We calculate the spectral dimension for nonperturbative quantum gravity defined via Euclidean dynamical triangulations. We find that it runs from a value of ∼3/2 at short distance to ∼4 at large ...distance scales, similar to results from causal dynamical triangulations. We argue that the short-distance value of 3/2 for the spectral dimension may resolve the tension between asymptotic safety and the holographic principle.
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≈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 MS¯-renormalized masses are mu(2 GeV)=2.130(41) MeV, md(2 GeV)=4.675(56) MeV, ms(2 GeV)=92.47(69) MeV, mc(3 GeV)=983.7(5.6) MeV, and mc(mc)=1273(10) MeV, with four active flavors; and mb(mb)=4195(14) MeV with five active flavors. We also obtain ratios of quark masses mc/ms=11.783(25), mb/ms=53.94(12), and mb/mc=4.578(8). The result for mc 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 αs4. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: Λ¯MRS=555(31) MeV in the minimal renormalon-subtracted (MRS) scheme, μπ2=0.05(22) GeV2, and μG2(mb)=0.38(2) GeV2. The MRS scheme Phys. Rev. D 97, 034503 (2018) is the key new aspect of our method.
A
bstract
We investigate a nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) with a non-trivial measure term in the path integral. We are motivated ...to revisit this older formulation of dynamical triangulations by hints from renormalization group approaches that gravity may be asymptotically safe and by the emergence of a semiclassical phase in causal dynamical triangulations (CDT).
We study the phase diagram of this model and identify the two phases that are well known from previous work: the branched polymer phase and the collapsed phase. We verify that the order of the phase transition dividing the branched polymer phase from the collapsed phase is almost certainly first-order. The nontrivial measure term enlarges the phase diagram, allowing us to explore a region of the phase diagram that has been dubbed the crinkled region. Although the collapsed and branched polymer phases have been studied extensively in the literature, the crinkled region has not received the same scrutiny. We find that the crinkled region is likely a part of the collapsed phase with particularly large finite-size effects. Intriguingly, the behavior of the spectral dimension in the crinkled region at small volumes is similar to that of CDT, as first reported in arXiv:1104.5505, but for sufficiently large volumes the crinkled region does not appear to have 4-dimensional semiclassical features. Thus, we find that the crinkled region of the EDT formulation does not share the good features of the extended phase of CDT, as we first suggested in arXiv:1104.5505. This agrees with the recent results of arXiv:1307.2270, in which the authors used a somewhat different discretization of EDT from the one presented here.
All lattice-QCD calculations of the hadronic-vacuum-polarization contribution to the muon's anomalous magnetic moment to date have been performed with degenerate up- and down-quark masses. Here we ...calculate directly the strong-isospin-breaking correction to a_{μ}^{HVP} for the first time with physical values of m_{u} and m_{d} and dynamical u, d, s, and c quarks, thereby removing this important source of systematic uncertainty. We obtain a relative shift to be applied to lattice-QCD results obtained with degenerate light-quark masses of δa_{μ}^{HVP,m_{u}≠m_{d}}=+1.5(7)%, in agreement with estimates from phenomenology.
We calculate the leptonic decay constants of heavy-light pseudoscalar mesons with charm and bottom quarks in lattice quantum chromodynamics on four-flavor QCD gauge-field configurations with ...dynamical u, d, s, and c quarks. We analyze over twenty isospin-symmetric ensembles with six lattice spacings down to a≈0.03 fm and several values of the light-quark mass down to the physical value 12(mu+md). We employ the highly-improved staggered-quark (HISQ) action for the sea and valence quarks; on the finest lattice spacings, discretization errors are sufficiently small that we can calculate the B-meson decay constants with the HISQ action for the first time directly at the physical b-quark mass. We obtain the most precise determinations to-date of the D- and B-meson decay constants and their ratios, fD+=212.7(0.6) MeV, fDs=249.9(0.4) MeV, fDs/fD+=1.1749(16), fB+=189.4(1.4) MeV, fBs=230.7(1.3) MeV, fBs/fB+=1.2180(47), where the errors include statistical and all systematic uncertainties. Our results for the B-meson decay constants are three times more precise than the previous best lattice-QCD calculations, and bring the QCD errors in the standard model predictions for the rare leptonic decays B¯(Bs→μ+μ−)=3.64(11)×10−9, B¯(B0→μ+μ−)=1.00(3)×10−11, and B¯(B0→μ+μ−)/B¯(Bs→μ+μ−)=0.00264(8) to well below other sources of uncertainty. As a byproduct of our analysis, we also update our previously published results for the light-quark-mass ratios and the scale-setting quantities fp4s, Mp4s, and Rp4s. We obtain the most precise lattice-QCD determination to date of the ratio fK+/fπ+=1.1950( −23+16) MeV.
