A large number of experimental discoveries especially in the heavy quarkonium sector that did not at all fit to the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy Among various explanations of the internal structure of these excitations, hadronic molecules, being analogues of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty We review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures Nonrelativistic effective field theories are the suitable framework for studying hadronic molecules, and are discussed in both the continuum and finite volumes Also pertinent lattice QCD results are presented Further, we discuss the production mechanisms and decays of hadronic molecules, and comment on the reliability of certain assertions often made in the literature

Hadronic molecules

We review lattice results related to pion, kaon, D-meson, B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \rightarrow \pi $ transition at zero momentum transfer, as well as the decay constant ratio $f_K/f_\pi $ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $SU(2)_L\times SU(2)_R$ and $SU(3)_L\times SU(3)_R$ Chiral Perturbation Theory. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha _s$. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.

FLAG Review 2019

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

QCD and strongly coupled gauge theories: challenges and perspectives

The existence and properties of the sigma meson have been controversial for almost six decades, despite playing a central role in the spontaneous chiral symmetry of QCD or in the nucleon-nucleon attraction. This controversy has also been fed by the strong indications that it is not an ordinary quark-antiquark meson. Here we review both the recent and old experimental data and the model independent dispersive formalisms which have provided precise determinations of its mass and width, finally settling the controversy and leading to its new name: $f_0(500)$. We then provide a rather conservative average of the most recent and advanced dispersive determinations of its pole position $\sqrt{s_\sigma}=449^{+22}_{-16}-i(275\pm12)$. 
In addition, after comprehensive introductions, we will review within the modern perspective of effective theories and dispersion theory, its relation to chiral symmetry, unitarization techniques, its quark mass dependence, popular models, as well as the recent strong evidence, obtained from the QCD $1/N_c$ expansion or Regge theory, for its non ordinary nature in terms of quarks and gluons.

/pdf/from-controversy-to-precision-on-the-sigma-meson-a-review-on-3umvi1vsss.pdf

From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance

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.

The $XYZ$ states: experimental and theoretical status and perspectives

We employ a variational basis with a number of $\overline{q}q$ and $\ensuremath{\pi}\ensuremath{\pi}$ lattice interpolating fields with quantum numbers of the $\ensuremath{\rho}$ resonance to extract the discrete energy spectrum in a finite volume. In the elastic region, this spectrum is related to the phase shift of the continuum scattering amplitude by L\"uscher's formula, and the relation allows the extraction of resonance parameters from the spectrum calculation. The simulations are performed at three different total momenta of the coupled $\overline{q}q\ensuremath{-}\ensuremath{\pi}\ensuremath{\pi}$ system, which allows us to extract the $p$-wave scattering phase at five values of pion relative momenta near the resonance region. The effective range formula describes the phase-shift dependence nicely, and we extract the resonance mass ${m}_{\ensuremath{\rho}}=792(7)(8)\text{ }\text{ }\mathrm{MeV}$ and the coupling ${g}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}=5.13(20)$ at our ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}266\text{ }\text{ }\mathrm{MeV}$. The coupling ${g}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}$ is directly related to the width of the $\ensuremath{\rho}$ meson, and our value is close to the value derived from the experimental width. The simulations are performed using dynamical gauge configurations with two mass-degenerate flavors of tree-level improved clover-Wilson fermions. Correlation functions are calculated using the recently proposed distillation method with Laplacian-Heaviside smearing of quarks, which enables flexible calculations, in many cases with unprecedented accuracy.

/pdf/coupled-channel-analysis-of-the-rho-meson-decay-in-lattice-1wam58htdy.pdf

Coupled channel analysis of the rho meson decay in lattice QCD

Erratum: Coupled channel analysis of the ρ meson decay in lattice QCD [Phys. Rev. D 84, 054503 (2011)]

We extract the P-wave pi-pi phase shift for five values of pion relative momenta, which gives information on the rho resonance The Breit-Wigner formula describes the pi-pi phase shift dependence nicely and we extract m(rho)=792(7)(8) MeV and the coupling g_{\rho\pi\pi}=513(20) at our mpi=266 MeV We extract the P-wave scattering length a_{l=1}^{\pi\pi}=0082(10)(3) fm^3 from the state with the lowest pion relative momenta 
We also determine the S-wave rho-pi phase shift for two values of relative momenta, which provides parameters of the lowest axial resonance a1(1260) Using the Breit-Wigner fit we extract m(a1)=144(4) GeV and the coupling g_{a_1\rho\pi}=11(3) GeV From the lowest state we also extract the rho-pi scattering length a_{l=0}^{\rho\pi}=023(12) fm for our mpi 
The simulation is performed using one Nf=2 ensemble of gauge configurations with clover-improved Wilson quarks The phase shifts are determined from the lowest two energy-levels, which are obtained by the variational analysis with a number of quark-antiquark and meson-meson interpolators The correlation functions are calculated using the distillation method with the Laplacian Heaviside (LapH) smearing of quarks

Decay of rho and a1 mesons on the lattice using distillation

We extract the P-wave ππ phase shift for five values of pion relative momenta, which gi ves information on the ρ resonance. The Breit-Wigner formula describes the ππ phase shift dependence nicely and we extract mρ = 792(7)(8) MeV and the coupling gρππ = 5.13(20) at our mπ = 266 MeV. We extract the P-wave scattering length a ππ=1 = 0.082(10)(3) fm 3 from the state with the lowest pion relative momenta. We also determine the S-wave ρπ phase shift for two values of relative momenta, which provides parameters of the lowest axial resonance a1(1260). Using the Breit-Wigner fit we extract ma1 = 1.44(4) GeV and the coupling ga1ρπ = 1.1(3) GeV. From the lowest state we also extract the ρπ scattering length a ρπ=0 = 0.23(12) fm for our mπ . The simulation is performed using one Nf = 2 ensemble of gauge configurations with cloverimproved Wilson quarks. The phase shifts are determined from the lowest two energy-levels, which are obtained by the variational analysis with a number of quark-antiquark and mesonmeson interpolators. The correlation functions are calcul ated using the distillation method with the Laplacian Heaviside (LapH) smearing of quarks.

Matija Vidmar

Papers

Coupled channel analysis of the rho meson decay in lattice QCD

Erratum: Coupled channel analysis of the ρ meson decay in lattice QCD [Phys. Rev. D 84, 054503 (2011)]

Decay of rho and a1 mesons on the lattice using distillation

Decay of rho and a1 mesons on the lattice using distillation

Decay of the rho and a1 mesons on the lattice using distillation