Pion Exchange Potential Research Articles

Possible Σc*Σ¯ molecular states

We investigate the possibility of deuteronlike Σc*Σ¯ bound states within the one-boson-exchange model and systematically analyze the effects of the contact range δ3(r→) potential, the tensor term from the vector-meson exchange, and nonlocal potentials due to the dependence on the sum of the initial and final state center-of-mass momenta. We find that the pion-exchange potential including the δ3(r→) term and the tensor term of the ρ-exchange potential exhibit comparable magnitudes but opposite signs for any S-wave baryon-antibaryon systems. For the Σc*Σ¯ system, it is most likely to form bound states with mass around 3.7 GeV in the I(JP)=0(2−) and 1(2−) channels. Published by the American Physical Society 2024

Heavy Hadronic Molecules Coupled with Multiquark States

We investigate the hidden-charm pentaquarks as a \(\varLambda _c{\bar{D}}^{(*)}-\varSigma _c^{(*)}{\bar{D}}^{(*)}\) hadronic molecule coupling to a compact five-quark state. The coupling to the compact state leads to an hadron short-range interaction generating an attraction. In addition, the one pion exchange potential (OPEP) as a long-range interaction is introduced by the Lagrangians satisfying the chiral and heavy quark spin symmetries. The OPEP has been known as a driving force to bind atomic nuclei, where the tensor term leading the coupled-channel effect generates a strong attraction. The mass degeneracy of heavy hadrons due to the heavy quark spin symmetry enhances the OPEP derived by the \(\pi D^{(*)}{\bar{D}}^{(*)}\) and \(\pi \varSigma _c^{(*)}\varSigma _c^{(*)}\) couplings. Introducing those interactions, we consistently explain the masses and widths of the \(P_c\) states reported by LHCb in 2019. The short range interaction has a dominant role to determine the energy-level structures, while the OPEP tensor term does the decay width.

One pion exchange and the quantum numbers of the Pc(4440) and Pc(4457) pentaquarks

The LHCb collaboration has recently discovered three pentaquark-like states---the ${P}_{c}(4312)$, ${P}_{c}(4440)$ and ${P}_{c}(4457)$---close to the $\overline{D}{\mathrm{\ensuremath{\Sigma}}}_{c}$ and the ${\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ meson-baryon thresholds. The standard interpretation is that they are heavy antimeson-baryon molecules. Their quantum numbers have not been determined yet, which implies two possibilities for the ${P}_{c}(4440)$ and ${P}_{c}(4457)$: ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ and ${J}^{P}={\frac{3}{2}}^{\ensuremath{-}}$. The preferred interpretation within a contact-range effective field theory is that the ${P}_{c}(4440)$ is the ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ molecule, while the ${P}_{c}(4457)$ is the ${J}^{P}={\frac{3}{2}}^{\ensuremath{-}}$ one. Here we show that when the one pion exchange potential between the heavy antimeson and heavy baryon is taken into account, this conclusion changes, with the contrary identification being as likely as the original one. The identification is however cutoff dependent, which suggests that improvements of the present description (e.g., the inclusion of subleading order corrections, like two-pion exchanges) are necessary in order to disambiguate the spectroscopy of the molecular pentaquarks.

