We investigate the Ξ* resonances within the molecular picture, where these states are dynamically generated as poles in the unitarized scattering amplitudes arising from the coupled-channel interactions of <math altimg='si2.svg'><mrow><msup><mi>K</mi><mrow><mo>*</mo><mo>&#8722;</mo></mrow></msup><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle></mrow></math>, <math altimg='si3.svg'><mrow><msup><mi>K</mi><mrow><mo>*</mo><mo>&#8722;</mo></mrow></msup><msup><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mn>0</mn></msup></mrow></math>, <math altimg='si4.svg'><mrow><msup><mi>&#961;</mi><mo>&#8722;</mo></msup><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mn>0</mn></msup></mrow></math>, <math altimg='si5.svg'><mrow><mspace width='0.16em' /><msup><mover><mrow><mspace width='-0.16em' /><mi>K</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mo>&#8722;</mo></msup></mrow></math>, <math altimg='si6.svg'><mrow><msup><mi>&#961;</mi><mn>0</mn></msup><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup></mrow></math>, <math altimg='si7.svg'><mrow><mi>&#969;</mi><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup></mrow></math>, and <math altimg='si9.svg'><mrow><mi>&#981;</mi><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup></mrow></math>. The interaction kernel is derived from the local hidden gauge formalism, while the unitarization procedure employs a hybrid method that combines cutoff and dimensional regularizations in the evaluation of the loop function. From a detailed spectroscopic analysis, we identify two <math altimg='si149.svg'><mrow><mi>S</mi><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>2</mn></mrow></math> baryon states whose properties are compatible with some of the &#926;* resonances listed in the Review of Particle Physics. To explore their possible experimental signatures, we compute the femtoscopic correlation functions for all the vector&#8211;baryon pairs considered in the present study, using realistic estimates of production weights and varying source sizes <math altimg='si150.svg'><mrow><mi>R</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo>,</mo><mn>1.1</mn><mo>,</mo><mn>1.2</mn><mo>,</mo><mn>1.3</mn><mo>,</mo><mn>1.5</mn></mrow></math> fm.

China

Spain

Jia-Xin Lin

Pablo Encarnación

Miguel Albaladejo

Albert Feijoo

Signatures of odd-parity <italic>s</italic>-wave &#926;* states in femtoscopic correlation functions

We study the feasibility of having the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Σ</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math> state, predicted within the chiral unitary approach and recently reported by the Belle Collaboration, as corresponding to a state of a nonmolecular nature. Starting from this assumption, since the state is observed in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi mathvariant="normal">Λ</mi></math> channel, we allow the coupling to this state and relate the coupling to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>N</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi mathvariant="normal">Σ</mi></math> using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> symmetry arguments. We find that it is possible to have such a state with negligible coupling to the molecular components with a bare mass of the state very close to the physical mass of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Σ</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math>. Yet this has consequences on other observables, since the width obtained is extremely small and incompatible with the Belle observations, and it leads to abnormally large values of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>N</mi></math> effective range. Conversely, such mismatches do not appear for large values of the bare mass of the state, but in this case, we observe that the state develops large molecular components. While one can rule out a largely nonmolecular nature for this state, its properties and detailed nature will need further experimental developments which one can anticipate will be coming in the near future.

Jing Song

Eulogio Oset

Testing the nature of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Σ</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math>

This work addresses the incorporation of Coulomb interactions into femtoscopy correlation functions (CFs) used to probe hadron interactions. Combining strong contact potentials with Coulomb effects, the derived scattering amplitudes and wave functions are used to compute CFs, accounting for both interactions coherently. Next, we analyze the nature of the corrections due to the finite range of the strong interaction, closely linked to off-shell effects, and propose an approximate method to account for them. We show how these corrections turn out to be essential to accurately extract the strong hadron–hadron scattering amplitudes from CF data. We compare the obtained expressions for the CFs with those reported in previous theoretical frameworks. Also, using proton–proton systems as a case study, we obtain a good comparison of our results with previous realistic theoretical calculations and with accurate recent data from the ALICE experiment. The framework enables precise CF calculations without numerical solution of the Schrödinger equation, offering a practical tool for femtoscopy analyses involving charged hadrons. In addition, the scheme allows for an easy connection with scattering amplitudes obtained from Effective Field Theories.

