Mass Spectrum and Decay Constants of Heavy Quarkonia

In this paper, a non-relativistic potential model is used to find the solution of radial Schrodinger wave equation by using Crank Nicolson discretization for heavy quarkonia ( ̅, ̅). After solving the Schrodinger radial wave equation, the mass spectrum and hyperfine splitting of heavy quarkonia are calculated with and without relativistic corrections. The root means square radii and decay constants for S and P states of c ̅ and ̅ mesons by using the realistic and simple harmonic oscillator wave functions. The calculated results of mass, hyperfine splitting, root means square radii and decay constants agreed with experimental and theoretically calculated results in the literature.

Chiral dynamics with confinement versus the standard chiral theory

Chiral dynamics is investigated using the chiral confining Lagrangian (CCL), previously derived from QCD with confinement interaction. Based on the calculations of the quark condensate, which is defined entirely by confinement in the zero quark mass limit, one can assert that chiral symmetry breaking is predetermined by confinement. It is shown that CCL retains all basic relations of the standard chiral theory but enables one to include quark degrees of freedom in the CCL. The expansion of the CCL provides the Gell–Mann–Oakes–Renner (GMOR) relations and the masses and decay constants of all chiral mesons, including [Formula: see text]. For the latter, one needs to define a nonchiral component due to confinement, while the orthogonality condition defines the wave functions and the eigenvalues. The resulting masses and decay constants of all chiral mesons are obtained in good agreement with the experimental and lattice data.

The ground states and the first radially excited states of D-wave vector ρ and ϕ mesons

In this paper, we first derive two QCD sum rules QCDSR I and QCDSR II which are, respectively, used to extract observable quantities of the ground states and the first radially excited states of the D-wave vector [Formula: see text] and [Formula: see text] mesons. In our calculations, we consider the contributions of vacuum condensates up to dimension-7 in the operator product expansion. The predicted masses for [Formula: see text] [Formula: see text] meson and [Formula: see text] [Formula: see text] meson are consistent well with the experimental data of [Formula: see text]([Formula: see text]) and [Formula: see text]([Formula: see text]), respectively. Besides, our analysis indicates that it is reliable to assign the recent reported [Formula: see text]([Formula: see text]) state as the [Formula: see text] [Formula: see text] meson. Finally, we obtain the decay constants of these states with QCDSR I and QCDSR II. These predictions are helpful not only to reveal the structure of the newly observed [Formula: see text]([Formula: see text]) state, but also to establish [Formula: see text] meson and [Formula: see text] meson families.

Aligned natural inflation in the Large Volume Scenario

We embed natural inflation in an explict string theory model and derive observables in cosmology. We achieve this by compactifying the type IIB string on a Calabi-Yau orientifold, stabilizing moduli via the Large Volume Scenario, and configuring axions using D7-brane stacks. In order to obtain a large effective decay constant, we employ the Kim-Nilles-Peloso alignment mechanism, with the required multiple axions arising naturally from generically anisotropic bulk geometries. The bulk volumes, and hence the axion decay constants, are stabilized by generalized one-loop corrections and subject to various conditions: the Kähler cone condition on the string geometry; the convex hull condition of the weak gravity conjecture; and the constraint from the power spectrum of scalar perturbations. We find that all constraints can be satisfied in a geometry with relatively small volume and thus heavy bulk axion mass. We also covariantize the convex hull condition for the axion-dilaton-instanton system and verify the normalization of the extremal bound.

