Dynamical Charm Research Articles

Static energy in ( 2+1+1 )-flavor lattice QCD: Scale setting and charm effects

We present results for the static energy in ($2+1+1$)-flavor QCD over a wide range of lattice spacings and several quark masses, including the physical quark mass, with ensembles of lattice-gauge-field configurations made available by the MILC Collaboration. We obtain results for the static energy out to distances of nearly $1$~fm, allowing us to perform a simultaneous determination of the scales $r_{1}$ and $r_{0}$, as well as the string tension $\sigma$. For the smallest three lattice spacings we also determine the scale $r_{2}$. Our results for $r_{0}/r_{1}$ and $r_{0}\sqrt{\sigma}$ agree with published ($2+1$)-flavor results. However, our result for $r_{1}/r_{2}$ differs significantly from the value obtained in the ($2+1$)-flavor case, which is most likely due to the effect of the charm quark. We also report results for $r_{0}$, $r_{1}$, and $r_{2}$ in~fm, with the former two being slightly lower than published ($2+1$)-flavor results. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest two lattices with the previously published ($2+1$)-flavor QCD results at similar lattice spacing. We find that for $r > 0.2$~fm our results on the static energy agree with the ($2+1$)-flavor result, implying the decoupling of the charm quark for these distances. For smaller distances, on the other hand, we find that the effect of the dynamical charm quark is noticeable. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects. This is the first time that the decoupling of the charm quark is observed and quantitatively analyzed on lattice data of the static energy.

Annihilation diagram contribution to charmonium masses * *Supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302), the National Key Research and Development Program of China (2020YFA0406400), and the National Natural Science Foundation of China (NSFC) (11935017, 11775229, 12075253, 12070131001) (CRC 110 by DFG and NNSFC)

In this work, we generate gauge configurations with dynamical charm quarks on anisotropic lattices. The mass shift of and charmonia due to the charm quark annihilation effect can be investigated directly in a manner of unitary theory. The distillation method is adopted to treat the charm quark annihilation diagrams at a very precise level. For charmonia, the charm quark annihilation effect barely changes the mass, but lifts the mass by approximately 3–4 MeV. For charmonia, this effect results in positive mass shifts of approximately 1 MeV for and , but decreases the mass by approximately 3 MeV. We did not obtain a reliable result for the mass shift of . In addition, we observed that the spin averaged mass of the spin-triplet charmonia is in good agreement with , as expected by the non-relativistic quark model and measured by experiments.

The glueball content of ηc

We carry out the first lattice QCD derivation of the mixing energy and the mixing angle of the pseudoscalar charmonium and glueball on two gauge ensembles with Nf=2 degenerate dynamical charm quarks. The mixing energy is determined to be 49(6) MeV on the near physical charm ensemble, which seems insensitive to charm quark mass. By the assumption that X(2370) is predominantly a pseudoscalar glueball, the mixing angle is determined to be approximately 4.6(6)∘, which results in a +3.9(9) MeV mass shift of the ground state pseudoscalar charmonium. In the mean time, the mixing can raise the total width of the pseudoscalar charmonium by 7.2(8) MeV, which explains to some extent the relative large total width of the ηc meson. As a result, the branching fraction of ηc→γγ can be understood in this cc¯-glueball mixing framework. On the other hand, the possible discrepancy of the theoretical predictions and the experimental results of the partial width of J/ψ→γηc cannot be alleviated by the cc¯-glueball mixing picture yet, which demands future precise experimental measurements of this partial width.

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 lattice QCD simulations provide results that can be compared with experiments or whether {N_mathrm{f}}=2+1+1 QCD including the charm quark in the sea needs to be simulated. We consider two theories, {N_mathrm{f}}=0 QCD and QCD with {N_mathrm{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 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.

