Hadronic Systems Research Articles

Generation of long- and short-range potentials from atom-molecules to quark-gluon systems by the GPT potential

The general particle transfer (GPT) potential generates not only the Yukawa-type potential but also the 1/r n -type potential in the hadron system, where the mass dependence of the transferred (exchanged) particle is clarified. The GPT potential from the atom-molecule system to the quark-gluon system was studied, where pico-meter physics could be highlighted. It is demonstrated that the long-range three-body Efimov potential is connected with the short-range three-body force potential by the GPT potential. Some applications for historical few-body problems in physics are summarized.

Mass Spectra of Mesonic Molecules at Finite Temperature

At a finite temperature, exotic hadronic systems, mass spectrum was studied using the quark structure and the radial Schrödinger equation with the Cornell interaction potential representing the hadronic interaction. The projective unitary representation has been used in the study of hadronic ground states in physics. A relativistic bound state's mass spectrum with temperature dependence is shown to have a unique feature. The resulting values are compared to experimental and theoretical values, and the study showed a high level of conformity with additional values wherever feasible.

Probing the tau electric dipole moment at the BEPC-II collider

We investigate the prospects of the search for a nonzero $\tau$ EDM form factor $d_\tau(s)$ in $\tau$ pair production by $e^+ e^-$ collisions at BEPC-II collider energies. We compute the expectation values and covariances of simple and optimal $CP$-odd observables for $\tau$-pair production at $\sqrt{s}=4.18$ GeV and $4.95$ GeV with subsequent decays of $\tau^\pm$ into major leptonic or semihadronic modes. For the $\tau$ decays to two pions and three charged pions we take the full kinematic information of the hadronic system into account. Applying cuts and using realistic assumptions on the eventually attainable integrated luminosities at these energies, ${\cal L}(4.18) = 3\times 10^4~{\rm pb}^{-1}$ and ${\cal L}(4.95) = 10^4~{\rm pb}^{-1}$, respectively, we find the following. By taking into account purely semihadronic and semihadronic-leptonic $\tau^+\tau^-$ decays one can achieve with optimal $CP$-odd observables the 1 s.d. sensitivities $\delta {\rm Re} d_\tau = 4.5\times 10^{-18}$ ecm ($5.3\times 10^{-18}$ ecm) and $\delta {\rm Im} d_\tau = 2.2 \times 10^{-18}$ ecm ($2.7\times 10^{-18}$ ecm) at $\sqrt{s}=4.18$ GeV ($4.95$ GeV).

Hadronic currents and form factors in three-body semileptonic tau decays

Three-body semileptonic tau -decays offer a path to understand the properties of light hadronic systems and CP symmetry violations through searches for electric dipole moments. In studies of electro-weak physics, the hadronic part of the final states has traditionally been described using the language of form factors. Spectroscopic information, resolved in terms of orbital angular momentum quantum-numbers, is best being derived from an explicit decomposition of the hadronic current in the orbital angular momentum basis. Motivated by the upcoming large data samples from mathrm {B} factories, we present the full description of the hadronic currents decomposed into quantum numbers of the hadronic final state using the isobar picture. We present formulas for orbital angular momenta up to three and apply the rules derived from hadron spectroscopy to formulate the decay chain of hadronic three-body systems of arbitrary mass. We also translate this formalism to the language of form factors and thereby correct insufficiencies found in previous analyses of three-body hadronic final states.

Three-Body Dynamics of the a_{1}(1260) Resonance from Lattice QCD.

Resonant hadronic systems often exhibit a complicated decay pattern in which three-body dynamics play a relevant or even dominant role. In this work we focus on the a_{1}(1260) resonance. For the first time, the pole position and branching ratios of a three-body resonance are calculated from lattice QCD using one-, two-, and three-meson interpolators and a three-body finite-volume formalism extended to spin and coupled channels. This marks a new milestone for abinitio studies of ordinary resonances along with hybrid and exotic hadrons involving three-body dynamics.

Highlights of light meson spectroscopy at the BESIII experiment.

