Lattice HQET Research Articles

Two Higgs Doublet Model III and Double-Lepton Polarization Asymmetries in Λb → Λμ+μ− Decays**Supported by the National Natural Science Foundation of China under Grant Nos. 11345005 and Key Scientific Research projects of Henan Educational Committee (13A140814), and the National Science Foundation under Grant No. U1332103

Using the form factors calculated both in lattice QCD and HQET, we analyze the branching ratio, double-lepton polarization asymmetries and averaged double-lepton polarization asymmetries of Λb Λμ+μ− decay in the 2HDM III, respectively. Combining the experimental constrains on the 2HDM III parameters, we take two set of representative parameter spaces in our calculations. For the branching ratio of Λb → Λμ+μ− decay, considering the uncertainties of the form factors and input parameters, we find the results of both SM and 2HDM III can satisfy the current experimental data in the framework of lattice QCD, but not in HQET. Then we calculate the double-lepton polarization asymmetries Pij and their averaged values 〈Pij〉, we find the double-lepton polarization asymmetries PLT, PNN, and PTT are sensitive to the 2HDM III. However, PLN, PNL, PNT, and PTN show the opposite results. The contribution of the 2HDM III to their averaged values have similar results.

HQET at order 1/m: I. Non-perturbative parameters in the quenched approximation

We determine non-perturbatively the parameters of the lattice HQET Lagrangian and those of the time component of the heavy-light axial-vector current in the quenched approximation. The HQET expansion includes terms of order 1/m b. Our results allow to compute, for example, the heavy-light spectrum and B-meson decay constants in the static approximation and to order 1/m b in HQET. The determination of the parameters is separated into universal and non-universal parts. The universal results can be used to determine the parameters for various discretizations. The computation reported in this paper uses the plaquette gauge action and the “HYP1/2” action for the b-quark described by HQET. The parameters of the current also depend on the light-quark action, for which we choose non-perturbatively O(a)-improved Wilson fermions.

Heavy-light mesons in lattice HQET and QCD

We present a study of a combination of HQET and relativistic QCD to extract the b-quark mass and the Bs-meson decay constant from lattice quenched simulations. We start from a small volume, where one can directly simulate the b-quark, and compute the connection to a large volume, where finite size effects are negligible, through a finite size technique. The latter consists of steps extrapolated to the continuum limit, where the b-region is reached through interpolations guided by the effective theory. With the lattice spacing given in terms of the Sommer's scale r0 and the experimental Bs and K masses, we get the final results for the renormalization group invariant mass Mb = 6.88(10) GeV, translating into mb(mb) = 4.42(6) GeV in the MSbar scheme, and fBs = 191(6) MeV for the decay constant. A renormalization condition for the chromo-magnetic operator, responsible, at leading order in the heavy quark mass expansion of HQET, for the mass splitting between the pseudoscalar and the vector channel in mesonic heavy-light bound states, is provided in terms of lattice correlations functions which well suits a non-perturbative computation involving a large range of renormalization scales and no valence quarks. The two-loop expression of the corresponding anomalous dimension in the Schroedinger functional (SF) scheme is computed starting from results in the literature; it requires a one-loop calculation in the SF scheme with a non-vanishing background field. The cutoff effects affecting the scale evolution of the renormalization factors are studied at one-loop order, and confirmed by non-perturbative quenched computations to be negligible for the numerical precision achievable at present.

Signal at subleading order in lattice HQET

We discuss the correlators in lattice HQET that are needed to go beyond the static theory. Based on our implementation in the Schr\"odinger functional we focus on their signal-to-noise ratios and check that a reasonable statistical precision can be reached in quantities like $f_{B_s}$ and $M_{B^\star}-M_B$.

Lattice HQET with exponentially improved statistical precision

We introduce an alternative discretization for static quarks on the lattice retaining the O(a)-improvement properties of the Eichten–Hill action. In this formulation, statistical fluctuations are reduced by a factor which grows exponentially with Euclidean time, x0. For the first time, B-meson correlation functions are computed with good statistical precision in the static approximation for x0>1 fm. At lattice spacings a≈0.1, 0.08, 0.07 fm, the Bs-meson decay constant is determined in the combined static and quenched approximation. A correction due to the finite mass of the b-quark is estimated by interpolating between the static result and a recent determination of FDs.