We report on a scale determination with gradient-flow techniques on the N sub(functionof)=2+1+1 highly improved staggered quark ensembles generated by the MILC Collaboration. The ensembles include ...four lattice spacings, ranging from approximately 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales radicalt sub(0)/a and w sub(0)/a and their tree-level improvements, radicalt sub(0,imp) and w sub(0,imp), are computed on each ensemble using Symanzik flow and the cloverleaf definition of the energy density E. Using a combination of continuum chiral-perturbation theory and a Taylor-series ansatz for the lattice-spacing and strong-coupling dependence, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. We determine the scales (ProQuest: Formulae and/or non-USASCII text omitted)and (ProQuest: Formulae and/or non-USASCII text omitted), where the errors are sums, in quadrature, of statistical and all systematic errors. The precision of w sub(0) and radicalt sub(0) is comparable to or more precise than the best previous estimates, respectively. We then find the continuum mass dependence of radicalt sub(0) and w sub(0), which will be useful for estimating the scales of new ensembles. We also estimate the integrated autocorrelation length of left angle bracketE(t)right angle bracket. For long flow times, the autocorrelation length of left angle bracketEright angle bracket appears to be comparable to that of the topological charge.
We calculate the contribution to the muon anomalous magnetic moment hadronic vacuum polarization from the connected diagrams of up and down quarks, omitting electromagnetism. We employ QCD ...gauge-field configurations with dynamical u, d, s, and c quarks and the physical pion mass, and analyze five ensembles with lattice spacings ranging from a≈0.06 to 0.15 fm. The up- and down-quark masses in our simulations have equal masses ml. We obtain, in this world where all pions have the mass of the π0, 1010aμll(conn.)=637.8(8.8), in agreement with independent lattice-QCD calculations. We then combine this value with published lattice-QCD results for the connected contributions from strange, charm, and bottom quarks, and an estimate of the uncertainty due to the fact that our calculation does not include strong-isospin breaking, electromagnetism, or contributions from quark-disconnected diagrams. Our final result for the total O(α2) hadronic-vacuum polarization to the muon's anomalous magnetic moment is 1010aμHVP,LO=699(15)u,d(1)s,c,b, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both ab-initio lattice-QCD calculations and phenomenological determinations from experimental e+e−-scattering data. It is 1.3σ below the "no new physics" value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of aμ with theoretical calculations of the other contributions.
We present a lattice calculation of the electromagnetic (EM) effects on the masses of light pseudoscalar mesons. The simulations employ 2+1 dynamical flavors of asqtad QCD quarks and quenched ...photons. Lattice spacings vary from ≈0.12 fm to ≈0.045 fm. We compute the quantity ε, which parametrizes the corrections to Dashen’s theorem for the K+–K0 EM mass splitting, as well as εK0, which parametrizes the EM contribution to the mass of the K0 itself. An extension of the nonperturbative EM renormalization scheme introduced by the BMW group is used in separating EM effects from isospin-violating quark mass effects. We correct for leading finite-volume effects in our realization of lattice electrodynamics in chiral perturbation theory, and remaining finite-volume errors are relatively small. While electroquenched effects are under control for ε, they are estimated only qualitatively for εK0 and constitute one of the largest sources of uncertainty for that quantity. We find ε=0.78(1)stat(+8−11)syst and εK0=0.035(3)stat(20)syst. We then use these results on 2+1+1 flavor pure QCD highly improved staggered quark (HISQ) ensembles and find mu/md=0.4529(48)stat(+150−67)syst.
We study the exclusive semileptonic B-meson decays B arrow right K(pi)scriptl super(+)scriptl super(-), B arrow right K(pi)nunu super(-), and B arrow right pitaunu, computing observables in the ...Standard Model using the recent lattice-QCD results for the underlying form factors from the Fermilab Lattice and MILC collaborations. These processes provide theoretically clean windows into physics beyond the Standard Model because the hadronic uncertainties are now under good control for suitably binned observables. For example, the resulting partially integrated branching fractions for B arrow right pi mu super(+) mu super(-) and B arrow right K mu super(+) mu super(-) outside the charmonium resonance region are 1-2sigma higher than the LHCb collaboration's recent measurements, where the theoretical and experimental errors are commensurate. The combined tension is 1.7sigma. Combining the Standard-Model rates with LHCb's measurements yields values for the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements V sub()td7.45(6 9)x10 super(-3), V sub(t)s35.7(1.5)x10 super(-3), and V sub(t)dV sub(t)s0.201(20), which are compatible with the values obtained from neutral B sub(()smeson oscillations and have competitive uncertainties. Alternatively, taking the CKM matrix elements from unitarity, we constrain new-physics contributions at the electroweak scale. The constraints on the Wilson coefficients Re(C sub(9)) and Re(C sub(10)) from B arrow right pi mu super(+) mu super(-) and B arrow right K mu super(+) mu super(-) are competitive with those from B arrow right K* mu super(+ ) mu super(-), and display a 2.0sigma tension with the Standard Model. Our predictions for B arrow right K(pi)nunu and B arrow right pitaunu are close to the current experimental limits.
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