Amador García-Lorenzo

Juan Nieves

Femtoscopy Correlation Functions and Hadron–Hadron Scattering Amplitudes in Presence of Coulomb Potential

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.

Pan-Pan Shi

Meng-Lin Du

Feng-Kun Guo

<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 have studied the feasibility of the experimental determination of the width of a D meson in a nuclear medium by using the method of the nuclear transparency. The cross section for inclusive production of a <math><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup></math> in different nuclei is evaluated, taking care of the <math><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup></math> absorption in the nucleus, or equivalently, the survival probability of the <math><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup></math> in its way out of the nucleus from the point of production. We use present values of the in medium width of D mesons and calculate ratios of the cross sections for different nuclei to the <math><mmultiscripts><mrow><mtext>C</mtext></mrow><mprescripts></mprescripts><none></none><mrow><mn>12</mn></mrow></mmultiscripts></math> nucleus as reference. We find ratios of the order of 0.6 for heavy nuclei, a large deviation from unity, which indicates that the method proposed is adequate to measure this relevant magnitude, so far only known theoretically.

Victor Montesinos

Japan

Natsumi Ikeno

Germany

Laura Tolos

On the determination of the Meson Width in the Nuclear Medium With the Transparency Ratio

We start from a recently favored picture in which the <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2940</mn><mo>)</mo></math> and <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2910</mn><mo>)</mo></math> correspond mostly to <math><mi>N</mi><msup><mi>D</mi><mo>*</mo></msup></math> bound states with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> respectively, and then add a <math><mi>D</mi></math> as a third particle, looking for the possible binding of the <math><mi>D</mi><mi>N</mi><msup><mi>D</mi><mo>*</mo></msup></math> three-body system within the framework of the fixed center approximation. We find that the system is bound with respect to the corresponding <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2940</mn><mo>)</mo><mi>D</mi></math>, <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2910</mn><mo>)</mo><mi>D</mi></math> thresholds with a binding of about 60 MeV and a width of about 90 MeV. Alternatively we assume a cluster of <math><mi>N</mi><mi>D</mi></math> and a <math><msup><mi>D</mi><mo>*</mo></msup></math> meson interacting with the cluster, and we find similar results. The observation of these states of <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math> would provide new and valuable information concerning the <math><mi>D</mi><mi>N</mi></math> and <math><msup><mi>D</mi><mo>*</mo></msup><mi>N</mi></math> interaction, an issue of current debate.

Wei-Hong Liang

Study of possible <math><mrow><mi>D</mi><mi>N</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> bound states

Recently, the LHCb Collaboration reported a near-threshold enhancement <math><mi>X</mi><mo>(</mo><mn>3960</mn><mo>)</mo></math> in the <math><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup></math> invariant mass distribution. We show that the data can be well described by either a bound or a virtual state below the <math><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup></math> threshold. The mass given by the pole position is (<math><mrow><mn>3928</mn><mo>±</mo><mn>3</mn></mrow></math>) MeV. Using this mass and the existing information on the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> and <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math> resonances, a complete spectrum of the <math><mi>S</mi></math>-wave hadronic molecules formed by a pair of ground state charmed and anticharmed mesons is established. Thus, pole positions of the partners of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>, <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math>, and the newly observed <math><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup></math> state are predicted. Calculations have been carried out at the leading order of nonrelativistic effective field theory and considering both heavy quark spin and light flavor SU(3) symmetries, though conservative errors from the breaking of these symmetries are provided.

