Search

The nature of the three narrow $P_c$ states, i.e., $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, is under intense discussion since their discovery from the updated analysis by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. \bf{124}, 072001 (2020)] by including the $\Lambda_c\bar{D}^{(*)}$ and $\eta_cp$ as explicitly in addition to the $J/\psi p$, as required by unitarity and heavy quark spin symmetry (HQSS). Since inelastic parameters are very badly constrained by the current data, three schemes are considered: (a) scheme I with pure contact interactions and without the $\Lambda_c\bar D^{(*)}$ interactions, (b) scheme II, where the one-pion exchange is added to scheme I, and (c) scheme III, where the $\Lambda_c \bar D^{(*)}$ are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with $S$-$D$ mixing contact terms. We demonstrate that the experimental data for the $J/\psi p$ invariant mass distribution are consistent with the interpretation of the $P_c(4312)$ and $P_c(4440)/P_c(4457)$ as $\Sigma_c\bar{D}$ and $\Sigma_c \bar{D}^{*}$ hadronic molecules, respectively, and that the data show clear evidence for a new narrow $P_c(4380)$, as a $\Sigma_c^*\bar D$ molecule, which should exist as a consequence of HQSS. While two equally good solutions are found in scheme I, only one of these solutions with the quantum numbers of the $P_c(4440)$ and $P_c(4457)$ being $J^P=3/2^-$ and $1/2^-$, respectively, survives the requirement of regulator independence once the OPE is included. Moreover, we predict the line shapes in the elastic and inelastic channels and demonstrate that those related to the $P_c(4440)$ and the $P_c(4457)$ in the corresponding $\Sigma_c^{(*)}\bar{D}$ and $\eta_cp$ mass distributions allow one to confirm the quantum numbers given above, once the data are available., Comment: 57 pages, 14 figures, and 13 tables

Recently, the LHCb Collaboration reported pronounced structures in the invariant mass spectrum of $J/\ensuremath{\psi}$ pairs produced in proton-proton collisions at the Large Hadron Collider. In this Letter, we argue that the data can be very well described within two variants of a coupled-channel approach employing $T$ matrices consistent with unitarity: (i) with just two channels, $J/\ensuremath{\psi}J/\ensuremath{\psi}$ and $\ensuremath{\psi}(2S)J/\ensuremath{\psi}$, as long as energy-dependent interactions in these channels are allowed, or (ii) with three channels $J/\ensuremath{\psi}J/\ensuremath{\psi}$, $\ensuremath{\psi}(2S)J/\ensuremath{\psi}$, and $\ensuremath{\psi}(3770)J/\ensuremath{\psi}$ with just constant contact interactions. Both formulations hint at the existence of a near-threshold state in the $J/\ensuremath{\psi}J/\ensuremath{\psi}$ system with the quantum numbers ${J}^{PC}={0}^{++}$ or ${2}^{++}$, which we refer to as $X(6200)$. We suggest experimental tests to check the existence of this state and discuss what additional channels need to be studied experimentally to allow for distinctive tests between the two mechanisms proposed. If the molecular nature of $X(6200)$, as hinted by the three-channel approach, is confirmed, many other double-quarkonium states should exist driven by the same binding mechanism. In particular, there should be an ${\ensuremath{\eta}}_{c}{\ensuremath{\eta}}_{c}$ molecule with a similar binding energy.

The dipion transitions $\mathrm{\ensuremath{\Upsilon}}(10860)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\mathrm{\ensuremath{\Upsilon}}(nS)$ ($n=1$, 2, 3) are studied in the framework of a unitary and analytic coupled-channel formalism previously developed for analyzing experimental data on the bottomoniumlike states ${Z}_{b}(10610)$ and ${Z}_{b}(10650)$ [Phys. Rev. D 98, 074023 (2018)] and predicting the properties of their spin partners [Phys. Rev. D 99, 094013 (2019)]. In this work we use a relatively simple but realistic version of this approach, where the scattering and production amplitudes are constructed employing only short-ranged interactions between the open- and hidden-flavor channels consistent with the constraints from heavy quark spin symmetry, for an extended analysis of the experimental line shapes. In particular, the transitions from the $\mathrm{\ensuremath{\Upsilon}}(10860)$ to the final states $\ensuremath{\pi}\ensuremath{\pi}{h}_{b}(mP)$ ($m=1$, 2) and $\ensuremath{\pi}{B}^{(*)}{\overline{B}}^{*}$ already studied before, are now augmented by the $\mathrm{\ensuremath{\Upsilon}}(10860)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\mathrm{\ensuremath{\Upsilon}}(nS)$ final states ($n=1$, 2, 3). This is achieved by employing dispersion theory to account for the final state interaction of the $\ensuremath{\pi}\ensuremath{\pi}$ subsystem including its coupling to the $K\overline{K}$ channel. Fits to the two-dimensional Dalitz plots for the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\mathrm{\ensuremath{\Upsilon}}$ final states were performed. Two real subtraction constants are adjusted to achieve the best description of the Dalitz plot for each $\mathrm{\ensuremath{\Upsilon}}(nS)$ ($n=1$, 2, 3) while all the parameters related to the properties of the ${Z}_{b}\mathrm{s}$ are kept fixed from the previous study. A good overall description of the data for all $\mathrm{\ensuremath{\Upsilon}}(10860)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\mathrm{\ensuremath{\Upsilon}}(nS)$ channels achieved in this work provides additional strong support for the molecular interpretation of the ${Z}_{b}$ states.

