S-wave State Research Articles

Magnetic dipole transitions of Bc and Bc* mesons in the relativistic independent quark model

We study M1-transitions involving mesons: $B_c(1s)$, $B_c^*(1s)$, $B_c(2s)$, $B_c^*(2s)$, $B_c(3s)$ and $B_c^*(3s)$ in the relativistic independent quark (RIQ) model based on a flavor independent average potential in the scalar-vector harmonic form. The transition form factor for $B_c^*\to B_c\gamma$ is found to have analytical continuation from spacelike to physical timelike region. Our predicted coupling constant $g_{B_c^* B_c}$ = 0.34 Ge$V^{-1}$ and decay width $\Gamma(B_c^*\to B_c\gamma)$ = 23 eV agree with other model predictions. In view of possible observation of $B_c$ and $B_c^*$ s-wave states at LHC and Z-factory and potential use of theoretical estimate on M1-transitions, we investigate the allowed as well as hindered transitions of orbitally excited $B_c$-meson states and predict their decay widths in overall agreement with other model predictions. We consider the typical case of $B_c^*(1s)\to B_c(1s)\gamma$, where our predicted decay width which is found quite sensitive to the mass difference between $B_c^*$ and $B_c$ mesons may help in determining the mass of $B_c^*$ experimentally.

AdS/QCD duality and the quarkonia holographic information entropy

Bottomonium and charmonium, representing quarkonia states, are scrutinized under the point of view of the information theory, in the AdS/QCD holographic setup. A logarithmic measure of information, comprised by the configurational entropy, is here employed to quantitatively study quarkonia radially excited S-wave states. The configurational entropy provides data regarding the relative dominance and the abundance of the bottomonium and charmonium states, whose underlying information is more compressed, in the Shannon's theory meaning. The derived configurational entropy, therefore, identifies the lower phenomenological prevalence of higher S-wave resonances and higher masses quarkonia in Nature.

Nematicity, magnetism, and superconductivity in FeSe under pressure: Unified explanation based on the self-consistent vertex correction theory

To understand the rich electronic phase diagram in FeSe under pressure that vividly demonstrates the strong interplay between the nematicity, magnetism and superconductivity, we analyze the electronic states by including the higher-order many-body effects called the vertex correction (VC). We predict the pressure-induced emergence of xy-orbital hole-pocket based on the first-principles analysis. Due to this pressure-induced Lifshitz transition, the spin fluctuations on the xy orbital are enhanced, whereas those on xz,yz orbitals are gradually reduced. For this reason, nonmagnetic orbital order $O = n_{xz} - n_{yz}$, which is driven by the spin fluctuations on xz,yz orbitals through the intra-orbital VCs, is suppressed, and it is replaced with the magnetism of xy-orbital d-electrons. The nodal s-wave state at ambient pressure ($O > 0$) and the enhancement of Tc under pressure are driven by the cooperation between the spin and orbital fluctuations.

Bound and resonance states of positronic copper atoms

We report a theoretical calculation for the bound and S-wave resonance states of the positronic copper atom (e+Cu). A positron is a positively charged particle; therefore, a positronic atom has an attractive correlation between the positron and electron. A Gaussian expansion method is adopted to directly describe this correlation as well as the strong repulsive interaction with the nucleus. The correlation between the positron and electron is much more important than that between electrons in an analogous system of Cu−, although the formation of a positronium (Ps) in e+Cu is not expressed in the ground state structure explicitly. Resonance states are calculated with a complex scaling method and identified above the first excited state of the copper atom. Resonance states below Ps (n = 2) + Cu+ classified to a dipole series show agreement with a simple analytical law. Comparison of the resonance energies and widths of e+Cu with those of e+K, of which the potential energy of the host atom resembles that of e+Cu, reveals that the positions of the resonance for the e+Cu dipole series deviate equally from those of e+K.

Tunable odd-frequency triplet pairing states and skyrmion modes in chiral p-wave superconductor

Bogliubov-de Gennes equations are solved self-consistently to investigate the properties of bound states in chiral p-wave superconductive disks. It shows that either an s-wave or the mixed d- and s-wave state with odd-frequency and spin-triplet symmetry is induced at the vortex core, depending both on the chirality of the pairing states and on the vortex topology. It is also found that the odd-frequency triplet even parity (OTE) bound state can be manipulated with a local non-magnetic potential. Interestingly, with an appropriate potential amplitude, the zero-energy OTE bound state can be stabilized at a distance from the vortex core and from the local potential. Possible existences of the Majorana fermion modes are expected if the particle-hole symmetry property is applied to the zero-energy OTE bound state. Moreover, skyrmion modes with an integer topological charge have been found to exist.

