Past, present, and future of precision determinations of the QCD coupling from lattice QCD
Mattia Dalla Brida
备注：
Contribution to the EPJA special issue "Lattice Field Theory during the COVID-19 pandemic" in replacement of a plenary talk at the 38th International Symposium on Lattice Field Theory (Lattice 2020); LaTeX source, 36 pages. Matches published version in EPJA
Non-perturbative scale-dependent renormalization problems are ubiquitous in lattice QCD as they enter many relevant phenomenological applications. They require solving non-perturbatively the renormalization group equations for the QCD parameters and matrix elements of interest in order to relate their non-perturbative determinations at low energy to their high-energy counterparts needed for phenomenology. Bridging the large energy separation between the hadronic and perturbative regimes of QCD, however, is a notoriously difficult task. In this contribution we focus on the case of the QCD coupling. We critically address the common challenges that state-of-the-art lattice determinations have to face in order to be significantly improved. In addition, we review a novel strategy that has been recently put forward in order to solve this non-perturbative renormalization problem and discuss its implications for future precision determinations. The new ideas exploit the decoupling of heavy quarks to match $N_{\rm f}$-flavor QCD and the pure Yang-Mills theory. Through this matching the computation of the non-perturbative running of the coupling in QCD can be shifted to the computationally much easier to solve pure-gauge theory. We shall present results for the determination of the $Λ$-parameter of $N_{\rm f}=3$-flavor QCD where this strategy has been applied and proven successful. The results demonstrate that these techniques have the potential to unlock unprecedented precision determinations of the QCD coupling from the lattice. The ideas are moreover quite general and can be considered to solve other non-perturbative renormalization problems.
Motivated by the recent discovery of a new tetra-quark $T_{cc}^+$ state with two charm quarks and two light quarks by LHCb collaboration, we calculate the spectroscopic parameters, namely, the mass and residues of beauty partners of $T_{cc}^+$ within QCD sum rules by using hadronic molecular $BB^*$ picture. The obtained results are compared with the predictions of different approaches in the literature.
We compute the decay constants of the lowest ccbar-states with quantum numbers J(PC)=0(-+) [eta_c], 1(--) [J/psi], and 1(+-) [hc] by using lattice QCD and QCD sum rules. We consider the coupling of J/psi to both the vector and tensor currents. Lattice QCD results are obtained from the unquenched (Nf=2) simulations using twisted mass QCD at four lattice spacings, allowing us to take the continuum limit. On the QCD sum rule side we use the moment sum rules. The results are then used to discuss the rate of eta_c --> gamma gamma decay, and to comment on the factorization in B --> X K decays, with …
The current status of determinations of the QCD running quark masses is reviewed. Emphasis is on recent progress on analytical precision determinations based on finite energy QCD sum rules. A critical discussion of the merits of this approach over other alternative QCD sum rules is provided. Systematic uncertainties from both the hadronic and the QCD sector have been recently identified and dealt with successfully, thus leading to values of the quark masses with unprecedented accuracy. Results currently rival in precision with lattice QCD determinations.
We compare lattice data for the short-distance part of the static energy in 2+1 flavor quantum chromodynamics (QCD) with perturbative calculations, up to next-to-next-to-next-to leading-logarithmic accuracy. We show that perturbation theory describes very well the lattice data at short distances, and exploit this fact to obtain a determination of the product of the lattice scale r_0 with the QCD scale Lambda_{MS}. With the input of the value of r_0, this provides a determination of the strong coupling alpha_s at the typical distance scale of the lattice data. We obtain alpha_s(1.5 GeV)=0.326\p…
We present an overview of the recent lattice determination of the QCD coupling $α_s$ by the ALPHA Collaboration. The computation is based on the non-perturbative determination of the $Λ$-parameter of $N_{\rm f}=3$ QCD, and the perturbative matching of the $N_{\rm f}=3$ and $N_{\rm f}=5$ theories. The final result: $α_s(m_Z)=0.11852(84)$, reaches sub-percent accuracy.
Freeze-out conditions in Heavy Ion Collisions are generally determined by comparing experimental results for ratios of particle yields with theoretical predictions based on applications of the Hadron Resonance Gas model. We discuss here how this model dependent determination of freeze-out parameters may eventually be replaced by theoretical predictions based on equilibrium QCD thermodynamics.
