Theoretical predictions of the spectrum of heavy meson-baryon bound states are a fundamental tool for disentangling the nature of the different pentaquark states that have been observed in experimental facilities. Here we explore this spectrum in a phenomenological model that describes the heavy meson-baryon interaction in terms of a contact-range interaction, where the coupling strength is saturated by the exchange of light scalar and vector mesons, i.e., <math><mi>σ</mi></math>, <math><mi>ρ</mi></math>, and <math><mi>ω</mi></math> exchanges. Saturation determines the couplings modulo an unknown proportionality constant that can be calibrated from a molecular candidate. If we use the <math><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo>(</mo><mn>4312</mn><mo>)</mo></math> as input, we predict a series of molecular pentaquarks including the <math><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo>(</mo><mn>4457</mn><mo>)</mo></math>, the recent <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></math> and the <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4459</mn><mo>)</mo></math>.

China

Zi-Ying Yang

Fang-Zheng Peng

Mao-Jun Yan

France

Spain

Mario Sánchez Sánchez

Manuel Pavon Valderrama

Molecular <math><msub><mi>P</mi><mi>ψ</mi></msub></math> pentaquarks from light-meson exchange saturation

We consider a possible resummation of subleading effects in two-body systems with a large scattering length as described by a short-range effective field theory (EFT). In particular, we investigate the consequences of a resummation of part of the range corrections. Explicit calculations of the two-body phase shifts and charge form factor indicate that, except for extreme choices, resummations do not alter the convergence of the EFT expansion and are often beneficial at the lowest orders. We have considered the expansion when the regulator cutoff is removed as well as when it is finite, and find that the cutoff is not an important factor for resummations. Our results connect with other works where the partial resummation is induced by potentials with finite cutoffs or interaction ranges.

Lorenzo Contessi

United States

Italy

Ubirajara van Kolck

Limits on an improved action for contact effective field theory in two-body systems

The spectrum of the <math><mi>c</mi><mi>q</mi><mi>q</mi></math> baryons contains a few states whose nature is not clearly a three-quark composite and which might have a sizable baryon-meson component. Examples include the <math><msub><mi>Σ</mi><mi>c</mi></msub><mo>(</mo><mn>2800</mn><mo>)</mo></math> or the <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2940</mn><mo>)</mo></math>. Here we explore the spectrum of two-body systems composed of a light, octet baryon and a charmed meson (or antimeson) within a simple contact-range theory in which the couplings are saturated by light-meson exchanges. This results in the prediction of a series of composite anticharmed pentaquarks (<math><mrow><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>q</mi><mi>q</mi><mi>q</mi><mi>q</mi></mrow></math>) and singly charmed baryons (<math><mi>c</mi><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>q</mi><mi>q</mi></math>). Among the latter we find <math><mi>J</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math> <math><mi>Ξ</mi><mi>D</mi></math> and <math><mi>J</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math> <math><mi>Ξ</mi><msup><mi>D</mi><mo>*</mo></msup></math> bound states with masses matching those of the recently observed <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>(</mo><mn>3185</mn><mo>)</mo></math> and <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>(</mo><mn>3327</mn><mo>)</mo></math> baryons.