Partial wave decomposition in Friedrichs model with self-interacting continua

We consider the nonrelativistic model of coupling bare discrete states with continuum states in which the continuum states can have interactions among themselves. By partial-wave decomposition and constraint to the conserved angular momentum eigenstates, the model can be reduced to Friedrichs-like model with additional interactions between the continua. If a kind of factorizable form factor is chosen, the model can be exactly solvable, that is, the generalized discrete eigenstates including bound states, virtual states, and resonances can all be represented using the original bare states, and so do the in-state and out-state. The exact S matrix is thus obtained. We then discuss the behaviors of the dynamically generated S-wave and P-wave discrete states as the coupling is varying when there is only one self-interacting bare continuum state. We find that even when the potential is repulsive there could also be resonances and virtual states. In the P-wave cases with attractive interaction, we find that when there is a near-threshold bound state, there will always be an accompanying virtual state and we also give a more general argument of this effect.

From microphysics to dynamics of magnetars

MeV-scale magnetic fields in the interiors of magnetars suppress the pairing of neutrons and protons in the S-wave state. In the case of a neutron condensate the suppression is the consequence of the Pauli-paramagnetism of the neutron gas, i.e., the alignment of the neutron spins along the magnetic field. The proton S-wave pairing is suppressed because of the Landau diamagnetic currents of protons induced by the field. The Ginzburg-Landau and BCS theories of the critical magnetic fields for unpairing are reviewed. The macrophysical implications of the suppression (unpairing) of the condensates are discussed for the rotational crust-core coupling in magnetars and the neutrino-dominated cooling era of their thermal evolution.

The evolution of meson masses in a strong magnetic field

Spectra of qoverline{q} hadrons are investigated in the framework of the Hamiltonian obtained from the relativistic path integral in external homogeneous magnetic field. The spectra of all 12 spin-isospin s-wave states, generated by π and ρ mesons with different spin projections, are studied both analytically and numerically on the lattice as functions of (magnetic field) eB. Results are in agreement and demonstrate three types of behavior, with characteristic splittings predicted by the theory.

Recent results on flavor physics by CMS

Differential production cross sections of the B+ meson and of J/ψ, ψ(2S), and ϒ(nS) (n=1,2,3) vector mesons are measured in pp collisions at 13 TeV, as a function of transverse momentum and rapidity, using data collected by the CMS detector in 2015. The B+ is reconstructed in the decay channel B+→J/ψK+ and the five S-wave quarkonium states are reconstructed in the dimuon decay channel.The simultaneous production of two ϒ(1S) mesons in observed at s=8 TeV in a data sample corresponding to an integrated luminosity of L=20.7 fb−1.The angular distributions and the differential branching fraction of the flavor changing neutral current decay B0→K⁎0μ+μ− are studied using data collected at s=8 TeV, as a function of the dimuon invariant mass squared.Flavor changing neutral currents in top quark couplings are searched through single top quark production in association with a photon, and in tt‾→Zq+Wb and tt‾→Hq+Wb decays, where Z→l+l− and H→γγ, WW, ZZ, τ+τ− and bb‾. The observed number of events agrees with the Standard Model prediction, and no evidence of flavor changing neutral currents is found.

Quarkonia at T > 0 and lattice QCD

We report here on recent progress in the determination of S-wave and P-wave heavy-quarkonium states at finite temperature. Our results are based on the combination of effective field theories with numerical lattice QCD simulations. These non-perturbative tools allow us to compute the heavy-quarkonium in-medium spectral functions, from which we in turn determine the melting temperatures of individual states and estimate phenomenologically relevant observables, such as the $\psi^\prime$ to J/$\psi$ ratio in heavy-ion collisions.

Mesons in ultra-intense magnetic field: an evaded collapse

Spectra of $q \bar q$ mesons are investigated in the framework of the Hamiltonian obtained from the relativistic path integral in external homogeneous magnetic field. The spectra of all 12 spin-isospin s-wave states generated by $\pi$- and $\rho$-mesons with different spin projections, are studied analytically as functions of the field strength. Three types of behavior with characteristic splittings are found. The results are in agreement with recent lattice calculations.