Heavy baryon-antibaryon molecules in effective field theory

We discuss the effective field theory description of bound states composed of a heavy baryon and antibaryon. This framework is a variation of the ones already developed for heavy meson-antimeson states to describe the $X(3872)$ or the $Z_c$ and $Z_b$ resonances. We consider the case of heavy baryons for which the light quark pair is in S-wave and we explore how heavy quark spin symmetry constrains the heavy baryon-antibaryon potential. The one pion exchange potential mediates the low energy dynamics of this system. We determine the relative importance of pion exchanges, in particular the tensor force. We find that in general pion exchanges are probably non-perturbative for the $\Sigma_Q \bar{\Sigma}_Q$, $\Sigma_Q^* \bar{\Sigma}_Q$ and $\Sigma_Q^* \bar{\Sigma}_Q^*$ systems, while for the $\Xi_Q' \bar{\Xi}_Q'$, $\Xi_Q^* \bar{\Xi}_Q'$ and $\Xi_Q^* \bar{\Xi}_Q^*$ cases they are perturbative If we assume that the contact-range couplings of the effective field theory are saturated by the exchange of vector mesons, we can estimate for which quantum numbers it is more probable to find a heavy baryonium state. The most probable candidates to form bound states are the isoscalar $\Lambda_Q \bar{\Lambda}_Q$, $\Sigma_Q \bar{\Sigma}_Q$, $\Sigma_Q^* \bar{\Sigma}_Q$ and $\Sigma_Q^* \bar{\Sigma}_Q^*$ and the isovector $\Lambda_Q \bar{\Sigma}_Q$ and $\Lambda_Q \bar{\Sigma}_Q^*$ systems, both in the hidden-charm and hidden-bottom sectors. Their doubly-charmed and -bottom counterparts ($\Lambda_Q {\Lambda}_Q$, $\Lambda_Q {\Sigma}_Q^{(*)}$, $\Sigma_Q^{(*)} {\Sigma}_Q^{(*)}$) are also good candidates for binding.

Line shapes of the Zb(10610) and Zb(10650) in the elastic and inelastic channels revisited

The most recent experimental data for all measured production and decay channels of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ are analysed simultaneously using solutions of the Lippmann-Schwinger equations which respect constraints from unitarity and analyticity. The interaction potential in the open-bottom channels $B^{(*)}\bar{B}^{*}+\mbox{c.c.}$ contains short-range interactions as well as one-pion exchange. It is found that the long-range interaction does not affect the line shapes as long as only $S$ waves are considered. Meanwhile, the line shapes can be visibly modified once $D$ waves, mediated by the strong tensor forces from the pion exchange potentials, are included. However, in the fit they get balanced largely by a momentum dependent contact term that appears to be needed also to render the results for the line shapes independent of the cut-off. The resulting line shapes are found to be insensitive to various higher-order interactions included to verify stability of the results. Both $Z_b$ states are found to be described by the poles located on the unphysical Riemann sheets in the vicinity of the corresponding thresholds. In particular, the $Z_b(10610)$ state is associated with a virtual state residing just below the $B\bar{B}^{*}/\bar B{B}^{*}$ threshold while the $Z_b(10650)$ state most likely is a shallow state located just above the $B^*\bar{B}^{*}$ threshold.

Spin degeneracy of Hadronic molecules in the heavy quark region

Hadronic molecules have been considered to appear close to the hadron-hadron threshold. For the heavy mesons, and B, the one pion exchange potential is enhanced by the mass degeneracy of heavy pseudoscalar and vector mesons, caused by the heavy quark spin symmetry. In this study, we investigate new hadronic molecules formed by the heavy meson and a nucleon N, being P(*)N. As the interaction between P(*) and N, the pion and vector meson (ρ and ω) exchanges are considered. By solving the coupled-channel Schrödinger equations for P N and P*N, we obtain the bound and resonant states in the charm and bottom sectors, and in the in nite heavy quark mass limit. In the molecular states, the PN − P*N mixing effect is important, where the tensor force of the one pion exchange potential generates the strong attraction. In the heavy quark limit, we obtain the degeneracy of the states for JP = 1/2− and 3/2−.