The leading order hadronic contribution to the muon magnetic moment anomaly, $a^{HAD}_μ$, is determined entirely in the framework of QCD. The result in the light-quark sector, in units of $10^{-10}$, is $a^{HAD}_μ|_{uds} =686 \pm 26$, and in the heavy-quark sector $a^{HAD}_μ|_{c} =14.4 \pm 0.1$, and $a^{HAD}_μ|_{b} =0.29 \pm 0.01$, resulting in $a^{HAD}_μ= 701 \pm 26$. The main uncertainty is due to the current lattice QCD value of the first and second derivative of the electromagnetic current correlator at the origin. Expected improvement in the precision of these derivatives may render this …
A full determination of the CKM matrix using recent results from lattice QCD is presented. To extract the CKM matrix in a uniform fashion, I exclusively use results from unquenched lattice QCD as the theory input for nonperturbative QCD effects. All 9 CKM matrix elements and all 4 Wolfenstein parameters are obtained from results for gold-plated quantities, which include semileptonic decay form factors and leptonic decay constants of B, D and K mesons, and B^0-\bar{B}^0 and K^0-\bar{K}^0 mixing amplitudes.
We supply recently obtained results from lattice EQCD with the correct UV limit to construct the collisional broadening kernel $C(b_\perp)$ in a QCD plasma. We discuss the limiting behavior of $C(b_\perp)$ at small and large impact parameters $b_\perp$, and illustrate how the results can be used to compute medium-induced radiation rates.
We present an update of our determination of the strong coupling alpha_s from the quantum chromodynamics static energy. This updated analysis includes new lattice data, at smaller lattice spacings and reaching shorter distances, the use of better suited perturbative expressions to compare with data in a wider distance range, and a comprehensive and detailed estimate of the error sources that contribute to the uncertainty of the final result. Our updated value for alpha_s at the Z-mass scale, M_Z, is alpha_s(M_Z)=0.1166^{+0.0012}_{-0.0008}, which supersedes our previous result.
Lattice QCD is an important tool for theoretical input for flavor physics. There have been four reviews by the Flavour Lattice Averaging Group (FLAG). This talk will review the current status of the magnitude of eight of the nine CKM matrix elements, borrowing heavily from the most recent FLAG review (co-authored by the speaker). Future prospects for improving the determination of the CKM matrix will be discussed.
We present an update on our previous determination of the Lambda parameter in QCD. The main emphasis is on results for two flavours of light dynamical quarks, where we can now almost double the amount of data used, including values at smaller lattice spacings. The calculations are performed using $O(a)$ improved Wilson fermions. Little change is found to previous numerical values.
In this talk I review some recent results from lattice QCD calculations which aim to a more accurate determination of the Standard Model parameters in the quark sector. After a review of our current knowledge of these parameters, I present lattice results for the strange, charm and bottom quark masses, the CKM matrix element $V_{ub}$ and the complex CKM phase $δ$, which induces CP violation effects in the Standard Model with three generations.
We determine the strong coupling constant $α_s(M_Z)$ from the static QCD potential by matching a lattice result and a theoretical calculation. We use a new theoretical framework based on operator product expansion (OPE), where renormalons are subtracted from the leading Wilson coefficient. We find that our OPE prediction can explain the lattice data at $Λ_{\rm QCD} r \lesssim 0.8$. This allows us to use a larger window in matching, which leads to a more reliable determination. We obtain $α_s(M_Z)=0.1179^{+0.0015}_{-0.0014}$.
We obtain a determination of the strong coupling alpha_s in quantum chromodynamics, by comparing perturbative calculations for the short-distance part of the static energy with lattice computations. Our result reads alpha_s(1.5GeV)=0.326\pm0.019, and when evolved to the scale M_Z (the Z-boson mass) it corresponds to alpha_s(M_Z)=0.1156^{+0.0021}_{-0.0022}.
We present a lattice determination of the $Λ$ parameter in three-flavor QCD and the strong coupling at the Z pole mass. Computing the nonperturbative running of the coupling in the range from $0.2\,$GeV to $70\,$GeV, and using experimental input values for the masses and decay constants of the pion and the kaon, we obtain $Λ_{\overline{\rm MS}}^{(3)}=341(12)\,$MeV. The nonperturbative running up to very high energies guarantees that systematic effects associated with perturbation theory are well under control. Using the four-loop prediction for $Λ_{\overline{\rm MS}}^{(5)}/Λ_{\overline{\rm MS}…
The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used MS-bar scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf=3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full…
The relativistic correction to the QCD static inter-quark potential at O(1/m) is investigated nonperturbatively for the first time by using lattice Monte Carlo QCD simulations. The correction is found to be comparable with the Coulombic term of the static potential when applied to charmonium, and amounts to one-fourth of the Coulombic term for bottomonium.
