Heavy-light Meson Masses Research Articles

Extraction of nonperturbative parameters for D(*) mesons from lattice data

Recent data for the masses of D and D* mesons determined using methods of lattice QCD for several values of the charm quark mass different from its physical mass are analyzed in heavy quark effective theory. Nonperturbative parameters are extracted that arise at order O(1/mc) in the heavy quark mass expansion of a heavy-light meson mass. The determined parameters are used to establish the charm quark masses corresponding to the employed lattice sets. Published by the American Physical Society 2024

Heavy-Light Meson Masses in the Framework of Trigonometric Rosen-Morse Potential Using the Generalized Fractional Derivative

Trigonometric Rosen-Morse Potential is employed as a mesonic potential interaction. The extended Nikiforov-Uvarov method is used to solve the N-radial Fractional Schrödinger equation analytically. Using the generalized fractional derivative, the energy eigenvalues are obtained in fractional forms. The current findings are used to calculate the masses of mesons such as charmonium, bottomonium, and heavy-light mesons. The current findings are superior to those of other recent studies and show good agreement with experimental data as a result, the fractional parameter is crucial in optimizing meson masses.

Optimal Perturbation Technique within the Asymptotic Iteration Method for Heavy-Light Meson Mass Splittings

For further insight into the perturbation technique within the framework of the asymptotic iteration method (PAIM), we suggest this method to be used as an alternative method to the traditional well-known perturbation techniques. We show by means of very simple algebraic manipulations that PAIM can be directly applied to obtain the symbolic expectation value of any perturbed potential piece without using the eigenfunction of the unperturbed problem. One of the fundamental advantages of PAIM is its ability to extract a reference unperturbed potential piece or pieces from the total Hamiltonian which can be solved exactly within AIM. After all, one can easily compute the symbolic expectation values of the remaining potential pieces. As an example, the present scheme is applied to the semi-relativistic wave equation with the harmonic-oscillator potential implemented with the Fermi–Breit potential terms. In particular, the non-trivial symbolic expectation values of the Dirac delta function, and the momentum-dependent orbit–orbit coupling terms are successfully calculated. Results are then used, as an illustration, to compute the semi-relativistic s-wave heavy-light meson masses. We obtain good agreement with experimental data for the meson mass splittings cu¯, cd¯, cs¯, bu¯, bd¯, bs¯.

The Relativistic and Nonrelativistic Solutions for the Modified Unequal Mixture of Scalar and Time-Like Vector Cornell Potentials in the Symmetries of Noncommutative Quantum Mechanics

Abstract: In this work, we have obtained analytically the bound state solution for both the relativistic modified Klein-Gordon equation MKG and non-relativistic modified Schrödinger equation for the modified unequal mixture of scalar and time-like vector Cornell (MUSVC) potentials in the relativistic noncommutative three-dimensional real space (RNC: 3D-RS) symmetries. The unequal mixture of scalar and time-like vector Cornell potentials is extended by including new radial terms. Also, MUSVC potentials are proposed as a quark-antiquark interaction potential for studying the masses of heavy and heavy-light mesons in (RNC: 3D-RSP) symmetries. The ordinary Bopp’s shift method and perturbation theory are surveyed to get generalized excited states’ energy as a function of shift energy and the energy of USVC potentials in the relativistic quantum mechanics RQM and NRQM. Furthermore, the obtained preservative solutions of discrete spectrum depended on the parabolic cylinder function, the gamma function, the ordinary discrete atomic quantum numbers, as well as the potential parameters and the two infinitesimal parameters (θ and σ) which are generated with the effect of (space-space) noncommutativity properties. We have also applied our obtained results for bosonic particles, like the charmonium cc ¯ and bottomonium bb ¯ mesons (that have quark and antiquark flavour) and cs ¯ mesons with spin-(0 and 1) and shown that MKG equation under MUSVC potentials becomes similar to the Duffin–Kemmer equation. We have shown that the degeneracy of the initial spectral under USVC potentials in RQM is changed radically and replaced by the newly triplet degeneracy of energy levels under the MUSVC potentials; this gives more precision in measurement and better results compared to the results of ordinary RQM under USVC potentials. Keywords: Klein-Gordon equation, Schrödinger equation, Unequal mixture of scalar and time-like vector Cornell potentials, Noncommutative quantum mechanics, Star product, Bopp’s shift method, Heavy–light mesons. PACS Nos.: 03.65.Ta; 03.65.Ca; 03.65.Ge.