Teng Ji

Xiang-Kun Dong

Establishing the heavy quark spin and light flavor molecular multiplets of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>, <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math>, and <math><mi>X</mi><mo>(</mo><mn>3960</mn><mo>)</mo></math>

We have performed a combined analysis of the BESIII data for both the <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math> and <math><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math> structures, assuming that the latter is an SU(3) flavor partner of the former one. We have improved on the previous analysis of Albaladejo et al. [Phys. Lett. B 755, 337 (2016)] by computing the amplitude for the <math><msub><mi>D</mi><mn>1</mn></msub><mover><mi>D</mi><mo>¯</mo></mover><msup><mi>D</mi><mo>*</mo></msup></math> triangle diagram considering both <math><mi>D</mi></math>- and <math><mi>S</mi></math>-wave <math><msub><mi>D</mi><mn>1</mn></msub><msup><mi>D</mi><mo>*</mo></msup><mi>π</mi></math> couplings. We have also investigated effects from SU(3) light-flavor violations, which are found to be moderate and of the order of 20%. The successful reproduction of the BESIII spectra, in both the hidden-charm and hidden-charm strange sectors, strongly supports that the <math><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math> and <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math> are SU(3) flavor partners placed in the same octet multiplet. The best results are obtained when an energy-dependent term in the diagonal <math><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><msubsup><mover><mi>D</mi><mo>¯</mo></mover><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup></math> interaction is included, leading to resonances (poles above the thresholds) to describe these exotic states. We have also made predictions for the isovector <math><msubsup><mi>Z</mi><mi>c</mi><mo>*</mo></msubsup></math> and isodoublet <math><msubsup><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow><mo>*</mo></msubsup></math>, <math><msup><mi>D</mi><mo>*</mo></msup><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math>, and <math><msup><mi>D</mi><mo>*</mo></msup><msubsup><mover><mi>D</mi><mo>¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math> molecules, with <math><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> and <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math>, respectively. These states would be heavy-quark spin symmetry (HQSS) partners of the <math><msub><mi>Z</mi><mi>c</mi></msub></math> and <math><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub></math>. Besides the determination of the masses and widths of the <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math> and <math><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math>, we also predict those of the <math><msubsup><mi>Z</mi><mi>c</mi><mo>*</mo></msubsup></math> and <math><msubsup><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow><mo>*</mo></msubsup></math> resonances.

Combined analysis of the <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math> and the <math><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math> exotic states

Since 2003 many new hadrons, including the lowest-lying positive-parity charm-strange mesons <math><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo>(</mo><mn>2317</mn><mo>)</mo></mrow></math> and <math><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>2460</mn><mo>)</mo></math>, have been observed that do not conform with quark-model expectations. It was recently demonstrated that various puzzles in the charm-meson spectrum find a natural resolution if the SU(3) multiplets for the lightest scalar and axial-vector states, among them the <math><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo>(</mo><mn>2317</mn><mo>)</mo></math> and the <math><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>2460</mn><mo>)</mo></math>, owe their existence to the nonperturbative dynamics of Goldstone-boson scattering off <math><msub><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></msub></math> and <math><msubsup><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>*</mo></msubsup></math> mesons. Most importantly the ordering of the lightest strange and nonstrange scalars becomes natural. We demonstrate for the first time that this mechanism is strongly supported by the recent high quality data on the <math><msup><mi>B</mi><mo>−</mo></msup><mo>→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> provided by the LHCb experiment. This implies that the lowest quark-model positive-parity charm mesons, together with their bottom counterparts, if realized in nature, do not form the ground-state multiplet. This is similar to the pattern that has been established for the scalar mesons made from light up, down, and strange quarks, where the lowest multiplet is considered to be made of states not described by the quark model. In a broader view, the hadron spectrum must be viewed as more than a collection of quark-model states.