First-Principles Determination of the QCD Contribution to the Axion-Photon Coupling Using Domain-Wall Fermions
School of Physics, Peking University（北京大学物理学院）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心（SCNT））；Department of Physics, University of Connecticut（康涅狄格大学物理系）
While the standard model is the most successfully theory to describe all interactions and constituents in elementary particle physics, it has been constantly examined for over four decades. Weak decays of charm quarks can measure the coupling strength of quarks in different families and serve as an ideal probe for CP violation. As the lowest charm-strange baryons with three different flavors, $Ξ_c$ baryons (made of $csu$ or $csd$) have been extensively studied in experiments at the large hadron collider and in electron-positron collision. However the lack of reliable knowledge in theory become…
We review the determination of the strong coupling alpha_s from the comparison of the perturbative expression for the Quantum Chromodynamics static energy with lattice data. We collect here all the perturbative expressions needed to evaluate the static energy at the currently known accuracy.
We compute the light and strange quark masses m_l = (m_u+m_d)/2 and m_s, respectively, in full lattice QCD with N_f=2 flavors of light dynamical quarks. The renormalization constants, which convert bare quark masses into renormalized quark masses, are computed nonperturbatively, including the effect of quark-line disconnected diagrams. We obtain m_l=4.7(2)(3) MeV and m_s=119(5)(8) MeV in the MSbar scheme at the scale 2 GeV.
A method suitable for extracting resonance parameters of unstable baryons in lattice QCD is examined. The method is applied to the strong decay of the Delta to a pion-nucleon state, extracting the pion-nucleon - Delta coupling constant and Delta decay width.
We determine the strong coupling constant $α_s$ from the static QCD potential by matching a theoretical calculation with a lattice QCD computation. We employ a new theoretical formulation based on the operator product expansion, in which renormalons are subtracted from the leading Wilson coefficient. We remove not only the leading renormalon uncertainty of $\mathcal{O}(Λ_{\rm QCD})$ but also the first $r$-dependent uncertainty of $\mathcal{O}(Λ_{\rm QCD}^3 r^2)$. The theoretical prediction for the potential turns out to be valid at the static color charge distance $Λ_{\rm \overline{MS}} r \les…
We determine the strange and light quark condensates in full lattice QCD for the first time. This is done by direct calculation of the expectation value of the trace of the quark propagator followed by subtraction of the appropriate perturbative contribution to convert to a value for the condensate in the MS-bar scheme at 2 GeV. We use lattice QCD configurations including u, d, s and c quarks in the sea with u/d quark masses going down to the physical value. We find the ratio of the strange to the light quark condensate to be 1.08(16).
We present a determination of the QCD parameter Lambda in the quenched approximation (n_f=0) and for two flavours (n_f=2) of light dynamical quarks. The calculations are performed on the lattice using O(a) improved Wilson fermions and include taking the continuum limit. We find Lambda_{n_f=0} = 259(1)(20) MeV and Lambda_{n_f=2} = 261(17)(26) MeV}, using r_0 = 0.467 fm to set the scale. Extrapolating our results to five flavours, we obtain for the running coupling constant at the mass of the Z boson alpha_s(m_Z) = 0.112(1)(2). All numbers refer to the MSbar scheme.
We present a lattice determination of the leptonic decay constant F_Ds of the Ds-meson using its mass and F_K as experimental input. Setting the scale with F_K=160 MeV, our final result is F_Ds = 252(9) MeV. The error contains all uncertainties apart from the quenched approximation. Setting the scale with the nucleon mass instead leads to an increase of 3(1) MeV of the leptonic decay constant which might indicate a small quenching error.
Existing lattice data on the QCD phase transition are analyzed in renormalized perturbation theory. In quenched QCD it is found that T_c scales for lattices with only 3 time slices, and that T_c/Lambda_msbar=1.15 \pm 0.05. A preliminary estimate in QCD with two flavours of dynamical quarks shows that this ratio depends on the quark mass. For realistic quark masses we estimate T_c/Lambda_msbar=0.49 \pm 0.02. We also investigate the equation of state in quenched QCD at 1-loop order in renormalised perturbation theory.