We present a comprehensive analysis of the deuteron charge and quadrupole form factors based on the latest two-nucleon potentials and charge density operators derived in chiral effective field theory. The single- and two-nucleon contributions to the charge density are expressed in terms of the proton and neutron form factors, for which the most up-to-date empirical parametrizations are employed. By adjusting the fifth-order short-range terms in the two-nucleon charge density operator to reproduce the world data on the momentum-transfer dependence of the deuteron charge and quadrupole form factors, we predict the values of the structure radius and the quadrupole moment of the deuteron: $r_{\rm str}=1.9729\substack{+0.0015\\ -0.0012}\ \text{fm},\ Q_d=0.2854\substack{+0.0038\\ -0.0017}\ \text{fm}^2. $ A comprehensive and systematic analysis of various sources of uncertainty in our predictions is performed. Following the strategy advocated in our recent publication Phys. Rev. Lett. 124, 082501 (2020), we employ the extracted structure radius together with the accurate atomic data for the deuteron-proton mean-square charge radii difference to update the determination of the neutron charge radius, for which we find: $r_n^2=-0.105\substack{+0.005\\ -0.006} \, \text{fm}^2$. Given the observed rapid convergence of the deuteron form factors in the momentum-transfer range of $Q \simeq 1-2.5$ fm$^{-1}$, we argue that this intermediate-energy domain is particularly sensitive to the details of the nucleon form factors and can be used to test different parametrizations., Comment: 39 pages, 9 figures

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 $\chi_{c1}(3872)$ and $T_{cc}^+$ states supporting the claim that these exotic states have a predominantly molecular nature., Comment: 15 pages, 1 figure

The photoproduction of the $J/\psi$ off the proton is believed to deepen our understanding of various physics issues. On the one hand, it is proposed to provide access to the origin of the proton mass, based on the QCD multipole expansion. On the other hand, it can be employed in a study of pentaquark states. The process is usually assumed to proceed through vector-meson dominance, that is the photon couples to a $J/\psi$ which rescatters with the proton to give the $J/\psi p$ final state. In this Letter, we provide a compelling hint for and propose measurements necessary to confirm a novel production mechanism via the $\Lambda_c \bar D^{(*)}$ intermediate states. In particular, there must be cusp structures at the $\Lambda_c \bar D^{(*)}$ thresholds in the energy dependence of the $J/\psi$ photoproduction cross section. The same mechanism also implies the $J/\psi$-nucleon scattering lengths of order 1 mfm. Given this, one expects only a minor contribution of charm quarks to the nucleon mass., Comment: 6 pages, 5 figures

Recently, the LHCb Collaboration reported pronounced structures in the invariant mass spectrum of J/ψ pairs produced in proton-proton collisions at the Large Hadron Collider. In this Letter, we argue that the data can be very well described within two variants of a coupled-channel approach employing T matrices consistent with unitarity: (i) with just two channels, J/ψJ/ψ and ψ(2S)J/ψ, as long as energy-dependent interactions in these channels are allowed, or (ii) with three channels J/ψJ/ψ, ψ(2S)J/ψ, and ψ(3770)J/ψ with just constant contact interactions. Both formulations hint at the existence of a near-threshold state in the J/ψJ/ψ system with the quantum numbers J^{PC}=0^{++} or 2^{++}, which we refer to as X(6200). We suggest experimental tests to check the existence of this state and discuss what additional channels need to be studied experimentally to allow for distinctive tests between the two mechanisms proposed. If the molecular nature of X(6200), as hinted by the three-channel approach, is confirmed, many other double-quarkonium states should exist driven by the same binding mechanism. In particular, there should be an η_{c}η_{c} molecule with a similar binding energy.

