^-\gamma }$$ <math> <mrow> <msup> <mi>η</mi> <mo>′</mo> </msup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <msup> <mi>π</mi> <mo>-</mo> </msup> <mi>γ</mi> </mrow> </math> and $$\varvec{\eta '\rightarrow \ell ^+\ell ^-\gamma }$$ <math> <mrow> <msup> <mi>η</mi> <mo>′</mo> </msup> <mo>→</mo> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <msup> <mi>ℓ</mi> <mo>-</mo> </msup> <mi>γ</mi> </mrow> </math>