Light Scalar Mesons Research Articles

Walking-dilaton hybrid inflation with B − L Higgs embedded in dynamical scalegenesis

We propose a hybrid inflationary scenario based on eight-flavor hidden QCD with the hidden colored fermions being in part gauged under U(1)B−L. This hidden QCD is almost scale-invariant, so-called walking, and predicts the light scalar meson (the walking dilaton) associated with the spontaneous scale breaking, which develops the Coleman-Weinberg (CW) type potential as the consequence of the nonperturbative scale anomaly, hence plays the role of an inflaton of the small-field inflation. The U(1)B−L Higgs is coupled to the walking dilaton inflaton, which is dynamically induced from the so-called bosonic seesaw mechanism. We explore the hybrid inflation system involving the walking dilaton inflaton and the U(1)B−L Higgs as a waterfall field. We find that observed inflation parameters tightly constrain the U(1)B−L breaking scale as well as the walking dynamical scale to be ~ 109 GeV and ~ 1014 GeV, respectively, so as to make the waterfall mechanism worked. The lightest walking pion mass is then predicted to be around 500 GeV. Phenomenological perspectives including embedding of the dynamical electroweak scalegenesis and possible impacts on the thermal leptogenesis are also addressed.

Hadronic structure on the light front. VIII. Light scalar and vector mesons

We use the QCD instanton vacuum model to discuss the emergence of the light scalar and vector mesons on the light front. We take into account both the instanton and anti-instanton single and molecular interactions on the light quarks, in the form of nonlocal effective interactions. Although the molecular induced interactions are suppressed by a power of the packing fraction, they are still sufficient to bind the vector mesons, while keeping most of the scalar spectrum relatively unchanged. We explicitly derive the light front distribution amplitudes and partonic functions for the scalar and vector mesons, and compare them after pertinent QCD evolution, to the available empirical and lattice measured counterparts. The Dirac electric form factors for both the pion and ρ meson are derived, and shown to compare well with current data. Published by the American Physical Society 2024

Form factors of B(s) to light scalar mesons with the B -meson light-cone sum rules

In this work, the transition form factors of the semileptonic decays of B(s) to the light scalar mesons with masses close to 1.5 GeV such as K0*(1430),a0(1450), and f0(1500) are calculated in the framework of the light-cone sum rules. For this purpose, the two- and three-particle B-meson distribution amplitudes (DAs) are used. Note that it is possible to use the B-meson DAs for the Bs meson in the SU(3)F symmetry limit. The transition form factors are obtained in terms of the two-particle DAs up to twist-five accuracy, and the three-particle up to twist-six level. We apply two classes of the phenomenological models for the DAs of the B meson. The longitudinal lepton polarization asymmetries and branching fractions for the semileptonic decays of B(s) to the light scalar mesons are estimated with the help of these form factors. Published by the American Physical Society 2024

Electromagnetic form factors in a contact interaction: scalar and pseudoscalar mesons

The determination of fundamental properties of hadrons is important to clearly understand the experimental measurements such as the anomalous magnetic moment of the muon. However, since a first principle approach is hard to find, several groups among the world are approaching phenomenologically to such description of hadrons. In this poster, we present a comprehensive survey of electromagnetic form factors of all light, heavy and heavy-light ground-state pseudoscalar and scalar mesons. Specifically, in this work we are interested on the determination of Elastic Meson Form Factors (EFF) for Scalar (S) and Pseudoscalar (PS) mesons. However, the calculation of all EFF requires the computation of the quark propagator, the Bethe-Salpeter (BS) equation and the Bethe-Salpeter Amplitudes (BSA) of mesons, their masses as well as the knowledge of the quark-photon interaction at different probing momenta.

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.

