Structure Of Mesons Research Articles

A short history of the smallest

Abstract This paper tells the story of the Standard Model of particle physics. That starts in the 1930s with the idea of the pion and then traces its roots from an embryonic quark theory to its contemporary form. Early scepticism towards the quark model dissolved as it elegantly elucidated baryon and meson structures, and helped to uncover the intricacies of the weak and strong interactions. The Δ++ particle’s existence demanded the introduction of ‘colour’ charge, giving birth to Quantum Chromodynamics. Successive discoveries of heavy quarks, heavy leptons and their corresponding neutrinos fortified the Standard Model. The verification of the existence of gluons, the discovery of the W and Z bosons, and - finally - the Higgs boson are considered triumphs of the theory. However, despite its success, the model has inadequacies, notably with regard to dark matter and energy, but also in explaining the very origin of its many free parameters. New ideas and discoveries are needed to help solve these mysteries.

Nuclear medium meson structures from the Schwinger proper-time Nambu–Jona-Lasinio model

In this paper, we report the results of our study on the nuclear medium modifications of the meson electromagnetic form factors in the framework of the Nambu–Jona-Lasinio model with the help of the Schwinger proper-time regularization scheme to tame the loop divergence and simulate the effect of QCD confinement. In our current approach, the meson structure and nuclear medium are constructed in the same Nambu–Jona-Lasinio model at the quark level. We examine the free-space and in-medium charge radii of kaon and pion, the spacelike elastic electromagnetic form factors of kaon and pion, and their quark-sector form factors, which reflect their internal structures. By comparing our result to experimental data, we found that the free-space elastic electromagnetic form factors of the mesons are consistent with the data, while the in-medium elastic electromagnetic form factors of the mesons are found to decrease as the nuclear matter density increases, leading to a rise of meson charge radius, which is consistent with the prediction of other theoretical calculations. We also predict the axial nucleon coupling constant gA in nuclear medium computed via the Goldberger-Treiman relation, which is crucial for searching the neutrinoless double beta decay (0νββ). Published by the American Physical Society 2024

Structure of heavy mesons in the light-front quark model

We investigate the structure of ground-state heavy mesons within the light-front quark model, utilizing wave functions derived from the single Gaussian ansatz (SGA) and the Gaussian expansion method (GEM). By performing a χ2 fit to static properties such as mass spectra and decay constants, we determine the model parameters for each approach. We then compare the impacts of both methods on the light-front wave functions and structural observables. Our analysis reveals significant differences in the distribution amplitudes ϕ2;M(x) near the end points, with GEM showing enhanced amplitudes and correct asymptotic behavior ϕ2;M(x→1)∝(1−x), consistent with perturbative QCD. This end point behavior is linked to the short-range (high-momentum) wave function governed by color Coulomb interaction and relativistic kinematics. GEM accurately reproduces a power-law damping ψ0(k→∞)∝1/k⊥2, aligning with perturbative QCD predictions. Furthermore, the electromagnetic form factors of pseudoscalar mesons in the low-Q2 region fall off faster with GEM than with SGA. Overall, while both methods adequately describe static properties, GEM provides a more accurate description of structural properties, being more sensitive to details and asymptotic behaviors. Published by the American Physical Society 2024

Investigation of vertex a1>>VP for hadronic tau decays

In the framework of U(3) symmetric quark model, triangular diagrams are calculated that describe the strongly interacting vertices a1>>rhopi and a1>>K*K. The divergences arising when considering quark loops are regularized by covariant cutoff parameter. Based on four-particle hadronic τ decays, the quark structure of the resonance with quantum numbers JPC=1++ was studied. Theoretical estimates of intermediate channels with the meson for the partial decay widths of tau>>pipipinu, tau>>KKpinu and tau>>KKetanu are obtained. Contributions from contact channels describing the direct production of 3pi, KKpi and KKeta mesons by τ lepton current are taken into account. The interference of contact and intermediate axial-vector channels in determining the integral decay widths is studied. The matrix elements of the processes are obtained in the leading approximation of 1/Nc expansion. It is shown that calculations on τ lepton mesonic decays confirm the quark-antiquark structure of the a1 meson and clarify the role of the intermediate non-strange axial-vector channel in determining the integral partial decay widths. The obtained results are compared with experimental data by BaBar and Belle collaborations at the BEPC II and KEK lepton colliders.

