Hadronic Mass Spectrum Research Articles

Black magic session of concordance: Regge mass spectrum from Casson’s invariant

Recently, there had been a great deal of interest in obtaining and describing all kinds of knots in links in hydrodynamics, electrodynamics, non-Abelian gauge field theories and gravity. Although knots and links are observables of the Chern–Simons (CS) functional, the dynamical conditions for their generation lie outside the scope of the CS theory. The nontriviality of dynamical generation of knotted structures is caused by the fact that the complements of all knots/links, say, in S3are 3-manifolds which have positive, negative or zero curvature. The ability to curve the ambient space is thus far attributed to masses. The mass theorem of general relativity requires the ambient 3-manifolds to be of nonnegative curvature. Recently, we established that, in the absence of boundaries, complements of dynamically generated knots/links are represented by 3-manifolds of nonnegative curvature. This fact opens the possibility to discuss masses in terms of dynamically generated knotted/linked structures. The key tool is the notion of knot/link concordance. The concept of concordance is a specialization of the concept of cobordism to knots and links. The logic of implementation of the concordance concept to physical masses results in new interpretation of Casson’s surgery formula in terms of the Regge trajectories. The latest thoroughly examined Chew–Frautschi (CF) plots associated with these trajectories demonstrate that the hadron mass spectrum for both mesons and baryons is nicely described by the data on the corresponding CF plots. The physics behind Casson’s surgery formula is similar but not identical to that described purely phenomenologically by Keith Moffatt in 1990. The developed topological treatment is fully consistent with available rigorous mathematical and experimentally observed results related to physics of hadrons.

Instanton contributions to the low-lying hadron mass spectrum

The role of instanton-like objects in the QCD vacuum on the mass spectrum of low-lying light hadrons is explored in lattice QCD. Using over-improved stout-link smearing, tuned to preserve instanton-like objects in the QCD vacuum, the evolution of the mass spectrum under smearing is examined. The calculation is performed using a $20^3\times40$ dynamical fat-link-irrelevant-clover (FLIC) fermion action ensemble with lattice spacing 0.126 fm. Through the consideration of a range of pion masses, the effect of the vacuum instanton content is compared at a common pion mass. While the qualitative features of ground-state hadrons are preserved on instanton-dominated configurations, the excitation spectrum experiences significant changes. The underlying physics revealed shows little similarity to the direct-instanton interaction predictions of the instanton liquid model.

Hadron masses in strong magnetic fields

Hadron masses under strong magnetic fields are studied. In the presence of strong magnetic fields exceeding the QCD energy scale $ eB \gg \Lambda^2_{\rm QCD} $, ${\rm SU(3)}_{\rm flavor} \otimes {\rm SU(2)}_{\rm spin}$ symmetry of hadrons is explicitly broken so that the quark components of hadrons differ from those with zero or weak magnetic fields $ eB \lesssim \Lambda^2_{\rm QCD} $. Also, squeezing of hadrons by strong magnetic fields affects the hadron mass spectrum. We develop a quark model which appropriately incorporates these features and analytically calculate various hadron masses including mesons, baryons and those with strangeness.

Parton-hadron matter at finite temperature and chemical potential

The dynamics of partons and hadrons in ultra-relativistic nucleus-nucleus collisions is analyzed within the Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for the partonic phase (DQPM) including a dynamical hadronization scheme while reproducing lattice QCD results in thermodynamic equilibrium for the equation-of-state as well as transport coefficients like shear and bulk viscosities or the electric conductivity of the hot QCD medium. The PHSD model reproduces a large variety of observables from SPS to LHC energies, e.g. the quark-number scaling of elliptic flow, transverse mass and rapidity spectra of charged hadrons, dilepton spectra, open and hidden charm production, collective flow coefficients etc., which are associated with the observation of a strongly interacting QGP (sQGP). The ’highlights’ of the latest results from LHC energies are presented with a focus on the correlation between the average transverse momentum < pT > and the number of charged particles Nch in p-p, p-Pb and Pb-Pb collisions at midrapidity as observed by the ALICE Collaboration.

On the meson mass spectrum in the covariant confined quark model

We provide a new insight into the problem of generating the hadron mass spectrum in the framework of the covariant confined quark model. One of the underlying principles of this model is the compositeness condition, which means that the wave function renormalization constant of the elementary hadron is equal to zero. In particular, this equation allows us to express the Yukawa coupling of the meson fields to the constituent quarks as a function of other model parameters. In addition to the compositeness condition, we also employ a further equation relating the meson mass function to the Fermi coupling. Both equations guarantee that the Yukawa-type theory is equivalent to the Fermi-type theory, thereby providing an interpretation of the meson field as the bound state of its constituent fermions (quarks). We evaluate the Fermi-coupling as a function of meson (pseudoscalar and vector) masses and vary the values of the masses in such a way to obtain a smooth behavior for the resulting curve. The mass spectrum obtained in this manner is found to be in good agreement with the experimental data.