Some very recent computations of $α_{\bar{\rm MS}}(M_Z)$ from $N_f=1+1$ lattice simulations and of the running of the Strong coupling, obtained from the lattice ghost-gluon vertex, over a large momentum window are very briefly reviewed.
A method suitable for extracting resonance parameters of unstable baryons in lattice QCD is examined. The method is applied to the strong decay of the Delta to a pion-nucleon state, extracting the pi-N - Delta coupling constant and Delta decay width.
We use the recently obtained theoretical expression for the complete QCD static energy at next-to-next-to-next-to leading-logarithmic accuracy to determine r_0Lambda_MS by comparison with available lattice data, where r_0 is the lattice scale and Lambda_MS is the QCD scale. We obtain r_0Lambda_MS=0.637^{+0.032}_{-0.030} for the zero-flavor case. The procedure we describe can be directly used to obtain r_0Lambda_MS in the unquenched case, when unquenched lattice data for the static energy at short distances becomes available. Using the value of the strong coupling alpha_s as an input, the unque…
We present lattice results for the non-perturbative Collins-Soper (CS) kernel, which describes the energy-dependence of transverse momentum-dependent parton distributions (TMDs). The CS kernel is extracted from the ratios of first Mellin moments of quasi-TMDs evaluated at different nucleon momenta.The analysis is done with dynamical $N_f=2+1$ clover fermions for the CLS ensemble H101 ($a=0.0854\,\mathrm{fm}$, $m_π=m_K=422\,\mathrm{MeV}$). The computed CS kernel is in good agreement with experimental extractions and previous lattice studies.
We calculate the chiral condensate of QCD with 2, 2+1 and 3 flavors of sea quarks. Lattice QCD simulations are performed employing dynamical overlap fermions with up and down quark masses covering a range between 3 and 100 MeV. On L ~ 1.8-1.9 fm lattices at a lattice spacing ~ 0.11 fm, we calculate the eigenvalue spectrum of the overlap-Dirac operator. By matching the lattice data with the analytical prediction from chiral perturbation theory at the next-to-leading order, the chiral condensate in the massless limit of up and down quarks is determined.
We implement a proposal made in [arXiv:1107.4388] to determine the lattice spacing by matching the lattice vector correlator at a reference distance scale with the same correlator obtained by a dispersion relation based on the $R$-ratio determined experimentally. We work with the isovector current, requiring a separation of the isovector hadronic final states on the phenomenological side. We also discuss the finite-size effect on the correlator, which must be controlled in order for the method to be applicable.
The I=2 pipi scattering length is calculated in fully-dynamical lattice QCD with domain-wall valence quarks on the asqtad-improved coarse MILC configurations (with fourth-rooted staggered sea quarks) at four light-quark masses. Two- and three-flavor mixed-action chiral perturbation theory at next-to-leading order is used to perform the chiral and continuum extrapolations. At the physical charged pion mass, we find m_pi a_pipi(I=2) = -0.04330 +- 0.00042, where the error bar combines the statistical and systematic uncertainties in quadrature.
We compute the strange and the average up/down quark masses in the quenched approximation of lattice QCD, by using the O(a)-improved Wilson action and operators and by implementing the non-perturbative renormalization. Our computation is performed at four values of the lattice spacing, from which we could extrapolate to the continuum limit. Our final result for the strange quark mass (in the MSbar scheme) is ms(2 GeV) = (106 +/- 2 +/- 8) MeV. For the average up/down quark mass we have ml(2 GeV) = (4.4 +/- 0.1 +/- 0.4) MeV. The ratio ms/ml = (24.3 +/- 0.2 +/- 0.6).