T-even TMDs for the spin-0 pseudo-scalar mesons upto twist-4 using light-front formalism

We have investigated the pseudo-scalar meson structure in the form of transverse momentum-dependent parton distribution functions (TMDs) in the light-front based holographic model and quark model. Starting from leading order, we have calculated all the time-reversal even TMDs for pion and kaon up to twist-4 in these models. We have shown the 3-dimensional structure as well as the 2-dimensional structure of these particles along with their average quark transverse momenta. The parton distribution functions (PDFs) of pseudo-scalar pion have been compared with E615 and modified E615 results. The sum rules, TMD transverse dependence, inverse moments and Gaussian transverse dependence ratio in these models have also been studied. Further, the transverse quark densities have also been analyzed in the momentum space plane for these particles. The higher twist kaon properties in light-front framework have been predicted for the first time in this work.

Algebraic model to study the internal structure of pseudoscalar mesons with heavy-light quark content

The internal structure of all lowest-lying pseudoscalar mesons with heavy-light quark content is studied in detail using an algebraic model that has been applied recently, and successfully, to the same physical observables of pseudoscalar and vector mesons with hidden-flavor quark content, from light to heavy quark sectors. The algebraic model consists on constructing simple and evidence-based of the meson’s Bethe-Salpeter amplitude (BSA) and quark’s propagator in such a way that the Bethe-Salpeter wave function (BSWF) can then be readily computed algebraically. Its subsequent projection onto the light front yields the light front wave function (LFWF) whose form allows us a simple access to the valence-quark parton distribution amplitude (PDA) by integrating over the transverse momentum squared. We exploit our current knowledge of the PDAs of lowest-lying pseudoscalar heavy-light mesons to compute their generalized parton distributions (GPDs) through the overlap representation of LFWFs. From these three dimensional knowledge, different limits/projections lead us to deduce the related parton distribution functions (PDFs), electromagnetic form factors (EFFs), and impact parameter space GPDs (IPS-GPDs). When possible, we make explicit comparisons with available experimental results and earlier theoretical predictions. Published by the American Physical Society 2024

The AMBER Experiment at CERN

NA66/AMBER has been approved by CERN in 2020 as a new multipurpose facility for experiments in meson and baryon physics. In a first beamtime in 2023, data have been taken for the determination of antiproton production cross-sections in proton-helium collisions, needed for the interpretation of cosmic antimatter observations. Preparations are ongoing for a measurement of the proton charge radius in high-energy muon-proton scattering. This measurement will feature substantially different systematics than other approaches and aims at clarifying the present discrepancies. Further, experiments to study the partonic structure of mesons in Drell-Yan processes and strange-meson spectroscopy are on the menu of AMBER.

Distribution amplitude and decay constant of 1S and 2S state light mesons in the light-front quark model

Studying meson structures is essential for gaining insights into the nonperturbative nature of Quantum Chromodynamics (QCD). This study will focus on calculating the decay constant and distribution amplitudes (DAs) of unflavored light mesons (π and ρ) in the 1S and 2S states using the Light Front Quark Model. This study utilizes the QCD-motivated Hamiltonian, taking into account both contact and smeared spin-spin interactions. The two lowest harmonic oscillator bases are employed in this work to achieve improved results for the 2S states. The study found the optimal mixing parameter in basis expansion coefficients to be θ = 10°. Light meson properties, including the mass spectrum, decay constant, and twist-2 DAs, are then predicted using model parameters fixed through the variational principle. While the contact spin-spin interaction yields poor accuracy, the results from the smeared interaction generally agree well with experimental data and other theoretical models with $ f_{\pi}^{1S}=130 $ MeV and $ f_{\rho}^{1S}=210 $ MeV in the mixed state. Unlike the case for the 1S state, it should be noted that the properties of the 2S state are sensitive to the mixing parameter θ. In addition, we observe that the decay constant for ρ(2S) is $ f_{\rho}^{2S}=116 $ MeV. While for π(2S) the decay constant is extremely small with the value of $ f_{\pi}^{2S}=0.9 $ MeV, which is mainly due to the dynamical chiral symmetry breaking.