The QGP dynamics in relativistic collisions

The dynamics of partons and hadrons in ultra-relativistic nucleus-nucleus collisions is analyzed within the Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for the partonic phase (DQPM) including a dynamical hadronization scheme while reproducing lattice QCD results in thermodynamic equilibrium for the equation-of-state as well as transport coefficients like shear and bulk viscosities or the electric conductivity of the hot QCD medium. The PHSD model reproduces a large variety of observables from SPS to LHC energies, e.g. the quark-number scaling of elliptic flow, transverse mass and rapidity spectra of charged hadrons, dilepton spectra, open and hidden charm production, collective flow coefficients etc., which are associated with the observation of a strongly interacting QGP (sQGP). The ‘highlights’ of the latest results from LHC energies are presented with a focus on observable effects from the non-equilibrium initial dynamics.

The form factors for hadronic tau decay using background field method

In the two body hadronic tau decays, such as τ→Kπ(η)ν, vector mesons play important role. Belle and Babar measured hadronic invariant mass spectrum of τ→Kπν decay. To compare the spectrum with theoretical prediction, we develop the chiral Lagrangian with vector mesons in [D. Kimura, K. Y. Lee and T. Morozumi, arXiv:1201.1794 [hep-ph]]. We compute the form factors of the hadronic τ decay taking account of the quantum corrections of Nambu Goldstone bosons. We also show how to renormalize the divergence of the Feynman diagrams with arbitrary number of loops and determine the counterterms within one loop using background field method. In this report, we discuss the renormalization of [D. Kimura, K. Y. Lee and T. Morozumi, arXiv:1201.1794 [hep-ph]] by considering the one loop Feynman diagrams.

Light-Front Holographic QCD and the Confinement Potential

Light-Front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time τ=t+z/c, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure. The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. In fact, the potential U has a unique form if one requires that the action for zero quark mass remains conformally invariant. We also show that the holographic mapping of gravity in AdS space to QCD with a specific soft-wall dilaton yields the same light-front Schrödinger equation. Light-front holography also leads to a precise relation between the bound-state amplitudes in the fifth dimension z of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The elastic and transition form factors of the pion and the nucleons are found to be well described in this framework. The predictions of the LF equations of motion include a zero-mass pion in the chiral mq→0 limit, and linear Regge trajectories M2(n,L)∝n+L with the same slope in the radial quantum number n and orbital angular momentum L. The light-front AdS/QCD holographic approach thus gives a frame-independent representation of color-confining dynamics, Regge spectroscopy, and the excitation spectra of relativistic light-quark meson and baryon bound states in QCD in terms of a single mass parameter. We also briefly discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant.

Elliptic-flow suppression due to hadron mass spectrum

Hadron resonance gas models provide a good description of the equation of state of quantum chromodynamics determined by lattice QCD calculations at temperatures $T\ensuremath{\sim}100--155$ MeV. In this paper we investigate the effects of an exponentially increasing hadron mass spectrum (Hagedorn spectrum) on the azimuthal anisotropy of the rapidly expanding matter formed in ultrarelativistic heavy-ion collisions. If the temperature at which the conversion from fluid degrees of freedom to hadrons is sufficiently close to the Hagedorn temperature, the production of Hagedorn resonances suppresses the differential elliptic flow of all hadron species.

Search for a doubly charmed hadron atBfactories

The doubly charmed hadron production at $B$ factories is of special importance for the study of the hadron structure and the color connections before hadronization. To suppress the combination background fluctuations of the reconstructed hadron mass spectra, we suggest a three-jet event shape trigger. After these three jets are identified by their energy and angular distributions, it is found that (1) the background process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}c\overline{c}\ensuremath{\rightarrow}{h}^{\ensuremath{'}}s$ in consideration of the final hadron system ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}+X$ is significantly suppressed, and (2) for the selected events, about half of the particles, ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$, ${K}^{\ensuremath{-}}$, ${\ensuremath{\pi}}^{+}$, which obviously cannot belong to the decay products of the doubly charmed hadron, can be vetoed. The relevant hadronization is investigated.

