Meson Spectrum Research Articles

Hydrodynamic description of D meson production in high-energy heavy-ion collisions * *Supported by the National Key Research and Development Program of China (2020YFE0202002); the National Natural Science Foundation of China (11935007, 11221504, 11861131009, 12075098, 11890714); the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of Nuclear Physics, of the U.S. Department of Energy (DOE) (DE-

The large values and constituent-quark-number scaling of the elliptic flow of low- D mesons imply that charm quarks, initially produced through hard processes, might be partially thermalized through strong interactions with quark-gluon plasma (QGP) in high-energy heavy-ion collisions. To quantify the degree of thermalization of low- charm quarks, we compare the meson spectra and elliptic flow from a hydrodynamic model to experimental data as well as transport model simulations. We use an effective charm chemical potential at the freeze-out temperature to account for the initial charm quark production from hard processes and assume that they are thermalized in the local comoving frame of the medium before freeze-out. mesons are sampled statistically from the freeze-out hyper-surface of the expanding QGP as described by the event-by-event (3+1)D viscous hydrodynamic model CLVisc. Both the hydrodynamic and transport models can describe the elliptic flow of mesons at GeV/c as measured in Au+Au collisions at GeV. Though the experimental data on spectra are consistent with the hydrodynamic result at small GeV/c, they deviate from the hydrodynamic model at high transverse momentum, GeV/c. The diffusion and parton energy loss mechanisms in the transport model can describe the measured spectra reasonably well within the theoretical uncertainty. Our comparative study indicates that charm quarks only approach local thermal equilibrium at small , even though they acquire sizable elliptic flow comparable to light-quark hadrons at both small and intermediate .

Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system

Hulthén plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. We solved the radial Schrödinger equation analytically using the Nikiforov-Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons such as charmonium and bottomonium. Four special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, Yukawa potential, Coulomb potential, and Hulthén potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

The case of equivalence of low and high energy constraints on Regge vector spectrum in AdS/QCD

The AdS/QCD models are believed to interpolate between low and high energy sectors of QCD. This belief is usually based on observations that many phenomenologically reasonable predictions follow from bounds imposed at high energies although the hypothetical range of applicability of semiclassical bottom-up holographic models is restricted by the gauge/gravity duality to low energies where QCD is strongly coupled. For testing the feasibility of high energy constraints it is interesting to calculate holographically some observable constants at low and high momenta independently and compare. We consider an AdS/QCD model describing the Regge-like linear spectrum of spin-1 mesons in a general form and show that under definite physical assumptions, the low-energy constraints on two-point correlation functions lead to nearly the same numerical values for the parameters of linear radial spectrum as the high energy ones. The found approximate coincidence looks surprising in view of the fact that such a property for observables is natural for conformal theories while real strong interactions are not conformal.

Effect of the anomalous magnetic moment of quarks on magnetized QCD matter and meson spectra

We systematically investigate the effects made by the anomalous magnetic moment (AMM) of quark in the magnetized QCD matter, including the magnetic susceptibility, the inverse magnetic catalysis around the critical temperature and the modified neutral and or charged pion and rho meson's spectra. The dynamical AMM of quark, coupling with magnetic field, causes Zeeman splitting in the energy dispersion of quark and thus changes the magnetism properties and masses of magnetized mesons. Unfortunately, we found that the lattice results of the quark matter under magnetic fields cannot fully be explained via including the AMM interaction. It is observed that the AMM of quark reduces the dynamical quark mass and therefore induces the inverse magnetic catalysis around ${T}_{c}$. The neutral pion is very sensitive to the AMM term and its mass decreases with magnetic field quickly. On the contrary, the charged pion mass shows a nontrivial behavior, i.e., linearly increases with the weak and moderate magnetic fields and then saturates at strong region. For rho mesons, AMM coupling modifies the masses of neutral rho particles for all ${s}_{z}$ consistently, while it reduces the masses of charged rho mesons for ${s}_{z}=+1$, 0 but enhances the mass of ${s}_{z}=\ensuremath{-}1$ state. The magnetic susceptibility at low temperatures can be either positive or negative with different strengths of AMM interaction.

Chiral effective Lagrangian for excited heavy-light mesons from QCD

We derive the chiral effective Lagrangian for excited heavy-light mesons from QCD under proper approximations. We focus on the chiral partners with and which amounts to (1+, 2+) and (1−, 2−) states respectively. The low energy constants including the masses of the chiral partners are calculated. The calculated spectrum for the excited mesons are found roughly consistent with experimental data. In addition, our results indicate that quantum numbers of B J (5970) can be identified with 1− or 2−.