Investigating Fully Strange Tetraquark System with Positive Parity in a Chiral Quark Model

Motivated by the intriguing discovery of X(6900) by the LHCb collaboration, we undertake a comprehensive study of the ss¯ss¯ tetraquark system with positive parity, employing the Gaussian expansion within the chiral quark model method. We consider two structures, the diquark–antidiquark (ss-s¯s¯) structure and meson–meson (ss¯-ss¯) structure, covering all conceivable color and spin configurations. Despite the absence of bound states in our calculations, we have identified potential resonant states with JP=0+, namely, R(0,2150) and R(0,2915), as well as a resonant state with JP=1+, denoted as R(1,2950), and a resonant state with JP=2+, denoted as R(2,2850), utilizing the real-scaling method. By comparing their energies and widths, we suggest that R(0,2915) and R(1,2950) may share characteristics with X(6900), while R(0,2150) could be a promising candidate for the experimental state f0(2100). We strongly advocate for experimental investigations to shed light on the existence and properties of these resonant states.

Semileptonic decays D → P/V/Sℓ+νℓ with the SU(3) flavor symmetry/breaking

Many exclusive c→d/sℓ+νℓ(ℓ=e,μ,τ) transitions have been well measured, and they can be used to test the theoretical calculations. Motivated by this, we study the D→P/V/Sℓ+νℓ decays induced by the c→d/sℓ+νℓ transitions with the SU(3) flavor symmetry approach, where P denotes the pseudoscalar meson, V denotes the vector meson, and S denotes the scalar meson with a mass below 1 GeV. The different decay amplitudes of the D→Pℓ+νℓ, D→Vℓ+νℓ or D→Sℓ+νℓ decays can be related by using the SU(3) flavor symmetry and by considering the SU(3) flavor breaking. Using relevant data, we predict the not yet measured or not yet well measured processes in the D→P/V/Sℓ+νℓ decays. We find that the SU(3) flavor symmetry approach works well in the D→P/Vℓ+νℓ decays. Many branching ratios of the D→Sℓ+νℓ decays are predicted by using the data of the Ds+→f0(980)e+νe and D→S(S→P1P2)ℓ+νℓ decays, in addition, the two quark and the four quark scenarios for the light scalar mesons are analyzed. The SU(3) flavor symmetry predictions of the D→Sℓ+νℓ decays need to be further tested, and our predictions of the D→Sℓ+νℓ decays are useful for probing the structure of light scalar mesons. Our results in this work could be used to test the SU(3) flavor symmetry approach in the semileptonic D decays by the future experiments at BESIII, LHCb and BelleII.

The unpolarized TMD valence quark distributions of light mesons in the statistical covariant parton model approach

We investigate the unpolarized transverse momentum dependent (TMD) structure of light mesons at low Q^2 scales in nonperturbative region of quantum chromodynamics (QCD). To this end, we calculate the unpolarized TMD valence quark distribution functions of pion and kaon based on the covariant parton model in which the flavour dependent covariant momentum distribution of quarks is needed. We apply the statistical model for this momentum distribution, for the first time, and also consider the quarks to be massive. The results of TMD valence distributions of light mesons show convenient general properties. We also obtain the integrated valence quark distributions of pion and kaon and compare our results with those of other models.