Trigonometric Rosen–Morse Potential as a Quark–Antiquark Interaction Potential for Meson Properties in the Non-relativistic Quark Model Using EAIM

Trigonometric Rosen-Morse potential is suggested as the quark-antiquark interaction potential for studying the thermodynamic properties and the masses of heavy and heavy-light mesons. For this purpose, N-radial Schrodinger equation is analytically solved using an exact analytical iteration method (EAIM). The eigenvalues of energy and corresponding wave functions are obtained in the N-dimensional space. The present results are applied for calculating the mass of heavy mesons such as charmonium, bottomonium, bc, and cs mesons and thermodynamic properties such as the mean-internal energy, the specific heat, the free energy, and the entropy. The effect of dimensional number is studied on the meson masses. A comparison is studied with other works and experimental data. The present potential provides satisfying results in comparison with other works and experimental data.

Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD

We calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from $a\ensuremath{\approx}0.15$ to 0.03 fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the $\overline{\mathrm{MS}}$-renormalized masses are ${m}_{u}(2\text{ }\text{ }\mathrm{GeV})=\phantom{\rule{0ex}{0ex}}2.130(41)\text{ }\text{ }\mathrm{MeV}$, ${m}_{d}(2\text{ }\text{ }\mathrm{GeV})=4.675(56)\text{ }\text{ }\mathrm{MeV}$, ${m}_{s}(2\text{ }\text{ }\mathrm{GeV})=92.47(69)\text{ }\text{ }\mathrm{MeV}$, ${m}_{c}(3\text{ }\text{ }\mathrm{GeV})=\phantom{\rule{0ex}{0ex}}983.7(5.6)\text{ }\text{ }\mathrm{MeV}$, and ${m}_{c}({m}_{c})=1273(10)\text{ }\text{ }\mathrm{MeV}$, with four active flavors; and ${m}_{b}({m}_{b})=4195(14)\text{ }\text{ }\mathrm{MeV}$ with five active flavors. We also obtain ratios of quark masses ${m}_{c}/{m}_{s}=11.783(25)$, ${m}_{b}/{m}_{s}=53.94(12)$, and ${m}_{b}/{m}_{c}=4.578(8)$. The result for ${m}_{c}$ matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of ${\ensuremath{\alpha}}_{s}^{4}$. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: ${\overline{\mathrm{\ensuremath{\Lambda}}}}_{\mathrm{MRS}}=555(31)\text{ }\text{ }\mathrm{MeV}$ in the minimal renormalon-subtracted (MRS) scheme, ${\ensuremath{\mu}}_{\ensuremath{\pi}}^{2}=0.05(22)\text{ }\text{ }{\mathrm{GeV}}^{2}$, and ${\ensuremath{\mu}}_{G}^{2}({m}_{b})=0.38(2)\text{ }\text{ }{\mathrm{GeV}}^{2}$. The MRS scheme [Phys. Rev. D 97, 034503 (2018)] is the key new aspect of our method.

Relations between heavy-light meson and quark masses

The study of heavy-light meson masses should provide a way to determine renormalized quark masses and other properties of heavy-light mesons. In the context of lattice QCD, for example, it is possible to calculate hadronic quantities for arbitrary values of the quark masses. In this paper, we address two aspects relating heavy-light meson masses to the quark masses. First, we introduce a definition of the renormalized quark mass that is free of both scale dependence and renormalon ambiguities, and discuss its relation to more familiar definitions of the quark mass. We then show how this definition enters a merger of the descriptions of heavy-light masses in heavy-quark effective theory and in chiral perturbation theory ($\chi$PT). For practical implementations of this merger, we extend the one-loop $\chi$PT corrections to lattice gauge theory with heavy-light mesons composed of staggered fermions for both quarks. Putting everything together, we obtain a practical formula to describe all-staggered heavy-light meson masses in terms of quark masses as well as some lattice artifacts related to staggered fermions. In a companion paper, we use this function to analyze lattice-QCD data and extract quark masses and some matrix elements defined in heavy-quark effective theory.