Scrutinizing the light scalar quarkonia from LSR at higher orders

We scrutinize, improve some determinations of the masses and couplings of light scalar quarkonia (q¯q and four-quark states) and present new results for the π+π−,K+K−,… molecules using QCD Laplace Sum Rule (LSR) truncated at the D=6 dimension vacuum condensates. We pay a special attention on the higher order perturbative (PT) corrections up to the (estimated) O(αs5) which improve the quality of the analysis. We request that the optimal results obey the rigorous constraint: Resonance ≥ QCD continuum contributions (RP/C≥1) in the LSR which excludes a Breit-Wigner/on-shell (not to be confused with a complex pole) scalar meson mass around (500-600) MeV obtained for values [tc≤(1∼1.5) GeV2] of the QCD continuum threshold. Mass-splittings due to SU(3) breakings are small. We discuss the different assignments of the observed scalar mesons below 2 GeV in the Conclusions where the I=0 states are compared with the scalar gluonia. The results are compiled in Tables 3 to 6. We hope that the systematic analysis done in this paper helps to clarify the complex spectra of the light scalar mesons.

Note on the definitions of branching ratios of overlapping resonances

Branching ratios for the decay of hadrons with large width or near thresholds depend on their definition. We test different definitions and show that rather different branching ratios can be obtained. For wide resonances and for sequential decays with wide intermediate resonances, integration over the spectral functions is mandatory. The tests are performed exploiting the latest solution of the Bonn-Gatchina multi-channel analysis and published values for residues of light scalar mesons. For a resonance overlapping with a threshold, in case its pole lies in a non-adjacent sheet, we show how the total width, needed for the branching ratios, does not correspond to the imaginary part of the pole position. We use the Madrid-Krakow dispersive parameterizations to illustrate this situation with the f0(980).

Electromagnetic form factors and charge radii of pseudoscalar and scalar mesons: A comprehensive contact interaction analysis

We carry out a comprehensive survey of electromagnetic form factors of all light, heavy and heavy-light ground-state pseudoscalar and scalar mesons. Our analysis is based upon a Schwinger-Dyson equations treatment of a vector $\times$ vector contact interaction. It incorporates confinement and ensures axial vector and vector Ward-Takahashi identities are satisfied along with the corresponding corollaries such as the Goldberger-Treiman relations. The algebraic simplicity of the model allows us to compute the form factors at arbitrarily large virtualities of the probing photon momentum squared with relative ease. Wherever possible and insightful, we compare our results for the electromagnetic form factors and the charge radii with those obtained earlier through Schwinger-Dyson equations, lattice and with experimental observations available. We also comment on the scope and shortcomings of the model.

Four-Quark Nature of Light Scalar Mesons

The contribution of Novosibirsk physicists to the discovery of the four-quark nature of light scalar mesons f0(980) and a0(980) is described.

Study of light scalar mesons through Ds+→π0π0e+νe and KS0KS0e+νe decays

Using 6.32~fb$^{-1}$ of $e^+e^-$ collision data recorded by the BESIII detector at center-of-mass energies between $4.178$ to $4.226$~GeV, we present the first measurement of the decay $D_s^+\to f_0(980)e^+\nu_e,\,f_0(980)\to \pi^0\pi^0$. The product branching fraction of $D_s^+\to f_0(980)e^+\nu_e,\,f_0(980)\to \pi^0\pi^0$ is measured to be $(7.9\pm1.4_{\rm stat} \pm0.3_{\rm syst})\times 10^{-4}$, with a statistical significance of $7.8\sigma$. Furthermore, the upper limits on the product branching fractions of $D_s^+\to f_0(500)e^+\nu_e$ with $f_0(500)\to \pi^0\pi^0$ and the branching fraction of $D_s^+\to K_{S}^{0}K_{S}^{0}e^+\nu_e$ are set to be $6.4\times 10^{-4}$ and $3.9\times 10^{-4}$ at 90\% confidence level, respectively. Our results provide valuable inputs to the understanding of the structures of light scalar mesons.