Hadron spectroscopy provides a way to understand the dynamics of the strong interaction. For light hadron systems, only phenomenological models or lattice quantum chromodynamics (QCD) are applicable, because of the failure of perturbation expansions for QCD at low energy. Experimental data on light hadron spectroscopy are therefore crucial to provide necessary constraints on various theoretical models. Light meson spectroscopy has been studied using charmonium decays with the Beijing Spectrometer Experiment (BES) at the Beijing Electron-Positron Collider, operating at 2.0–4.6 GeV center-of-mass energy, for nearly three decades. Charmonium data with unprecedented statistics and well-defined initial and final states provide BESIII with unique opportunities to search for glueballs, hybrids and multi-quark states, as well as perform systematic studies of the properties of conventional light mesons. In this article, we review BESIII results that address these issues.

Proton and deuteron mass radii from near-threshold ϕ -meson photoproduction

We analyze the exclusive $\phi$-meson photoproduction on both hydrogen and deuterium targets based on the published data of CLAS, SAPHIR and LEPS collaborations. A dipole-form scalar gravitational form factor is applied to describe the $|t|$-dependence of the differential cross section. Based on the average of all the near-threshold data from CLAS, SAPHIR and LEPS, we find that the proton and deuteron mass radii are $0.75 \pm 0.02$ fm and $1.95 \pm 0.19$ fm respectively. The coherent and near-threshold quarkonium photoproduction seems to be sensitive to the radius of the hadronic system. The vector-meson-dominance model together with a low-energy QCD theorem well describe the data of near-threshold $\phi$ photoproduction on the hadronic systems.

Hyperons in Neutron Stars

I review the issues related to the appearance of hyperons in neutron star matter, focusing in particular on the problem of the maximum mass supported by hyperonic equations of state. I discuss the general mechanism that leads to the formation of hyperons in the core of neutron stars and I review the main techniques and many-body methods used to construct an appropriate equation of state to describe the strongly interacting system of hadrons hosted in the core of neutron stars. I outline the consequences on the structure and internal composition of neutron stars and also discuss the possible signatures of the presence of hyperons in astrophysical dynamical systems like supernova explosions and binary neutron star mergers. Finally, I briefly report about the possible important role played by hyperons in the transport properties of neutron star matter and on the consequences of neutron star cooling and gravitational wave instabilities induced by the presence of hyperons.

Mass Spectrum of exotic Hyperatoms

The hyperatoms belong to the group of exotic atoms. An exotic hyperatom is a system where a negative muon as an electron in a normal atom is captured into an hyperatomic orbit around hypernuclei. Our knowledge of the non-relativistic quantum mechanics is a good method for the exotic hyperatoms containing one muon. We theoretically have been investigated exotic muonic hyperatoms. Theoretically, the mass spectra of muonic hyperatoms have been determined in the framework of the non-relativistic Schrodinger equation with Coulomb type potential describing the interaction between a muon and the hypernuclei core. The studies of exotic systems have achieved great progress both in theory and experiments. Mass spectrum and binding energy have been provided useful information for exotic hadronic systems and for hypernuclei which participate in the experimental reaction and also the interaction between them. The analytic method based on quantum field theories, the behavior of the correlation function, Feynman path integral, and oscillator representation method is suggested. Within all of these different frameworks, we have presented the theoretical approach to describing the mass spectrum of muonic hyperatoms in the ground and orbital excited states.

Uncovering an axion mechanism with the EDM portfolio

Effective field theory arguments suggest that if BSM sectors contain new sources of CP-violation that couple to QCD, these sources will renormalize the $\theta$ term and frustrate ultraviolet solutions to the strong CP problem. Simultaneously, they will generate distinctive patterns of low-energy electric dipole moments in hadronic, nuclear, atomic, and molecular systems. Observing such patterns thus provides evidence that strong CP is solved by an infrared relaxation mechanism. We illustrate the renormalization of $\theta$ and the collections of EDMs generated in a several models of BSM physics, confirming effective field theory expectations, and demonstrate that measurements of ratios of electric dipole moments at planned experiments can provide valuable input on the resolution of the strong CP problem.

Phase transitions and critical behavior in hadronic transport with a relativistic density functional equation of state

We develop a flexible, relativistically covariant parametrization of the dense nuclear matter equation of state suited for inclusion in computationally demanding hadronic transport simulations. Within an implementation in the hadronic transport code smash, we show that effects due to bulk thermodynamic behavior are reproduced in dynamic hadronic systems, demonstrating that hadronic transport can be used to study critical behavior in dense nuclear matter, both at and away from equilibrium. We also show that two-particle correlations calculated from hadronic transport simulation data follow theoretical expectations based on the second-order cumulant ratio, and constitute a clear signature of the crossover region above the critical point.