We study the effective monopole action obtained in the Maximal Abelian projection of quenched SU(2) lattice QCD. We determine the quadratic part of the lattice action using analytical blocking from continuum dual superconductor model to the lattice model. The leading contribution to the quadratic action depends explicitly on value of the monopole condensate. We show that the analytical monopole action matches the numerically obtained action in quenched SU(2) QCD with a good accuracy. The comparison of numerical and analytical results gives us the value of the monopole condensate in quenched SU…
We present two determinations of the strong coupling \(α_s\). The first one is from the static energy at three-loop accuracy, and may be considered an update of earlier determinations by some of us. The new analysis includes new lattice data at smaller lattice spacings, and reaches distances as short as \(0.0237\,{\rm fm}\). We present a comprehensive and detailed estimate of the error sources that contribute to the uncertainty of the final result, $α_s(M_Z)=0.11660^{+0.00110}_{-0.00056}$. The second determination is based on lattice data for the singlet free energy at finite temperature up to…
QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the $\bar{MS}$ scheme. Both the high and the low energy expansion of the vector current correlator are involved in this determination. The optimal integration kernel turns out to be of the form $p(s) = 1 - (s_0/s)^2$, where $s_0$ is the onset of perturbative QCD. This kernel enhances the contribution of the well known narrow resonances, and reduces the impact of the data in the range $s \simeq 20 - 25 GeV^2$. This feature leads to a substantial reduction in the sensit…
We extend HPQCD's earlier $n_f=4$ lattice-QCD analysis of the ratio of $\overline{\mathrm{MSB}}$ masses of the $b$ and $c$ quark to include results from finer lattices (down to 0.03fm) and a new calculation of QED contributions to the mass ratio. We find that $\overline{m}_b(μ)/\overline{m}_c(μ)=4.586(12)$ at renormalization scale $μ=3$\,GeV. This result is nonperturbative. Combining it with HPQCD's recent lattice QCD$+$QED determination of $\overline{m}_c(3\mathrm{GeV})$ gives a new value for the $b$-quark mass: $\overline{m}_b(3\mathrm{GeV}) = 4.513(26)$GeV. The $b$-mass corresponds to $\ove…
We discuss the determination of the strong coupling $α_\mathrm{\overline{MS}}^{}(m_\mathrm{Z})$ or equivalently the QCD $Λ$-parameter. Its determination requires the use of perturbation theory in $α_s(μ)$ in some scheme, $s$, and at some energy scale $μ$. The higher the scale $μ$ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the $Λ$-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to $α_s = 0.1$ and below. We find that (continuu…
The determination of the charm quark mass is now possible to 1% from QCD, with lattice QCD pushing the error down below 1%. I will describe the ingredients of this approach and how it can achieve this accuracy. Results for quark mass ratios, m_c/m_s and m_b/m_c, can also be determined to 1% from lattice QCD, allowing accuracy for the heavy quark masses to be leveraged into the light quark sector. I will discuss the prospects for, and importance of, improving results in future calculations.
This paper reports on the determination of $α_S$ 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.
The temperature dependence of the sum of the QCD up- and down-quark masses, $(m_u + m_d)$ and the pion decay constant, $f_π$, are determined from two thermal finite energy QCD sum rules for the pseudoscalar-current correlator. This quark-mass remains mostly constant for temperatures well below the critical temperature for deconfinement/chiral-symmetry restoration. As this critical temperature is approached, the quark-mass increases sharply with increasing temperature. This increase is far more pronounced if the temperature dependence of the pion mass (determined independently from other method…
In this talk I present the current status of a precise first-principles calculation of the quark connected, quark disconnected, and leading QED and strong isospin-breaking contributions to the leading-order hadronic vacuum polarization by the RBC and UKQCD collaborations. The lattice data is also combined with experimental $e^+ e^-$ scattering data, consistency between the two datasets is checked, and a combined result with smaller error than the lattice data and $e^+ e^-$ scattering data individually is presented.
We develop a strategy for the non-perturbative determination of the O(a)-improvement coefficient c_sw for Wilson fermions with massive sea quarks. The improvement condition is defined via the PCAC relation in the Schrödinger functional. It is imposed along a line of constant physics designed to be close to the correct mass of the charm quark. The numerical work uses the tree-level improved Lüscher-Weisz gauge action in N_f=3+1 Lattice QCD.