Hadronic three-body D decays mediated by scalar resonances

We study the quasi-two-body $D\ensuremath{\rightarrow}SP$ decays and the three-body $D$ decays proceeding through intermediate scalar resonances, where $S$ and $P$ denote scalar and pseudoscalar mesons, respectively. Our main results are the following: (i) Certain external and internal $W$-emission diagrams with the emitted meson being a scalar meson are na\"{\i}vely expected to vanish, but they actually receive contributions from vertex and hard spectator-scattering corrections beyond the factorization approximation. (ii) For light scalars with masses below or close to 1 GeV, it is more sensible to study three-body decays directly and compare with experiment as the two-body branching fractions are either unavailable or subject to large finite-width effects of the scalar meson. (iii) We consider the two-quark (scheme I) and four-quark (scheme II) descriptions of the light scalar mesons, and find the latter generally in better agreement with experiment. This is in line with recent BESIII measurements of semileptonic charm decays that prefer the tetraquark description of light scalars produced in charmed meson decays. (iv) The topological amplitude approach fails here as the $D\ensuremath{\rightarrow}SP$ decay branching fractions cannot be reliably inferred from the measurements of three-body decays, mainly because the decay rates cannot be factorized into the topological amplitude squared and the phase space factor. (v) The predicted rates for ${D}^{0}\ensuremath{\rightarrow}{f}_{0}P,{a}_{0}P$ are generally smaller than experimental data by one order of magnitude, presumably implying the significance of $W$-exchange amplitudes. (vi) The $W$-annihilation amplitude is found to be very sizable in the $SP$ sector with $|A/T{|}_{SP}\ensuremath{\sim}1/2$, contrary to its suppression in the $PP$ sector with $|A/T{|}_{PP}\ensuremath{\sim}0.18$. (vii) Finite-width effects are very important for the very broad $\ensuremath{\sigma}/{f}_{0}(500)$ and $\ensuremath{\kappa}/{K}_{0}^{*}(700)$ mesons. The experimental branching fractions $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}\ensuremath{\sigma}{\ensuremath{\pi}}^{+})$ and $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{\overline{\ensuremath{\kappa}}}^{0}{\ensuremath{\pi}}^{+})$ are thus corrected to be $(3.8\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $(6.{7}_{\ensuremath{-}4.5}^{+5.6})%$, respectively.

Perturbative QCD analysis of neutral B-meson decays into sigma sigma , sigma f_0 and f_0 f_0

The decays of B_{d,s}^0 rightarrow sigma sigma , sigma f_0, f_0 f_0, with sigma and f_0 denoting the light scalar mesons f_0(500) and f_0(980) in the two-quark picture, are studied in the perturbative QCD approach based on k_T factorization. With the referenced value of the mixing angle |varphi | sim 25^circ for the sigma -f_0 mixing in the quark-flavor basis, it is of great interest to obtain that: (a) these neutral B-meson decays into sigma sigma , sigma f_0, and f_0 f_0 have large branching ratios in the order of 10^{-6}{-}10^{-4}, which mean the possibly constructive interferences existed in the decays with different flavor states, and then are expected to be tested at the Large Hadron Collider beauty and/or Belle-II experiments in the (near) future; (b) the large direct CP violations could be easily found in the B_d^0 rightarrow sigma sigma , f_0 f_0 and B_{d,s}^0 rightarrow sigma f_0 decays, which indicate the considerable interferences between the tree and the penguin decay amplitudes involved in these four modes, and would be confronted with the future measurements; (c) these neutral B-meson decays could be examined through the secondary decay chain sigma /f_0 rightarrow pi ^+ pi ^-, namely, the four-body decays of B_{d,s}^0 rightarrow (pi ^+ pi ^-)_{sigma (f_0)} (pi ^+ pi ^-)_{sigma (f_0)} with still large branching ratios. On the other side, it seems that other 4 four-body decays of B_d^0 rightarrow (pi ^+ pi ^-)_{sigma } (K^+ K^-)_{f_0}, B_s^0 rightarrow (pi ^+ pi ^-)_{sigma (f_0)} (K^+ K^-)_{f_0}, and B_s^0 rightarrow (K^+ K^-)_{f_0} (K^+ K^-)_{f_0} could also be detected at the relevant experiments, if the f_0 rightarrow K^+ K^- could be identified from the phi rightarrow K^+ K^- clearly. The (near) future experimental confirmations with good precision would help to further study the perturbative and/or nonperturbative QCD dynamics involved in these considered decay modes, as well as to explore the intrinsic characters of these scalar mesons sigma and/or f_0 and to constrain both of the magnitude and the sign of varphi .