Hidden-charm and bottom meson-baryon molecules coupled with five-quark states

In this paper, we investigate the hidden-charm pentaquarks as $\bar{D}^{(\ast)}\Lambda_{\rm c}$ and $\bar{D}^{(\ast)}\Sigma^{(\ast)}_{\rm c}$ molecules coupled to the five-quark states. Furthermore, we extend our calculations to the hidden-bottom sector. The coupling to the five-quark states is treated as the short range potential, where the relative strength for the meson-baryon channels is determined by the structure of the five-quark states. We found that resonant and/or bound states appear in both the charm and bottom sectors. The five-quark state potential turned out to be attractive and, for this reason, it plays an important role to produce these states. In the charm sector, we need the five-quark potential in addition to the pion exchange potential in producing bound and resonant states, whereas, in the bottom sector, the pion exchange interaction is strong enough to produce states. Thus, from this investigation, it emerges that the hidden-bottom pentaquarks are more likely to form than their hidden-charm counterparts; for this reason, we suggest that the experimentalists should look for states in the bottom sector.

Mass spectra of meson molecular states for heavy and light sectors

We obtain mass spectra of the light and heavy meson-antimeson (molecular states) sectors by using a nonrelativistic potential model with Coulomb and one pion exchange potential terms for meson-meson interaction. The digamma decay widths are also obtained for the light sector. We compare our results with available experimental and theoretical data.

Dimesonic states with the heavy-light flavour mesons

In this work, we have calculated the mass spectra and decay properties of dimesonic states in the variational scheme. The inter-mesonic interaction considered as the Hellmann potential and One Pion Exchange potential. The mass spectra of the $D\overline{D^{*}}$, $D^{*}\overline{D^{*}}$, $D\overline{B^{*}}$, $B^{*}\overline{D}$, $B\overline{B^{*}}$, $B^{*}\overline{B^{*}}$ bound states are calculated. The states X(3872), $X_{2c}(4013)$, $Z_{b}(10610)/X_{b}$ and $Z_{b}(10650)/X_{b2}$ are compared with $D\overline{D^{*}}$, $D^{*}\overline{D^{*}}$, $B\overline{B^{*}}$ and $B^{*}\overline{B^{*}}$ dimesonic bound states. {\bf To probe the molecular structure of the compared states, we have calculated the decay properties sensitive to their long and short distance structure of the hadronic molecule. The radiative decay for the state X(3872) into $J/\psi \gamma$ and $\psi(2S) \gamma$ have been calculated and the ratio is found to be ten times lesser than the experimental value whereas the other decay modes are comparable with other theoretical and experimental results. This results restrict us to assigned the pure molecular structure to the X(3872). But, Our results suggests that the compared states are close to the molecular structure or have dominant molecular component in their wave function. Apart from these, the other calculated mass spectra of dimesonic states are predicted and for such bound states, the experimental search are suggested.}

Heavy-quark spin symmetry partners of the X(3872) revisited

We revisit the consequences of the heavy-quark spin symmetry for the possible spin partners of the $X(3872)$. We confirm that, if the $X(3872)$ were a $D\bar{D}^*$ molecular state with the quantum numbers $J^{PC}=1^{++}$, then in the strict heavy-quark limit there should exist three more hadronic molecules degenerate with the $X(3872)$, with the quantum numbers $0^{++}$, $1^{+-}$, and $2^{++}$ in line with previous results reported in the literature. We demonstrate that this result is robust with respect to the inclusion of the one-pion exchange interaction between the $D$ mesons. However, this is true only if all relevant partial waves as well as particle channels which are coupled via the pion-exchange potential are taken into account. Otherwise, the heavy-quark symmetry is destroyed even in the heavy-quark limit. Finally, we solve the coupled-channel problem in the $2^{++}$ channel with nonperturbative pions beyond the heavy-quark limit and, contrary to the findings of previous calculations with perturbative pions, find for the spin-2 partner of the $X(3872)$ a significant shift of the mass as well as a width of the order of 50 MeV.