HQE parameters from unquenched lattice data on pseudoscalar and vector heavy-light meson masses

We present a new lattice determination of some of the parameters appearing both in the Operator Product Expansion (OPE) analysis of the inclusive semileptonic B-meson decays and in the Heavy Quark Expansion (HQE) of the pseudoscalar (PS) and vector (V) heavy-light meson masses. We perform a lattice QCD (LQCD) computation of PS and V heavy-light meson masses for heavy-quark masses mh in the range from [see formula in PDF] to ≃ [see formula in PDF]. We employed the Nf = 2 + 1 + 1 gauge configurations of the European Twisted Mass Collaboration (ETMC) at three values of the lattice spacing a ≃ (0.062,0.082,0.089) fm with pion masses in the range Mπ ≃ (210 - 450) MeV. The heavy-quark mass is simulated directly on the lattice up to ≃ [see formula in PDF]. The interpolation to the physical [see formula in PDF] is performed using the ETMC ratio method and adopting the kinetic mass scheme. We obtain [see formula in PDF] (1 GeV) = 4.61(20) GeV (m̅b(m̅b) = 4.26(18) GeV in the MS scheme). The lattice data are analyzed in terms of the HQE and the matrix elements of dimension-4 and dimension-5 operators are extracted with good precision, namely: [see formula in PDF] and [see formula in PDF]. The data also allow for an estimate of the dimension-6 operator matrix elements.

Ground State Mass Predictions of Heavy-Light Hybrids from QCD Sum-Rule Analysis (JP = {0±,1±})

We present QCD Laplace sum-rule predictions of ground state masses of heavy-light open-flavour hybrid mesons. Having computed leading-order diagonal correlation functions, including up to dimension six gluon condensate contributions, we extract hybrid mass predictions for all JP∈{0±,1±}, and explore possible mixing effects with conventional meson states. Similarities are found in the mass hierarchy in both charm and bottom systems with some exceptions that are discussed.

Relation between the mass modification of heavy–light mesons and the chiral symmetry structure in dense matter

We point out that the study of the density dependences of the masses of heavy-light mesons give some clues to the chiral symmetry structure in nuclear matter. We include the omega meson effect as well as the sigma meson effect at mean field level on the density dependence of the masses of heavy-light mesons with chiral partner structure. It is found that the omega meson affects the masses of the heavy-light mesons and their antiparticles in the opposite way, while it affects the masses of chiral partners in the same way. This is because the omega meson is sensitive to the baryon number of the light degrees included in the heavy-light mesons. We also show that the mass difference between chiral partners is proportional to the mean field of sigma, reflecting the partial restoration of chiral symmetry in the nuclear matter. In addition to the general illustration of the density dependence of the heavy-light meson masses, we consider two concrete models for nuclear matter, the parity doublet model and skyrmion crystal model in the sense of mean field approximation.

Extraction of heavy-quark-expansion parameters from unquenched lattice data on pseudoscalar and vector heavy-light meson masses

We present a precise lattice computation of pseudoscalar and vector heavy-light meson masses for heavy-quark masses ranging from the physical charm mass up to $\simeq 4$ times the physical b-quark mass. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range $M_\pi \simeq 210 - 450$ MeV. The heavy-quark mass is simulated directly on the lattice up to $\simeq 3$ times the physical charm mass. The interpolation to the physical $b$-quark mass is performed using the ETMC ratio method, based on ratios of the meson masses computed at nearby heavy-quark masses, and adopting the kinetic mass scheme. The extrapolation to the physical pion mass and to the continuum limit yields $m_b^{\rm kin}(1~\mbox{GeV}) = 4.61 (20)$ GeV, which corresponds to $\overline{m}_b(\overline{m}_b) = 4.26 (18)$ GeV in the $\overline{MS}$ scheme. The lattice data are analyzed in terms of the Heavy Quark Expansion (HQE) and the matrix elements of dimension-4 and dimension-5 operators are extracted with a good precision, namely: $\overline{\Lambda} = 0.552 (26)$ GeV, $\mu_\pi^2 = 0.321 (32)$ GeV$^2$ and $\mu_G^2(m_b) = 0.253 (25)$ GeV$^2$. The data also allow for a rough estimate of the dimension-6 operator matrix elements. As the HQE parameters play a crucial role in the inclusive determination of the Cabibbo-Kobayashi-Maskawa matrix elements $V_{ub}$ and $V_{cb}$, their precise determination on the lattice may eventually validate and improve the analyses based on fits to the semileptonic moments.