Pedro Fernandez-Soler

Christoph Hanhart

Ulf-G. Meißner

De-Liang Yao

Towards a new paradigm for heavy-light meson spectroscopy

The masses of the $$D^*_{s0}(2317)$$ <math><mrow><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>∗</mo></msubsup><mrow><mo>(</mo><mn>2317</mn><mo>)</mo></mrow></mrow></math> and $$D_{s1}(2460)$$ <math><mrow><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mrow><mo>(</mo><mn>2460</mn><mo>)</mo></mrow></mrow></math> resonances lie below the DK and $$D^*K$$ <math><mrow><msup><mi>D</mi><mo>∗</mo></msup><mi>K</mi></mrow></math> thresholds respectively, which contradicts the predictions of naive quark models and points out to non-negligible effects of the $$D^{(*)}K$$ <math><mrow><msup><mi>D</mi><mrow><mo>(</mo><mrow></mrow><mo>∗</mo><mo>)</mo></mrow></msup><mi>K</mi></mrow></math> loops in the dynamics of the even-parity scalar ($$J^\pi =0^+$$ <math><mrow><msup><mi>J</mi><mi>π</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></mrow></math> ) and axial-vector ($$J^\pi =1^+$$ <math><mrow><msup><mi>J</mi><mi>π</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></mrow></math> ) $$c\bar{s}$$ <math><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> systems. Recent lattice QCD studies, incorporating the effects of the $$D^{(*)}K$$ <math><mrow><msup><mi>D</mi><mrow><mo>(</mo><mrow></mrow><mo>∗</mo><mo>)</mo></mrow></msup><mi>K</mi></mrow></math> channels, analyzed these spin-parity sectors and correctly described the $$D^*_{s0}(2317)-D_{s1}(2460)$$ <math><mrow><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>∗</mo></msubsup><mrow><mo>(</mo><mn>2317</mn><mo>)</mo></mrow><mo>-</mo><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mrow><mo>(</mo><mn>2460</mn><mo>)</mo></mrow></mrow></math> mass splitting. Motivated by such works, we study the structure of the $$D_{s0}^*(2317)$$ <math><mrow><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>∗</mo></msubsup><mrow><mo>(</mo><mn>2317</mn><mo>)</mo></mrow></mrow></math> and $$D_{s1}(2460)$$ <math><mrow><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mrow><mo>(</mo><mn>2460</mn><mo>)</mo></mrow></mrow></math> resonances in the framework of an effective field theory consistent with heavy quark spin symmetry, and that incorporates the interplay between $$D^{(*)}K$$ <math><mrow><msup><mi>D</mi><mrow><mo>(</mo><mrow></mrow><mo>∗</mo><mo>)</mo></mrow></msup><mi>K</mi></mrow></math> meson–meson degrees of freedom and bare P-wave $$c\bar{s}$$ <math><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> states predicted by constituent quark models. We extend the scheme to finite volumes and fit the strength of the coupling between both types of degrees of freedom to the available lattice levels, which we successfully describe. We finally estimate the size of the $$D^{(*)}K$$ <math><mrow><msup><mi>D</mi><mrow><mo>(</mo><mrow></mrow><mo>∗</mo><mo>)</mo></mrow></msup><mi>K</mi></mrow></math> two-meson components in the $$D^*_{s0}(2317)$$ <math><mrow><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>∗</mo></msubsup><mrow><mo>(</mo><mn>2317</mn><mo>)</mo></mrow></mrow></math> and $$D_{s1}(2460)$$ <math><mrow><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mrow><mo>(</mo><mn>2460</mn><mo>)</mo></mrow></mrow></math> resonances, and we conclude that these states have a predominantly hadronic-molecular structure, and that it should not be tried to accommodate these mesons within $$c\bar{s}$$ <math><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> constituent quark model patterns.

Pablo Ortega

Contribution of constituent quark model $$c\bar{s}$$ <math><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> states to the dynamics of the $$D_{s0}^*(2317)$$ <math><mrow><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>∗</mo></msubsup><mrow><mo>(</mo><mn>2317</mn><mo>)</mo></mrow></mrow></math> and $$D_{s1}(2460)$$ <math><mrow><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mrow><mo>(</mo><mn>2460</mn><mo>)</mo></mrow></mrow></math> resonances