Physical states are characterised uniquely by their pole positions and the corresponding residues. Accordingly, in those parameters also the nature of the states should be encoded. For bound states (poles on the real $s$-axis below the lowest threshold on the physical sheet) there is an established criterion formulated originally by Weinberg in the 1960s, which allows one to estimate the amount of compact and molecular components in a given state. We demonstrate in this paper that this criterion can be straightforwardly extended to shallow virtual states (poles on the real $s$-axis below the lowest threshold on the unphysical sheet) which should be classified as molecular. We argue that predominantly non-molecular or compact states exist either as bound states or as resonances (poles on the unphysical sheet off the real energy axis) but not as virtual states. We also discuss the limitations of the mentioned classification scheme., 12 pages, 8 figures

One-pion exchange defines the longest-range part of the NN interaction, controls the near-threshold energy dependence of the scattering amplitude and imposes correlations between the coefficients in the effective range expansion. These correlations may be regarded as low-energy theorems. We discuss the low-energy theorems for unphysical pion masses and consider various applications to test recent lattice QCD results. In particular, we demonstrate that the binding energies of the deuteron and dineutron obtained by the NPLQCD Collaboration at a pion mass of $M_\pi=450$ MeV are inconsistent with the low-energy behavior of the corresponding phase shifts within the quoted uncertainties. Using the binding energies of the deuteron and dineutron as input, we employ the low-energy theorems to predict the phase shifts and extract the scattering length and the effective range in the ${}^3S_1$ and ${}^1S_0$ channels.

Three hidden-charm pentaquark ${P}_{c}$ states, ${P}_{c}(4312)$, ${P}_{c}(4440)$, and ${P}_{c}(4457)$ were revealed in the ${\mathrm{\ensuremath{\Lambda}}}_{b}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}p{K}^{\ensuremath{-}}$ process measured by LHCb using both run I and run II data. Their nature is under lively discussion, and their quantum numbers have not been determined. We analyze the $J/\ensuremath{\psi}p$ invariant mass distributions under the assumption that the crossed-channel effects provide a smooth background. For the first time, such an analysis is performed employing a coupled-channel formalism with the scattering potential involving both one-pion exchange as well as short-range operators constrained by heavy quark spin symmetry. We find that the data can be well described in the hadronic molecular picture, which predicts seven ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{\overline{D}}^{(*)}$ molecular states in two spin multiplets, such that the ${P}_{c}(4312)$ is mainly a ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}$ bound state with ${J}^{P}=1/{2}^{\ensuremath{-}}$, while ${P}_{c}(4440)$ and ${P}_{c}(4457)$ are ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ bound states with quantum numbers $3/{2}^{\ensuremath{-}}$ and $1/{2}^{\ensuremath{-}}$, respectively. We also show that there is evidence for a narrow ${\mathrm{\ensuremath{\Sigma}}}_{c}^{*}\overline{D}$ bound state in the data which we call ${P}_{c}(4380)$, different from the broad one reported by LHCb in 2015. With this state included, all predicted ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}$, ${\mathrm{\ensuremath{\Sigma}}}_{c}^{*}\overline{D}$, and ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ hadronic molecules are seen in the data, while the missing three ${\mathrm{\ensuremath{\Sigma}}}_{c}^{*}{\overline{D}}^{*}$ states are expected to be found in future runs of the LHC or in photoproduction experiments.

Three hidden-charm pentaquark P_{c} states, P_{c}(4312), P_{c}(4440), and P_{c}(4457) were revealed in the Λ_{b}^{0}→J/ψpK^{-} process measured by LHCb using both run I and run II data. Their nature is under lively discussion, and their quantum numbers have not been determined. We analyze the J/ψp invariant mass distributions under the assumption that the crossed-channel effects provide a smooth background. For the first time, such an analysis is performed employing a coupled-channel formalism with the scattering potential involving both one-pion exchange as well as short-range operators constrained by heavy quark spin symmetry. We find that the data can be well described in the hadronic molecular picture, which predicts seven Σ_{c}^{(*)}D[over ¯]^{(*)} molecular states in two spin multiplets, such that the P_{c}(4312) is mainly a Σ_{c}D[over ¯] bound state with J^{P}=1/2^{-}, while P_{c}(4440) and P_{c}(4457) are Σ_{c}D[over ¯]^{*} bound states with quantum numbers 3/2^{-} and 1/2^{-}, respectively. We also show that there is evidence for a narrow Σ_{c}^{*}D[over ¯] bound state in the data which we call P_{c}(4380), different from the broad one reported by LHCb in 2015. With this state included, all predicted Σ_{c}D[over ¯], Σ_{c}^{*}D[over ¯], and Σ_{c}D[over ¯]^{*} hadronic molecules are seen in the data, while the missing three Σ_{c}^{*}D[over ¯]^{*} states are expected to be found in future runs of the LHC or in photoproduction experiments.