Investigating full-heavy tetraquarks composed of cc{bar{c}}{bar{b}} and bb{bar{b}}{bar{c}}

The full-heavy tetraquarks cc{bar{c}}{bar{b}} and bb{bar{b}}{bar{c}} are systematically investigated within a quark model. The meson–meson structure, diquark–antidiquark structure and K-structure are considered in this work. There is no bound state for cc{bar{c}}{bar{b}} and bb{bar{b}}{bar{c}} systems in IJ^{P}=00^{+},01^{+} and 02^{+} channels. However, for cc{bar{c}}{bar{b}} system, three possible resonance states with energy of 10{,}079~textrm{MeV} , 10{,}081~textrm{MeV} and 10{,}177~textrm{MeV} are found in IJ^{P}=00^{+},01^{+} and 02^{+}, respectively, and their decay width Gamma are 6.7–8.4 MeV, 1.4–7.2 MeV and 9.1–11.1 MeV. For bb{bar{b}}{bar{c}} system, there also exist three possible resonance states with energy of 16{,}474~textrm{MeV} , 16{,}474~textrm{MeV} and 16{,}541~textrm{MeV} in IJ^{P}=00^{+},01^{+} and 02^{+}, respectively, and the decay widths Gamma of them are 2.2–6.1 MeV, 2.2–6.9 MeV and 5.3–8.5 MeV. bc{bar{c}}{bar{c}} and cb{bar{b}}{bar{b}} systems will have the same results as cc{bar{c}}{bar{b}} and bb{bar{b}}{bar{c}}, respectively. These full-heavy resonance states are worthy to be searched in the future experiments.

Cornering large-Nc QCD with positivity bounds

The simple analytic structure of meson scattering amplitudes in the large-Nc limit, combined with positivity of the spectral density, provides precise predictions on low-energy observables. Building upon previous studies, we explore the allowed regions of chiral Lagrangian parameters and meson couplings to pions. We reveal a structure of kinks at all orders in the chiral expansion and develop analytical tools to show that kinks always correspond to amplitudes with a single light pole. We build (scalar- and vector-less) deformations of the Lovelace-Shapiro and Coon UV-complete amplitudes, and show that they lie close to the boundaries. Moreover, constraints from crossing-symmetry imply that meson couplings to pions become smaller as their spin increases, providing an explanation for the success of Vector Meson Dominance and holographic QCD. We study how these conclusions depend on assumptions about the high-energy behavior of amplitudes. Finally, we emphasize the complementarity between our results and Lattice computations in the exploration of large-Nc QCD.

Isospin-conserving hadronic decay of the D s1(2460) into D s π + π −

The internal structure of the charm-strange mesons and D s1(2460) are the subject of intensive studies. Their widths are small because they decay dominantly through isospin-breaking hadronic channels and . The D s1(2460) can also decay into the hadronic final states , conserving isospin. In that case there is, however, a strong suppression from phase space. We study the transition in the scenario that the D s1(2460) is a D * K hadronic molecule. The π π final state interaction is taken into account through dispersion relations. We find that the ratio of the partial widths of the obtained in the molecular picture is consistent with the existing experimental measurement. More interestingly, we demonstrate that the π + π − invariant mass distribution shows a double bump structure, which can be used to disentangle the hadronic molecular picture from the compact state picture for the D s1(2460)+. Predictions on the are also made.

Light-front wave functions of vector mesons in an algebraic model

Inspired by the recent development of an algebraic model which provides an adequate and unified description of the internal structure of the lowest-lying pseudoscalar mesons, belonging both to the light quarks sector and to the one of heavy quarks, we perform its first extension to the vector-meson case. The algebraic model describes the meson's structure in terms of the spectral density function that appears in a Nakanishi integral representation of the covariant quark-antiquark bound-state amplitude, i.e., the Bethe-Salpeter amplitude. We compute the leading-twist light-front wave functions of the $\ensuremath{\rho}(770)$, $\ensuremath{\phi}(1020)$, $J/\ensuremath{\psi}$, and $\mathrm{\ensuremath{\Upsilon}}(1S)$ mesons through their connection with the parton distribution amplitudes. Among the results we present, the following are of particular interest: (i) transverse light-front wave functions can be obtained algebraically from the corresponding parton distribution amplitudes, whereas that is not the case for longitudinal light-front wave functions, which requires an intermediate step where a spectral density function must be derived from the particular parton distribution amplitude; (ii) the derived spectral density functions show marked differences between light and heavy vector mesons, the latter being narrower as compared to the former, and these are also nonpositive definite, although the integral over the entire curve is larger than zero as expected; and (iii) the longitudinal and transverse light-front wave functions of vector mesons with light quark content exhibit steep $x$ and ${p}_{\ensuremath{\perp}}^{2}$ dependence, while those of the $J/\ensuremath{\psi}$ and $\mathrm{\ensuremath{\Upsilon}}(1S)$ mesons are characterized by narrow distributions in the $x$ range but, comparatively, much more gradual falloffs with respect to the ${p}_{\ensuremath{\perp}}^{2}$ range depicted.