Exotic Baryons from a Heavy Meson and a Nucleon

Hadronic molecules have been considered to be one of the candidate of exotic hadron structures near the threshold. In the heavy quark sector, new symmetry, called the heavy quark symmetry, plays an important role to form the molecules. This symmetry has an essential role which is to enhance the one pion exchange potential arising through the mixing of heavy pseudoscalar and heavy vector mesons. In this study, we investigate new hadronic molecule formed by the heavy meson $$P^{(*)}=\bar{D}^{(*)},B^{(*)}$$ and a nucleon N, being $$P^{(*)}N$$ and $$P^{(*)}NN$$ few-body states. As the interaction between P and N, the $$\pi $$ exchange and vector meson ( $$\rho $$ and $$\omega $$ ) exchanges are considered. By solving the coupled-channel schrödinger equations for PN(N) and $$P^{(*)}N(N)$$ , we predict the bound and resonant states in the charm and bottom sectors. In the bound and resonant states, the $$PN-P^*N$$ mixing effect is important, where the tensor force of the one pion exchange potential generates the strong attraction.

The mass spectra and decay properties of dimesonic states, using the Hellmann potential

Mass spectra of the dimesonic (meson-antimeson) molecular states are computed using the Hellmann potential in variational approach, which consists of relativistic correction to kinetic energy term as well as to the potential energy term. For the study of molecular bound state system, the Hellmann potential of the form $V(r)=-\frac{\alpha_{s}}{r} + \frac{B e^{-Cr}}{r}$ is being used. The one pion exchange potential (OPEP) is also incorporated in the mass calculation. The digamma decay width and decay width of the dimesonic system are evaluated using the wave function. The experimental states such as $f_{0}(980)$, $b_{1}(1235)$, $h_{1}(1380)$, $a_{0}(1450)$, $f_{0}(1500)$, $f_{2}'(1525)$,$f_{2}(1565)$, $h_{1}(1595)$, $a_{2}(1700)$, $f_{0}(1710)$, $f_{2}(1810)$ are compared with dimesonic states. Many of these states (masses and their decay properties) are close to our theoretical predictions.

Two Pion versus σ-Meson Exchange Potentials

The two pion exchange potentials are evaluated by carrying out the numerical integrations of three Feynman parameters in the corresponding Feynman diagrams. The two pion exchange potentials give rise to the attractive force which is quite similar to the effective scalar meson with its mass of mss4.7mπ and its strength of at T = 0 channel. However, there is a strong isospin dependence of (t1·t2)2 which should be different from the phenomenological σ-meson exchange calculations. Therefore, the medium range attraction of the T = 0 nuclear interaction should be due to the two pion exchange processes, but the T = 1 channel is still an open problem.

$\bar{D}$ and B nuclei with one pion exchange potential

We discuss the possible existence of exotic dibaryons with a heavy antiquark, being realized three-body systems, [Formula: see text] and B(*)NN. These are genuinely exotic states with no quark-antiquark annihilation. We consider the heavy quark spin symmetry and chiral symmetry, and introduce the one pion exchange potential between a [Formula: see text] meson and a nucleon N. As for the NN interaction, we employ the Argonne [Formula: see text] potential. By solving the coupled-channel equations for PNN and [Formula: see text], we find bound and resonant states near the thresholds both in charm and bottom sectors.

Exotic dibaryons with a heavy antiquark

We discuss the possible existence of exotic dibaryons with a heavy antiquark, being realized three-body systems, Dbar^(*)NN and B^(*)NN. These are genuinely exotic states with no quark-antiquark annihilation. We consider the heavy quark spin and chiral symmetries, and introduce the one pion exchange potential between a Dbar^(*) (B^(*)) meson and a nucleon N. As for the NN interaction, we employ the Argonne v^\prime_8 potential. By solving the coupled-channel equations for PNN and P^* NN (P^(*)=Dbar^(*) and B^(*)), we find bound states for (I,J^P)=(1/2,0^-) as well as resonant states for (I,J^P)=(1/2,1^-) both in Dbar^(*)NN and B^(*)NN systems. We also discuss the heavy quark limit, and find that the spin degeneracy is realized in the bound states with (I,J^P)=(1/2,0^-) and (1/2,1^-).