We present a high-accuracy calculation of the deuteron structure radius in chiral effective field theory. Our analysis employs the state-of-the-art semilocal two-nucleon potentials and takes into account two-body contributions to the charge density operators up to fifth order in the chiral expansion. The strength of the fifth-order short-range two-body contribution to the charge density operator is adjusted to the experimental data on the deuteron charge form factor. A detailed error analysis is performed by propagating the statistical uncertainties of the low-energy constants entering the two-nucleon potentials and by estimating errors from the truncation of the chiral expansion as well as from uncertainties in the nucleon form factors. Using the predicted value for the deuteron structure radius together with the very accurate atomic data for the difference of the deuteron and proton charge radii we, for the first time, extract the charge radius of the neutron from light nuclei. The extracted value reads $r_n^2 = - 0.106 \substack{ +0.007\\ -0.005\\} \, \text{fm}^2$ and its magnitude is about $1.7\sigma$ smaller than the current value given by the Particle Data Group. In addition, given the high accuracy of the calculated deuteron charge form factor and its careful and systematic error analysis, our results open the way for an accurate determination of the nucleon form factors from elastic electron-deuteron scattering data measured at the Mainz Microtron and other experimental facilities., Comment: 5 pages, 1 figure, supplementary material available in source package

In a recent paper [Phys. Rev. D 98, 074023 (2018)], the most up-to-date experimental data for all measured production and decay channels of the bottomoniumlike states ${Z}_{b}(10610)$ and ${Z}_{b}(10650)$ were analyzed in a field-theoretical coupled-channel approach which respects analyticity and unitarity and incorporates both the pion exchange and a short-ranged potential nonperturbatively. All parameters of the interaction were fixed directly from data, and pole positions for both ${Z}_{b}$ states were determined. In this work we employ the same approach to predict in a parameter-free way the pole positions and the line shapes in the elastic and inelastic channels of the (still to be discovered) spin partners of the ${Z}_{b}$ states. They are conventionally referred to as ${W}_{bJ}$'s with the quantum numbers ${J}^{PC}={J}^{++}$ ($J=0$, 1, 2). It is demonstrated that the results of our most advanced pionful fit, which gives the best ${\ensuremath{\chi}}^{2}/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ for the data in the ${Z}_{b}$ channels, are consistent with all ${W}_{bJ}$ states being above-threshold resonances which manifest themselves as well-pronounced hump structures in the line shapes. On the contrary, in the pionless approach, all ${W}_{bJ}$'s are virtual states which can be seen as enhanced threshold cusps in the inelastic line shapes. Since the two above scenarios provide different imprints on the observables, the role of the one-pion exchange in the ${B}^{(*)}{\overline{B}}^{(*)}$ systems can be inferred from the once available experimental data directly.

We study baryon-baryon scattering by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. We derive the corresponding diagrammatic rules paying special attention to complications caused by momentum-dependent interactions and propagators of particles with non-zero spin. We define the effective potential as a sum of two-baryon irreducible contributions of time-ordered diagrams and derive a system of integral equations for the scattering amplitude, which provides a coupled-channel generalization of the Kadyshevsky equation. The obtained leading-order baryon-baryon potentials are perturbatively renormalizable, and the corresponding integral equations have unique solutions in all partial waves. We discuss the issue of additional finite subtractions required to improve the ultraviolet convergence of (finite) loop integrals on the example of nucleon-nucleon scattering in the $^3P_0$ partial wave. Assuming that corrections beyond leading order can be treated perturbatively, we obtain a fully renormalizable formalism which can be employed to study baryon-baryon scattering., 13 pages, 4 figures, final version published in Phys. Lett. B

The possibility for a common effective field theory for hadronic molecules with different heavy-quark flavours is examined critically. It is argued that such a theory does not allow one to draw definite conclusions for doubly heavy molecules. In particular, it does not allow one to relate binding energies for the molecules in the c-quark and b-quark sectors with controlled uncertainties. Therefore, while this kind of reasoning does not preclude from employing heavy-quark spin symmetry for charmonium- and bottomonium-like states separately within a well established effective field theory framework, relations between different heavy-quark sectors can only be obtained using phenomenological approaches with uncontrolled uncertainties., Comment: 7 pages, extended discussions, added references, version to appear in Eur. Phys. J. C

The experimental line shapes available in the B$ \bar {B} $*, B*$ \bar {B} $*, hb(1P)π and hb(2P)π channels are analysed using a theoretical EFT-based framework manifestly consistent with unitarity and analyticity. The line shapes are calculated using a system of coupled channel integral equations with the potential consisting of the one-pion and one-eta meson exchange interactions from the lightest Goldstone boson octet as well as of several contact terms at leading and subleading orders which are adjusted to minimise the overall chi squared. The pole positions of the Zb(10610) and Zb(10650) are extracted for the best fits corresponding to χ2/d.o.f. of the order of one.