Binding of antikaons and $$\varLambda (1405)$$ clusters in light kaonic nuclei

The energy spectra of light-mass kaonic nuclei were investigated using the theoretical framework of the $0s$-orbital model with zero-range $\bar{K} N$ and $\bar{K}\bar{K}$ interactions of effective single-channel real potentials. The energies of the $\bar{K} NN$, $\bar{K} NNN$, $\bar{K} NNNN$, $\bar{K}\bar{K} N$, and $\bar{K}\bar{K} NN$ systems were calculated in the cases of weak- and deep-binding of the $\bar{K} N$ interaction, which was adjusted to fit the $\Lambda(1405)$ mass with the energy of the $\bar{K} N$ bound state. The results qualitatively reproduced the energy systematics of kaonic nuclei calculated via other theoretical approaches. In the energy spectra of the $\bar{K} NN$ and $\bar{K}\bar{K} NN$ systems, the lowest states $\bar{K} NN(J^\pi,T=0^-,1/2)$ and $\bar{K}\bar{K} NN(0^+,0)$ were found to have binding energies approximately twice and four times as large as that of the $\bar{K} N(1/2^-,0)$ state, respectively. Higher $(J^\pi,T)$ states including $\bar{K} NN(1^-,1/2)$, $\bar{K}\bar{K} NN(0^+,1)$, and $\bar{K}\bar{K} NN(1^+,1)$ were predicted at energies of 9--25 MeV below the antikaon-decay threshold. The effective $\Lambda(1405)$-$\Lambda(1405)$ interaction in the $\bar{K}\bar{K} N N$ system was also investigated via a $\bar{K} N+\bar{K} N$-cluster model. Strong and weak $\Lambda(1405)$-$\Lambda(1405)$ attractions were obtained in the $S^\pi=0^+$ and $S^\pi=1^-$ channels, respectively. The $\Lambda(1405)$-$\Lambda(1405)$ interaction in the $$\bar{K}\bar{K} NN$ system was compared with the effective $d$-$d$ interaction in the $NNNN$ system, and the properties of dimer-dimer interactions in hadron and nuclear systems were discussed.

Electric dipole moment of the tau lepton revisited

We reconsider the issue of the search for a nonzero electric dipole form factor (EDM) ${d}_{\ensuremath{\tau}}(s)$ using optimal observables in ${\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$ production by ${e}^{+}{e}^{\ensuremath{-}}$ collisions in the center-of-mass energy range from the $\ensuremath{\tau}$-pair threshold to about $\sqrt{s}\ensuremath{\sim}15\text{ }\text{ }\mathrm{GeV}$. We discuss the general formalism of optimal observables and apply it to two $CP$-odd observables that are sensitive to the real and imaginary part of ${d}_{\ensuremath{\tau}}(s)$, respectively. We compute the expectation values and covariances of these optimal $CP$ observables for $\ensuremath{\tau}$-pair production at $\sqrt{s}=10.58\text{ }\text{ }\mathrm{GeV}$ with subsequent decays of ${\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}$ into major leptonic or semihadronic modes. For the $\ensuremath{\tau}$ decays to two pions and three charged pions we take the full kinematic information of the hadronic system into account. Assuming that the Belle II experiment at the KEKB accelerator will eventually analyze data corresponding to an integrated luminosity of $50\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$ and applying acceptance cuts on the final-state pions, we find that 1 s.d. sensitivities $\ensuremath{\delta}\mathrm{Re}{d}_{\ensuremath{\tau}}=6.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }e\text{ }\mathrm{cm}$ and $\ensuremath{\delta}\mathrm{Im}{d}_{\ensuremath{\tau}}=4.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }e\text{ }\mathrm{cm}$ can be obtained with events where both $\ensuremath{\tau}$'s decay semihadronically. We consider also the ideal case that no cuts on the final-state particles are applied. With $50\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$ at $\sqrt{s}=10.58\text{ }\text{ }\mathrm{GeV}$ corresponding to $4.5\ifmmode\times\else\texttimes\fi{}{10}^{10}$ ${\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$ events we find the 1 s.d. sensitivities $\ensuremath{\delta}\mathrm{Re}{d}_{\ensuremath{\tau}}=5.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }e\text{ }\mathrm{cm}$ and $\ensuremath{\delta}\mathrm{Im}{d}_{\ensuremath{\tau}}=3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }e\text{ }\mathrm{cm}$, again for events where both $\ensuremath{\tau}$ leptons decay semihadronically. Furthermore, we analyze the potential magnitude of the $\ensuremath{\tau}$ EDM form factor in the type-II two-Higgs doublet extension and in two scalar leptoquark extensions of the Standard Model, taking into account phenomenological constraints.