Mass of heavy-light mesons in a constituent quark picture with partially restored chiral symmetry

We probe effects of the partial chiral symmetry restoration to the mass of heavy-light mesons in a constituent quark model by changing the constituent quark mass of the light quark. Due to the competing effect between the quark mass and the linearly rising potential, whose contribution to the energy increases as the quark mass decreases, the heavy-light meson mass has a minimum value near the constituent quark mass typically used in the vacuum. Hence, the meson mass increases as one decreases the constituent quark mass consistent with recent QCD sum rule analyses, which show an increasing $D$ meson mass as the chiral order parameter decreases.

Effects of a dressed quark-gluon vertex in pseudoscalar heavy-light mesons

Using a simple model in the context of the Dyson-Schwinger-Bethe-Salpeter approach, we investigate the effects of a dressed-quark-gluon vertex on pseudoscalar meson masses. In particular, we focus on the unequal-mass case and investigate heavy-light meson masses; in addition, we study the premise of the effective treatment of heavy quarks in our approach.

Masses of heavy-light mesons in Regge phenomenology

The masses of some orbitally and radially excited heavy-light mesons are calculated in Regge phenomenology. The results are in reasonable agreement with the experimental data and those given in many other theoretical approaches. Based on the calculation, we suggest that the recently observed D(2550), D(2600) and D(2760) can be assigned as the charmed members of the 21S0, 23S1 and 13D1 multiplets, respectively. D*s1(2700)± may be assigned as the charm-strange member of the 23S1 state. The results may be helpful in understanding the nature of current and future experimentally observed heavy-light mesons.

Precise heavy-light meson masses and hyperfine splittings from lattice QCD including charm quarks in the sea

We present improved results for the B and D meson spectrum from lattice QCD including the effect of u/d,s and c quarks in the sea. For the B mesons the Highly Improved Staggered Quark action is used for the sea and light valence quarks and NonRelativistic QCD for the b quark including O(\alpha_s) radiative corrections to many of the Wilson coefficients for the first time. The D mesons use the Highly Improved Staggered Quark action for both valence quarks on the same sea. We find M_{B_s}-M_B=84(2) MeV, M_{B_s}=5.366(8) GeV, M_{B_c}=6.278(9) GeV, M_{D_s}=1.9697(33) GeV, and M_{D_s}-M_{D}=101(3) MeV. Our results for the B meson hyperfine splittings are M_{B^*}-M_{B}=50(3) MeV, M_{B_s^*}-M_{B_s}=52(3) MeV, in good agreement with existing experimental results. This demonstrates that our perturbative improvement of the NRQCD chromo-magnetic coupling works for both heavyonium and heavy-light mesons. We predict M_{B_c^*}-M_{B_c}=54(3) MeV. We also present first results for the radially excited B_c states as well as the orbitally excited scalar B_c0^* and axial vector B_c1 mesons.

Hadron properties in AdS/QCD

We discuss a holographic soft-wall model developed for the description of mesons and baryons with adjustable quantum numbers n,J,L,S. This approach is based on an action which describes hadrons with broken conformal invariance and which incorporates confinement through the presence of a background dilaton field. Results obtained for heavy-light meson masses and decay constants are consistent with predictions of HQET. In the baryon sector, applications to the baryon masses, nucleon electromagnetic form factors and generalized parton distributions are discussed.