Molecular charmed baryons and pentaquarks from light-meson exchange saturation

The spectrum of the charmed meson-(anti)meson system is a fundamental tool for disentangling the nature of a few exotic hadrons, including the recently discovered <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo>(</mo><mn>3875</mn><mo>)</mo></math> tetraquark, the <math><mi>X</mi><mo>(</mo><mn>3960</mn><mo>)</mo></math>, or the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>, the nature of which is still not clear after almost two decades of its discovery. Here we consider that the charmed meson-(anti)meson short-range interaction is described by the exchange of light mesons (<math><mi>σ</mi></math>, <math><mi>ρ</mi></math>, <math><mi>ω</mi></math>). The effects of light-meson exchanges are recast into a simple contact-range theory by means of a saturation procedure, resulting in a compact description of the two-hadron interaction. From this, if the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> were to be an isoscalar <math><msup><mi>D</mi><mo>*</mo></msup><mi>D</mi></math> molecule, then there should exist an isoscalar <math><mi>J</mi><mo>=</mo><mn>1</mn></math> <math><msup><mi>D</mi><mo>*</mo></msup><msup><mi>D</mi><mo>*</mo></msup></math> partner, as constrained by heavy-quark spin symmetry. Yet, within our model, the most attractive two charmed meson configurations are the isovector <math><mi>J</mi><mo>=</mo><mn>0</mn></math> <math><msup><mi>D</mi><mo>*</mo></msup><msup><mi>D</mi><mo>*</mo></msup></math> molecule and its sextet <math><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><msup><mi>D</mi><mo>*</mo></msup></math> and <math><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup></math> flavor partners. Finally, we find a tension between the molecular descriptions of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> and that of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> and <math><mi>X</mi><mo>(</mo><mn>3960</mn><mo>)</mo></math>, where most parameter choices suggest that if the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> is purely molecular then the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> overbinds [or conversely, if the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> is a molecule the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> does not bind]. This might be consequential for determining the nature of these states.

Heavy- and light-flavor symmetry partners of the <math><mrow><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>(</mo><mn>3875</mn><mo>)</mo></mrow></math>, the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>, and the <math><mrow><mi>X</mi><mo>(</mo><mn>3960</mn><mo>)</mo></mrow></math> from light-meson exchange saturation

The nature of the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>4312</mn><mo>)</mo></math>, <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> pentaquarks is a fascinating theoretical question. Within the molecular picture their more usual interpretation is that of <math><mi>I</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> <math><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mi>Σ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> and <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Σ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> bound states. Here we argue in favor of interpreting the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> pentaquark as a <math><mi>I</mi><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Σ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> bound state (with spin <math><mi>J</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math>) instead. Owing to isospin symmetry breaking effects, with this identification the partial decay width of the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mo>(</mo><mn>4457</mn><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup></math> into <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>p</mi></math> will be of the same order of magnitude as the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mo>(</mo><mn>4312</mn><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup></math> and <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mo>(</mo><mn>4440</mn><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup></math>, in contrast with the considerably larger partial decay width in the <math><mi>I</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> scenario. In turn, this leads to a different hidden-charm molecular pentaquark spectrum, in which there are only four or five <math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ψ</mi></mrow><mrow><mi>N</mi></mrow></msubsup></math> bound states instead of the usual seven, which might explain why the predicted <math><mi>J</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> and <math><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> (<math><mi>I</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math>) <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msubsup><mrow><mi>Σ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math> molecular partners of the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>4312</mn><mo>)</mo></math> and <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> have not been observed.

Rethinking the (4457) As the Isoquartet Molecule

The LHCb collaboration has detected a new hidden-charm pentaquark with the quantum numbers of a <math><mi>Λ</mi></math> baryon: the <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></math>. This pentaquark will be interpreted as a <math><msub><mover><mi>D</mi><mo>¯</mo></mover><mi>s</mi></msub><msub><mi>Λ</mi><mi>c</mi></msub><mo>−</mo><mover><mi>D</mi><mo>¯</mo></mover><msub><mi>Ξ</mi><mi>c</mi></msub></math> resonance within a contact-range theory. Here we briefly comment on the relation of the new <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></math> with the <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4459</mn><mo>)</mo></math>. We find that the <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></math> and <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4459</mn><mo>)</mo></math> both accept a common description in terms of the same parameters, which predicts the existence of a few additional <math><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup></math>, <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup></math>, <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Σ</mi></msubsup></math>, and <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi><mi>s</mi></mrow><mi>Ξ</mi></msubsup></math> molecular pentaquarks composed of a charmed antimeson and an antitriplet charmed baryon. The most robust of these predicted pentaquarks is a <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup></math> with a mass in the <math><mo>(</mo><mn>4235</mn><mi>–</mi><mn>4255</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> range, while other two interesting ones are a <math><msubsup><mi>P</mi><mi>ψ</mi><mi>N</mi></msubsup><mo>(</mo><mn>4150</mn><mo>)</mo></math> and a <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Σ</mi></msubsup><mo>(</mo><mn>4335</mn><mo>)</mo></math>, the latter basically at the same mass as the <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></math>, with which it might mix owing to isospin symmetry breaking effects.

