Narrow Results

It is pointed out that the diagonal amplitude of the E1–E1 chromo-electric interaction with soft gluon fields (chromo-polarizability) can be measured directly for the J/ψ and ϒ resonances in the decays J/ψ→ππℓ⁺ℓ^- and ϒ→ππℓ⁺ℓ^- with soft pions. For the J/ψ this amplitude is often discussed in connection with the J/ψ interaction with nuclear matter, while for the ϒ the chromo-polarizability enters the estimates of the nonperturbative mass shift of the resonance relevant to precision determination of the b quark mass from the ϒ mass.

The paper is devoted to theoretical consideration of inclusive η_{c, b} meson production at LHC. It is shown that existing experimental data on η_c meson production at LHCb detector can be described in the framework of NRQCD formalism and color singlet component with phenomenological value of matrix element |R(0)|² gives main contribution. Using this model, we present theoretical prediction for integrated cross-sections and transverse momentum distributions for inclusive η_c production at other LHC detectors. The case of η_b meson production at LHC is also considered.

We study the energy spectra of Schrödinger Hamiltonian in N-dimensional space with Coulomb plus inverse quadratic term $V(r)=-\frac{\alpha }{r}+\frac{g}{r^2}$ and energy-dependent confining potential of the form $a(E)r+b(E)r^2$. It is found that the energy spectra exhibit saturation effect, where these spectra are suppressed to finite values at large quantum numbers n and/or $\ell$ at any dimensional space N. As a typical application, we obtained a compact mass formula for the spectra of heavy quarkonia ($c\bar{c}$, $b\bar{b}$). It is found that the model is capable of reproducing the mass spectra of these systems with observed saturation governed by a factor $\gamma$. The comparison of this work predictions with available experimental data as well as other relevant theoretical works is also presented. The eigenfunctions are expressed in terms of the bi-confluent Heun functions.

Heavy $c\bar{c}$ and $b\bar{b}$ quarkonia are considered as systems confined within a hard-wall potential shaped after a linear combination of a cotangent — with a square co-secant function. Wave functions and energy spectra are then obtained in closed forms in solving by the Nikiforov–Uvarov method the associated radial Schrödinger equation in the presence of a centrifugal term. The interest in this potential is that in one parametrization, it can account for a conformal symmetry of the strong interaction, and in another for its perturbation, a reason for which we here employ it to study status of conformal symmetry in the heavy flavor sector. The resulting predictions on heavy quarkonia mass spectra and root mean square radii are compared with the available experimental data, as well as with predictions by other theoretical approaches. We observe that a relatively small conformal symmetry perturbing term in the potential suffices to achieve good agreement with data.

We reproduce masses of the self-conjugate and non-self-conjugate mesons in the context of the spinless Salpeter equation taking into account the relativistic kinematics and the quark spins. The hyperfine splittings for the 2S charmonium and 1S bottomonium are also calculated. Further, the pseudoscalar and vector decay constants of the B_c meson and the unperturbed radial wave function at the origin are also calculated. We have obtained a local equation with a complete relativistic corrections to a class of three attractive static interaction potentials of the general form V(r) = -Ar^-β + κr^β + V₀, with β = 1, 1/2, 3/4 decomposed into scalar and vector parts in the form V_V(r) = -Ar^-β + (1-∊)κr^β and V_S(r) = ∊κr^β + V₀; where 0≤∊≤1. We have used the shifted large-N-expansion technique (SLNET) to solve the reduced equation for the scalar (∊ = 1), equal mixture of scalar-vector (∊ = 1/2), and vector (∊ = 0) confinement interaction kernels. The energy eigenvalues are carried out up to the third order approximation.

Heavy quarkonium production is a powerful implement to study the strong interaction dynamics and QCD theory. Fragmentation is the dominant production mechanism for heavy quarkonia with large transverse momentum. With the large heavy quark mass, the relative motion of the heavy quark pair inside a heavy quarkonium is effectively nonrelativistic and it is also well known that their fragmentation functions can be calculated in the perturbative QCD framework. Here, we analytically calculate the process-independent fragmentation functions for a gluon to split into the spin-singlet and spin-triplet $S$-wave heavy quarkonia using three different scenarios. We will show that the fragmentation probability of the gluon into the spin-triplet bound-state is the biggest one.

In this work, we study the dynamics of particles coupled to a dissipative environment from Bohmian trajectory perspective. The dissipation is modeled using the concept of memory-dependent derivative (MDD), which is characterized by its time-delay constant $\tau$ and nonsingular kernel $K(x,t)$ of two parameters $a$, $b$. By assuming a Gaussian packet wave function, we derived a MDD-Langevin equation (MDDLE). The general behavioral solution $x_c(t)$ of the MDDLE is investigated for the case of Gaussian fluctuation force. Based on the miscellaneous choices of $a$, $b$, $\tau$, the findings are that $x_c(t)$ can exhibit distinct behaviors, such as monotonic and nonmonotonic decay without zero crossings, oscillatory-like without zero and with zero crossing. Therefore, we have either diffusion or oscillatory dominate based on the problem parameters. For a harmonically bound heavy quarkonium, characterized by the angular frequency $\omega$, the position correlation function $C_x(t)$ is then obtained and analyzed numerically. The analysis shows that this correlation function is also sensitive to the various choices of $\tau$ and kernel parameters. Based on these choices, the correlation function exhibits distinct behaviors: oscillation without damping, damping, and enhanced. This wide range of behavior coverage increases the versatility to fit nonlinear or memory-dependent experimental findings. The results are compared with the fractional Langevin equation.