Meson spectrum in the large N limit

We present the result of our computation of the lowest lying meson masses for SU(N) gauge theory in the large N limit (with Nf /N → 0). The final values are given in units of the square root of the string tension, and with errors which account for both statistical and systematic errors. By using 4 different values of the lattice spacing we have seen that our results scale properly. We have studied various values of N (169, 289 and 361) to monitor the N-dependence of the most sensitive quantities. Our methodology is based upon a first principles approach (lattice gauge theory) combined with large N volume independence. We employed both Wilson fermions and twisted mass fermions with maximal twist. In addition to masses in the pseudoscalar, vector, scalar and axial vector channels, we also give results on the pseudoscalar decay constant and various remormalization factors.

Predictions for the beauty meson spectrum

We predict the spectrum of the four $1S$ and eight $1P$ nonstrange and strange states in the beauty meson family in the context of effective field theory. By the union of heavy quark effective theory and chiral perturbation theory, the mass formalisms for the heavy-light mesons are defined. Our analysis uses mass expressions involving, for the first time, the full leading self-energy corrections and leading power corrections to the heavy quark and chiral limits. The counterterms present in these expressions are fitted using available experimental and theoretical information on the charmed meson masses and couplings. The results from charm sector are used to make theoretical expectations on the analog beauty meson spectrum. The observed spectrum of the ground state, $B^{(*)}_{(s)}$, and excited, $B_{(s)1}$ and $B^*_{(s)2}$, beauty mesons are well reproduced in our theoretical calculations. The excited scalar, $B^*_{(s)0}$, and axial-vector, $B^\prime_{(s)1}$, beauty mesons have not yet been discovered. Hopefully our predictions may provide valuable clues to further experimental exploration of these missing resonances.

Coupling Hadron-Hadron Thresholds within a Chiral Quark Model Approach

Heavy hadron spectroscopy was well understood within the naive quark model until the end of the past century. However, in 2003, the X(3872) was discovered, with puzzling properties difficult to understand in the simple naive quark model picture. This state made clear that excited states of heavy mesons should be coupled to two-meson states in order to understand not only the masses but, in some cases, unexpected decay properties. In this work, we will give an overview of a way in which the naive quark model can be complemented with the coupling to two hadron thresholds. This program has been already applied to the heavy meson spectrum with the chiral quark model, and we show some examples where thresholds are of special relevance.

The large limit of QCD on the lattice.

We review recent progress in the study of the large N_c limit of gauge theories from lattice simulations. The focus is not only the planar limit but also the size of {{mathcal {O}}}(N_c^{-1}) corrections for values of N_cgtrsim 3. Some concrete examples of the topics we include are tests of large-N_c factorization, the topological susceptibility, the glueball, meson and baryon spectra, the chiral dependence of masses and decay constants, and weak matrix elements related to the varDelta I=1/2 rule in kaon decays.

Gauge/gravity dual dynamics for the strongly coupled sector of composite Higgs models

A holographic model of chiral symmetry breaking is used to study the dynamics plus the meson and baryon spectrum of the underlying strong dynamics in composite Higgs models. The model is inspired by top-down D-brane constructions. We introduce this model by applying it to Nf = 2 QCD. We compute meson masses, decay constants and the nucleon mass. The spectrum is improved by including higher dimensional operators to reflect the UV physics of QCD. Moving to composite Higgs models, we impose perturbative running for the anomalous dimension of the quark condensate in a variety of theories with varying number of colors and flavours. We compare our results in detail to lattice simulations for the following theories: SU(2) gauge theory with two Dirac fundamentals; Sp(4) gauge theory with fundamental and sextet matter; and SU(4) gauge theory with fundamental and sextet quarks. In each case, the holographic results are encouraging since they are close to lattice results for masses and decay constants. Moreover, our models allow us to compute additional observables not yet computed on the lattice, to relax the quenched approximation and move to the precise fermion content of more realistic composite Higgs models not possible on the lattice. We also provide a new holographic description of the top partners including their masses and structure functions. With the addition of higher dimension operators, we show the top Yukawa coupling can be made of order one, to generate the observed top mass. Finally, we predict the spectrum for the full set of models with top partners proposed by Ferretti and Karateev.