<math><mrow><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ψ</mi><mi>s</mi></mrow><mrow><mi>Λ</mi></mrow></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></mrow></math> pentaquark and its partners in the molecular picture

The heavy hadron spectrum is constrained by symmetries, of which two of the most important ones are heavy-quark spin and SU(3)-flavor symmetries. Here we argue that in the molecular picture the <math><mi>Y</mi><mo>(</mo><mn>4230</mn><mo>)</mo></math> [or <math><mi>Y</mi><mo>(</mo><mn>4260</mn><mo>)</mo></math>], the <math><mi>Y</mi><mo>(</mo><mn>4360</mn><mo>)</mo></math>, and the recently discovered <math><mi>Y</mi><mo>(</mo><mn>4500</mn><mo>)</mo></math> and <math><mi>Y</mi><mo>(</mo><mn>4620</mn><mo>)</mo></math> vectorlike resonances are linked by these two symmetries. By formulating a contact-range effective field theory for the <math><mi>D</mi><msub><mover><mi>D</mi><mo>¯</mo></mover><mn>1</mn></msub></math> and <math><msub><mi>D</mi><mi>s</mi></msub><msub><mover><mi>D</mi><mo>¯</mo></mover><mrow><mi>s</mi><mn>1</mn></mrow></msub></math> family of <math><mi>S</mi></math>- and <math><mi>P</mi></math>-wave charmed meson-antimeson systems, we find that if the <math><mi>Y</mi><mo>(</mo><mn>4230</mn><mo>)</mo></math> were to be a pure <math><mi>D</mi><msub><mover><mi>D</mi><mo>¯</mo></mover><mn>1</mn></msub></math> molecular state, there would be a <math><msup><mi>D</mi><mo>*</mo></msup><msub><mover><mi>D</mi><mo>¯</mo></mover><mn>1</mn></msub></math> partner with a mass similar to the <math><mi>Y</mi><mo>(</mo><mn>4360</mn><mo>)</mo></math>, a <math><msub><mi>D</mi><mi>s</mi></msub><msub><mover><mi>D</mi><mo>¯</mo></mover><mrow><mi>s</mi><mn>1</mn></mrow></msub></math> partner with a mass close to the <math><mi>Y</mi><mo>(</mo><mn>4500</mn><mo>)</mo></math>, and three <math><mi>J</mi><mo>=</mo><mn>1</mn></math>, 2 <math><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><msub><mover><mi>D</mi><mo>¯</mo></mover><mrow><mi>s</mi><mn>1</mn></mrow></msub></math> and <math><mi>J</mi><mo>=</mo><mn>3</mn></math> <math><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><msubsup><mover><mi>D</mi><mo>¯</mo></mover><mrow><mi>s</mi><mn>2</mn></mrow><mo>*</mo></msubsup></math> bound states with a mass in the vicinity of 4630 MeV, of which the first one (<math><mi>J</mi><mo>=</mo><mn>1</mn></math>) might correspond with the <math><mi>Y</mi><mo>(</mo><mn>4620</mn><mo>)</mo></math>. The previous predictions can in turn be improved by modifying the assumptions we have used to build the effective field theory. In particular, if we consider the closeness of the <math><msup><mi>D</mi><mo>*</mo></msup><msub><mover><mi>D</mi><mo>¯</mo></mover><mn>1</mn></msub><mtext>−</mtext><msup><mi>D</mi><mo>*</mo></msup><msubsup><mover><mi>D</mi><mo>¯</mo></mover><mn>2</mn><mo>*</mo></msubsup></math> and <math><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><msub><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi><mn>1</mn></mrow></msub><mtext>−</mtext><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><msubsup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi><mn>2</mn></mrow><mrow><mo>*</mo></mrow></msubsup></mrow></math> thresholds and include the related coupled channel dynamics, we predict a <math><mi>J</mi><mo>=</mo><mn>2</mn></math> positive <math><mi>C</mi></math>-parity state with a mass around 4650 MeV. This hidden-strange and hidden-charm state might in turn be identified with the <math><mi>X</mi><mo>(</mo><mn>4630</mn><mo>)</mo></math> that has been discovered during the past year by the LHCb in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ϕ</mi></math> invariant mass distribution.