SHARE with CHARM

SHARE with CHARM program (SHAREv3) implements the statistical hadronization model description of particle production in relativistic heavy-ion collisions. Given a set of statistical parameters, SHAREv3 program evaluates yields and therefore also ratios, and furthermore, statistical particle abundance fluctuations. The physical bulk properties of the particle source is evaluated based on all hadrons produced, including the fitted yields. The bulk properties can be prescribed as a fit input complementing and/or replacing the statistical parameters. The modifications and improvements in the SHARE suite of programs are oriented towards recent and forthcoming LHC hadron production results including charm hadrons. This SHAREv3 release incorporates all features seen previously in SHAREv1.x and v2.x and, beyond, we include a complete treatment of charm hadrons and their decays, which further cascade and feed lighter hadron yields. This article is a complete and self-contained manual explaining and introducing both the conventional and the extended capabilities of SHARE with CHARM. We complement the particle list derived from the Particle Data Group tabulation composed of up, down, strange $u,d,s$ quarks (including resonances) with hadrons containing charm $c,\bar c$ quarks. We provide a table of the charm hadron decays including partial widths. The branching ratios of each charm hadron decays add to unity, which is achieved by including some charm hadron decay channels based on theoretical consideration in the absence of direct experimental information. A very successful interpretation of all available LHC results has been already obtained using this program.

The form factors of τ → K π (η) ν and the predictions for CP violation beyond the standard model

We study the hadronic form factors of $\tau$ lepton decays $\tau \to K \pi(\eta) \nu$. We compute one loop corrections to the form factors using the chiral Lagrangian including vector mesons. The counterterms which subtract the divergence of the one-loop amplitudes are determined by using background field method. In the vector form factor, $K^\ast$ resonance behavior is reproduced because the diagram with a vector meson propagator is included. We fit the data of the hadronic invariant mass spectrum measured by Belle by determining some of the counterterms of the Lagrangian. Besides the hadronic invariant mass spectrum, the forward-backward asymmetry is predicted. We also study the effect of CP violation of a two Higgs doublet model. In the model, CP violation of the neutral Higgs sector generates the mixing of CP even Higgs and CP odd Higgs. We show how the mixing leads to the direct CP violation of the $\tau$ decays and predict the CP violation of the forward-backward asymmetry.

The QGP dynamics in relativistic heavy-ion collisions

The dynamics of partons and hadrons in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for the partonic phase (DQPM) including a dynamical hadronization scheme. The PHSD model reproduces a large variety of observables from SPS to LHC energies, e.g. the quark-number scaling of elliptic flow, transverse mass and rapidity spectra of charged hadrons, dilepton spectra, open and hidden charm production, collective flow coefficients etc., which are associated with the observation of a sQGP. The ‘highlights’ of the latest results on collective flow are presented and open questions/perspectives are discussed.

Nonextensivity of hadronic systems

The predictions from a non-extensive self-consistent theory recently proposed are investigated. Transverse momentum ($p_T$) distribution for several hadrons obtained in $p+p$ collisions are analyzed to verify if there are evidence for a limiting effective temperature and a limiting entropic factor. In addition, the hadron-mass spectrum proposed in that theory is confronted with available data. It turns out that all $p_T$-distributions and the mass spectrum obtained in the theory are in good agreement with experiment with constant effective temperature and constant entropic factor. The results confirm that the non-extensive statistics plays an important role in the description of the termodynamics of hadronic systems, and also that the self-consistent principle holds for energies as high as those achieved in the LHC. A discussion on the best $p_T$-distirbution formula for fitting experimental data is presented.

The form factors of -&gt; K ( ) and the predictions for CP violation beyond the standard model

We study the hadronic form factors of the τ lepton decays |$\tau \rightarrow K \pi (\eta) \nu $|⁠. We compute one-loop corrections to the form factors using the chiral Lagrangian including vector mesons. The counterterms that subtract the divergence of the one-loop amplitudes are determined by using the background field method. In the vector form factor, K* resonance behavior is reproduced because a diagram with a vector meson propagator is included. We fit the data of the hadronic invariant mass spectrum measured by Belle by determining some of the counterterms of the Lagrangian. Besides the hadronic invariant mass spectrum, forward–backward asymmetry is predicted. We also study the effect of CP violation of a two Higgs doublet model. In the model, CP violation of the neutral Higgs sector generates the mixing of CP-even Higgs and CP-odd Higgs. We show how the mixing leads to direct CP violation of the τ decays and predict the CP violation of the forward–backward asymmetry.

Particle Production in Ultrarelativistic Heavy-Ion Collisions: A Statistical-Thermal Model Review

The current status of various thermal and statistical descriptions of particle production in the ultrarelativistic heavy-ion collisions experiments is presented in detail. We discuss the formulation of various types of thermal models of a hot and dense hadron gas (HG) and the methods incorporated in the implementing of the interactions between hadrons. It includes our new excluded-volume model which is thermodynamically consistent. The results of the above models together with the experimental results for various ratios of the produced hadrons are compared. We derive some new universal conditions emerging at the chemical freeze-out of HG fireball showing independence with respect to the energy as well as the structure of the nuclei used in the collision. Further, we calculate various transport properties of HG such as the ratio of shear viscosity-to-entropy using our thermal model and compare with the results of other models. We also show the rapidity as well as transverse mass spectra of various hadrons in the thermal HG model in order to outline the presence of flow in the fluid formed in the collision. The purpose of this review article is to organize and summarize the experimental data obtained in various experiments with heavy-ion collisions and then to examine and analyze them using thermal models so that a firm conclusion regarding the formation of quark-gluon plasma (QGP) can be obtained.

