Hyperfine Splitting In Charmonium Research Articles

Meson mass decomposition from lattice QCD

Hadron masses can be decomposed as a sum of quark and glue components which are defined through hadronic matrix elements of QCD operators. The components consist of the quark mass term, the quark energy term, the glue energy term, and the trace anomaly term. We calculate these components for mesons with lattice QCD for the first time. The calculation is carried out with overlap fermion on $2+1$ flavor domain-wall fermion gauge configurations. We confirm that $\sim 50\%$ of the light pion mass comes from the quark mass term and $\sim 10\%$ comes from the quark energy; whereas, while for the $\rho$ meson, the quark energy contributes roughly half of its mass but the quark mass term contributes little. The combined glue components contribute $\sim 40 - 50\%$ for both mesons. It is interesting to observe that the quark mass contribution to the mass of the vector meson is almost linear in quark mass over a large quark mass region below the charm quark mass. For heavy mesons, the quark mass term dominates the masses, while the contribution from the glue components is about $200$ MeV (a bare value around 2GeV) for the heavy pseudoscalar and vector mesons. The charmonium hyperfine splitting is found to be dominated by the quark energy term which is consistent with the picture of the quark potential model.

Charm annihilation effects on the hyperfine splitting in charmonium

In calculations of the hyperfine splitting in charmonium, the contributions of the disconnected diagrams are considered small and are typically ignored. We aim to estimate nonperturbatively the size of the resulting correction, which may eventually be needed in high precision calculations of the charmonium spectrum. We study this problem in the quenched and unquenched QCD cases. On dynamical ensembles the disconnected charmonium propagators contain light modes which complicate the extraction of the signal at large distances. In the fully quenched case, where there are no such light modes, the interpretation of the signal is simplified. We present results from lattices with $a\ensuremath{\approx}0.09\text{ }\text{ }\mathrm{fm}$ and $a\ensuremath{\approx}0.06\text{ }\text{ }\mathrm{fm}$.

Estimate of the flavor singlet contributions to the hyperfine splitting in charmonium

We explore the splitting between flavor singlet and non-singlet mesons in charmonium using unquenched lattice QCD. The non-perturbatively improved clover formalism is used for both the sea and valence quarks. This has implications for lattice calculations of the hyperfine splitting in charmonium.

Mass of the eta b and alpha s from the nonrelativistic renormalization group.

We sum up the next-to-leading logarithmic corrections to the heavy-quarkonium hyperfine splitting, using the nonrelativistic renormalization group. On the basis of this result, we predict the mass of the eta(b) meson to be M(eta(b))=9421+/-11(th)+9-8(delta alpha(s)) MeV. The experimental measurement of M(eta(b)) with a few MeV error would be sufficient to determine alpha(s)(M(Z)) with an accuracy of +/-0.003. For the hyperfine splitting in charmonium, the use of the nonrelativistic renormalization group brings the perturbative prediction significantly closer to the experimental figure.

Mass and the E1 decay rate of the singlet P state of charmonium.

We calculate the hyperfine splitting of the [ital P] states of charmonium using the perturbative QCD hyperfine interaction to order [alpha][sub [ital s]][sup 2], in an improved quasistatic approximation whereby the quark-antiquark scattering amplitude is expanded in powers of [ital p][sup 2]/[ital p][sub 0][sup 2] instead of [ital p][sup 2]/[ital m][sup 2] and terms of up to first order in [ital p][sup 2]/[ital p][sub 0][sup 2] are kept. We evaluated the hyperfine splitting using the wave functions obtained from the unperturbed Hamiltonian of Gupta, Radford, and Suchyta. We find the splitting [Delta][ital M][sub [ital P]]=[ital M][sub c.o.g.][sup 3][ital P][sub [ital J]][minus][ital M][sup 1][ital P][sub 1] to be [minus]0.63 MeV. Our result is very similar to the result of Halzen, Olson, Olsson, and Stong who find [Delta][ital M][sub [ital P]]=[minus]0.7[plus minus]0.2 MeV, using various potential models. It also confirms the recent published experimental result on [Delta][ital M][sub [ital P]]. We also note that if we had used the improved quasistatic approximation of Gupta to extract the hyperfine interaction from the [ital q[bar q]] scattering amplitude to order [alpha][sub [ital s]][sup 2] in QCD, we would have obtained entirely different results for the [ital P]-wave hyperfine splitting in charmonium. We also calculatemore » the electric dipole decay rate of the process 1 [sup 1][ital P][sub 1][r arrow]1 [sup 1][ital S][sub 0]+[gamma] and find it to be about 630 keV for charmonium.« less

Charmed meson spectroscopy and matrix elements with an O(a)-improved clover fermion action

We present preliminary results for the spectrum and decay matrix elements for heavy-light and heavy-heavy mesons, obtained on the 64-node Meiko Computing Surface at the University of Edinburgh. Quark propagators are computed with an O(a)-improved fermion action on m24 3 × 48 lattices at β = 6.2, using three values of the quark mass up to around the strange quark mass, and four values of the quark mass in the region of the charm quark mass. We compare results for the hyperfine splitting in charmonium with those obtained using the conventional Wilson fermion action and find that the splitting is 1.83(15) times larger with the improved action. Our measurements of f b indicate non-scaling corrections of the order of 20% to the Heavy Quark Effective Theory expectation. A comparison is made with results obtained on 16 3 × 48 lattices at β = 6.0.

The hyperfine splitting in charmonium. Lattice computations using the Wilson and clover fermion actions

We compute the hyperfine splitting m J ψ −m η c on the lattice, using both the Wilson and O (α)-improved (clover) actions for quenched quarks. The computations are performed on a 24 3×48 lattice at β = 6.2, using the same set of 18 gluon configurations for both fermion actions. We find that the splitting is 1.83 −15 +13 times larger with the clover action than with the Wilson action, demonstrating the sensitivity of the spin-splitting to the magnetic moment term which is present in the clover action. However, even with the clover action the result is less than half of the physical mass-splitting. We also compute the decay constants ƒ ηc and ƒ J ψ −1 both of which are considerably larger when computed using the clover action than with the Wilson action. For example for the ratio ƒ J ψ −1 ƒ ϱ −1 we find 0.32 −2 +1 with the Wilson action and 0.48±3 with the clover action (the physical value is 0.44 (2)).

Quarkonia from charmonium and renormalization group equations

A prediction of the upsilon and strangeonium spectra is made from the charmonium spectrum by solving the Salpeter equation using an identical potential to that used in charmonium. Effective quark masses and coupling parameters αs are functions of the inter-quark distance according to the renormalization group equations. The use of the Fermi-Breit-Hamiltonian for obtaining the charmonium hyperfine splitting is criticized.