The validity range of the time-honored effective range expansion can be very limited due to the presence of a left-hand cut close to the two-particle threshold. Such a left-hand cut arises in the two-particle interaction involving a light particle exchange with a small mass or a mass slightly heavier than the mass difference of the two particles, identified as a long-range force, a scenario encountered in a broad range of systems. This can hinder a precise extraction of low-energy scattering observables and resonance poles. To address this issue, we propose a new parametrization for the low-energy scattering amplitude that accounts for the left-hand cut. The parametrization is like a Padé approximation but with nonanalytic terms from the left-hand cut and can be regarded as an extension of the effective range expansion. This parametrization is versatile and applicable to a broad range of systems with Yukawa-type interactions, including particle, hadronic, nuclear, cold atom, and quantum gas systems. In particular, it should be invaluable in understanding various near-threshold hadron resonances. As byproducts, we also show that the parametrization can be used to extract the couplings of the exchanged particle to the scattering particles, and derive expressions for amplitude zeros caused by the interplay between the short- and long-range interactions.

China

Meng-Lin Du

Feng-Kun Guo

Bing Wu

Effective-Range Expansion with a Long-Range Force

The absence of observed charmonium-like states with the exotic quantum numbers <math altimg='si1.svg'><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math> has prompted us to investigate the production rates of the <math altimg='si2.svg'><msup><mrow><mn>1</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math> <math altimg='si3.svg'><mi>D</mi><mspace width='0.2em' /><msub><mrow><mover accent='true'><mrow><mi>D</mi></mrow><mo>&#8254;</mo></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy='false'>(</mo><mn>2420</mn><mo stretchy='false'>)</mo></math> and <math altimg='si4.svg'><msup><mrow><mi>D</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup><mspace width='0.2em' /><msub><mrow><mover accent='true'><mrow><mi>D</mi></mrow><mo>&#8254;</mo></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy='false'>(</mo><mn>2420</mn><mo stretchy='false'>)</mo></math> hadronic molecules, which we refer to as <math altimg='si131.svg'><msub><mrow><mi>&#951;</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub></math> and <math altimg='si128.svg'><msubsup><mrow><mi>&#951;</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow><mrow><mo>&#8242;</mo></mrow></msubsup></math>, respectively, in electron-positron collisions. Assuming a hadronic molecular nature for the vector charmonium-like states <math altimg='si7.svg'><mi>&#968;</mi><mo stretchy='false'>(</mo><mn>4360</mn><mo stretchy='false'>)</mo></math> and <math altimg='si8.svg'><mi>&#968;</mi><mo stretchy='false'>(</mo><mn>4415</mn><mo stretchy='false'>)</mo></math>, we evaluate the radiative decay widths of <math altimg='si9.svg'><mi>&#968;</mi><mo stretchy='false'>(</mo><mn>4360</mn><mo stretchy='false'>)</mo><mo stretchy='false'>&#8594;</mo><mi>&#947;</mi><msub><mrow><mi>&#951;</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub></math> and <math altimg='si10.svg'><mi>&#968;</mi><mo stretchy='false'>(</mo><mn>4415</mn><mo stretchy='false'>)</mo><mo stretchy='false'>&#8594;</mo><mi>&#947;</mi><msubsup><mrow><mi>&#951;</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow><mrow><mo>&#8242;</mo></mrow></msubsup></math>. Using these decay widths, we estimate the cross sections for producing <math altimg='si131.svg'><msub><mrow><mi>&#951;</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub></math> and <math altimg='si128.svg'><msubsup><mrow><mi>&#951;</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow><mrow><mo>&#8242;</mo></mrow></msubsup></math> in electron-positron annihilations, as well as the event numbers at the planned Super <italic>&#964;</italic>-Charm Facility. Our results suggest that the ideal energy region for observing these states is around 4.44 and 4.50 GeV, just above the <math altimg='si4.svg'><msup><mrow><mi>D</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup><mspace width='0.2em' /><msub><mrow><mover accent='true'><mrow><mi>D</mi></mrow><mo>&#8254;</mo></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy='false'>(</mo><mn>2420</mn><mo stretchy='false'>)</mo></math> and <math altimg='si11.svg'><msup><mrow><mi>D</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup><mspace width='0.2em' /><msubsup><mrow><mover accent='true'><mrow><mi>D</mi></mrow><mo>&#8254;</mo></mover></mrow><mrow><mn>2</mn></mrow><mrow><mo>&#8270;</mo></mrow></msubsup><mo stretchy='false'>(</mo><mn>2460</mn><mo stretchy='false'>)</mo></math> thresholds, respectively.

Xiao-Yu Zhang

Spain

Pan-Pan Shi

Production of 1 &#8722;+ exotic charmonium-like states in electron-positron collisions