Quenched and first unquenched lattice HQET determination of the Bs-meson width difference

We present recent results for the prediction of the B 0 s - B 0 s lifetime difference from lattice Heavy Quark Effective Theory simulations. In order to get a next-to-leading order result we have calculated the matching between QCD and HQET and the two-loop anomalous dimensions in the HQET for all the Δ B=2 operators, in particular for the operators which enter the width difference. We present results from quenched and, for the first time, from unquenched simulations. We obtain for the B 0 s - B 0 s lifetime difference, ▪ and ▪ from the quenched and unquenched simulations respectively.

NNLO unquenched calculation of the b quark mass

By combining the first unquenched lattice computation of the B-meson binding energy with the recently calculated two-loop contribution to the lattice HQET mass, we determine the MS b-quark mass, m b( m b) at the NNLO. We find m b( m b) = (4.26 ± 0.03 ± 0.05) GeV. The inclusion of the two-loop is one of the steps necessary to extract m b( m b) with a precision better than O( Λ QCD ), which is the uncertainty due to the presence of an IR renormalon singularity in the perturbative series of the residual mass. Our results have been obtained on a sample of 60 lattices of size 24 3 × 40 at β = 5.6, using the unquenched Wilson action with two degenerate sea quarks. The quark propagators have been computed using the unquenched links generated by the T ζ L Collaboration.

NNLO unquenched calculation of the b quark mass

By combining the first unquenched lattice computation of the B-meson binding energy and the two-loop contribution to the lattice HQET residual mass, we determine the (\bar{{MS}}) (b)-quark mass, (\bar{m}_{b}(\bar{m}_{b})). The inclusion of the two-loop corrections is essential to extract (\bar{m}_{b}(\bar{m}_{b})) with a precision of ({\cal O}(\Lambda^{2}_{QCD}/m_{b})), which is the uncertainty due to the renormalon singularities in the perturbative series of the residual mass. Our best estimate is (\bar{m}_{b}(\bar{m}_{b}) = (4.26 \pm 0.09) {\rm GeV}), where we have combined the different errors in quadrature. A detailed discussion of the systematic errors contributing to the final number is presented. Our results have been obtained on a sample of (60) lattices of size (24^{3}\times 40) at (\beta =5.6), using the Wilson action for light quarks and the lattice HQET for the (b) quark, at two values of the sea quark masses. The quark propagators have been computed using the unquenched links generated by the T(\chi)L Collaboration.

Matrix elements of four-fermion operators in the HQET

The B- B mixing, B-meson lifetimes, the B 3- B 3 lifetime difference and SUSY FCNC effects in ΔB = 2 processes are very important measurable quantities in B-meson phenomenology whose theoretical predictions depend on unknown matrix elements of several four-fermion operators. We present preliminary results for the matrix elements of the relevant four-fermion operators computed on a sample of 600 lattices of size 24 2 × 40 at β = 6.0, using the SW-Clover action for light quarks with rotated light quark propagators and the lattice version of the HQET for heavy quarks. As a necessary ingredient of the calculation, we also present results for the next-to-leading order matching of the full theory to the lattice HQET (one- and two-loop anomalous dimensions, one-loop QCD-HQET matching coefficients and one-loop continuum-lattice HQET matching coefficients).

Formula omitted] mixing in the HQET

We present a high statistics, quenched lattice calculation of the B-parameters B B d and B B s , computed at lowest order in the HQET. The results were obtained using a sample of 600 quenched gauge field configurations, generated by Monte Carlo simulation at β = 6.0 on a 24 3 × 40 lattice. For the light quarks the SW-Clover action was used; the propagator of the lattice HQET was also tree-level improved. Our best estimate of the renormalization scale independent B-parameter is B B d = 1.08 ± 0.06 ± 0.08 . B B d has been obtained by using “boosted” perturbation theory to calculate the renormalization constants which relate the matrix elements of the lattice operators to the corresponding amplitudes in the continuum. Due to the large statistics, the errors in the extraction of the matrix elements of the relevant bare operators are rather small. The main systematic error, corresponding to ±0.08 in the above result, comes from the uncertainty in the evaluation of the renormalization constants, for which the one-loop corrections are rather large. The non-perturbative evaluation of these constants will help to reduce the final error. We also obtain B B s B B d = 1.01 ± 0.01 and f B s 2 B B s f B d 2 B B d = 1.38 ± 0.07 .