Charged multihadron systems in lattice QCD+QED

Systems with the quantum numbers of up to twelve charged and neutral pseudoscalar mesons, as well as one-, two-, and three-nucleon systems, are studied using dynamical lattice quantum chromodynamics and quantum electrodynamics (QCD+QED) calculations and effective field theory. QED effects on hadronic interactions are determined by comparing systems of charged and neutral hadrons after tuning the quark masses to remove strong isospin breaking effects. A non-relativistic effective field theory, which perturbatively includes finite-volume Coulomb effects, is analyzed for systems of multiple charged hadrons and found to accurately reproduce the lattice QCD+QED results. QED effects on charged multi-hadron systems beyond Coulomb photon exchange are determined by comparing the two- and three-body interaction parameters extracted from the lattice QCD+QED results for charged and neutral multi-hadron systems.

Triple- X and beyond: Hadronic systems of three and more X(3872)

The $X(3872)$ resonance has been conjectured to be a $J^{PC} = 1^{++}$ charm meson-antimeson two-body molecule. Meanwhile, there is no experimental evidence for larger, few-body compounds of multiple charm meson-antimeson pairs which would resemble larger molecules or nuclei. Here, we investigate such multi-meson states to the extent of what can be deduced theoretically from essentials of the interaction between uncharged $D^{0}$ and $D^{*0}$ mesons. From a molecular $X(3872)$, we predict a $4X$ ($4^{++}$) octamer with a binding energy \mbox{$B_{4X} > 2.08\,{\rm MeV}$,} assuming a $D^{*0} \bar{D}^0$ system close to the unitary limit (as suggested by the mass of the $X(3872)$). If we consider heavy-quark spin symmetry explicitly, the $D^{*0} \bar{D}^{*0}$ ($2^{++}$) system is close to unitarity, too. In this case, we predict a bound $3X$ ($3^{++}$) hexamer with $B_{3X} > 2.29\,{\rm MeV}$ and a more deeply bound $4X$ octamer with $B_{4X} > 11.21\,{\rm MeV}$. These results exemplify with hadronic molecules a more general phenomenon of equal-mass two-species Bose systems comprised of equal number of either type: the emergence of unbound four- and six-boson clusters in the limit of a short-range two-body interaction which acts only between bosons of different species. Finally, we also study the conditions under which a $2X$ ($2^{++}$) tetramer might form.

Euclidean formulation of relativistic quantum mechanics of N particles

A Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales. While direct interaction approaches to relativistic quantum mechanics have proved to be useful, they have two disadvantages. One is that cluster properties are difficult to realize for systems of more than two particles. The second is that the relation to quantum field theories is indirect. Euclidean formulations of relativistic quantum mechanics provide an alternative representation that does not have these difficulties. More surprising, the theory can be formulated entirely in the Euclidean representation without the need for analytic continuation. In this work a Euclidean representation of a relativistic $N$-particle system is discussed. Kernels for systems of N free particles of any spin are given and shown to be reflection positive. Explicit formulas for generators of the Poincar\'e group for any spin are constructed and shown to be self-adjoint on the Euclidean representation of the Hilbert space. The structure of correlations that preserve both the Euclidean covariance and reflection positivity is discussed.

Spin density matrix elements in exclusive omega meson muoproduction

We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive omega meson muoproduction on the proton at COMPASS using 160 GeV/c polarised mu ^{+} and mu ^{-} beams impinging on a liquid hydrogen target. The measurement covers the range 5.0 GeV/c^2< W< 17.0 GeV/c^2, with the average kinematics langle Q^{2} rangle = 2.1 (GeV/c)^2, langle W rangle = 7.6 GeV/c^2, and langle p^{2}_{mathrm{T}} rangle = 0.16 (GeV/c)^2. Here, Q^2 denotes the virtuality of the exchanged photon, W the mass of the final hadronic system and p_T the transverse momentum of the omega meson with respect to the virtual-photon direction. The measured non-zero SDMEs for the transitions of transversely polarised virtual photons to longitudinally polarised vector mesons (gamma ^*_T rightarrow V_L) indicate a violation of s-channel helicity conservation. Additionally, we observe a sizeable contribution of unnatural-parity-exchange (UPE) transitions that decreases with increasing W. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow to evaluate in a model-dependent way the contribution of UPE transitions and assess the role of parton helicity-flip GPDs in exclusive omega production.