Superconductivity in FeSe Thin Films Driven by the Interplay between Nematic Fluctuations and Spin-Orbit Coupling.

The origin of the high-temperature superconducting state observed in FeSe thin films, whose phase diagram displays no sign of magnetic order, remains a hotly debated topic. Here we investigate whether fluctuations arising due to the proximity to a nematic phase, which is observed in the phase diagram of this material, can promote superconductivity. We find that nematic fluctuations alone promote a highly degenerate pairing state, in which both s-wave and d-wave symmetries are equally favored, and T_{c} is consequently suppressed. However, the presence of a sizable spin-orbit coupling or inversion symmetry breaking at the film interface lifts this harmful degeneracy and selects the s-wave state, in agreement with recent experimental proposals. The resulting gap function displays a weak anisotropy, which agrees with experiments in monolayer FeSe and intercalated Li_{1-x}(OH)_{x}FeSe.

In-medium quarkonium properties from a lattice QCD based effective field theory

In order to understand the experimental data on heavy quarkonium production in heavy ion collisions at RHIC and LHC it is necessary (though not sufficient) to pinpoint the properties of heavy QQ‾ bound states in the deconfined quark-gluon plasma, including their dissolution. Here we present recent results on the temperature dependence of bottomonium and charmonium correlators, as well as their spectral functions in a lattice QCD based effective field theory called NRQCD, surveying temperatures close to the crossover transition 140MeV<T<249MeV. The spectra are reconstructed based on a novel Bayesian prescription, whose systematic uncertainties are assessed. We present indications for sequential melting of different quarkonium species with respect to their vacuum binding energies and give estimates on the survival of S-wave and P-wave ground states.

Semileptonic decays of $$B_c$$ B c meson to S-wave charmonium states in the perturbative QCD approach

Inspired by the recent measurement of the ratio of $B_c$ branching fractions to $J/\psi \pi^+$ and $J/\psi \mu^+\nu_{\mu}$ final states at the LHCb detector, we study the semileptonic decays of $B_c$ meson to the S-wave ground and radially excited 2S and 3S charmonium states with the perturbative QCD approach. After evaluating the form factors for the transitions $B_c\rightarrow P,V$, where $P$ and $V$ denote pseudoscalar and vector S-wave charmonia, respectively, we calculate the branching ratios for all these semileptonic decays. The theoretical uncertainty of hadronic input parameters are reduced by utilizing the light-cone wave function for $B_c$ meson. It is found that the predicted branching ratios range from $10^{-6}$ up to $10^{-2}$ and could be measured by the future LHCb experiment. Our prediction for the ratio of branching fractions $\frac{\mathcal {BR}(B_c^+\rightarrow J/\Psi \pi^+)}{\mathcal {BR}(B_c^+\rightarrow J/\Psi \mu^+\nu_{\mu})}$ is in good agreement with the data. For $B_c\rightarrow V l \nu_l$ decays, the relative contributions of the longitudinal and transverse polarization are discussed in different momentum transfer squared regions. These predictions will be tested on the ongoing and forthcoming experiments.

In-medium P-wave quarkonium from the complex lattice QCD potential

We extend our lattice QCD potential based study arXiv:1509.07366 (JHEP 1512 (2015) 101) of the in-medium properties of heavy quark bound states to P-wave bottomonium and charmonium. Similar to the behavior found in the S-wave channel their spectra show a characteristic broadening, as well as mass shifts to lower energy with increasing temperature. In contrast to the S-wave states, finite angular momentum leads to the survival of spectral peaks even at temperatures, where the continuum threshold reaches below the bound state remnant mass. We elaborate on the ensuing challenges in defining quarkonium dissolution, present estimates of melting temperatures for the spin averaged $\chi_b$ and $\chi_c$ states and contrast the findings to recent direct lattice NRQCD studies of P-wave quarkonium. As an application to heavy-ion collisions we estimate the contribution of feed down to S-wave quarkonium through the P-wave states after freezeout.