Radiative decays of heavy-light mesons and the $$ {f}_{H,{H}^{\ast },{H}_1}^{(T)} $$ decay constants

The on-shell matrix elements, or couplings $$ {g}_{H{H}^{\ast}\left({H}_1\right)\upgamma} $$ g H H ∗ H 1 γ , describing the $$ B{(D)}_q^{\ast } $$ B D q ∗ → B(D)qγ and B1q → Bqγ (q = u, d, s) radiative decays, are determined from light-cone sum rules at next-to-leading order for the first time. Two different interpolating operators are used for the vector meson, providing additional robustness to our results. For the D*-meson, where some rates are experimentally known, agreement is found. The couplings are of additional interest as they govern the lowest pole residue in the B(D) → γ form factors which in turn are connected to QED-corrections in leptonic decays B(D) → ℓ$$ \overline{\nu} $$ ν ¯ . Since the couplings and residues are related by the decay constants $$ {f}_{H^{\ast}\left({H}_1\right)} $$ f H ∗ H 1 and $$ {f}_{H^{\ast}\left({H}_1\right)}^T $$ f H ∗ H 1 T , we determine them at next-leading order as a by-product. The quantities $$ \left\{{f}_{H^{\ast}}^T,{f}_{H_1}^T\right\} $$ f H ∗ T f H 1 T have not previously been subjected to a QCD sum rule determination. All results are compared with the existing experimental and theoretical literature.

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.

Masses and decay constants of the η and η′ mesons from lattice QCD

We determine the masses, the singlet and octet decay constants as well as the anomalous matrix elements of the η and η′ mesons in Nf = 2 + 1 QCD. The results are obtained using twenty-one CLS ensembles of non-perturbatively improved Wilson fermions that span four lattice spacings ranging from a ≈ 0.086 fm down to a ≈ 0.050 fm. The pion masses vary from Mπ = 420 MeV to 126 MeV and the spatial lattice extents Ls are such that LsMπ ≳ 4, avoiding significant finite volume effects. The quark mass dependence of the data is tightly constrained by employing two trajectories in the quark mass plane, enabling a thorough investigation of U(3) large-Nc chiral perturbation theory (ChPT). The continuum limit extrapolated data turn out to be reasonably well described by the next-to-leading order ChPT parametrization and the respective low energy constants are determined. The data are shown to be consistent with the singlet axial Ward identity and, for the first time, also the matrix elements with the topological charge density are computed. We also derive the corresponding next-to-leading order large-Nc ChPT formulae. We find F8 = 115.0(2.8) MeV, θ8 = −25.8(2.3)°, θ0 = −8.1(1.8)° and, in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme for Nf = 3, F0(μ = 2 GeV) = 100.1(3.0) MeV, where the decay constants read $$ {F}_{\eta}^8 $$ F η 8 = F8 cos θ8, $$ {F}_{\eta \prime}^8 $$ F η ′ 8 = F8 sin θ8, $$ {F}_{\eta}^0 $$ F η 0 = −F0 sin θ0 and $$ {F}_{\eta \prime}^0 $$ F η ′ 0 = F0 cos θ0. For the gluonic matrix elements, we obtain aη(μ = 2 GeV) = 0.0170(10) GeV3 and aη′(μ = 2 GeV) = 0.0381(84) GeV3, where statistical and all systematic errors are added in quadrature.

Numerical Solution of Radioactive Core Decay Activity Rate of Actinium Series Using Matrix Algebra Method

The Actinium 235 series is one of the radioactive series which is widely used as a raw material for reactors and nuclear activities. The existence of this series is found in several countries such as West USA, Canada, Australia, South Africa, Russia, and Zaire. The purpose of this study was to determine the activity value and the number of radioactive nucleus decay atoms on the actinium 235 rendered in a very long decay time of 4.3 x 109 years. The decay count in this study uses an algebraic matrix method to simplify the chain decay solution, which generally uses the concept of differential equations. The solution using this method can be computationally simulated using the Matlab program. This study indicates that the value of the decay activity experienced by each element in this series is the same, which is equal to 2,636 x 1011 Bq. This condition causes the actinium 235 series to experience secular equilibrium because the half-life of the parent nuclide is greater than the nuclide derivatives. The decay activity of the radioactive nucleus under the actinium 235 series is strongly influenced by the half-life of the nuclides, the decay constants, and the number of atoms after decay