Study ofψ(3686)→π0hc,hc→γηcviaηcexclusive decays

The process ψ(3686)→π0hc, hc→γηc has been studied with a data sample of 106±4 million ψ(3686) events collected with the BESIII detector at the BEPCII storage ring. The mass and width of the P-wave charmonium spin-singlet state hc(P11) are determined by simultaneously fitting distributions of the π0 recoil mass for 16 exclusive ηc decay modes. The results, M(hc)=3525.31±0.11(stat)±0.14(syst) MeV/c2 and Γ(hc)=0.70±0.28±0.22 MeV, are consistent with and more precise than previous measurements. We also determine the branching ratios for the 16 exclusive ηc decay modes, five of which have not been measured previously. New measurements of the ηc line-shape parameters in the E1 transition hc→γηc are made by selecting candidates in the hc signal sample and simultaneously fitting the hadronic mass spectra for the 16 ηc decay channels. The resulting ηc mass and width values are M(ηc)=2984.49±1.16±0.52 MeV/c2 and Γ(ηc)=36.4±3.2±1.7 MeV.Received 22 September 2012DOI:https://doi.org/10.1103/PhysRevD.86.092009© 2012 American Physical Society

Hadron mass spectrum and the shear viscosity to entropy density ratio of hot hadronic matter

Lattice calculations of the QCD trace anomaly at temperatures $T<160$ MeV have been shown to match hadron resonance gas model calculations, which include an exponentially rising hadron mass spectrum. In this paper we perform a more detailed comparison of the model calculations to lattice data that confirms the need for an exponentially increasing density of hadronic states. Also, we find that the lattice data is compatible with a hadron density of states that goes as $\rho(m) \sim m^{-a}\exp(m/T_H) $ at large $m$ with $a> 5/2$ (where $T_H \sim 167$ MeV). With this specific subleading contribution to the density of states, heavy resonances are most likely undergo 2-body decay (instead of multi-particle decay), which facilitates their inclusion into hadron transport codes. Moreover, estimates for the shear viscosity and the shear relaxation time coefficient of the hadron resonance model computed within the excluded volume approximation suggest that these transport coefficients are sensitive to the parameters that define the hadron mass spectrum.

Dilaton in a soft-wall holographic approach to mesons and baryons

We discuss a holographic soft-wall model developed for the description of mesons and baryons with adjustable quantum numbers n, J, L, S. This approach is based on an action which describes hadrons with broken conformal invariance and which incorporates confinement through the presence of a background dilaton field. We show that in the case of the bound-state problem (hadronic mass spectrum) two versions of the model with a positive and negative dilaton profile are equivalent to each other by a special transformation of the bulk field. We also comment on recent works which discuss the dilaton sign in the context of soft-wall approaches.

Lattice quantum chromodynamics at the physical point and beyond

We review the work of the PACS-CS Collaboration, which aimed to realize lattice quantum chromodynamics (QCD) calculations at the physical point, i.e., those with quark masses set at physical values. This has been a long-term goal of lattice QCD simulation since its inception in 1979. After reviewing the algorithmic progress, which played a key role in this development, we summarize the simulations that explored the quark mass dependence of hadron masses down to values close to the physical point. In addition to allowing a reliable determination of the light hadron mass spectrum, this work provided clues on the validity range of chiral perturbation theory, which is widely used in phenomenology. We then describe the application of the technique of quark determinant reweighting, which enables lattice QCD calculations exactly on the physical point. The physical quark masses and the strong coupling constants are fundamental constants of the strong interaction. We describe a non-perturbative Schrödinger functional approach to figure out the non-perturbative renormalization needed to calculate them. There are a number of physical applications that can benefit from lattice QCD calculations carried out either near or at the physical point. We take up three illustrative examples: calculation of the physical properties of the ρ meson as a resonance, the electromagnetic form factor and charge radius of the pion, and charmed meson spectroscopy. Bringing single hadron properties under control opens up a number of new areas for serious lattice QCD research. One such area is electromagnetic effects in hadronic properties. We discuss the combined QCD plus QED simulation strategy and present results on electromagnetic mass difference. Another area is multi-hadron states, or nuclei. We discuss the motivations and difficulties in this area, and describe our work for deuteron and helium as our initial playground. We conclude with a brief discussion on the future perspective of lattice QCD.