arXiv subjects
Publications and source records attributed to E. Epelbaum.
We offer a brief response to the criticism put forward by Pavon Valderrama about our recent paper on "How (not) to renormalize integral equations with singular potentials in effective field theory".
Recently, we have shown that the continuity equation for the nuclear vector and axial current operators acquires additional terms if the latter depend on the energy transfer. We analyze in detail the electromagnetic single-nucleon four-current operators and verify the validity of the modified continuity equation for all one- and two-nucleon contributions up to fourth order in the chiral expansion. We also derive, for the first time, the leading contribution to the three-nucleon charge operator which appears at this order. Our study completes the derivation of the electroweak nuclear currents to fourth order in the chiral expansion.
In a recent paper Phys.Rev. D98, 074023 (2018), the most up-to-date experimental data for all measured production and decay channels of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ were analysed in a field-theoretical coupled-channel approach which respects analyticity and unitarity and incorporates both the pion exchange as well as 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 $χ^2/{\rm d.o.f.}$ 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 $B^{(*)}\bar{B}^{(*)}$ systems can be inferred from the once available experimental data directly.
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.
We discuss the connection between the perturbative and non-perturbative renormalization and related conceptual issues in the few-nucleon sector of the low-energy effective field theory of the strong interactions. General arguments are supported by examples from effective theories with and without pions as dynamical degrees of freedom. A quantum mechanical potential with explicitly specified short- and long-range parts is considered as an "underlying fundamental theory" and the corresponding effective field theory potential is constructed. Further, the problem of the effective field theoretical renormalization of the Skornyakov-Ter-Martyrosian equation is revisited.
We present a complete calculation of nucleon-deuteron scattering as well as ground and low-lying excited states of light nuclei in the mass range A=3-16 up through next-to-next-to-leading order in chiral effective field theory using semilocal coordinate-space regularized two- and three-nucleon forces. It is shown that both of the low-energy constants entering the three-nucleon force at this order can be reliably determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. The inclusion of the three-nucleon force is found to improve the agreement with the data for most of the considered observables.
We analyze the longest-range two-pion exchange contributions to the three-nucleon force at leading-loop order in the framework of heavy-baryon chiral effective field theory with explicit $Δ(1232)$ degrees of freedom. All relevant low-energy constants which appear in the calculation are determined from pion-nucleon scattering. Comparing our results with the ones obtained in the $Δ$-less theory at N4LO, we find effects of the $Δ$ isobar for this particular topology to be rather well represented in terms of resonance saturation of various low-energy constants in the $Δ$-less approach.
We employ a variety of ab initio methods including Faddeev-Yakubovsky equations, No-Core Configuration Interaction Approach, Coupled-Cluster Theory and In-Medium Similarity Renormalization Group to perform a comprehensive analysis of the nucleon-deuteron elastic and breakup reactions and selected properties of light and medium-mass nuclei up to 48Ca using the recently constructed semilocal coordinate-space regularized chiral nucleon-nucleon potentials. We compare the results with those based on selected phenomenological and chiral EFT two-nucleon potentials, discuss the convergence pattern of the chiral expansion and estimate the achievable theoretical accuracy at various chiral orders using the novel approach to quantify truncation errors of the chiral expansion without relying on cutoff variation. We also address the robustness of this method and explore alternative ways to estimate the theoretical uncertainty from the truncation of the chiral expansion.
We introduce new semilocal two-nucleon potentials up to fifth order in the chiral expansion. We employ a simple regularization approach for the pion-exchange contributions which (i) maintains the long-range part of the interaction, (ii) is implemented in momentum space and (iii) can be straightforwardly applied to regularize many-body forces and current operators. We discuss in detail the two-nucleon contact interactions at fourth order and demonstrate that three terms out of fifteen used in previous calculations can be eliminated via suitably chosen unitary transformations. The removal of the redundant contact terms results in a drastic simplification of the fits to scattering data and leads to interactions which are much softer (i.e. more perturbative) than our recent semilocal coordinate-space regularized potentials. Using the pion-nucleon low-energy constants from matching pion-nucleon Roy-Steiner equations to chiral perturbation theory, we perform a comprehensive analysis of nucleon-nucleon scattering and the deuteron properties up to fifth chiral order and study the impact of the leading F-wave two-nucleon contact interactions which appear at sixth order. The resulting chiral potentials lead to an outstanding description of the proton-proton and neutron-proton scattering data from the self-consistent Granada-2013 database below the pion production threshold, which is significantly better than for any other chiral potential. For the first time, the chiral potentials match in precision and even outperform the available high-precision phenomenological potentials, while the number of adjustable parameters is, at the same time, reduced by about ~40%. Last but not least, we perform a detailed error analysis and, in particular, quantify for the first time the statistical uncertainties of the fourth- and the considered sixth-order contact interactions.
The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an illustration, a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained. The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed.
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.
We compare the subtractive renormalization and the Wilsonian renormalization group approaches in the context of an effective field theory for the two-nucleon system. Based on an exactly solvable model of contact interactions, we observe that the standard Wilsonian renormalization group approach with a single cutoff parameter does not cover the whole space spanned by the renormalization scale parameters of the subtractive formalism. In particular, renormalization schemes corresponding to Weinberg's power counting in the case of an unnaturally large scattering length are beyond the region covered by the Wilsonian renormalization group approach. In the framework of pionless effective field theory, also extended by the inclusion of a long-range interaction of separable type, we demonstrate that Weinberg's power counting scheme is consistent in the sense that it leads to a systematic order-by-order expansion of the scattering amplitude.
Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion-nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the $Δ(1232)$ as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the $Δ$ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the $Δ$-less theory the resummation of $1/m_N$ corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation.
We consider renormalization of the three-body scattering problem in low-energy effective field theory of self-interacting scalar particles by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation. The obtained leading-order equation is perturbatively renormalizable and non-perturbatively finite and does not require a three-body counter term in contrast to its non-relativistic approximation.
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.
We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of the continuity equation.
The recently developed semi-local improved chiral nucleon-nucleon interaction is used for the first time to study several electromagnetic and weak processes at energies below the pion production threshold. Cross sections and selected polarization observables for deuteron photodisintegration, nucleon-deuteron radiative capture, three-body $^3$He photodisintegration as well as capture rates for decays of the muonic $^2$H and $^3$He atoms are calculated. The Lippmann-Schwinger and Faddeev equations in momentum space are solved to obtain nuclear states. The electromagnetic current operator is taken as a single nucleon current supplemented by many-body contributions induced via the Siegert theorem. For muon capture processes the nonrelativistic weak current together with the dominant relativistic corrections is used. Our results compare well with experimental data, demonstrating the same quality as is observed for the semi-phenomenological AV18 potential. Compared to the older version of the chiral potential with a nonlocal regularization, a much smaller cut-off dependence is found for the state-of-art chiral local interaction employed in this paper. Finally, estimates of errors due to the truncation of the chiral expansion are given.
We consider the nucleon-nucleon scattering problem by applying time-ordered perturbation theory to the Lorentz invariant formulation of baryon chiral perturbation theory. Using a symmetry preserving higher derivative form of the effective Lagrangian, we exploit the freedom of the choice of the renormalization condition and obtain an integral equation for the scattering amplitude with an improved ultraviolet behavior. The resulting formulation is used to quantify finite regulator artifacts in two-nucleon phase shifts as well as in the chiral extrapolations of the S-wave scattering lengths and the deuteron binding energy. This approach can be straightforwardly extended to analyze few-nucleon systems and processes involving external electroweak sources.