A new variational approach and its application toheavy quarkonia

By combining the variational principle with Heisenberg uncertaintyprinciple in an effective Hamiltonian for heavy flavored mesons, we in-troduce a framework to estimate masses and radii of these states froman analytical constraint. In a novel manner, a model for quark velocityand a model for quark momentum width are introduced. These kinemat-ical model parameters are obtained as analytical functions of inter quarkseparation in heavy quarkonia. The values of such quark parameters arethen used in the calculation of S-wave annihilation decay rates of \bar{c}c and\bar{b} b. To test the accuracy of our technique we first calculate the spin averaged masses, scalar radii and annihilation decay rates of charmoniumand bottomonium without and with relativistic corrections by solving theSchrödinger wave equation with the appropriate parametrization of the Song-Lin potential. The Schrödinger wave equation is solved numericallywith the matrix Numerov method and we observe a good agreement withthe experimental measurements and other theoretical calculations and extract strong running coupling constant for \bar{c}c and \bar{b}b systems. In non rel-ativistic settings, heavy meson spectra have been obtained and extended to rather higher excited states within our framework by using bare masses of c and b quarks which we have extracted from analysis of experimentaldata

Light neutral meson production in heavy ion collisions with ALICE in the era of precision physics at the LHC

The production of light neutral mesons in AA collisions probes the physics of the Quark-Gluon Plasma (QGP), which is formed in heavy-ion collisions at the LHC. More specifically, the centrality dependent neutral meson spectra in AA collisions compared to its spectra in minimum-bias pp collisions, scaled with the number of hard collisions, provides information on the energy loss of partons traversing the QGP. The measurement allows to test with high precision the predictions of theoretical model calculations. In addition, the decay of the π0 and η mesons are the dominant back- grounds for all direct photon measurements. Therefore, pushing the limits of the precision of neutral meson production is key to learning about the temperature and space-time evolution of the QGP.In the ALICE experiment neutral mesons can be detected via their decay into two photons. The latter can be reconstructed using the two calorimeters EMCal and PHOS or via conversions in the detector material. The excellent momentum resolution of the conversion photons down to very low pT and the high reconstruction efficiency and triggering capability of calorimeters at high pT, allow us to measure the pT dependent invariant yield of light neutral mesons over a wide kinematic range.Combining state-of-the-art reconstruction techniques with the high statistics delivered by the LHC in Run 2 gives us the opportunity to enhance the precision of our measurements. In these proceedings, new ALICE run 2 preliminary results for neutral meson production in pp and Pb–Pb collisions at LHC energies are presented.

Pion quasiparticles and QCD phase transitions at finite temperature and isospin density from holography

Spectra of pions, which are known as the pseudo-Goldstone bosons of spontaneous chiral symmetry breaking, as well as their relationship with chiral phase transition and pion superfluidity phase transition, have been investigated in the framework of soft-wall AdS/QCD. In chiral limit, it is proved both numerically and analytically that pions are massless Goldstone bosons even at finite temperature, which was usually considered as an assumption in soft-wall models. Above $T_c$, at which chiral condensate $\langle \bar{q}q\rangle$ vanishes, the spectra of pions and scalar mesons merge together, showing the evidence of the restored chiral symmetry in hadronic spectrum level. Extending to finite quark mass, pion masses increase with quark mass. Further, it is more interesting to observe that the pole masses of pions decrease with temperature below $T_c$, which agrees with the analysis in Phys.Rev.Lett.88(2002)202302. Meanwhile, symmetry restoration above $T_c$ could be seen in the spectra of scalar and pseudo-scalar mesons. With finite temperature and isospin chemical potential $\mu_I$, it is shown that the masses of charged pions would split. The mass of positive charged pion $\pi^+$ decreases almost linearly to zero when $\mu_I$ grows to $\mu_{I}^c$, where pion condensation starts to form. This reveals the Goldstone nature of $\pi^+$ after pion superfluidity transition, which are closely related to the experimental observation.

Analytical Solutions of the Schrödinger Equation with Class of Yukawa Potential for a Quarkonium System Via Series Expansion Method

A class of Yukawa potential is adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. The potential was made to be temperature-dependent by replacing the screening parameter with Debye mass. We solved the radial Schrödinger equation analytically using the series expansion method and obtained the energy eigenvalues. The present results are applied for calculating the mass spectra of heavy mesons such as charmonium and bottomonium . Two special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, and Coulomb potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