Parton Distribution Functions for Pseudoscalar Mesons in the Confining Effective Chiral Quark Theory

This review paper presents the gluon, sea, and valence quark distributions of the pseudoscalar (PS) mesons. The calculations of the parton structure of PS mesons are performed using the Bethe-Salpeter equation-Nambu--Jona-Lasinio (BSE-NJL) model, which offers a clear description of the dynamical chiral symmetry breaking (D$\chi$SB) of the low-energy nonperturbative quantum chromodynamics (QCD), with the help of the Schwinger proper-time regularization scheme that simulates the color QCD confinement. Our results for the dynamical quark mass -- which emerged from the spontaneous chiral symmetry breaking (S$\chi$SB) -- are generated via the chiral condensate in the chiral limit and beyond. Results for the valence parton distribution functions for the PS meson at the factorization scale $Q = 2$ GeV are in excellent agreement with experimental data and the gluon distribution for the pion fitted well with the lattice QCD and Jefferson Lab Angular Momentum (JAM) QCD global fit analysis.

Next-to-leading order (NLO) perturbative effects in QCD sum-rule analyses of light tetraquark systems: A case study in the scalar-isoscalar channel

QCD sum-rule mass predictions for tetraquark states provide insights on the interpretations and internal structure of experimentally-observed exotic mesons. However, the overwhelming majority of tetraquark QCD sum-rule analyses have been performed at leading order (LO), which raises questions about the underlying theoretical uncertainties from higher-loop corrections. The impact of next-to-leading order (NLO) perturbative effects are systematically examined in scalar (JPC=0++) isoscalar light-quark tetraquark systems where comprehensive LO sum-rule analyses have been performed and NLO perturbative corrections to the correlators have previously been calculated. Using the scalar-isoscalar state as a detailed case study to illustrate the differences between LO and NLO analyses, it is shown that NLO effects in individual Laplace sum-rules are numerically significant and have an important role in improving the reliability of the sum-rule analyses by widening the Borel window. However, ratios of sum-rules are found to be less sensitive to NLO effects with the additional advantage of cancelling the anomalous dimension that emerges from the NLO corrections. NLO mass predictions based on these sum-rule ratios are thus remarkably robust despite the slow perturbative convergence of the underlying correlator. The mass predictions 0.52GeV<mσ<0.77GeV for the lightest scalar-isoscalar σ state are in good agreement with the four-quark interpretation of the f0(500), and the relative coupling strengths of the f0(980) and f0(500) to the tetraquark current agree with the pattern found in chiral Lagrangian analyses. Effects of the σ resonance width are studied for different models, including resonance shapes inspired by chiral Lagrangians.

Hadron structure from basis light-front quantization

We present our recent progress in applying basis light-front quantization approach to investigate the structure of the light mesons and the nucleon.

Hadron research with AMBER at CERN

The recently approved NA66/AMBER experiment (Apparatus for Meson and Baryon Experimental Research) at the CERN Super Proton Synchrotron pursues a broad research program in quantum chromodynamics. It ranges in its first phase from a precision measurement of the proton radius with a 100 GeV muon beam to investigating the quark-gluon structure of mesons in Drell-Yan processes. In a second phase, radio-frequency separated kaon beams will allow to extend such investigations to the strangeness sector.

Internal structure of pion and kaon: an algebraic model and its implications

We describe an algebraic approach to address aspects of the structure of pseudo-scalar mesons through their corresponding generalized parton distributions, from which parton distribution functions and electromagnetic form factors can be derived. A direct relation between such distributions and the so-called parton distribution amplitudes can be established since the generalized parton distributions are obtained from the overlap of light-front wave functions.