Abstract
The properties of charmonium states are or will be intensively studied by the B-factories Belle II and BESIII, the LHCb and PANDA experiments and at a future Super-c-tau Factory. Precise lattice calculations provide valuable input and several results have been obtained by simulating up, down and strange quarks in the sea. We investigate the impact of a charm quark in the sea on the charmonium spectrum, the renormalization group invariant charm–quark mass M_{mathrm{c}} and the scalar charm–quark content of charmonium. The latter is obtained by the direct computation of the mass-derivatives of the charmonium masses. We do this investigation in a model, QCD with two degenerate charm quarks. The absence of light quarks allows us to reach very small lattice spacings down to 0.023~hbox {fm}. By comparing to pure gauge theory we find that charm quarks in the sea affect the hyperfine splitting at a level around 2%. The most significant effects are 5% in M_c and 3% in the value of the charm quark content of the eta _c meson. Given that we simulate two charm quarks these estimates are upper bounds for the contribution of a single charm quark. We show that lattice spacings <0.06~hbox {fm} are needed for safe continuum extrapolations of the charmonium spectrum with O(a) improved Wilson quarks. A useful relation for the projection to the desired parity of operators in two-point functions computed with twisted mass fermions is proven.
Highlights
We investigate the impact of a charm quark in the sea on the charmonium spectrum, the renormalization group invariant charm–quark mass Mc and the scalar charm–quark content of charmonium
By comparing to pure gauge theory we find that charm quarks in the sea affect the hyperfine splitting at a level around 2%
We show that lattice spacings < 0.06 fm are needed for safe continuum extrapolations of the charmonium spectrum with O(a) improved Wilson quarks
Summary
C (2019) 79:607 multi-hadron channels need to be included for a full treatment The masses of these resonances can be computed in the approximation that they are treated as stable and are accurate up to the hadronic width [10,11]. For the computation of the charmonium spectrum the relevant quarks to include in the lattice simulations are u, d, s, and c. For processes at energies E which are much smaller than the charm–quark mass Mc the charm quark decouples [17,18]. S ∂M where M is the renormalization group invariant mass of the heavy quark, is universal (i.e. it does not depend on the specific scale chosen) up to non-perturbative 1/M2 corrections ηNMP. 4 we present our results for the charm loop effects, in the charmonium spectrum and the renormalized charm–quark mass. We compute the generalization of the mass-scaling function in Eq (1.1)
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