Two-photon decays of a tensor D∗D¯∗ molecule are studied and the suggested approach is applied to the X(3915) charmonium-like state under the assumption of the latter being a 2++ molecule — a spin partner of the X(3872). It is argued that the existing experimental data disfavour such an identification of this state. Therefore, it is suggested that either the X(3915) has a different exotic nature or it has to be identified as a scalar.

Heavy-quark spin-symmetry (HQSS) partners of the isovector bottomonium like states Zb(10610) and Zb(10650) are predicted within the molecular picture. Treating both Zb’s as shallow bound states, we solve the system of coupled-channel integral equations for the contact plus one-pion exchange (OPE) potentials to predict the location of the partner states with the quantum numbers J++ (J = 0,1,2). In particular, we predict the existence of a narrow tensor 2++ state residing a few MeV below the B∗ B¯∗ threshold. It is emphasised that the tensor part of the OPE potential in combination with HQSS breaking due to the nonvanishing B∗ -B mass splitting has a significant impact on the location of this partner state.

The most recent experimental data for all measured production and decay channels of the bottomoniumlike states ${Z}_{b}(10610)$ and ${Z}_{b}(10650)$ are analyzed simultaneously using solutions of the Lippmann-Schwinger equations which respect constraints from unitarity and analyticity. The interaction potential in the open-bottom channels ${B}^{(*)}{\overline{B}}^{*}+\mathrm{c}.\mathrm{c}.$ contains short-range interactions as well as a 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 cutoff. 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 $B{\overline{B}}^{*}/\overline{B}{B}^{*}$ threshold while the ${Z}_{b}(10650)$ state most likely is a shallow state located just above the ${B}^{*}{\overline{B}}^{*}$ threshold.

Implications of heavy-quark spin-symmetry are investigated for the isoscalar charmonium-like state $X(3872)$ and the isovector bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ under the assumption of the latter being bound states of the nearby heavy meson-antimeson pairs. We formulate and solve a system of the integral equations for a coupled-channel problem involving the $P\bar P$, $P\bar V$, and $V\bar V$ channels (with $P$ and $V$ being either $D$ and $D^*$ or $B$ and $B^*$ mesons) to determine the scattering amplitudes in the channels with the quantum numbers $J^{PC} = 1^{++}, 1^{+-}, 0^{++}$, and $2^{++}$. The coupled-channel potentials incorporate the contact and one-pion exchange interactions derived in a chiral effective field theory approach and iterated to all orders. Once two contact terms at leading order are adjusted to reproduce the binding energies of the states used as input, the approach can be employed to predict the mass and the prominent contributions to the width of the spin-partner states with the quantum numbers $J^{++}$ ($J=0,1,2$).

Antikaon-deuteron scattering is studied at low energies within the non-relativistic effective field theory (EFT) approach. The largest contribution to the \(\bar K d\) scattering length stems from the multiple scattering series with infinitely heavy (static) nucleons. While the leading static contribution is inherently non-perturbative and requires resummation, the correction to the scattering length due to the nucleon recoil (retardation) effect is amenable to the perturbative treatment with respect to the small parameter ξ=MK/mN. The first order correction to the K−d scattering length due to single insertion of the retardation term in the multiple-scattering series is calculated. The leading recoil effect turns out to be reasonably small and contributes less than 10 % to the scattering length.

We study the implications of the heavy-quark spin symmetry for the possible spin partners of the exotic states $Z_b(10610)$ and $Z_b(10650)$ in the spectrum of bottomonium. We formulate and solve numerically the coupled-channel equations for the $Z_b$ states that allow for a dynamical generation of these states as hadronic molecules. The force includes short-range contact terms and the one-pion exchange potential, both treated fully nonperturbatively. The strength of the potential at leading order is fixed completely by the pole positions of the $Z_b$ states such that the mass and the most prominent contributions to the width of the isovector heavy-quark spin partner states $W_{bJ}$ with the quantum numbers $J^{++}$ ($J=0,1,2$) come out as predictions. Since the accuracy of the present experimental data does not allow one to fix the pole positions of the $Z_b$'s reliably enough, we also study the pole trajectories of their spin partner states as functions of the $Z_b$ binding energies. It is shown that, once the heavy-quark spin symmetry is broken by means of the physical $B$ and $B^*$ masses, especially the pion tensor force has a significant impact on the location of the partner states clearly demonstrating the need of a coupled-channel treatment of pion dynamics to understand the spin multiplet pattern of hadronic molecules., 21 pages, 5 figures, 1 table

