By solving the Lippmann-Schwinger equation, possible hadronic molecules in the <math altimg='si1.svg'><msup><mrow><mi>D</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup><mover accent='true'><mrow><mi>K</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math>- <math altimg='si4.svg'><mi>D</mi><msup><mrow><mover accent='true'><mrow><mi>K</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></mrow><mrow><mo>&#8270;</mo></mrow></msup></math> coupled-channel system are investigated with the one-meson exchange potentials, where both vector and pseudoscalar mesons are considered as exchange particles. We find an S-wave virtual state with mass <math altimg='si5.svg'><mi>M</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>2487</mn></math> MeV, and a resonance with <math altimg='si6.svg'><mi>M</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>2759</mn></math> and width <math altimg='si7.svg'><mi mathvariant='normal'>&#915;</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>18</mn></math> MeV. In the <math altimg='si1.svg'><msup><mrow><mi>D</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup><mover accent='true'><mrow><mi>K</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math> invariant mass distribution, the virtual state appears as a cusp at the <math altimg='si1.svg'><msup><mrow><mi>D</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup><mover accent='true'><mrow><mi>K</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math> threshold, while the resonance potentially manifests as a dip. In particular, we take into account the <math altimg='si8.svg'><mi>D</mi><mover accent='true'><mrow><mi>K</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover><mi>&#960;</mi></math> three-body dynamics due to the on-shell pion exchange and the finite decay width for <math altimg='si9.svg'><msup><mrow><mover accent='true'><mrow><mi>K</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></mrow><mrow><mo>&#8270;</mo></mrow></msup></math>.

Spain

Pan-Pan Shi

China

F. Gil-Domínguez

R. Molina

Meng-Lin Du

Pole analysis for the <math altimg='si1.svg'><msup><mrow><mi>D</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup><mover accent='true'><mrow><mi>K</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math>- <math altimg='si2.svg'><mi>D</mi><mover accent='true'><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math> coupled-channel system

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.

Feng-Kun Guo

Bing Wu

Effective-Range Expansion with a Long-Range Force

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

Motivated by the recent observation of <math><msub><mi>T</mi><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow></msub><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mn>0</mn></msup></math> and <math><msub><mi>T</mi><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow></msub><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> in the <math><msub><mi>D</mi><mi>s</mi></msub><mi>π</mi></math> invariant mass distributions, we investigate <math><msup><mi>D</mi><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> interactions in a coupled-channel approach. Within the hidden local symmetry formalism, a sizable attraction interaction is found in the <math><mi>J</mi><mo>=</mo><mn>0</mn></math> isospin triplet sector that can form a bound or a virtual state, which is consistent with the experimentally observed <math><msub><mi>T</mi><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math>. By reproducing a <math><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><mi>ρ</mi><mtext>−</mtext><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> bound/virtual state with the pole mass equal to that of the <math><msub><mi>T</mi><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> measured by LHCb in the sector <math><mo>(</mo><mi>I</mi><mo>,</mo><mi>J</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math>, we determine the unknown parameter in the loop function, and then search for possible poles in the sectors of <math><mi>I</mi><mo>=</mo><mn>1</mn></math>, <math><mi>J</mi><mo>=</mo><mn>1</mn></math>, 2 and <math><mi>I</mi><mo>=</mo><mn>0</mn></math>, <math><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2. The predicted resonances provide a useful reference for the future experimental studies of the <math><mo>(</mo><mi>C</mi><mo>,</mo><mi>S</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math> systems and can be also helpful to unravel the nature of the <math><msub><mi>T</mi><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math>.

Man-Yu Duan

Zhi-Hui Guo

En Wang

Dian-Yong Chen

Coupled-channel <math><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mtext>−</mtext><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><mi>ρ</mi></mrow></math> interactions and the origin of <math><msub><mi>T</mi><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math>

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.

