Hadron–hadron interactions from imaginary-time Nambu–Bethe–Salpeter wave function on the lattice
TL;DR: In this paper, the Nambu-Bethe-Salpeter wave function was used to extract non-local hadron-hadron potential and phase shift in the S 0 1 channel.
About: This article is published in Physics Letters B.The article was published on 2012-06-12 and is currently open access. It has received 186 citations till now. The article focuses on the topics: Lattice QCD & Scattering length.
Citations
More filters
01 Jan 1990
TL;DR: In this paper, a method to calculate the elastic scattering amplitude at low energies in two-dimensional quantum field theories is proposed and tested in a numerical simulation of the 0(3) non-linear if-model on a simple square lattice.
Abstract: A method to calculate the elastic scattering amplitude at low energies in two-dimensional quantum field theories is proposed and tested in a numerical simulation of the 0(3) non-linear if-model on a simple square lattice. We also compute the isospin current form factor in this model and compare our results with the known exact expressions for the S-matrix and the form factor in the continuum limit. As a technical improvement, we introduce a two-cluster simulation algorithm which leads to significantly reduced statistical errors in the calculation of four-point correlation functions.
430 citations
TL;DR: In the last decade, there has been an explosion of data from both e+e− and hadron colliders, and many recently observed states that do not fit into this picture are called generically "exotics" as discussed by the authors.
428 citations
Ludwig Maximilian University of Munich1, Technische Universität München2, Russian Academy of Sciences3, Novosibirsk State University4, Budker Institute of Nuclear Physics5, Forschungszentrum Jülich6, National Research Nuclear University MEPhI7, Moscow Institute of Physics and Technology8, Fudan University9, Beihang University10, University of Cambridge11, Chinese Academy of Sciences12
TL;DR: A review of the progress in the field of exotic $XYZ$ hadrons can be found in this article, with a summary on future prospects and challenges, as well as a survey of the current state-of-the-art.
Abstract: The quark model was formulated in 1964 to classify mesons as bound states made of a quark-antiquark pair, and baryons as bound states made of three quarks. For a long time all known mesons and baryons could be classified within this scheme. Quantum Chromodynamics (QCD), however, in principle also allows the existence of more complex structures, generically called exotic hadrons or simply exotics. These include four-quark hadrons (tetraquarks and hadronic molecules), five-quark hadrons (pentaquarks) and states with active gluonic degrees of freedom (hybrids), and even states of pure glue (glueballs). Exotic hadrons have been systematically searched for in numerous experiments for many years. Remarkably, in the past fifteen years, many new hadrons that do not exhibit the expected properties of ordinary (not exotic) hadrons have been discovered in the quarkonium spectrum. These hadrons are collectively known as $XYZ$ states. Some of them, like the charged states, are undoubtedly exotic. Parallel to the experimental progress, the last decades have also witnessed an enormous theoretical effort to reach a theoretical understanding of the $XYZ$ states. Theoretical approaches include not only phenomenological extensions of the quark model to exotics, but also modern non-relativistic effective field theories and lattice QCD calculations. The present work aims at reviewing the rapid progress in the field of exotic $XYZ$ hadrons over the past few years both in experiments and theory. It concludes with a summary on future prospects and challenges.
298 citations
TL;DR: In this paper, the authors review progress in the study of few-hadron reactions in which resonances and bound states appear using lattice QCD techniques and present a leading approach that takes advantage of the periodic finite spatial volume used in lattice-QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box.
Abstract: The vast majority of hadrons observed in nature are not stable under the strong interaction; rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy nonperturbative region, and in addition many probes of the limits of the electroweak sector of the standard model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required nonperturbative evaluation of hadron observables. This article reviews progress in the study of few-hadron reactions in which resonances and bound states appear using lattice QCD techniques. The leading approach is described that takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. An explanation is given of how from explicit lattice QCD calculations one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. The challenges which currently limit the field are discussed along with the steps being taken to resolve them.
269 citations
Cites methods from "Hadron–hadron interactions from ima..."
...Lastly we consider the potential method, which has been championed by the HAL QCD collaboration (Aoki et al., 2012a, 2010, 2013; Ishii et al., 2012, 2007)....
[...]
TL;DR: In the last decade, there has been an explosion of data from both $e^+e^-$ and hadron colliders and there are many recently observed states that do not fit into this picture as mentioned in this paper.
Abstract: For many decades after the invention of the quark model in 1964 there was no evidence that hadrons are formed from anything other than the simplest pairings of quarks and antiquarks, mesons being formed of a quark-antiquark pair and baryons from three quarks. In the last decade, however, in an explosion of data from both $e^+e^-$ and hadron colliders, there are many recently observed states that do not fit into this picture. These new particles are called generically "exotics". They can be either mesons or baryons. Remarkably, they all decay into at least one meson formed of either a $c\overline{c}$ or $b\overline{b}$ pair. In this review, after the introduction, we explore each of these new discoveries in detail first from an experimental point of view, then subsequently give a theoretical discussion. These exotics can be explained if the new mesons contain two-quarks and two-antiquarks (tetraquarks), while the baryons contain four-quarks plus an antiquark (pentquarks). The theoretical explanations for these states take three divergent tracks: tightly bound objects, just as in the case of normal hadrons, but with more constituents, or loosely bound "molecules" similar to the deuteron, but formed from two mesons, or a meson or baryon, or more wistfully, they are not multiquark states but appear due to kinematic effects caused by different rescatterings of virtual particles; most of these models have all been post-dictions. Both the tightly and loosely bound models predict the masses and related quantum numbers of new, as yet undiscovered states. Thus, future experimental discoveries are needed along with theoretical advances to elucidate the structure of these new exotic states.