It has been proposed recently (Phys. Rev. Lett. 115 (2015), 022001) that the charmoniumlike state named X(3915) and suggested to be a $0^{++}$ scalar, is just the helicity-0 realisation of the $2^{++}$ tensor state $\chi_{c2}(3930)$. This scenario would call for a helicity-0 dominance, which were at odds with the properties of a conventional tensor charmonium, but might be compatible with some exotic structure of the $\chi_{c2}(3930)$. In this paper, we investigate, if such a scenario is compatible with the assumption that the $\chi_{c2}(3930)$ is a $D^*\bar D^*$ molecular state - a spin partner of the $X(3872)$ treated as a shallow bound state. We demonstrate that for a tensor molecule the helicity-0 component vanishes for vanishing binding energy and accordingly for a shallow bound state a helicity-2 dominance would be natural. However, for the $\chi_{c2}(3930)$, residing about 100 MeV below the $D^*\bar D^*$ threshold, there is no a priori reason for a helicity-2 dominance and thus the proposal formulated in the above mentioned reference might indeed point at a molecular structure of the tensor state. Nevertheless, we find that the experimental data currently available favour a dominant contribution of the helicity-2 amplitude also in this scenario, if spin symmetry arguments are employed to relate properties of the molecular state to those of the X(3872). We also discuss what research is necessary to further constrain the analysis., Comment: LaTeX2e, 23 pages, 2 figures, version to appear in JHEP

The heavy-quark spin symmetry (HQSS) partners of the X(3872) molecule are investigated in a chiral effective field theory (EFT) approach which incorporates contact and one-pion exchange interactions. The integral equations of the Lippmann-Schwinger type are formulated and solved for the coupled-channel problem for the DD , DD *, and D*D * systems with the quantum numbers J PC = 1 ++ , 1+− , 0 ++ , and 2 ++ . We confirm that, if the X (3872) is a 1 ++ DD * molecular state then, in the strict heavy-quark limit, there exist three partner states, with the quantum numbers 1 +− , 0 ++ , and 2 ++ , which are degenerate in mass. At first glance, this result looks natural only for the purely contact pionless theory since pions contribute differently to different transition potentials and, therefore, may lift the above degeneracy. Nevertheless, it is shown that, by an appropriate unitary transformation, the Lippmann-Schwinger equation in each channel still can be brought to a block-diagonal form, with the same blocks for all quantum numbers, so that the degeneracy of the bound states in different channels is preserved. We stress that neglecting some of the coupled-channel transitions in an inconsistent manner leads to a severe violation of HQSS and yields regulator-dependent results for the partner states. The effect of HQSS violation in combination with nonperturbative pion dynamics on the pole positions of the partner states is discussed.

The most recent experimental data for the decays of the vector bottomonium γ(10860) proceeding through the formation of the states Zb(10610) and Zb(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^*} $ contains short-range interactions as well as the one-pion exchange; both types of the interaction are taken into account fully nonperturbatively. This way, all parameters of the interaction are fixed directly from the data and the pole positions for the Zb’s are determined as a prediction. In particular, both Zb states are found to be described by resonance poles located on the unphysical Riemann sheets in the vicinity of the corresponding thresholds. The heavy quark spin symmetry (HQSS) is employed to predict, in a parameter-free way, the pole positions and the line shapes in the elastic and inelastic channels for the Zbs’ spin partner states WbJ with the quantum numbers J++ (J = 0, 1, 2). Such spin partners can be produced in radiative decays of the vector bottomonium Υ(10860) and are expected to be detected in the Belle-II experiment.

We explore the quark-mass dependence of the pole position of the X ( 3872 ) state within the molecular picture. The calculations are performed within the framework of a nonrelativistic Faddeev-type three-body equation for the D D ¯ π system in the J P C = 1 + + channel. The πD interaction is parametrised via a D ⁎ pole, and a three-body force is included to render the equations well defined. Its strength is adjusted such that the X ( 3872 ) appears as a D D ¯ ⁎ bound state 0.5 MeV below the neutral threshold. We find that the trajectory of the X ( 3872 ) depends strongly on the assumed quark-mass dependence of the short-range interactions which can be determined in future lattice QCD calculations. At the same time we are able to provide nontrivial information on the chiral extrapolation in the X channel.