Two-Photon Exchange in Elastic Electron Scattering on Hadronic Systems

In the present review, we discuss different aspects of the two-photon exchange (TPE) physics in elastic ep scattering at high Q2, as well as at low Q2. The imaginary part of the TPE amplitude gives rise to beam and target single-spin asymmetries. Different theoretical approaches to the calculation of these observables are considered. The real part of the TPE amplitude influences the unpolarized cross-section and double-spin observables and is, most likely, responsible for the discrepancy between two methods of measurements of the proton form factors. We review different methods of calculations of the TPE amplitudes in the framework of the “hadron” and “quark-gluon” approaches. We discuss the dispersion approach suitable for low and intermediate Q2, which includes elastic and inelastic intermediate hadronic states, as well as the connection of TPE with the proton radius puzzle. The present situation with direct experimental searches for the TPE amplitude in the e+p/e−p charge asymmetry is also discussed, as well as attempts to extract the TPE amplitudes from existing experimental data obtained by the Rosenbluth and double polarization techniques. The TPE physics in other processes such as elastic мp, e-nucleus, and еп scattering is also reviewed.

Neutrino(antineutrino)–nucleus interactions in the shallow- and deep-inelastic scattering regions

In –nucleon/nucleus interactions shallow inelastic scattering (SIS) is technically defined in terms of the four-momentum transfer to the hadronic system as non-resonant meson production with Q 2 ⪅ 1 GeV2. This non-resonant meson production intermixes with resonant meson production in a regime of similar effective hadronic mass W of the interaction. As Q 2 grows and surpasses this ≈1 GeV2 limit, non-resonant interactions begin to take place with quarks within the nucleon indicating the start of deep inelastic scattering (DIS). To essentially separate this resonant plus non-resonant meson production from DIS quark-fragmented meson production, a cut of 2 GeV in W of the interactions is generally introduced. However, since experimentally mesons from resonance decay cannot be separated from non-resonant produced mesons, SIS for all practical purposes in this review has been defined as inclusive meson production that includes non-resonant plus resonant meson production and the interference between them. Experimentally then for W ⪅ 2 GeV inclusive meson production with W ⪆ (M N + M π ) and all Q 2 is here defined as SIS, while for W ⪆ 2 GeV, the kinematic region with Q 2 ⪆ 1 GeV2 is defined as DIS. The so defined SIS and DIS regions have received varying degrees of attention from the community. While the theoretical/phenomenological study of ν–nucleon and ν–nucleus DIS scattering is advanced, such studies of a large portion of the SIS region, particularly the SIS to DIS transition region, have hardly begun. Experimentally, the SIS and the DIS regions for ν–nucleon scattering have minimal results and only in the experimental study of the ν–nucleus DIS region are there significant results for some nuclei. Since current and future neutrino oscillation experiments have contributions from both higher W SIS and DIS kinematic regions and these regions are in need of both considerable theoretical and experimental study, this review will concentrate on these SIS to DIS transition and DIS kinematic regions surveying our knowledge and the current challenges.

0+ fully-charmed tetraquark states

Motivated by the LHCb's new observation of structures in the $J/\psi$-pair invariant mass spectrum, for which could be classified as possible $cc\bar{c}\bar{c}$ tetraquark candidates, we systematically study $0^{+}$ fully-charmed tetraquark states through QCD sum rules. Making the development of calculation techniques to fourfold heavy hadronic systems, four different configuration currents with $0^{+}$ are considered and vacuum condensates up to dimension $6$ are included in the operator product expansion (OPE). Finally, mass values acquired for $0^{+}$ $cc\bar{c}\bar{c}$ tetraquark states agree well with the experimental data of the broad structure, which supports that it could be a $0^{+}$ fully-charmed tetraquark state.