Scaling behaviors of heavy flavor meson suppression and flow in different nuclear collision systems at the LHC

We explore the system size dependence of heavy-quark-QGP interaction by studying the heavy flavor meson suppression and elliptic flow in Pb–Pb, Xe–Xe, Ar–Ar and O–O collisions at the LHC. The space-time evolution of the QGP is simulated using a $$(3+1)$$ ( 3 + 1 ) -dimensional viscous hydrodynamic model, while the heavy-quark-QGP interaction is described by an improved Langevin approach that includes both collisional and radiative energy loss inside a thermal medium. Within this framework, we provides a reasonable description of the D meson suppression and flow coefficients in Pb–Pb collisions, as well as predictions for both D and B meson observables in other collision systems yet to be measured. We find a clear hierarchy for the heavy meson suppression with respect to the size of the colliding nuclei, while their elliptic flow coefficient relies on both the system size and the geometric anisotropy of the QGP. Sizable suppression and flow are predicted for both D and B mesons in O–O collisions, which serve as a crucial bridge of jet quenching between large and small collision systems. Scaling behaviors between different collision systems are shown for heavy meson suppression factor and the bulk-eccentricity-rescaled heavy meson elliptic flow as functions of the number of participant nucleons in heavy-ion collisions.

Study on the Applicability of Varshni Potential to Predict the Mass Spectra of the Quark-Antiquark Systems in a Non-relativistic Framework

In this work, we obtain the Schrödinger equation solutions for the Varshni potential using the Nikiforov-Uvarov method. The energy eigenvalues are obtained in non-relativistic regime. The corresponding eigenfunction is obtained in terms of Laguerre polynomials. We applied the present results to calculate heavy-meson masses of charmonium cc ¯ and bottomonium bb ¯. The mass spectra for charmonium and bottomonium multiplets have been predicted numerically. The results are in good agreement with experimental data and the works of other researchers. Keywords: Schrödinger equation, Varshni potential, Nikiforov-Uvarov method, Heavy meson. PACs: 14.20.Lq; 03.65.-w; 14.40.Pq; 11.80.Fv.

A self-consistent framework of topological amplitude and its SU(N) decomposition

We propose a systematic theoretical framework for the topological amplitudes of the heavy meson decays and their SU(N) decomposition. In the framework, the topologies are expressed in invariant tensors and classified into tree- and penguin-operator-induced diagrams according to which four-quark operators, tree or penguin, being inserted into their effective weak vertexes. The number of possible topologies contributing to one type of decay can be counted by permutations and combinations. The Wigner-Eckhart theorem ensures the topological amplitudes under flavor symmetry are the same for different decay channels. By decomposing the four-quark operators into irreducible representations of SU(N) group, one can get the SU(N) irreducible amplitudes. Taking the D → PP decay (P denoting a pseudoscalar meson) with SU(3)F symmetry as an example, we present our framework in detail. The linear correlation of topologies in the SU(3)F limit is clarified in group theory. It is found there are only nine independent topologies in all tree- and penguin-operator-induced diagrams contributing to the D → PP decays in the Standard Model. If a large quark-loop diagram, named TLP, is assumed, the large ∆ACP and the very different D0→ K+K− and D0→ π+π− branching fractions can be explained with a normal U-spin breaking. Moreover, our framework provides a simple way to analyze the SU(N) breaking effects. The linear SU(3)F breaking and the high order U-spin breaking in charm decays are re-investigated in our framework, which are consistent with literature. Analogous to the degeneracy and splitting of energy levels, we propose the concepts of degeneracy and splitting of topologies to describe the flavor symmetry breaking effects in decay. As applications, we analyze the strange-less D decays in SU(3)F symmetry breaking into Isospin symmetry and the charm-less B decays in SU(4)F symmetry breaking into SU(3)F symmetry.