The low-energy theorems (LET) for NN scattering provide important relations between the coefficients in the effective-range expansion (ERE) of the amplitude, which are governed by the long-range part of the potential. In this work we extend the LET to the case of unphysical pion masses. It is emphasized that correlations provided by LET can be used as nontrivial consistency checks for lattice calculations. As an example, we use the Mπ dependence of the effective range suggested in the recent lattice study by NPLQCD collaboration [1] as input to predict the Mπ dependence of the binding energy and the shape parameters.

We apply the low-energy theorems to analyze the recent lattice QCD results for the two-nucleon system at a pion mass of ${M}_{\ensuremath{\pi}}\ensuremath{\simeq}450$ MeV obtained by the NPLQCD Collaboration. We find that the binding energies of the deuteron and dineutron are inconsistent with the low-energy behavior of the corresponding phase shifts within the quoted uncertainties and vice versa. Using the binding energies of the deuteron and dineutron as input, we employ the low-energy theorems to predict the phase shifts and extract the scattering length and the effective range in the $^{3}S_{1}$ and $^{1}S_{0}$ channels. Our results for these quantities are consistent with those obtained by the NPLQCD Collaboration from effective field theory analyses but are in conflict with their determination based on the effective-range approximation.

The reaction $NN \to NN \pi$ offers a good testing ground for chiral effective field theory at intermediate energies. It challenges our understanding of the first inelastic channel in nucleon-nucleon scattering and of the charge-symmetry breaking pattern in hadronic reactions. In our previous studies, we presented a complete calculation of the pion-production operator for s-wave pions up-to-and-including next-to-next-to-leading order (NNLO) in the formulation of chiral effective field theory, which includes pions, nucleons and $\Delta(1232)$ degrees of freedom. In this paper we calculate the near threshold cross section for the $pp \to d \pi^{+}$ reaction by performing the convolution of the obtained operators with nuclear wave functions based on modern phenomenological and chiral potentials. The available chiral $NN$ wave functions are constructed with a cutoff comparable with the momentum transfer scale inherent in pion production reactions. Hence, a significant portion of the dynamical intermediate-range physics is thereby cut off by them. On the other hand, the NNLO amplitudes evaluated with phenomenological wave functions appear to be largely independent of the $NN$ model used and give corrections to the dominant leading order contributions as expected from dimensional analysis. The result gives support to the counting scheme used to classify the pion production operators, which is a precondition for a reliable investigation of the chirally suppressed neutral pion production. The explicit inclusion of the $\Delta(1232)$ is found to be important but smaller than expected due to cancellations., Comment: 25 pages, 7 figures, 2 tables

Chiral extrapolations of the binding energy of the X (3872) molecular state are investigated using an explicitly renormalizable framework free of finite cut-off artefacts. Insights into the binding mechanisms are discussed: if the X is less bound with the growing pion mass, its binding energy is governed by the explicit pion mass dependence from one-pion exchange; an opposite behaviour would indicate the importance of the pionmass dependent short-range interactions, in addition to pionic effects. The important role of the three-body DDπ dynamics is emphasised.

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., 17 pages, 3 figures, 1 table, version published in Phys.Lett.B

The differential cross section d σ / d Ω and analysing power A y of the p → p → { p p } s π 0 reaction have been measured at COSY-ANKE at 353 MeV. The final proton pair was detected at very low excitation energy, leading to an S -wave diproton, denoted here as { p p } s . The angular dependence of both d σ / d Ω and A y can be described in terms of s - and d -wave pion production. By using phase information from elastic pp scattering, unique solutions are derived for the corresponding amplitudes only as a result of the combined analysis of both experimental observables. The large d -wave term thus obtained is important for the tests of the current state-of-the-art chiral perturbation theory approach. The amplitudes will also help towards determining the isospin dependence of pion production in nucleon–nucleon collisions with diproton formation.

In order to test chiral perturbation theory and establish links between p-wave pion production in nucleon–nucleon collisions and low energy three-nucleon scattering, an extensive programme of experiments on pion production is currently underway at COSY-ANKE. The final proton pair is measured at very low excitation energy, leading to an S-wave diproton, denoted here as {pp}s. By using a deuterium target we have obtained data on the differential cross section and analysing power of the quasi-free p→n→{pp}sπ− reaction at 353 MeV. The spectator proton psp was either measured directly in silicon tracking telescopes or reconstructed using the momentum of a detected π−. Both observables can be described in terms of s-, p-, and d-wave pion production amplitudes. Taken together with the analogous data on the p→p→{pp}sπ0 reaction, full partial wave decompositions of both processes were carried out.