A proposal for B-physics on current lattices

A method to extract B-physics parameters (b-quark mass and f B , $ {f_{{B_s}}} $ decay constants) from currently available lattice data is presented and tested. The approach is based on the idea of constructing appropriate ratios of heavy-light meson masses and decay constants, respectively, possessing a precisely known static limit, and evaluating them at various pairs of heavy quark masses around the charm. Via a smooth interpolation in the heavy quark mass from the easily accessible charm region to the asymptotic point, B-physics parameters are computed with a few percent (statistical + systematic) error using recently produced N f = 2 maximally twisted Wilson fermions data.

Nonperturbatively determined relativistic heavy quark action

We present a method to nonperturbatively determine the parameters of the on-shell, O(a)-improved relativistic heavy quark action. These three parameters, m{sub 0}, {zeta}, and c{sub B}=c{sub E}, are obtained by matching finite-volume, heavy-heavy, and heavy-light meson masses to the exact relativistic spectrum through a finite-volume, step-scaling recursion procedure. We demonstrate that accuracy on the level of a few percent can be achieved by carrying out this matching on a pair of lattices with equal physical spatial volumes but quite different lattice spacings. A fine lattice with inverse lattice spacing 1/a=5.4 GeV and 24{sup 3}x48 sites and a coarse, 1/a=3.6 GeV, 16{sup 3}x32 lattice are used together with a heavy quark mass m approximately that of the charm quark. This approach is unable to determine the initially expected, four heavy quark parameters: m{sub 0}, {zeta}, c{sub B}, and c{sub E}. This apparent nonuniqueness of these four parameters motivated the analytic result, presented in a companion paper, that this set is redundant and that the restriction c{sub E}=c{sub B} is permitted through order a|p-vector| and to all orders in ma where p-vector is the heavy quark's spatial momenta.

A Canonical Ds Spectrum

Quark mass dependence induced by one loop corrections to the Breit-Fermi spin-dependent one gluon exchange potential permits an accurate determination of heavy-light meson masses. Thus the Ds(2317) is a canonical cs̄ meson. Good agreement is also obtained with the properties of two recently announced Ds mesons identified as Ds0(2860) = cs̄(2P) and D*s(2700) = cs̄(2S; 3S1).

Charm as a domain wall fermion in quenched lattice QCD

We report a study describing the charm quark by a domain-wall fermion (DWF) in lattice quantum chromodynamics (QCD). Our study uses a quenched gauge ensemble with the DBW2 rectangle-improved gauge action at a lattice cutoff of $a^{-1} \sim 3$ GeV. We calculate masses of heavy-light (charmed) and heavy-heavy (charmonium) mesons with spin-parity $J^P = 0^\mp$ and $1^\mp$, leptonic decay constants of the charmed pseudoscalar mesons ($D$ and $D_s$), and the $D^0$-$\bar{D^0}$ mixing parameter. The charm quark mass is found to be $m^{\bar{\rm MS}}_{c}(m_{c})=1.24(1)(18)$ GeV. The mass splittings in charmed-meson parity partners $\Delta_{q,J=0}$ and $\Delta_{q, J=1}$ are degenerate within statistical errors, in accord with experiment, and they satisfy a relation $\Delta_{q=ud, J} > \Delta_{q=s, J}$, also consistent with experiment. A C-odd axial vector charmonium state, $h_c), lies 22(11) MeV above the $\chi_{c1}$ meson, or $m_{h_{c}} = 3533(11)_{\rm stat.}$ MeV using the experimental $\chi_{c1}) mass. However, in this regard, we emphasize significant discrepancies in the calculation of hyperfine splittings on the lattice. The leptonic decay constants of $D$ and $D_s$ mesons are found to be $f_D=232(7)_{\rm stat.}(^{+6}_{-0})_{\rm chiral}(11)_{\rm syst.}$ MeV and $f_{D_s}/f_{D} = 1.05(2)_{\rm stat.}(^{+0}_{-2})_{\rm chiral}(2)_{\rm syst.}$, where the first error is statistical, the second a systematic due to chiral extrapolation and the third error combination of other known systematics. The $D^0$-$\bar{D^0}$ mixing bag parameter, which enters the $\Delta C = 2$ transition amplitude, is found to be $B_D(2{GeV})=0.845(24)_{\rm stat.}(^{+24}_{-6})_{\rm chiral}(105)_{\rm syst.}$.