Light-meson scattering dispersive analyses and light-scalar meson spectroscopy. Where do we stand?

In this talk I reviewed the present status and recent progress on lightmeson scattering analyses, by means of dispersive or analytic methods. The recent application of these model independent techniques have settled the controversy about the existence and parameters of long debated light meson resonances. I will thus discuss here the state of the art and recent changes on our knowledge about the spectroscopy of light scalar mesons when observed from such scattering processes.

Cabibbo-favored [formula omitted] decay in the final state interaction

The anti-triplet charmed baryon decays with the light scalar mesons are rarely measured, whereas the recent observation of the Cabibbo-favored Λc+→Ληπ+ decay hints a possible Λc+→Λa0(980)+,a0(980)+→ηπ+ process. We hence study the Λc+→Λa0(980)+ decay. Particularly, it is found that the final state interaction can give a significant contribution, where Σ+(1385) and η in Λc+→Σ+(1385)η by exchanging a charged pion are transformed as Λ and a0(980)+, respectively. Accordingly, we predict B(Λc+→Λa0(980)+)=(1.7−1.0+2.8±0.3)×10−3, accessible to the BESIII, BELLEII and LHCb experiments.

Meson and glueball spectroscopy within the graviton soft wall model

The graviton soft wall (GSW) model provides a unified description of the scalar glueball and meson spectra with a unique energy scale. This success has led us to extend the analysis to the description of the spectra of other hadrons. We use this model to calculate masses of the odd and even ground states of glueballs for various spins, and show that the GSW model is able to reproduce the Regge trajectory of these systems. In addition, the spectra of the $\ensuremath{\rho}$, ${a}_{1}$ and $\ensuremath{\eta}$ mesons will be addressed. Results are in excellent agreement with current experimental data. Furthermore such an achievement is obtained without any additional parameters. Indeed, the only two parameters appearing in these spectra are those that were previously fixed by the light scalar meson and glueball spectra. Finally, in order to describe the $\ensuremath{\pi}$ meson spectrum, a suitable modification of the dilaton profile function has been included in the analysis to properly take into account the Goldstone realization of chiral symmetry. The present investigation confirms that the GSW model provides an excellent description of the spectra of mesons and glueballs with only a small number of parameters unveiling a relevant predicting power.

Spinless mesons and glueballs mixing patterns in SU(3) flavor limit

We present a detailed study of the interactions among scalar and pseudoscalar mesons and glueballs within the framework of the generalized linear sigma model in the SU(3) flavor limit. The basis of our approach is to develop a global understanding of light scalar and pseudoscalar mesons (up to around 2 GeV) and thereby explore the underlying mixings among composite quark matter fields and glueballs. The chiral sector of the Lagrangian is formulated in terms of two chiral nonets representing quark-antiquarks and tetraquarks (in the leading order, this sector contains terms with eight or fewer number of quark or antiquark lines). The Lagrangian also contains a sector that represents scalar and pseudoscalar glueballs and their interactions with the matter chiral fields, in a manner that the axial and trace anomalies of QCD are exactly realized. In this construct, the model has two scalar octets and two pseudoscalar octets (each a linear combination of two- and four-quark components), as well as three scalar SU(3) singlets and three pseudoscalar SU(3) singlets (each a linear combination of two- and four-quark components as well as a glueball component). With the inputs of the experimental masses of a0(980), a0(1450), and the masses of π(137), π(1300) and their decay constants, we perform an extensive numerical simulation to determine the boundaries of the parameter space of the model. We further incorporate experimental data on the mass spectrum of eta states as well as on several decay widths and decay ratios of f0 states to zoom in on the parameter space and make predictions for the substructure of pseudoscalar and scalar SU(3) octets and singlets as well as for the pseudoscalar and scalar glueball masses. We find the scalar and pseudoscalar glueball masses around 1.6 and 2.0 GeV, respectively.

