Regge Trajectories For Mesons Research Articles

Towards a theory of bottom-up holographic models for linear Regge trajectories of light mesons

We advance in constructing a bottom-up holographic theory of linear meson Regge trajectories that generalizes and unites into one logical framework various bottom-up holographic approaches proposed in the past and scattered in the literature. The starting point of the theory is a quadratic in fields holographic five-dimensional action in which the Poincaré invariance along the holographic coordinate is violated in the most general way compatible with the linear Regge behavior of the discrete spectrum in four dimensions. It is further demonstrated how different Soft Wall (SW) like holographic models existing in the literature plus some new ones emerge from our general setup. Various interrelations between the emerging models are studied. These models include the known SW models with different sign in the exponential background, the SW models with certain generalized backgrounds, with modified metrics, and No Wall models with 5D mass depending on the holographic coordinate in a simple polynomial way. We argue that this dependence allows to describe the effects caused by the main non-local phenomena of strongly coupled 4D gauge theory, the confinement and chiral symmetry breaking, in terms of a local 5D dual field theory in the AdS space. We provide a detailed comparison of our approach with the Light Front holographic QCD, with the spectroscopic predictions of the dual Veneziano like amplitudes, and with the experimental Regge phenomenology. We apply our general approach to a holographic study of confinement, chiral symmetry breaking, and the pion form factor.

On Asymptotic Regge Trajectories of Heavy Meson Resonances

We performed the analysis of the asymptotic behavior of Regge trajectories of nonstrange and strange mesons and found that thewidth of heavy hadrons for these trajectories cannot linearly depend on their mass. Such a finding clearly demonstrates that a widely spread belief on the linear mass dependence of the resonance width contradicts the linearity of Regge trajectories on theMandelstam variable s. Using the data on masses and widths for ρJ––, ωJ––, aJ++,, and fJ++ mesons with the spin values J ≤ 6 and for K*J mesons with J ≤ 5, we extracted the parameters of the asymptotically linear Regge trajectories predicted by the finite-width model of quark gluon bags. It is shown that the parameters obtained for the data sets B and D are consistent with the cross-over temperaturedetermined by the lattice QCD simulations at the vanishing baryonic density and with the kinetic freeze-out temperature of early hadronizing particles found in relativistic heavy ion collisions at and above the highest SPS energy. Comparing the resonance width of sets B and D evaluated at the masses of Z and W bosons, respectively, we discovered that the calculated width values match that of the gauge bosons. We argue that such matches provide us with indirect, but the first experimental evidence for the compositeness of Z and W bosons. Based on these findings, we assume that Z, W, and Higgs bosons have the Regge trajectories which are similar to the asymptotic trajectories of the studied mesons. The predictions for the masses and widths of the Regge partners of Z and W bosons and for the mass dependence of the widths of Higgs boson Regge partners along with the values for the mass and width of the scalar Higgs mesons are made as well.

Regge theory in a holographic dual of QCD in the Veneziano limit

We initiate the study of Regge theory in a bottom-up holographic model for QCD in the Veneziano limit, where the backreaction of the quarks to the gluon dynamics is included. We determine the parameters of the model by carrying out a precise fit to the meson spectrum in QCD. The spectrum for spin-one and pseudoscalar mesons is well reproduced. We then generalise the model to incluce higher spin fields in the bulk trajectories dual to the Pomeron and meson Regge trajectories at the boundary. With this setting, we fit the masses of the mesons with spins J = 2, 3, and 4, as well as the experimental data of the total cross-sections σ(γγ → X), σ(γp → X) and σ(pp → X). For the cross sections we obtain a {chi}_{mathrm{d}.mathrm{o}.mathrm{f}}^2 of 0.74 for a total of 199 experimental points.

Structure of the meson Regge trajectories

We investigate the structure of the meson Regge trajectories based on the quadratic form of the spinless Salpeter-type equation. It is found that the forms of the Regge trajectories depend on the energy region. As the employed Regge trajectory formula does not match the energy region, the fitted parameters neither have explicit physical meanings nor obey the constraints although the fitted Regge trajectory can give the satisfactory predictions if the employed formula is appropriate mathematically. Moreover, the consistency of the Regge trajectories obtained from different approaches is discussed. And the Regge trajectories for different mesons are presented. Finally, we show that the masses of the constituents will come into the slope and explain why the slopes of the fitted linear Regge trajectories vary with different kinds of mesons.