Light- and heavy-quark symmetries and the <math><mi>Y</mi><mo>(</mo><mn>4230</mn><mo>)</mo></math>, <math><mi>Y</mi><mo>(</mo><mn>4360</mn><mo>)</mo></math>, <math><mi>Y</mi><mo>(</mo><mn>4500</mn><mo>)</mo></math>, <math><mi>Y</mi><mo>(</mo><mn>4620</mn><mo>)</mo></math>, and <math><mi>X</mi><mo>(</mo><mn>4630</mn><mo>)</mo></math> resonances

The discovery of three pentaquark peaks — the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>4312</mn><mo>)</mo></math>, <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> — by the LHCb collaboration has a series of interesting consequences for hadron spectroscopy. If these hidden-charm objects are indeed hadronic molecules, as suspected, they will be constrained by heavy-flavor and SU(3)-flavor symmetries. The combination of these two symmetries will imply the existence of a series of five-flavor pentaquarks with quark content <math><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>c</mi><mi>s</mi><mi>d</mi><mi>u</mi></math> and <math><mi>b</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>s</mi><mi>d</mi><mi>u</mi></math>, that is, pentaquarks that contain each of the five quark flavors that hadronize. In addition, from SU(3)-flavor symmetry alone we expect the existence of light-flavor partners of the three <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub></math> pentaquarks with strangeness <math><mi>S</mi><mo>=</mo><mo>−</mo><mn>1</mn></math> and <math><mi>S</mi><mo>=</mo><mo>−</mo><mn>2</mn></math>. The resulting structure for the molecular pentaquarks is analogous to the light-baryon octet — we can label the pentaquarks as <math><msubsup><mrow><mi>P</mi></mrow><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>N</mi></mrow></msubsup></math>, <math><msubsup><mrow><mi>P</mi></mrow><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>Λ</mi></mrow></msubsup></math>, <math><msubsup><mrow><mi>P</mi></mrow><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>Σ</mi></mrow></msubsup></math>, <math><msubsup><mrow><mi>P</mi></mrow><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>Ξ</mi></mrow></msubsup></math> depending on their heavy- and light-quark content (with N, Λ, Σ, Ξ the member of the light-baryon octet to which the light-quark structure resembles and <math><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup></math>, <math><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> the heavy quark-antiquark pair). In total we predict 45 new pentaquarks from heavy- and light-flavor symmetries alone, which extend up to 109 undiscovered states if we also consider heavy-quark spin symmetry. If an isoquartet (<math><mi>I</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></math>) hidden-charm pentaquark is ever observed, this will in turn imply a second multiplet structure resembling the light-baryon decuplet: <math><msubsup><mrow><mi>P</mi></mrow><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>Δ</mi></mrow></msubsup></math>, <math><msubsup><mrow><mi>P</mi></mrow><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><msup><mrow><mi>Σ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow></msubsup></math>, <math><msubsup><mrow><mi>P</mi></mrow><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow></msubsup></math>, <math><msubsup><mrow><mi>P</mi></mrow><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>Ω</mi></mrow></msubsup></math>.