Scalar mesons and the fragmented glueball

The center-of-gravity rule is tested for heavy and light-quark mesons. In the heavy-meson sector, the rule is excellently satisfied. In the light-quark sector, the rule suggests that the a0(980) could be the spin-partner of a2(1320), a1(1260), and b1(1235); f0(500) the spin-partner of f2(1270), f1(1285), and h1(1170); and f0(980) the spin-partner of f2′(1525), f1(1420), and h1(1415). From the decay and the production of light scalar mesons we find a consistent mixing angle θs=(14±4)∘. We conclude that f0(980) is likely “octet-like” in SU(3) with a slightly larger ss¯ content and f0(500) is SU(3) “singlet-like” with a larger nn¯ component. The a0(1450), K0⁎(1430), f0(1500) and f0(1370) are suggested as nonet of radial excitations. The scalar glueball is discussed as part of the wave function of scalar isoscalar mesons and not as additional “intruder”. It seems not to cause supernumerosity.

Light quarks at finite temperature: chiral restoration and the fate of the $$U(1)_A$$ symmetry

We review recent results on the role of light quark states within the QCD phase diagram. In particular, we will discuss how the combined use of theoretical techniques such as Effective Theories, Unitarization and Ward Identities helps to shed light on several important issues regarding chiral symmetry restoration, building bridges with recent lattice analyses. Special attention will be paid to the role of chiral and $U(1)_A$ partners in the interplay between those symmetries, which is crucial to properly understand the transition pattern. Light scalar mesons at finite temperature will be shown to be responsible for the description of susceptibilities encoding chiral and $U(1)_A$ restoration properties.

Flavor-dependent U(3) Nambu–Jona-Lasinio coupling constant

A non-perturbative one gluon exchange quark-antiquark interaction is considered to compute flavor dependent U(3) Nambu-Jona-Lasinio (NJL)-type interaction of the form $G_{ij, \Gamma} (\bar{\psi} \lambda_i \Gamma \psi ) ( \bar{\psi} \lambda_j \Gamma \psi)$ for $i,j=0...8$ and $\Gamma=I, i \gamma_5$ from one loop polarization process with non degenerate u-d-s quark effective masses. The resulting NJL-type coupling constants in all channels are resolved in the long-wavelength limit and numerical results are presented for different choices of an effective gluon propagator. Leading deviations with respect to a flavor symmetric coupling constant are found to be of the order of $(M_{f_2}^*-M_{f_1}^*)^n/(M_{f_2}^*+M_{f_1}^*)^n$, for $n=1,2$, where $M_{f_i}^*$ are the effective masses of quarks $f_1,f_2=u, d$ and $s$. The scalar channel coupling constants $G_{ij, s}$ can be considerably smaller than pseudoscalar ones. The effect of the flavor-dependence of coupling constants for the masses of pions and kaons may be nearly of the same order of magnitude as the effect of the u,d and s quark mass non-degeneracy. The effect of these coupling constants is also verified for some of the light scalar mesons masses, usually described by quark-antiquark states, and for some observables of the pseudoscalar mesons.

Where Is the Lightest Charmed Scalar Meson?

The lightest charmed scalar meson is known as the D_{0}^{*}(2300), which is one of the earliest new hadron resonances observed at modern B factories. We show here that the parameters assigned to the lightest scalar D meson are in conflict with the precise LHCb data of the decay B^{-}→D^{+}π^{-}π^{-}. On the contrary, these data can be well described by an unitarized chiral amplitude containing a much lighter charmed scalar meson, the D_{0}^{*}(2100). We also extract the low-energy S-wave Dπ phase of the decay B^{-}→D^{+}π^{-}π^{-} from the data in a model-independent way, and show that its difference from the Dπ scattering phase shift can be traced back to an intermediate ρ^{-} exchange. Our work highlights that an analysis of data consistent with chiral symmetry, unitarity, and analyticity is mandatory in order to extract the properties of the ground-state scalar mesons in the singly heavy sector correctly, in analogy to the light scalar mesons f_{0}(500) and K_{0}^{*}(700).