We present a calculation of the π − d scattering length with an accuracy of a few percent using chiral perturbation theory. For the first time isospin-violating corrections are included consistently. Using data on pionic deuterium and pionic hydrogen atoms, we extract the isoscalar and isovector pion–nucleon scattering lengths and obtain a + = ( 7.6 ± 3.1 ) ⋅ 10 − 3 M π − 1 and a − = ( 86.1 ± 0.9 ) ⋅ 10 − 3 M π − 1 . Via the Goldberger–Miyazawa–Oehme sum rule, this leads to a charged-pion–nucleon coupling constant g c 2 / 4 π = 13.69 ± 0.20 .

We perform a complete calculation of charge symmetry breaking effects for the reaction p n → d π 0 at leading order in chiral perturbation theory. A new leading-order operator is included. From our analysis we extract δ m N str , the strong contribution to the neutron–proton mass difference. The value obtained, δ m N str = ( 1.5 ± 0.8 (exp.) ± 0.5 (th.) ) MeV , is consistent with the result based on the Cottingham sum rule. This agreement provides a non-trivial test of our current understanding of the chiral structure of QCD.

The effect of the nucleon recoil for antikaon-deuteron scattering is studied in the framework of effective field theory. In particular, we performed a calculation of the nucleon recoil effect for the double scattering process. It is shown that the leading correction to the static term that emerges at order ξ1/2, where ξ = mK/MN, vanishes due to a complete cancellation of individually large terms. The resulting recoil effect for the double scattering process is found to be of order of 10–15% compared to the static term. We also developed a method to include the nucleon recoil effect in the calculation of the multiple scattering diagrams.

We investigate the role of the delta isobar in the reaction π d → π d at threshold in chiral effective field theory. We discuss the corresponding power counting and argue that this calculation completes the evaluation of diagrams up to the order χ 3 / 2 , with χ the ratio of the pion to the nucleon mass. The net effect of all delta contributions at this order to the pion–deuteron scattering length is δ a π d Δ = ( 2.4 ± 0.4 ) × 10 −3 m π −1 .

In a recent paper Phys.Rev.Lett. 111, 042002 (2013) (arXiv:1304.0846), the charmonium state X(3872) is studied in the framework of an effective field theory. In that work it is claimed that (i) the one-pion exchange (OPE) alone provides sufficient binding to produce the X as a shallow bound state at the $D^0\bar{D}^{*0}$ threshold, (ii) short-range dynamics (described by a contact interaction) provides only moderate corrections to the OPE, and (iii) the X-pole disappears as the pion mass is increased slightly and therefore the X should not be seen on the lattice, away from the pion physical mass point, if it were a molecular state. In this paper we demonstrate that the results of Phys.Rev.Lett. 111, 042002 (2013) (arXiv:1304.0846) suffer from technical as well as conceptual problems and therefore do not support the conclusions drawn by the authors.

Chiral extrapolation of the $X(3872)$ binding energy is investigated using the modified Weinberg formulation of chiral effective field theory for the $D \bar{D}^*$ scattering. Given its explicit renormalisability, this approach is particularly useful to explore the interplay of the long- and short-range $D \bar{D}^*$ forces in the $X(3872)$ from studying the light-quark (pion) mass dependence of its binding energy. In particular, the parameter-free leading-order calculation shows that the $X$-pole disappears for unphysical large pion masses. On the other hand, without contradicting the naive dimensional analysis, the higher-order pion-mass-dependent contact interaction can change the slope of the binding energy at the physical point yielding the opposite scenario of a stronger bound $X$ at pion masses larger than its physical value. An important role of the pion dynamics and of the 3-body $D\bar{D}\pi$ effects for chiral extrapolations of the $X$-pole is emphasised. The results of the present study should be of practical value for the lattice simulations since they provide a non-trivial connection between lattice points at unphysical pion masses and the physical world., Comment: 24 pages, 4 figures

The longest-range part of the nuclear force due to the one-pion exchange governs the energy dependence of the scattering amplitude in the near-threshold region and imposes correlations between the coefficients in the effective range expansion. These correlations may be regarded as low-energy theorems and are known to hold to a high accuracy in the neutron-proton 3S1 partial wave. We generalize the low-energy theorems to the case of unphysical pion masses and provide results for the correlations between the coefficients in the effective range expansion in this partial wave for pion masses up to Mpi ~ 400 MeV. We discuss the implications of our findings for the available and upcoming lattice-QCD simulations of two-nucleon observables., Comment: 17 pages, 7 figures, 3 tables