Chiral observables and topology in hot QCD with two families of quarks

We present results on QCD with four dynamical flavors in the temperature range $150$ MeV $\lesssim T \lesssim 500$ MeV. We have performed lattice simulations with Wilson fermions at maximal twist and measured Polyakov loop, chiral condensate and disconnected susceptibility, on lattices with spacings as fine as 0.065 fm. For most observables spacing effects are below statistical errors, which enables us to identify lattice results with continuum estimates. Our estimate of the pseudocritical temperature compares favorably with continuum results from staggered and domain wall fermions, confirming that a dynamical charm does not contribute in the transition region. From the high temperature behaviour of the disconnected chiral susceptibility we infer the topological susceptibility, which encodes relevant properties of the QCD axion, a plausible Dark Matter candidate. The topological susceptibility thus measured exhibits a power-law decay for $T/T_c \gtrsim 2$, with an exponent close to the one predicted by the Dilute Instanton Gas Approximation (DIGA). Close to $T_c$ the temperature dependent effective exponent seems to approach the DIGA result from above, a behaviour which would support recent analytic calculations based on an Instantons-dyons model. These results constrain the mass of a hypothetic QCD post-inflationary axion, once an assumption concerning the relative contribution of axions to Dark Matter is made.

Symanzik improvement with dynamical charm: a 3+1 scheme for Wilson quarks

We discuss the problem of lattice artefacts in QCD simulations enhanced by the introduction of dynamical charmed quarks. In particular, we advocate the use of a massive renormalization scheme with a close to realistic charm mass. To maintain O(a) improvement for Wilson type fermions in this case we define a finite size scheme and carry out a nonperturbative estimation of the clover coefficient csw. It is summarized in a fit formula csw(g02) that defines an improved action suitable for future dynamical charm simulations.

Charm quark effects on the strong coupling extracted from the static force

We compute the fermionic contribution to the strong coupling αqq extracted from the static force in Lattice QCD up to order g4 in perturbation theory. This allows us to subtract the leading fermionic lattice artifacts from recent determinations of αqq produced in simulations of two dynamical charm quarks. Moreover, by using a suitable parametrization of the βqq-function, we can evaluate the charm loop effects on αqq in the continuum limit.

Topology (and axion's properties) from lattice QCD with a dynamical charm

We present results on QCD with four dynamical flavors in the temperature range 0.9≲T/Tc≲2. We have performed lattice simulations with Wilson fermions at maximal twist and measured the topological charge with gluonic and fermionic methods. The topological charge distribution is studied by means of its cumulants, which encode relevant properties of the QCD axion, a plausible Dark Matter candidate. The topological susceptibility measured with the fermionic method exhibits a power-law decay for T/Tc≳2, with an exponent close to the one predicted by the Dilute Instanton Gas Approximation (DIGA). Close to Tc the temperature dependent effective exponent approaches the DIGA result from above, in agreement with recent analytic calculations. These results constrain the axion window, once an assumption on the fraction of axions contributing to Dark Matter is made.

Equation of state, fluctuations and other recent results from LQCD

We report on a continuum extrapolated result [1] for the equation of state (EoS) of QCD with Nf = 2 + 1 dynamical quark flavors and discuss preliminary results obtained with an addition dynamical charm quark (Nf = 2 + 1 + 1). Recent results on fluctuations of conserved charges (ratios of generalized susceptibilites) are reviewed and an update on crosscheck calculations using other complementary lattice actions is given. For all our final results, the systematics are controlled, quark masses are set to their physical values, and the continuum limit is taken using at least three lattice spacings corresponding to temporal extents up to Nt = 16.