Using the concept of conformable fractional derivative, we study the properties of fractional $N$-dimensional Schrödinger equation for the potential $V(r)=-\frac{k}{r}+\frac{g}{r^2}+ar+b{r}^2$. The extended Nikiforov–Uvarov method is generalized to the fractional domain and then employed to obtain the analytic exact energy eigenvalues and eigenfunctions and their dependence on the fractional order $\alpha$ and the dimension $N$. To test its applicability, we apply the method on heavy quarkonia systems, and reproduce their mass spectra and fractional radial probabilities at different values of $\alpha$ and $N$. Comparing the mass spectra with the experimental data, we discuss to what extent fractional models can account for some features in the description of heavy quarkonia at certain dimensional space.

Study of the mechanism of heavy quarkonia production is a powerful tool for a better understanding of the dynamics of strong interactions and probably to search for new physics. It is well-known that the fragmentation mechanism is dominant for heavy quarkonia production and forms the nonperturbative aspect of hadron production. Since the main contribution of $J∕\psi$ production in high energy processes results from the gluon fragmentation, through this work, we study the fragmentation mechanism of gluon into S-wave vector heavy charmonium $J∕\psi$ at lowest order perturbative QCD and extend our work to the noncommutative standard model. To investigate the effects of space–time noncommutativity, we employ the Seiberg–Witten maps. Our results show that the noncommutative effects are considerable, specifically when the gluon transverse momentum is small; $p_T<30$GeV.

The variational method is used to study the hard confinement of a two-particle quantum system in two potential models, the Cornell potential and the global potential, with Dirichlet-type boundary conditions at various cut-off radii. The trial wave function is constructed as the product of the $1S$ free hydrogen atom wave function or $1S$ harmonic oscillator wave function times a linear cut-off function of the form $(r-z)$ to ensure hard entrapment within a sphere of radius z. The behavior of $|\psi {|}^2$, the wave function at the origin (WFO) and the mean radius $〈r〉$ are computed for different situations and compared for the two potential models.

We review how quark models are able to describe the phenomenology of the charm meson sector. The spectroscopy and decays of charmonium and open charm mesons are described in a particular quark model and compared with the data and the results of other existing models in the literature. A quite reasonable global description of the heavy meson spectra is reached. A new assignment of the ψ(4415) resonance as a 3D state leaving aside the 4S state to the X(4360) is tested through the analysis of the resonance structure in e⁺e^- exclusive reactions around the ψ(4415) energy region. We make tentative assignments of some of the XYZ mesons. To elucidate the structure of the 1⁺cs states, i.e., D_s1(2460) and D_s1(2536), we study the strong decay properties of the D_s1(2536) meson. We also perform a calculation of the branching fractions for the semileptonic decays of B and B_s mesons into final states containing orbitally excited charmed and charmed-strange mesons, which have become a very important source of information about the structure of heavy mesons. Analysis of the nonleptonic B-meson decays into D^(*)D_sJ are also included.

A few of the newly discovered XYZ states might be bound states of a heavy meson and antimeson. These molecular states, as they are also known, respect heavy quark symmetries at the potential level and as a consequence they might appear in multiplets. Here we exploit their symmetry to predict new states from already known ones. For instance, we expect the existence of a bottom counterpart of the X(3872) at 10580 MeV. Conversely, the assumption that the Z_b(10610) and are molecular implies a pair of analogous resonances with hidden charm located at 3870 and 4010 MeV. They might be identified with the Z_c(3900) and Z_c(4025), supporting the idea that they are and bound states.

Linearly polarized gluons inside an unpolarized proton contribute to the transverse momentum distributions of (pseudo)scalar particles produced in hadronic collisions, such as Higgs bosons and quarkonia with even charge conjugation (η_c, η_b, χ_c0, χ_b0). Moreover, they can produce azimuthal asymmetries in the associated production of a photon and a J/ψ or a Υ particle, in a kinematic configuration in which they are almost back to back. These observables, which can be measured in the running experiments at the LHC, could lead to a first extraction of both the polarized and the unpolarized gluon distributions and allow for a study of their process and energy scale dependences.

The X(3872) is a charmonium-like hadron with a mass close to the threshold. It was first observed in 2003 by the Belle Collaboration and confirmed shortly after by the CDF collaboration. The quantum numbers were recently determined by the LHCb experiment to be J^PC = 1⁺⁺³. Yet, the nature of the X(3872) is not fully understood. In future, lattice QCD calculations should be able to obtain observables and are expected to contribute to a better understanding of the X…