Relative scale setting for two-color QCD with $N_f=2$ Wilson fermions

Abstract We determine the scale-setting function and the pseudocritical temperature on the lattice in $N_f=2$ two-color quantum chromodynamics (QCD) using the Iwasaki gauge and Wilson fermion actions. Although two-color QCD does not correspond to the real world, it is very useful as a good testing ground for three-color QCD. The scale-setting function gives the relative lattice spacings of simulations performed at different values of the bare coupling. It is a necessary tool for taking the continuum limit. First, we measure the meson spectra for various combinations of ($\beta,\kappa$) and find a line of constant physics in the $\beta$–$\kappa$ plane. Next, we determine the scale-setting function via $w_0$ scale in the gradient flow method. Furthermore, we estimate the pseudocritical temperature at zero chemical potential from the chiral susceptibility. Combining these results, we can discuss the QCD phase diagram in which both axes are given by dimensionless quantities, namely the temperature normalized by the pseudocritical temperature on the lattice and the chemical potential normalized by the pseudoscalar meson mass. This makes it easy to compare among several lattice studies, and also makes it possible to compare theoretical analyses and lattice studies in the continuum limit.

A new machine learning approach for predicting the spectra of meson bound states

In this paper, we investigate the benefits of machine learning (ML) approaches in predicting the spectra of meson bound states. A linear model (LM) approach is used to predict the spectra of some heavy mesons. Our proposed method has been successfully reproduced in recent experiments, to validate known outcomes. Our results are compared favorably to those obtained using other techniques. This novel perspective opens up a new future in the use of ML in the field of particle physics.

Vector mesons spectrum in a medium with a chiral imbalance induced by the vacuum of fermions

The properties of the light vector mesons in the presence of local parity breaking medium with a chiral imbalance are considered in the vector-meson dominance model. Applying the finite lowest-order radiatively induced local effective Lagrangian, initially developed for the QED, for the vector ρ and ω mesons, we obtained the mass spectrum as a function of momentum and chiral chemical potential μ5. We showed that in addition to the Chern–Simons term, splitting the transverse polarisations of the mesons, there is another radiatively induced contribution that becomes important at momentum and μ 5 around a few hundred MeV.

Relativistic Friedrichs\u2013Lee model and quark-pair creation model

In this paper, we present how the Friedrichs–Lee model could be extended to the relativistic scenario and be combined with the relativistic quark pair creation model in a consistent way. This scheme could be applied to study the “unquenched” effect of the meson spectra. As an example, if the lowest J^{PC}=0^{++}(ubar{u}+dbar{d})/sqrt{2} bound state in the potential model is coupled to the pi pi continuum, two resonance poles could be found from the scattering amplitude for the continuum states. One of them could correspond to the f_0(500)/sigma and the other probably f_0(1370). This scheme might shed more light on why extra states could appear in the hadron spectrum other than the prediction of the quark potential model.

Relativistic Cornell-type mechanism of exotic scalar resonances

The physical masses of the lowest scalar mesons strongly disagree with the calculated $q\overline{q}$ pole values. It is the purpose of this paper to explain theoretically the unusual spectrum of scalar mesons for both the ground and excited states, using the known spectra of the corresponding $q\overline{q}$ states and their connection to the meson resonances. The well-known Cornell coupled-channel mechanism is exploited for this connection together with the quark-chiral Lagrangian without fitting parameters. In addition to the scalars previously obtained using this method, ${f}_{0}(500)$, ${f}_{0}(980)$, ${a}_{0}(980)$, we predict all ground and first excited scalar states, ${f}_{0}(500)$, ${f}_{0}(980)$, ${a}_{0}(980)$, ${a}_{0}(1450)$, ${K}_{0}^{*}(700)$, ${K}_{0}^{*}(1430)$, ${f}_{0}(1370)$, ${f}_{0}(1710)$, which are in reasonably good agreement with experimental data.

Scalar spectrum in a graviton soft wall model

In this study we present a unified phenomenological analysis of the scalar glueball and scalar meson spectra within an AdS/QCD framework in the bottom up approach. For this purpose we generalize the recently developed graviton soft-wall (GSW) model, which has shown an excellent agreement with the lattice QCD glueball spectrum, to a description of glueballs and mesons with a unique energy scale. In this scheme, dilatonic effects, are incorporated in the metric as a deformation of the AdS space. We apply the model also to the heavy meson spectra with success. We obtain quadratic mass equations for all scalar mesons while the glueballs satisfy an almost linear mass equation. Besides their spectra, we also discuss the mixing of scalar glueball and light scalar meson states within a unified framework: the GSW model. To this aim, the light-front (LF) holographic approach, which connects the mode functions of AdS/QCD to the LF wave functions, is applied. This relation provides the probabilistic interpretation required to properly investigate the mixing conditions.