Determination of|Vus|from a Lattice QCD Calculation of theK→πℓνSemileptonic Form Factor with Physical Quark Masses

We calculate the kaon semileptonic form factor f+(0) from lattice QCD, working, for the first time, at the physical light-quark masses. We use gauge configurations generated by the MILC Collaboration with Nf = 2 + 1 + 1 flavors of sea quarks, which incorporate the effects of dynamical charm quarks as well as those of up, down, and strange. We employ data at three lattice spacings to extrapolate to the continuum limit. Our result, f+(0) = 0.9704(32), where the error is the total statistical plus systematic uncertainty added in quadrature, is the most precise determination to date. Combining our result with the latest experimental measurements of K semileptonic decays, one obtains the Cabibbo-Kobayashi-Maskawa matrix element |V(us)| = 0.22290(74)(52), where the first error is from f+(0) and the second one is from experiment. In the first-row test of Cabibbo-Kobayashi-Maskawa unitarity, the error stemming from |V(us)| is now comparable to that from |V(ud)|.

High statistics determination of the strong coupling constant in Taylor scheme and its OPE Wilson coefficient from lattice QCD with a dynamical charm

This paper reports on the determination of $\alpha_S$ from lattice simulations with 2+1+1 twisted-mass dynamical flavours {\it via} the computation of the ghost-gluon coupling renormalized in the MOM Taylor scheme. A high-statistics sample of gauge configurations, used to evaluate the coupling from ghost and gluon propagators, allows for the appropriate update of previous results, now performing an improved analysis of data with reduced statistical errors and the systematical uncertainties under a better control.

Intrinsic strangeness and charm of the nucleon using improved staggered fermions

We calculate the intrinsic strangeness of the nucleon, <N|ss|N> - <0|ss|0>, using the MILC library of improved staggered gauge configurations using the Asqtad and HISQ actions. Additionally, we present a preliminary calculation of the intrinsic charm of the nucleon using the HISQ action with dynamical charm. The calculation is done with a method which incorporates features of both commonly-used methods, the direct evaluation of the three-point function and the application of the Feynman- Hellman theorem. We present an improvement on this method that further reduces the statistical error, and check the result from this hybrid method against the other two methods and find that they are consistent. The values for <N|ss|N> and <N|cc|N> found here, together with perturbative results for heavy quarks, show that dark matter scattering through Higgs-like exchange receives roughly equal contributions from all heavy quark flavors.

Testing the operator product expansion Wilson coefficient forA2from lattice QCD with a dynamical charm

Gluon and ghost propagators data, obtained in Landau gauge from lattice simulations with two light and two heavy dynamical quark flavours ($N_f$=2+1+1), are described here with a running formula including a four-loop perturbative expression and a nonperturbative OPE correction dominated by the local operator $A^2$. The Wilson coefficients and their variation as a function of the coupling constant are extracted from the numerical data and compared with the theoretical expressions that, after being properly renormalized, are known at ${\cal O}(\alpha^4)$. As also $\Lambda_{\msbar}$ is rather well known for $N_f$=2+1+1, this allows for a precise consistency test of the OPE approach in the joint description of different observables.

Ghost-gluon coupling, power corrections, andΛMS¯from lattice QCD with a dynamical charm

This paper is a first report on the determination of $\Lambda_{\msbar}$ from lattice simulations with 2+1+1 twisted-mass dynamical flavours {\it via} the computation of the ghost-gluon coupling renormalized in the MOM Taylor scheme. We show this approach allows a very good control of the lattice artefacts and confirm the picture from previous works with quenched and ${\rm N}_f$=2 twisted-mass field configurations which prove the necessity to include non-perturbative power corrections in the description of the running. We provide with an estimate of $\Lambda_{\msbar}$ in very good agreement with experimental results. To our knowledge it is the first calculation with a dynamical charm quark which makes the running up to $\alpha_s(M_Z)$ much safer.

One-loop lattice artifacts of a dynamical charm quark

For a few observables in O(a) improved lattice QCD, we compute discretization effects arising from the vacuum polarization of a heavy quark at one-loop order. In particular, the force between static quarks, the running coupling in the Schrödinger functional and a related quantity, v¯, are considered. Results show that the cutoff effects of a dynamical charm quark are typically smaller than those present in the pure gauge theory. This perturbative result is a good indication that dynamical charm quarks are feasible already now.