Exotic Baryons from a Heavy Meson and a Nucleon

We evaluate a hadronic molecule formed by a heavy meson and a nucleon respecting heavy quark symmetry. The tensor force of pion exchange potential plays a dominate role to produce an strong attraction in this system. Solving coupled channel Schr\"odinger equations for PN and P* N, we find many bound and resonant states with isospin I=0 while there are few resonances in I=1 state. The rich structures with I=0 indicate that the spectrum of heavy baryons near the threshold is influenced by the contributions from such hadron composite structures.

On the Renormalization of the One–Pion Exchange Potential and the Consistency of Weinberg’s Power Counting

Nogga, Timmermans and van Kolck recently argued that Weinberg’s power counting in the few–nucleon sector is inconsistent and requires modifications. Their argument is based on the observed cutoff dependence of the nucleon–nucleon scattering amplitude calculated by solving the Lippmann–Schwinger equation with the regularized one–pion exchange potential and the cutoff Λ varied in the range Λ = 2 . . . 20 fm−1. In this paper we discuss the role the cutoff plays in the application of chiral effective field theory to the two–nucleon system and study carefully the cutoff–dependence of phase shifts and observables based on the one–pion exchange potential. We show that (i) there is no need to use the momentum–space cutoff larger than Λ ~ 3 fm−1; (ii) the neutron–proton low–energy data show no evidence for an inconsistency of Weinberg’s power counting if one uses Λ ~ 3 fm−1.

Power counting and perturbative one pion exchange in heavy meson molecules

We discuss the possible power counting schemes that can be applied in the effective field theory description of heavy meson molecules, such as the X(3872) or the recently discovered Zb(10610) and Zb(10650) states. We argue that the effect of coupled channels is suppressed by at least two orders in the effective field theory expansion, meaning that they can be safely ignored at lowest order. The role of the one pion exchange potential between the heavy mesons, and in particular the tensor force, is also analyzed. By using techniques developed in atomic physics for handling power-law singular potentials, which have been also successfully employed in nuclear physics, we determine the range of center-of-mass momenta for which the tensor piece of the one pion exchange potential is perturbative. In this momentum range, the one pion exchange potential can be considered a subleading order correction, leaving at lowest order a very simple effective field theory consisting only on contact-range interactions.

Perturbative renormalizability of chiral two-pion exchange in nucleon-nucleon scattering:PandDwaves

We study the perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering for p- and d-waves within the effective field theory approach. The one pion exchange potential is fully iterated at the leading order in the expansion, a choice generating a consistent and well-defined power counting that we explore in detail. The results show that perturbative chiral two pion exchange reproduces the data up to a center-of-mass momentum of k_cm ~300 MeV at NNLO and that the effective field theory expansion convergences up to k_cm ~ 350 MeV.

Deriving the existence ofBB¯*bound states from theX(3872)and heavy quark symmetry

We discuss the possibility and the description of bound states between $B$ and $\bar{B}^*$ mesons. We argue that the existence of such a bound state can be deduced from (i) the weakly bound X(3872) state, (ii) certain assumptions about the short range dynamics of the $D\bar{D}^*$ system and (iii) heavy quark symmetry. From these assumptions the binding energy of the possible $B\bar{B}^*$ bound states is determined, first in a theory containing only contact interactions which serves as a straightforward illustration of the method, and then the effects of including the one pion exchange potential are discussed. In this latter case three isoscalar states are predicted: a positive and negative C-parity $^3S_1-{}^3D_1$ state with a binding energy of $20\,{\rm MeV}$ and $6\,{\rm MeV}$ below threshold respectively, and a positive C-parity $^3P_0$ shallow state located almost at the $B\bar{B}^*$ threshold. However, large uncertainties are generated as a consequence of the $1/m_Q$ corrections from heavy quark symmetry. Finally, the newly discovered isovector $Z_b(10610)$ state can be easily accommodated within the present framework by a minor modification of the short range dynamics.