We reanalyze, considering the contribution of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave charmonia, lattice data for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>–</mi><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> coupled-channel of Prelovsek et al. [<a href="http://dx.doi.org/10.1007/JHEP06(2021)035">J. High Energy Phys. 06 (2021) 035</a>.] and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> systems of Prelovsek et al. [<a href="http://dx.doi.org/10.1103/PhysRevLett.111.192001">Phys. Rev. Lett. 111, 192001 (2013)</a>.] with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>≃</mo><mn>280</mn></math> and 266 MeV, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mo>=</mo><mn>24</mn><mi>a</mi><mo>/</mo><mn>32</mn><mi>a</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>≃</mo><mn>0.09</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mo>=</mo><mn>16</mn><mi>a</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>≃</mo><mn>0.1239</mn><mo stretchy="false">(</mo><mn>13</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math>), respectively. The hidden-charm 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>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</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> quantum numbers are then searched for. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>, the analysis reveals three poles in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>–</mi><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> coupled-channel amplitude, corresponding to three states. Two of these poles, located near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mrow><mi>D</mi></mrow><mo stretchy="false">¯</mo></mover></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub><msub><mover accent="true"><mrow><mi>D</mi></mrow><mo stretchy="false">¯</mo></mover><mi>s</mi></msub></math> thresholds, can be interpreted as mostly molecular states. A third pole above the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub><msub><mover accent="true"><mrow><mi>D</mi></mrow><mo stretchy="false">¯</mo></mover><mi>s</mi></msub></math> threshold is originated from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo></math> charmonium state. The number of poles found in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>–</mi><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> system is the same as that found in the original lattice analysis though the position of the third pole changes sizeably. In the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> sector, we find two poles in the complex energy plane. The first one is related to the molecular <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> state, with a compositeness exceeding 90%, while the second one, stemming from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo></math> charmonium, appears above the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> threshold and it likely corresponds to the recently discovered <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>4010</mn><mo stretchy="false">)</mo></math> state. In the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> sector, we also report two poles and find that the dressed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo></math> is lighter than the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> molecular state, with the dynamics of the latter closely related to that of the heavy-quark spin-symmetry partner 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>. Our exploratory study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</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> sectors offers valuable insights into their dynamics, but given that the fits that we carry out are underconstrained, more lattice data are required to draw robust conclusions.

Miguel Albaladejo

Juan Nieves

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave charmonium contribution to hidden-charm states from a reanalysis of lattice QCD data

We calculate the nucleon mass in a manifestly relativistic baryon chiral perturbation theory up to the leading two-loop order. Through dimensional counting analysis, we perform the chiral expansion and verify the validity of the extended-on-mass-shell scheme at the two-loop level. As a result, we obtain the complete chiral representation of the nucleon mass up to $$ \mathcal{O} $$ ($\textit{p}$ ), which preserves the original analytic properties and satisfies the correct power counting. The obtained chiral result is well-suited for chiral extrapolation and provides an excellent description of lattice QCD data across a broad range of pion masses. We find that the $$ \mathcal{O} $$ ($\textit{p}$ ) contribution is small, approximately 10 MeV, and varies only mildly with increasing pion mass, demonstrating good convergence of the nucleon mass up to pion masses of about 350 MeV at two-loop order.

Ze-Rui Liang

Han-Xue Chen

Zhi-Hui Guo

De-Liang Yao

Chiral representation of the nucleon mass at leading two-loop order

The possible existence of nucleon-antinucleon bound states has been studied for decades. We investigate 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><mo stretchy="false">→</mo><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></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>n</mi><mover accent="true"><mi>n</mi><mo stretchy="false">¯</mo></mover></math> cross sections in the nonrelativistic effective field theory framework. The proton-antiproton and neutron-antineutron coupled-channel final state interactions are considered and found responsible for near-threshold enhancements. Both the proton-neutron mass difference and the Coulomb interaction between <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"><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></math> are considered, and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mover accent="true"><mi>N</mi><mo stretchy="false">¯</mo></mover></math> strong interactions are taken into account through a short-distance optical potential. By fitting the low energy constants in the amplitudes to the data for the near-threshold <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>N</mi><mover accent="true"><mi>N</mi><mo stretchy="false">¯</mo></mover></math> cross sections from the BESIII and SND collaborations, a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mover accent="true"><mi>N</mi><mo stretchy="false">¯</mo></mover></math> quasibound state is found just above the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></math> threshold, and another <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mover accent="true"><mi>N</mi><mo stretchy="false">¯</mo></mover></math> pole is found on the unphysical Riemann sheet, farther away from the threshold. The constructed coupled-channel amplitude with Coulomb effects also offers a framework that can be used directly in experimental analyses on fine structures near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mover accent="true"><mi>N</mi><mo stretchy="false">¯</mo></mover></math> thresholds.

Zhao-Sai Jia

Zhen-Hua Zhang

Gang Li

Coupled-channel analysis of the near-threshold <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>N</mi><mover accent="true"><mi>N</mi><mo stretchy="false">¯</mo></mover></math> cross sections

Since 2003, plenty of resonant structures have been observed in the heavy quarkonium regime. Many of them are close to the thresholds of a few pairs of heavy hadrons. They are candidates of exotic hadrons and have attracted immense attentions. Based on a coupled-channel nonrelativistic effective field theory, we classify the near-threshold structures of a symmetry-related two-channel system by studying the evolution of the scattering amplitude line shapes and pole positions with the variation of the single-channel scattering length and channel coupling strength. We show that the evolution of the scattering amplitude line shapes can be understood from the pole trajectories in the complex energy plane, and the pole evolution can be traced back to the renormalization group fixed points. We provide a dictionary of correspondence between the evolution of line shapes and pole trajectories along with varying interaction and channel coupling strengths, which can be used to understand the experimental observations of the near-threshold structures.

Classification of coupled-channel near-threshold structures

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.

Yi-Lin Song

Yu Zhang

Germany

Vadim Baru

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

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 investigate the feasibility of measuring the proton charge radius through dimuon photoproduction off a proton target. Our findings indicate that the Bethe-Heitler mechanism, which dominates at small momentum transfers, allows for an extraction of the proton electromagnetic form factors in the extremely low <math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></math> region below <math><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> GeV$^{2}$ in the spacelike region, when the incident photon beam energy exceeds several hundred MeV. The optimal kinematical region and a sensitivity study of the proton charge radius from dimuon photoproduction are presented. Such a measurement is expected to provide an alternative to the elastic muon-proton scattering measurements such as MUSE at PSI and AMBER at CERN.

Yong-Hui Lin

The proton charge radius from dimuon photoproduction off the proton

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