Deep inelastic scattering from string/gauge duality with soft IR cutoff and exponentially small Bjorken parameter

In this work we use the string/gauge duality within the Softwall Model (SW). In this model a dilaton field is introduced in the action for the fields playing the role of a soft infrared (IR) cutoff. The SW model is very useful as it provides linear Regge trajectories for mesons. Here, using a 10–dimensional SW model, we calculate the corresponding structure functions for deep inelastic scattering (DIS) in which electrons are scattered off hadrons in a kinematical regime where the hadrons are broken apart, with high virtuality q, in the exponentially small x (Bjorken parameter) regime. Our results for this regime are consistent with those achieved using other holographic and non-holographic approaches.

Effects of nucleon resonances on η photoproduction off the neutron reexamined

We investigate $\eta$ photoproduction off the neutron target, i.e., $\gamma n \to \eta n$, employing an effective Lagrangian method combining with a Regge approach. As a background, we consider nucleon exchange in the $s$-channel diagram and $\rho$- and $\omega$-meson Regge trajectories in the $t$ channel. The role of nucleon resonances given in the Review of Particle Data Group in the range of $W \approx 1500 - 2100$ MeV and the narrow nucleon resonance $N(1685,1/2^+)$ is extensively studied. The numerical results of the total and differential cross sections, double polarization observable $E$, and helicity-dependent cross sections $\sigma_{1/2}$, $\sigma_{3/2}$ are found to be in qualitative agreement with the recent A2 experimental data. The predictions of the beam asymmetry are also given.

Glueballs and deconfinement temperature in AdS/QCD

We put forward an alternative way to estimate the deconfinement temperature in bottom-up holographic models. The deconfinement in AdS/QCD is related to the Hawking-Page phase transition, in which the critical Hawking temperature is identified with the deconfinement one in the gauge theory. The numeric estimation of the latter is only possible when the parameters of a $5D$ dual model are previously determined from consistency with other physical aspects, standardly, providing a description of the QCD resonances. The traditional way to fix parameters in the simplest AdS/QCD models is to reproduce the mass of the $\rho$ meson or the slope of the approximate radial Regge trajectory of the $\rho$ excitations. Motivated by a general idea that the slope value originates in gluodynamics, we propose calculating the deconfinement temperature using the trajectory of scalar glueballs. We consider several holographic models and use the recent idea of isospectral potentials to make an additional check of the relevance of our approach. It is demonstrated that different models from an isospectral family (i.e. the models leading to identical predictions for spectrum of hadrons with fixed quantum numbers) result in different predictions for the deconfinement temperature. This difference is found to be quite small in the scalar glueball channel but very large in the vector meson channel. The observed stability in the former case clearly favours the choice of the glueball channel for thermodynamic predictions in AdS/QCD models. For a balanced approach, we argue that either assuming $f_0(1500)$ to have a dominating component of $0^{++}$ glueball or accepting the idea of the universality in the radial Regge trajectories of light non-strange vector mesons one can reproduce the results for the deconfinement temperature obtained before in the lattice simulations in the background of non-dynamical quarks.

S-Wave Heavy Quarkonium Spectra: Mass, Decays, and Transitions

In this paper we revisited phenomenological potentials. We studied S-wave heavy quarkonium spectra by two potential models. The first one is power potential and the second one is logarithmic potential. We calculated spin averaged masses, hyperfine splittings, Regge trajectories of pseudoscalar and vector mesons, decay constants, leptonic decay widths, two-photon and two-gluon decay widths, and some allowed M1 transitions. We studied ground and 4 radially excited S-wave charmonium and bottomonium states via solving nonrelativistic Schrödinger equation. Although the potentials which were studied in this paper are not directly QCD motivated potential, obtained results agree well with experimental data and other theoretical studies.

Concavity of the meson Regge trajectories

It is illustrated by the fitted Regge trajectories for a large majority of mesons that the radial and orbital Regge trajectories for mesons prefer being concave in the (nr,M2) and (l,M2) planes, respectively. The concavity of the meson Regge trajectories is model-independent. The concavity is expected to act as a criterion to choose a newly observed meson or to assign a particle to the unwell-established state. The concavity of the meson Regge trajectories can assist in model construction and in the choice of the appropriate model to describe mesons. The appropriate models should yield the spectra which can produce the concave Regge trajectories according to the concavity of the meson Regge trajectories. If the large majority of the meson Regge trajectories are concave while a few meson Regge trajectories are convex which neither have been confirmed nor have been completely excluded at present, many existing models should be corrected or even be reconstructed, which will lead to the further understanding of the meson dynamics.