Ming-Zhu Liu

Ya-Wen Pan

Five-flavor pentaquarks and other light- and heavy-flavor symmetry partners of the LHCb hidden-charm pentaquarks

If known, the spectrum of heavy-hadron molecules will be a key tool to disentangle the nature of the exotic states that are being discovered in experiments. Here we argue that the general features of the molecular spectrum can be deduced from the idea that the short-range interaction between the heavy hadrons is effectively described by scalar- and vector-meson exchange, i.e., the <math><mi>σ</mi></math>, <math><mi>ρ</mi></math>, and <math><mi>ω</mi></math> mesons. By means of a contact-range theory, where the couplings are saturated by the aforementioned light mesons, we are indeed able to postdict the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> (as a <math><msup><mi>D</mi><mo>*</mo></msup><mover><mi>D</mi><mo>¯</mo></mover></math> molecule) from the three <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4312</mn><mo>)</mo></math>, <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math>, and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> pentaquarks (as <math><mover><mi>D</mi><mo>¯</mo></mover><msub><mi>Σ</mi><mi>c</mi></msub></math> and <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msub><mi>Σ</mi><mi>c</mi></msub></math> molecules). We predict a <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><mtext> </mtext><mtext> </mtext><mi>D</mi><msub><mover><mi>D</mi><mo>¯</mo></mover><mn>1</mn></msub></math> molecule at <math><mrow><mn>4240</mn><mi>–</mi><mn>4260</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>, which might support the hypothesis that the <math><mi>Y</mi><mo>(</mo><mn>4260</mn><mo>)</mo></math> is at least partly molecular. The extension of these ideas to the light baryons requires minor modifications, after which we recover approximate SU(4)-Wigner symmetry in the two-nucleon system and approximately reproduce the masses of the deuteron and the virtual state.

Heavy-hadron molecular spectrum from light-meson exchange saturation

Recently, the LHCb Collaboration announced the discovery of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> tetraquark. Being merely a few hundred keV below the <math><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi>D</mi><mn>0</mn></msup></math> threshold, the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> is expected to have a molecular component, for which there is a good separation of scales that can be exploited to make reasonably accurate theoretical predictions about this tetraquark. Independently of its nature, the most important decay channels will be <math><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math>, <math><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math>, and <math><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mi>γ</mi></mrow></math>. Its closeness to threshold suggests that the mass and particularly the width of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> tetraquark depend on the resonance profile. While the standard Breit-Wigner parametrization generates a <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> that is too broad for current theoretical calculations to reproduce, a three-body unitarized Breit-Wigner shape reveals instead a decay width (<math><mrow><msub><mrow><mi>Γ</mi></mrow><mrow><mi>pole</mi></mrow></msub><mo>=</mo><mn>48</mn><mo>±</mo><msubsup><mrow><mn>2</mn></mrow><mrow><mo>−</mo><mn>12</mn></mrow><mrow><mo>+</mo><mn>0</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>keV</mi></mrow></math>) consistent with theoretical expectations. Here, we consider subleading-order contributions to the decay amplitude, which, though having at most a moderate impact in the width, still indicate potentially significant differences with the experimental width that can be exploited to disentangle the nature of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>. Concrete calculations yield <math><mrow><msup><mrow><mi>Γ</mi></mrow><mrow><mi>LO</mi></mrow></msup><mo>=</mo><mn>49</mn><mo>±</mo><mn>16</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi></mrow></math> and <math><mrow><msup><mrow><mi>Γ</mi></mrow><mrow><mi>NLO</mi></mrow></msup><mo>=</mo><mn>5</mn><msubsup><mrow><mn>8</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow><mrow><mo>+</mo><mn>7</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>keV</mi></mrow></math>, though we expect further corrections to the next-to-leading-order (NLO) decay widths from asymptotic normalization effects. We find that a detailed comparison of the NLO total and partial decay widths with experiment suggests the existence of a small (but distinguishable from zero) nonmolecular component of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>.