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.

Spain

Miguel Albaladejo

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.

China

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

Eulogio Oset

Germany

Laura Tolos

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

We investigate the Λ c  → Λℓ + ν  ℓ  decay with a focus on potential new physics (NP) effects in the ℓ = μ channel. We employ an effective Hamiltonian within the framework of the Standard Model Effective Field Theory (SMEFT) to consider generalized dimension-6 semileptonic c → s operators of scalar, pseudoscalar, vector, axial-vector and tensor types. We rely on Lattice QCD (LQCD) for the hadronic transition form factors, using heavy quark spin symmetry (HQSS) to determine those that have not yet been obtained on the lattice. Uncertainties due to the truncation of the NP Hamiltonian and different implementations of HQSS are taken into account. As a result, we unravel the NP discovery potential of the Λ c  → Λ semileptonic decay in different observables. Our findings indicate high sensitivity to NP in lepton flavour universality ratios, probing multi-TeV scales in some cases. On the theoretical side, we identify LQCD uncertainties in axial and vector form factors as critical for improving NP sensitivity, alongside better SMEFT uncertainty estimations.

Fernando Alvarado

Luis Alvarez-Ruso

Eliecer Hernández

Neus Penalva

The Λ c  → Λ ℓ + ν  ℓ  weak decay including new physics

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.

Jing Song

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

We benefit from the lattice QCD determination by the HPQCD of the Standard Model (SM) form factors for the <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msub> <mi>D</mi> <mi>s</mi> </msub> </math> $$ {\overline{B}}_s\to {D}_s $$ [Phys. Rev. D 101 (2020) 074513] and the SM and tensor ones for the <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mo>∗</mo> </msubsup> </math> $$ {\overline{B}}_s\to {D}_s^{\ast } $$ ( arXiv:2304.03137 [hep-lat]) semileptonic decays, and the heavy quark effective theory (HQET) relations for the analogous B → D (*) decays obtained by F.U. Bernlochner et al. in Phys. Rev. D 95 (2017) 115008, to extract the leading and sub-leading Isgur-Wise functions for the <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mfenced> <mo>∗</mo> </mfenced> </msubsup> </math> $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)} $$ decays. Further use of the HQET relations allows us to evaluate the corresponding scalar, pseudoscalar and tensor form factors needed for a phenomenological study of new physics (NP) effects on the <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mfenced> <mo>∗</mo> </mfenced> </msubsup> </math> $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)} $$ semileptonic decay. At present, the experimental values for the ratios <math> <msub> <mi>R</mi> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> <mo>=</mo> <mi>Γ</mi> <mfenced> <mrow> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> <msup> <mi>τ</mi> <mo>−</mo> </msup> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> <mfenced> <mrow> <mo>/</mo> <mi>Γ</mi> </mrow> </mfenced> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> <msup> <mi>e</mi> <mo>−</mo> </msup> <mfenced> <msup> <mi>μ</mi> <mo>−</mo> </msup> </mfenced> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mrow> <mi>e</mi> <mfenced> <mi>μ</mi> </mfenced> </mrow> </msub> </mrow> </mfenced> </math> $$ {\mathcal{R}}_{D^{\left(\ast \right)}}=\Gamma \left[\overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau}\left]/\Gamma \right[\overline{B}\to {D}^{\left(\ast \right)}{e}^{-}\left({\mu}^{-}\right){\overline{\nu}}_{e\left(\mu \right)}\right] $$ are the best signal in favor of lepton flavor universality violation (LFUV) seen in charged current (CC) b → c decays. In this work we conduct a study of NP effects on the <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mfenced> <mo>∗</mo> </mfenced> </msubsup> <msup> <mi>τ</mi> <mo>−</mo> </msup> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math> $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } $$ semileptonic decays by comparing tau spin, angular and spin-angular asymmetry distributions obtained within the SM and three different NP scenarios. As expected from SU(3) light-flavor symmetry, we get results close to the ones found in a similar analysis of the <math> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </math> $$ \overline{B}\to {D}^{\left(\ast \right)} $$ case. The measurement of the <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mfenced> <mo>∗</mo> </mfenced> </msubsup> <mi>ℓ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>ℓ</mi> </msub> </math> $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)}\ell {\overline{\nu}}_{\ell } $$ semileptonic decays, which is within reach of present experiments, could then be of relevance in helping to establish or rule out LFUV in CC b → c transitions.

United Kingdom

Jonathan Flynn

Study of new physics effects in <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mfenced> <mo>∗</mo> </mfenced> </msubsup> <msup> <mi>τ</mi> <mo>−</mo> </msup> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math> $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } $$ semileptonic decays using lattice QCD form factors and heavy quark effective theory

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.

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 have a look at the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub></math> states generated from the interaction of <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msup><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>⁎</mo><mo>)</mo></mrow></msubsup></math> coupled channels. We consider the blocks of pseudoscalar-baryon <math><mo>(</mo><msup><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math> and vector-baryon <math><mo>(</mo><msup><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math>, and find 10 resonant states coupling mostly to <math><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mo>,</mo><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mo>,</mo><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math> and <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math>. A novel aspect of the work is the realization that the <math><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><msub><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> or <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><msubsup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> channels, with a strong transition potential, collaborate to produce a larger attraction than the corresponding states <math><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mi>Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> or <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><mo>,</mo><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> appearing in the generation of the strangenessless <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub></math> states, since in the latter case the transition potential between those channels is zero. The extra attraction obtained in the <math><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> pairs preclude the association of these channels to the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4338</mn><mo>)</mo></math> and <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4459</mn><mo>)</mo></math> states respectively. Then we find a natural association of the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4338</mn><mo>)</mo></math> state coupling mostly to <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> while the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4459</mn><mo>)</mo></math> is associated to the state found that couples mostly to <math><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup></math>. Four more states appear, like in other molecular pictures, and some of the states are degenerate in spin. Counting different spin states we find 10 states, which we hope can be observed in the near future.

Albert Feijoo

Wen-Fei Wang

Chu-Wen Xiao

Jia-Jun Wu

Bing-Song Zou

A new look at the States From a Molecular Perspective

Erratum to: Visible energy and angular distributions of the charged particle from the τ-decay in <math> <mi>b</mi> <mo>→</mo> <mi>cτ</mi> <mfenced> <mrow> <mi>μ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>μ</mi> </msub> <msub> <mi>ν</mi> <mi>τ</mi> </msub> </mrow> <mrow> <mi>π</mi> <msub> <mi>ν</mi> <mi>τ</mi> </msub> </mrow> <mrow> <mi>ρ</mi> <msub> <mi>ν</mi> <mi>τ</mi> </msub> </mrow> </mfenced> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math> $$ b\to c\tau \left(\mu {\overline{\nu}}_{\mu }{\nu}_{\tau },\pi {\nu}_{\tau },\rho {\nu}_{\tau}\right){\overline{\nu}}_{\tau } $$ reactions

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.

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>?