Central production of η via double Pomeron exchange and double Reggeon exchange in the Sakai-Sugimoto model

We use holographic QCD to study Pomeron- and Reggeon-mediated central production in Regge regime hadronic scattering. We focus specifically on $\eta$ production in proton-proton collisions. While previous work studied the Pomeron-mediated process, the mesonic Regge trajectories ("Reggeons") we now incorporate contribute significantly at experimentally probed energies. We use the five-point open string amplitude (in flat space) to construct approximate propagators for the Reggeon states, and the five-point closed string amplitude for the Pomeron. Using these "holographic" Reggeons and Pomerons, and low-energy couplings derived in the Sakai-Sugimoto model, we compute the differential and total cross sections at $\sqrt{s}$ =29.1 GeV. Our calculation of the total cross section is $\sigma =236 \ \mathrm{nb}$, while the experimentally measured value is $\sigma = 3859 \ \mathrm{nb}$. The discrepancy between our result and the measured value may indicate that our model systematically underestimates the values of the relevant coupling constants.

Excited state mass spectra, decay properties and Regge trajectories of charm and charm-strange mesons**Supported by Department of Science of Technology, India under SERB fast track scheme SR/FTP/PS-152/2012 and also to SVNIT (Institute Research Grant (Dean (R&C)/1488/2013-14))

The framework of a phenomenological quark-antiquark potential (Coulomb plus linear confinement) model with a Gaussian wave function is used for detailed study of masses of the ground, orbitally and radially excited states of heavy-light Qq̅, (Q=c,q=u/d,s) mesons. We incorporate a correction to the potential energy term and relativistic corrections to the kinetic energy term of the Hamiltonian. The spin-hyperfine, spin-orbit and tensor interactions incorporating the effect of mixing are employed to obtain the pseudoscalar, vector, radially and orbitally excited state meson masses. The Regge trajectories in the (J,M2) and (nr,M2) planes for heavy-light mesons are investigated with their corresponding parameters. Leptonic and radiative leptonic decay widths and corresponding branching ratios are computed. The mixing parameters are also estimated. Our predictions are in good agreement with experimental results as well as lattice and other theoretical models.

Extended soft wall model with background related to features of QCD thermodynamics

The soft wall model is extended to accommodate at the same time (i) approximately linear $\rho$ meson Regge trajectories at zero temperature $T$, (ii) various options for the thermodynamics with reference to QCD (cross over or second-order transition or first-order transition at $T_c$), and (iii) the appearance of vector meson states at $T \leq T_c$. While the vector meson masses display some modest model dependence very near to $T_c$, they stay below $T_c$ to good accuracy independent of the temperature, that is nearly as at $T=0$, thus being very consistent with the thermo-statistical models widely employed in analyses of the hadron yields in relativistic heavy-ion collisions in a region where baryon densitiy effects can be neglected and the vacuum hadron masses are used.

Analysis of recent CLAS data onΣ*(1385) photoproduction off a neutron target

Based on recent experimental data obtained by the CLAS Collaboration, the $\Sigma(1385)$ photoproduction off a neutron target at laboratory photon energies $E_\gamma$ up to 2.5\,GeV is investigated in an effective Lagrangian approach including $s$-, $u$-, and $t$-channel Born-term contributions. The present calculation does not take into account any explicit $s$-channel baryon-resonance contributions, however, in the spirit of duality, we include $t$-channel exchanges of mesonic Regge trajectories. The onset of the Regge regime is controlled by smoothly interpolating between Feynman-type single-meson exchanges and full-fledged Regge-trajectory exchanges. Gauge invariance broken by the Regge treatment is fully restored by introducing contact-type interaction currents that result from the implementation of \textit{local} gauge invariance in terms of generalized Ward-Takahashi identities. The cross sections for the $\gamma n\to K^+\Sigma^*(1385)^-$ reaction are calculated and compared with experimental results from the CLAS and LEPS collaborations. Despite its simplicity, the present theoretical approach provides a good description of the main features of the data. However, the parameters fitted to the data show that the gauge-invariance-restoring contact term plays a large role which may point to large contributions from final-state interactions.

Mass spectra and Regge trajectories of light mesons in the Bethe-Salpeter approach

We extend the calculation of relativistic bound-states of a fermion anti-fermion pair in the Bethe-Salpeter formalism to the case of total angular momentum $J=3$. Together with results for $J \le 2$ this allows for the investigation of Regge trajectories in this approach. We exemplify such a study for ground and excited states of light unflavored mesons as well as strange mesons within the rainbow-ladder approximation. For the $\rho$- and $\phi$-meson we find a linear Regge trajectory within numerical accuracy. Discrepancies with experiment in other channels highlight the need to go beyond rainbow-ladder and to consider effects such as state mixing and more sophisticated quark-antiquark interaction kernels.