Can X(5568) be a tetraquark state?**Supported by National Natural Science Foundation of China (11575110), Natural Science Foundation of Shanghai (15DZ2272100, 15ZR1423100), China Postdoctoral Science Foundation, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y5KF111CJ1), and Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry

Very recently, the D0 collaboration has reported the observation of a narrow structure, X(5568), in the decay process using the 10.4fb−1 data of pp̄ collision at . This structure is of great interest since it is the first hadronic state with four different valence quark flavors, b, s, u, d. In this work, we investigate tetraquarks with four different quark flavors. Based on the diquark-antidiquark scheme, we study the spectroscopy of the tetraquarks with one heavy bottom/charm quark and three light quarks. We find that the lowest-lying S-wave state, a tetraquark with the flavor [su][b̄d̄] and the spin-parity JP = 0+, is about 150 MeV higher than the X(5568). Further detailed experimental and theoretical studies of the spectrum, production and decays of tetraquark states with four different flavors are vital to gain a better understanding of the nature and classification of hadron exotic states.

Holographic model for heavy-vector-meson masses

The experimentally observed spectra of heavy-vector-meson radial excitations show a dependence on two different energy parameters. One is associated with the quark mass and the other with the binding energy levels of the quark-antiquark pair. The first is present in the large mass of the first state while the other corresponds to the small mass splittings between radial excitations. In this article we show how to reproduce such a behavior with reasonable precision using a holographic model. In the dual picture, the large energy scale shows up from a bulk mass and the small scale comes from the position of anti-de Sitter (AdS) space where field correlators are calculated. The model determines the masses of four observed S-wave states of charmonium and six S-wave states of bottomonium with 6.1% rms error. In consistency with the physical picture, the large energy parameter is flavor dependent, while the small parameter, associated with quark-antiquark interaction is the same for charmonium and bottomonium states.

Quarkonium cross sections and polarizations in pp collisions with CMS

According to NRQCD, quarkonium production starts with the production of a pre-resonant quark-antiquark (QQ‾) pair that then binds into the observed quarkonium state through a possible interaction with surroundings. Understanding this interaction would play a crucial role in the interpretation of the quarkonium suppression patterns as signatures of quark-gluon plasma formation. Unlike the measurements of quarkonium differential cross sections, which reflect partonic processes and are sensitive to initial-state effects, the polarization measurements are unambiguous probes of the final-state quarkonium formation process, determined by the quantum properties of the QQ‾: a change in polarization would be a direct signal, virtually unaffected by initial-state phenomena, of a change in binding mechanism. This report presents the ψ(nS) and ϒ(nS) cross sections and polarizations measured by CMS, using dimuon samples collected in pp collisions at s=7 TeV. The cross sections of five S-wave states extend up to or exceed pT=100 GeV, probing kinematical windows where the theory calculations are supposed to be the most reliable. The polarizations are measured up to high pT at midrapidity, and the Upsilon polarizations are also shown as a function of the number of charged particles produced in the pp collision.

Little–Parks effect in proximity superconductor-ferromagnet coaxial cylinders

The linearized Usadel equations in a generalized form containing both the spin singlet and the odd frequency spin triplet pair amplitudes in an s-wave state are used to study the oscillatory behavior of the superconducting critical temperature Tc due to the influence of an external magnetic field in proximity coaxial cylinders of a ferromagnetic core surrounded by a superconducting shell. Such geometry modifies the pairing wavefunction periodically with the vortex number L. The exchange field in the ferromagnetic core is chosen to be of the spiral type which rotates in the plane with a spiral wave vector Q. The external magnetic field assumes a constant value and is directed perpendicularly to the plane. The switching phenomena of the induced superconductivity in the ferromagnet with various vortex numbers are investigated in detail by solving self-consistently the Usadel equations to determine the Little–Parks effect i.e., the behavior of Tc versus a magnetic flux threading the ferromagnetic core.

Unconventional superconducting states on doped Shastry–Sutherland lattice

By using a renormalized mean-field theory, we investigate the phase diagram of t–t′–J–J′ model on a two dimensional Shastry–Sutherland (SS) lattice which can be realized in a group of layered compounds such as SrCu2(BO3)2, Yb2Pt2Pb. We find that the symmetry of ground state depends on frustration parameter η=t′/t and doping concentration. For weak and intermediate |η|, dx2−y2-wave superconducting state is robust in a wide region. While for larger |η| > 1 cases, the superconducting ground state has s–s-wave symmetry. Around the most frustrated η=±1 point, dx2−y2-wave state, s–s-wave state as well as staggered-flux state appear, the energy favorable state is the ground state. The order of the phase transition between different states depends on the continuity of the mean field order parameters.