Germany

Arseniy Filin

Vadim Baru

Xiang-Kun Dong

Evgeny Epelbaum

Christoph Hanhart

Slovenia

Portugal

Alexey Nefediev

Qian Wang

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>

We use a <math><mi>O</mi><mo>(</mo><msub><mi>α</mi><mi>s</mi></msub><mo>,</mo><msub><mi>Λ</mi><mi>QCD</mi></msub><mo>/</mo><msub><mi>m</mi><mi>c</mi></msub><mo>)</mo></math> heavy quark effective theory scheme, where only <math><mi>O</mi><mo>(</mo><msub><mi>Λ</mi><mi>QCD</mi></msub><mo>/</mo><msub><mi>m</mi><mi>b</mi></msub><mo>)</mo></math> corrections are neglected, to study the matrix elements of the scalar, pseudoscalar, vector, axial-vector and tensor currents between the <math><msub><mi>Λ</mi><mi>b</mi></msub></math> ground state and the odd parity charm <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><msup><mo>)</mo><mo>+</mo></msup></math> and <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2625</mn><msup><mo>)</mo><mo>+</mo></msup></math> resonances. We show that in the near-zero recoil regime, the scheme describes reasonably well, taking into account uncertainties, the results for the 24 form factors obtained in lattice QCD (LQCD) just in terms of only four Isgur-Wise (IW) functions. We also find some support for the possibility that the <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><msup><mo>)</mo><mo>+</mo></msup></math> and <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2625</mn><msup><mo>)</mo><mo>+</mo></msup></math> resonances might form a heavy quark spin symmetry (HQSS) doublet. However, we argue that the available LQCD description of these two resonances is not accurate enough to disentangle the possible effects of the <math><msub><mi>Σ</mi><mi>c</mi></msub><mi>π</mi></math> and <math><msubsup><mi>Σ</mi><mi>c</mi><mo>*</mo></msubsup><mi>π</mi></math> thresholds, located only a few MeV above their position, and that it cannot be ruled out that these states are not HQSS partners. Finally, we study the ratio <math><mfrac><mrow><mi>d</mi><mi>Γ</mi><mo>[</mo><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mrow><mi>c</mi><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>*</mo></msubsup><mo>ℓ</mo><msub><mover><mi>ν</mi><mo>¯</mo></mover><mo>ℓ</mo></msub><mo>]</mo><mo>/</mo><mi>d</mi><msup><mi>q</mi><mn>2</mn></msup></mrow><mrow><mi>d</mi><mi>Γ</mi><mo>[</mo><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mrow><mi>c</mi><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>*</mo></msubsup><mo>ℓ</mo><msub><mover><mi>ν</mi><mo>¯</mo></mover><mo>ℓ</mo></msub><mo>]</mo><mo>/</mo><mi>d</mi><msup><mi>q</mi><mn>2</mn></msup></mrow></mfrac></math> of the Standard Model differential semileptonic decay widths, with <math><mi>q</mi></math> the four-momentum transferred between the initial and final hadrons. We provide a natural explanation for the existence of large deviations, near the zero recoil, of this ratio from <math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> (value predicted in the infinite heavy quark mass limit, assuming that the <math><msubsup><mi>Λ</mi><mrow><mi>c</mi><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>*</mo></msubsup></math> and <math><msubsup><mi>Λ</mi><mrow><mi>c</mi><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>*</mo></msubsup></math> are the two members of a HQSS doublet) based on S-wave contributions to the <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mrow><mi>c</mi><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>*</mo></msubsup></math> decay amplitude driven by a subleading IW function.

Eliecer Hernández

Is the <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2625</mn><msup><mo>)</mo><mo>+</mo></msup></math> the heavy quark spin symmetry partner of the <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><msup><mo>)</mo><mo>+</mo></msup></math>?

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

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 benefit from a recent lattice determination of the full set of vector, axial and tensor form factors for the <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>*</mo></msubsup><mo>(</mo><mn>2595</mn><mo>)</mo><mi>τ</mi><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>τ</mi></msub></math> and <math><msubsup><mi>Λ</mi><mi>c</mi><mo>*</mo></msubsup><mo>(</mo><mn>2625</mn><mo>)</mo><mi>τ</mi><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>τ</mi></msub></math> semileptonic decays to study the possible role of these two reactions in lepton flavor universality violation studies. Using an effective theory approach, we analyze different observables that can be accessed through the visible kinematics of the charged particles produced in the tau decay, for which we consider the <math><msup><mi>π</mi><mo>−</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub><mo>,</mo><msup><mi>ρ</mi><mo>−</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub></math> and <math><msup><mi>μ</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>μ</mi></msub><msub><mi>ν</mi><mi>τ</mi></msub></math> channels. We compare the results obtained in the Standard Model and other schemes containing new physics (NP) interactions, with either left-handed or right-handed neutrino operators. We find a discriminating power between models similar to the one of the <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Λ</mi><mi>c</mi></msub></math> decay, although somewhat hindered in this case by the larger errors of the <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>*</mo></msubsup></math> lattice form factors. Notwithstanding this, the analysis of these reactions is already able to discriminate between some of the NP scenarios and its potentiality will certainly improve when more precise form factors are available.

Neus Penalva

New physics effects on <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>*</mo></msubsup><mi>τ</mi><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>τ</mi></msub></math> decays

We discuss some general features of the effective range expansion, the content of its parameters with respect to the nature of the pertinent near-threshold states and the necessary modifications in the presence of coupled channels, isospin violations and unstable constituents. As illustrative examples, we analyse the properties of the <math><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>3872</mn><mo>)</mo></math> and <math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math> states supporting the claim that these exotic states have a predominantly molecular nature.

Effective range expansion for narrow near-threshold resonances

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