Mesonic and baryonic Regge trajectories with quantized masses

We have constructed some Regge trajectories for mesons and baryons by taking the 70 MeV spinless mass quanta as the ultimate building block for the light hadrons. In order to make masses integral multiples of seventy, small changes in masses has been made with due explanation. We have shown how a linear relationship between J and M2 is maintained by considering quantized hadron masses, which is a direct consequence of the string model and gives a strong clue for quark confinement. It has also been established that mesons and baryons have different slopes and the slopes of baryons is less than the slope of the mesons. This clearly defies the concept of universality of slopes (α ≈ 1.1 GeV2) of hadrons, which can only be achieved if the strings joining the quarks have constant string tension α = 1/(2πσ) (where σ is the string tension).

Hadrons in AdS/QCD Models

We discuss applications of gauge/gravity duality to describe the spectrum of light hadrons. We compare two particular 5-dimensional approaches: a model with an infrared deformed Anti-de Sitter metric and another one based on a dynamical AdS/QCD framework with back-reacted geometry in a dilaton/gravity background. The models break softly the scale invariance in the infrared region and allow mass gap for the field excitations in the gravity description, while keeping the conformal property of the metric close to the four-dimensional boundary. The models provide linear Regge trajectories for light mesons, associated with specially designed infrared gravity properties. We also review the results for the decay widths of the f0's into two pions, as overlap integrals between mesonic string amplitudes, which are in qualitative agreement with data.

Spectroscopy and Regge trajectories of heavy baryons in the relativistic quark-diquark picture

Mass spectra of heavy baryons are calculated in the heavy-quark--light-diquark picture in the framework of the QCD-motivated relativistic quark model. The dynamics of light quarks in the diquark as well as the dynamics of the heavy quark and light diquark in the baryon are treated completely relativistically without application of nonrelativistic v/c and heavy quark 1/m_Q expansions. Such approach allows us to get predictions for the heavy baryon masses for rather high orbital and radial excitations. On this basis the Regge trajectories of heavy baryons for orbital and radial excitations are constructed, and their linearity, parallelism, and equidistance are verified. The relations between the slopes and intercepts of heavy baryons are considered and a comparison of the slopes of Regge trajectories for heavy baryons and heavy-light mesons is performed. All available experimental data on heavy baryons fit nicely to the constructed Regge trajectories. The possible assignment of the quantum numbers to the observed excited charmed baryons is discussed.

Holographic approach to Regge trajectory and rotating D5 brane

We study the Regge trajectories of holographic mesons and baryons by considering rotating strings and D5 brane, which is introduced as the baryon vertex. Our model is based on the type IIB superstring theory with the background of asymptotic $AdS_5\times S^5$. This background is dual to a confining supersymmetric Yang-Mills theory (SYM) with gauge condensate, $<F^2>$, which determines the tension of the linear potential between the quark and anti-quark. Then the slope of the meson trajectory ($\alpha'_{M}$) is given by this condensate as $\alpha'_{M}=1/\sqrt{\pi <F^2>}$ at large spin $J$. This relation is compatible with the other theoretical results and experiments. For the baryon, we show the importance of spinning baryon vertex to obtain a Regge slope compatible with the one of $N$ and $\Delta$ series. In both cases, mesons and baryons, the trajectories are shifted to large mass side with the same slope for increasing current quark mass.

Asymptotic Regge trajectories of non-strange mesons

We analyze the asymptotic behavior of Regge trajectories of non-strange mesons. In contrast to an existing belief, it is demonstrated that for the asymptotically linear Regge trajectories the width of heavy hadrons cannot linearly depend on their mass. Using the data on masses and widths of rho_J, omega_J, a_J and f_J mesons for the spin values J \leq 6, we extract the parameters of the asymptotically linear Regge trajectory predicted by the finite width model of quark gluon bags. As it is shown the obtained parameters for the data set B correspond to the cross-over temperature lying in the interval 170.9-175.3 MeV which is consistent with the kinetic freeze-out temperature of early hadronizing particles found in relativistic heavy ion collisions at and above the highest SPS energy.

Intercepts of meson Regge trajectories inSU(Nc)quantum chromodynamics with massless quarks

By means of solving the Bethe-Salpeter equation with the minimal perturbative kernel (ladder approximation) in the arbitrary covariant gauge, there was found a series of intercepts of meson Regge trajectories associated with colorless singularities of the four-quark Green function in SU($N_c$) quantum chromodynamics with massless quarks. The gauge and renorm-invariance of the result is grounded.