We develop a method to determine accurately the binding energy of the X(3872) from lattice data for the $D \bar D^*$ interaction. We show that, because of the small difference between the neutral and charged components of the X(3872), it is necessary to differentiate them in the energy levels of the lattice spectrum if one wishes to have a precise determination of the the binding energy of the X(3872). The analysis of the data requires the use of coupled channels. Depending on the number of levels available and the size of the box we determine the precision needed in the lattice energies to fi…
We present preliminary results towards a fully non-perturbative determination of the equation of state of QCD at very high-temperatures, $T\approx 3-80\,{\rm GeV}$. The key ingredient is the lattice formulation of QCD in a moving reference frame, which allows us for a neat determination of the entropy density from simple expectation values of the momentum-components of the energy-momentum tensor. For the computation we employ $N_{\rm f}=3$ flavours of non-perturbatively O($a$)-improved Wilson-fermions. We present an analysis of the O($a$)-improvement of the expectation values entering the dete…
The scale parameter $Λ_{\overline{MS}}$ is computed on the lattice in the quenched approximation and for $N_f = 2$ flavors of light dynamical quarks. The dynamical calculation is done with non-perturbatively $O(a)$ improved Wilson fermions. In the continuum limit we obtain $Λ_{\overline{MS}}^{N_f=0} = 243(1)(10)$ MeV and $Λ_{\overline{MS}}^{N_f=2} = 217(16)(11)$ MeV, respectively.
By matching Wilson loop ratios on anisotropic lattices we measure the coefficients $\cs$ and $\ct$, which are required for the calculation of the energy density. The results are compared to that of an indirect method of determination. We find similar behaviour, the differences are attributed to different discretization errors.
We analyze the static QCD potential in the distance region 0.1 fm < r < 1 fm. We combine most recent lattice computations and perturbative computations of the potential, in the framework of operator-product expansion (OPE). We determine simultaneously the non-perturbative contribution to the potential, delta E_US(r), and the relation between the lattice scale (Sommer scale) and Lambda_MSbar in the quenched approximation. We find that (1) large part of the short-distance linear potential belongs to the perturbative Wilson coefficient, (2) delta E_US(r) =0 is disfavored, and (3) r_0 Lambda_MSbar…
We obtain a new value for the QCD coupling constant by combining lattice QCD simulations with experimental data for hadron masses. Our lattice analysis is the first to: 1) include vacuum polarization effects from all three light-quark flavors (using MILC configurations); 2) include third-order terms in perturbation theory; 3) systematically estimate fourth and higher-order terms; 4) use an unambiguous lattice spacing; and 5) use an $\order(a^2)$-accurate QCD action. We use 28~different (but related) short-distance quantities to obtain $α_{\bar{\mathrm{MS}}}^{(5)}(M_Z) = 0.1170(12)$.
We perform a precise calculation of the chiral condensate in QCD using lattice QCD with 2+1 flavors of dynamical overlap quarks. Up and down quark masses cover a range between 3 and 100 MeV on a 16^3x48 lattice at a lattice spacing around 0.11 fm. At the lightest sea quark mass, the finite volume system on the lattice is in the epsilon-regime. By matching the low-lying eigenvalue spectrum of the Dirac operator with the prediction of chiral perturbation theory at the next-to-leading order, we determine the chiral condensate in 2+1-flavor QCD with strange quark mass fixed at its physical value a…
We present a fully non-perturbative determination of the $O(a)$ improvement coefficient $c_{\rm SW}$ in three-flavor dynamical QCD for the RG improved as well as the plaquette gauge actions, using the Schrödinger functional scheme. Results are compared with one-loop estimates at weak gauge coupling.
We use lattice QCD simulations, with MILC gluon configurations and HISQ c-quark propagators, to make very precise determinations of moments of charm-quark pseudoscalar, vector and axial-vector correlators. These moments are combined with new four-loop results from continuum perturbation theory to obtain several new determinations of the MSbar mass of the charm quark and of the MSbar coupling. We find m_c(3GeV)=0.986(10)GeV, or, equivalently, m_c(m_c)=1.268(9)GeV, both for n_f=4 flavors; and alpha_msb(3GeV,n_f=4)=0.251(6), or, equivalently, alpha_\msb(M_Z,n_f=5)=0.1174(12). The new mass agrees …
We review our new strategy and current status towards a high precision computation of the Lambda parameter from three-flavour simulations in QCD. To reach this goal we combine specific advantages of the Schrödinger functional and gradient flow couplings.
Based on universal arguments it is believed that there is a critical point (E) in QCD on the temperature (T) versus chemical potential (μ) plane, which is of extreme importance for heavy-ion experiments. Using finite size scaling and a recently proposed lattice method to study QCD at finite μwe determine the location of E in QCD with n_f=2+1 dynamical staggered quarks with semi-realistic masses on $L_t=4$ lattices. Our result is T_E=160 \pm 3.5 MeV and μ_E= 725 \pm 35 MeV. For the critical temperature at μ=0 we obtained T_c=172 \pm 3 MeV.