265 citations
Cites methods from "Hadron–hadron interactions from ima..."
...This is studied by the method of coupled-channel scattering involving the final states DD̄∗, πJ/ψ and ρηc, for which the HALQCD approach [81] is used....
[...]
...Likewise, the HALQCD approach [81], which is based...
[...]
References
More filters
Book•
16 Jun 1972
772 citations
TL;DR: In this paper, a method to calculate the elastic scattering amplitude at low energies in two-dimensional quantum field theories is proposed and tested in a numerical simulation of the O(3) non-linear σ-model on a simple square lattice.
651 citations
01 Jan 1990
TL;DR: In this paper, a method to calculate the elastic scattering amplitude at low energies in two-dimensional quantum field theories is proposed and tested in a numerical simulation of the 0(3) non-linear if-model on a simple square lattice.
Abstract: A method to calculate the elastic scattering amplitude at low energies in two-dimensional quantum field theories is proposed and tested in a numerical simulation of the 0(3) non-linear if-model on a simple square lattice. We also compute the isospin current form factor in this model and compare our results with the known exact expressions for the S-matrix and the form factor in the continuum limit. As a technical improvement, we introduce a two-cluster simulation algorithm which leads to significantly reduced statistical errors in the calculation of four-point correlation functions.
430 citations
TL;DR: In this article, the PACS-CS project presented the first results of a simulation of a 2+1$ flavor lattice QCD on the physical point with the nonperturbatively improved Wilson quark action and the Iwasaki gauge action.
Abstract: We present the first results of the PACS-CS project which aims to simulate $2+1$ flavor lattice QCD on the physical point with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action. Numerical simulations are carried out at $\ensuremath{\beta}=1.9$, corresponding to the lattice spacing of $a=0.0907(13)\text{ }\text{ }\mathrm{fm}$, on a ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ lattice with the use of the domain-decomposed HMC algorithm to reduce the up-down quark mass. Further algorithmic improvements make possible the simulation whose up-down quark mass is as light as the physical value. The resulting pseudoscalar meson masses range from 702 MeV down to 156 MeV, which clearly exhibit the presence of chiral logarithms. An analysis of the pseudoscalar meson sector with SU(3) chiral perturbation theory reveals that the next-to-leading order corrections are large at the physical strange quark mass. In order to estimate the physical up-down quark mass, we employ the SU(2) chiral analysis expanding the strange quark contributions analytically around the physical strange quark mass. The SU(2) low energy constants ${\overline{l}}_{3}$ and ${\overline{l}}_{4}$ are comparable with the recent estimates by other lattice QCD calculations. We determine the physical point together with the lattice spacing employing ${m}_{\ensuremath{\pi}}$, ${m}_{K}$ and ${m}_{\ensuremath{\Omega}}$ as input. The hadron spectrum extrapolated to the physical point shows an agreement with the experimental values at a few % level of statistical errors, albeit there remain possible cutoff effects. We also find that our results of ${f}_{\ensuremath{\pi}}$, ${f}_{K}$ and their ratio, where renormalization is carries out perturbatively at one loop, are compatible with the experimental values. For the physical quark masses we obtain ${m}_{ud}^{\overline{\mathrm{MS}}}$ and ${m}_{s}^{\overline{\mathrm{MS}}}$ extracted from the axial-vector Ward-Takahashi identity with the perturbative renormalization factors. We also briefly discuss the results for the static quark potential.
422 citations
TL;DR: In this article, the nucleon-nucleon potential is studied by lattice QCD simulations in the quenched approximation, using the plaquette gauge action and the Wilson quark action on a ${32}^{4}$ [$\ensuremath{\simeq}(4.4
Abstract: The nucleon-nucleon ($NN$) potential is studied by lattice QCD simulations in the quenched approximation, using the plaquette gauge action and the Wilson quark action on a ${32}^{4}$ [$\ensuremath{\simeq}(4.4\text{ }\text{ }\mathrm{fm}{)}^{4}$] lattice. A $NN$ potential ${V}_{NN}(r)$ is defined from the equal-time Bethe-Salpeter amplitude with a local interpolating operator for the nucleon. By studying the $NN$ interaction in the $^{1}S_{0}$ and $^{3}S_{1}$ channels, we show that the central part of ${V}_{NN}(r)$ has a strong repulsive core of a few hundred MeV at short distances ($r\ensuremath{\lesssim}0.5\text{ }\text{ }\mathrm{fm}$) surrounded by an attractive well at medium and long distances. These features are consistent with the known phenomenological features of the nuclear force.
412 citations