Quark-hadron duality for heavy meson mixings in the ’t Hooft model

We study local quark-hadron duality and its violation for the $$ {D}^0-{\overline{D}}^0 $$ D 0 − D ¯ 0 , $$ {B}_d^0-{\overline{B}}_d^0 $$ B d 0 − B ¯ d 0 and $$ {B}_s^0-{\overline{B}}_s^0 $$ B s 0 − B ¯ s 0 mixings in the ’t Hooft model, offering a laboratory to test QCD in two-dimensional spacetime together with the large-Nc limit. With the ’t Hooft equation being numerically solved, the width difference is calculated as an exclusive sum over two-body decays. The obtained rate is compared to inclusive one that arises from four-quark operators to check the validity of the heavy quark expansion (HQE). In view of the observation in four-dimensions that the HQE prediction for the width difference in the $$ {D}^0-{\overline{D}}^0 $$ D 0 − D ¯ 0 mixing is four orders of magnitude smaller than the experimental data, in this work we investigate duality violation in the presence of the GIM mechanism. We show that the order of magnitude of the observable in the $$ {D}^0-{\overline{D}}^0 $$ D 0 − D ¯ 0 mixing is enhanced in the exclusive analysis relative to the inclusive counterpart, when the 4D-like phase space function is used for the inclusive analysis. By contrast, it is shown that for the $$ {B}_d^0-{\overline{B}}_d^0 $$ B d 0 − B ¯ d 0 and $$ {B}_s^0-{\overline{B}}_s^0 $$ B s 0 − B ¯ s 0 mixings, small yet non-negligible corrections to the inclusive result emerge, which are still consistent with what is currently indicated in four-dimensions.

Symmetries, Partners and Thresholds: The Case of the Xb

The discovery of the X(3872) meant the revival of the heavy meson spectroscopy beyond naive qq¯ structures. Since the SU(3) scheme, which was very useful in the dawn of the quark models, does not work for these states, one has to use new symmetries, like Heavy Quark Spin Symmetry (HQSS) and Heavy Flavor Symmetry (HFS), to look for new states. However, at the energy regions where these new states appear, new factors are involved and it is not straightforward to relate the predictions of the symmetries with the data. In this work, we present a critical analysis of this problem and show, in a coupled-channels model, how the relative position of the bare QQ¯ states with respect to meson-meson thresholds and the coupling with other channels modulate the strength of the interaction and, hence, modify the structure of the predicted states. We found a possible candidate to the X(3872) partner at 10,599 MeV/c2.

Charm sea effects on charmonium decay constants and heavy meson masses

We estimate the effects on the decay constants of charmonium and on heavy meson masses due to the charm quark in the sea. Our goal is to understand whether for these quantities $${N_\mathrm{f}}=2+1$$ N f = 2 + 1 lattice QCD simulations provide results that can be compared with experiments or whether $${N_\mathrm{f}}=2+1+1$$ N f = 2 + 1 + 1 QCD including the charm quark in the sea needs to be simulated. We consider two theories, $${N_\mathrm{f}}=0$$ N f = 0 QCD and QCD with $${N_\mathrm{f}}=2$$ N f = 2 charm quarks in the sea. The charm sea effects (due to two charm quarks) are estimated comparing the results obtained in these two theories, after matching them and taking the continuum limit. The absence of light quarks allows us to simulate the $${N_\mathrm{f}}=2$$ N f = 2 theory at lattice spacings down to 0.023 fm that are crucial for reliable continuum extrapolations. We find that sea charm quark effects are below 1% for the decay constants of charmonium. Our results show that decoupling of charm works well up to energies of about 500 MeV. We also compute the derivatives of the decay constants and meson masses with respect to the charm mass. For these quantities we again do not see a significant dynamical charm quark effect, albeit with a lower precision. For mesons made of a charm quark and a heavy antiquark, whose mass is twice that of the charm quark, sea effects are only about 1‰ in the ratio of vector to pseudoscalar masses.