Sum Rule Predictions Research Articles

Nucleon Resonance Masses from QCD Sum Rules

We calculate the masses of the nucleon resonances [N+(1440), N-(1535), N- (1650), N+(1710), N+(1880), N-(1895), N+(2100)] using an adaptation of the method of finite energy QCD sum rules (FESR) introduced recently in the determination of the masses of the vector meson resonances. This variation of finite energy sum rules involves as usual integration over a closed contour consisting of a circle of a large radius R and a cut in the complex energy (squared) plane. A specific integration kernel is used, however, which minimizes the integral over the cut. We obtain remarkably stable results over a wide range R, where R is the radius of the integration contour. The sum rule predictions agree well with the experimental values. We make use of the nucleonic correlator discussed in our previous FESR calculation of the nucleon mass.

Precision calculations of Bd,s → π, K decay form factors in soft-collinear effective theory

We improve QCD calculations of the semileptonic Bd,s→ π, K decay form factors at large hadronic recoil by implementing the next-to-leading-logarithmic resummation for the obtained leading-power light-cone sum rules in the soft-collinear effective theory (SCET) framework and by computing for the first time the non-vanishing spectator-quark mass correction dictating the SU(3)-flavour symmetry breaking effects between these fundamental quantities at the one-loop accuracy. Additionally, we endeavour to investigate a variety of the subleading-power contributions to these heavy-to-light form factors at mathcal{O}left({alpha}_s^0right) with the same methodology, by including the higher-order terms in the heavy-quark expansion of the hard-collinear quark propagator, by evaluating the desired effective matrix element of the next-to-leading-order term in the SCETI representation of the weak transition current, by taking into account the off-light-cone contributions of the two-body heavy-quark effective theory (HQET) matrix elements as well as the three-particle higher-twist corrections from the subleading bottom-meson light-cone distribution amplitudes (LCDAs), and by computing the twist-five and twist-six four-body higher-twist effects with the aid of the factorization approximation. Having at our disposal the SCET sum rules for the exclusive B-meson decay form factors under discussion, we further explore in detail numerical implications of the newly computed subleading-power corrections by employing the three-parameter model for both the leading-twist and higher-twist B-meson distribution amplitudes. Taking advantage of the customary Bourrely-Caprini-Lellouch (BCL) parametrization for the complete set of the semileptonic Bd,s→ π, K form factors, we then determine the correlated numerical results for the interesting series coefficients, by carrying out the simultaneous fit of the exclusive B-meson decay form factors to both the achieved SCET sum rule predictions at small momentum transfer (q2) and the available lattice QCD results at large momentum transfer. Subsequently, we perform a comprehensive phenomenological analysis of the full angular observables, the lepton-flavour university ratios and the lepton polarization asymmetries for the flavour-changing charged- current Bto pi ell {overline{nu}}_{ell } and {B}_sto Kell {overline{nu}}_{ell } decays (with ℓ = μ, τ) together with the differential q2-distribution for the exclusive rare Bto K{nu}_{ell }{overline{nu}}_{ell } decays in the Standard Model.

Isovector meson masses from QCD sum rules

We present a calculation of the masses of the isovector mesons (vector, scalar and pseudoscalar including the established recurrences) using a new method of finite energy QCD sum rules. The method is based on the idea of choosing a suitable integration kernel which minimizes the occurring integral over the cut in the complex energy (squared) plane. We obtain remarkably stable results in a wide range [Formula: see text], where [Formula: see text] is the radius of the integration contour. The sum rule predictions agree with the experimental values within the expected accuracy showing that QCD describes single resonances.

Heavy-light hybrid mesons with different spin-parities

The spectroscopic parameters of the heavy-light hybrid mesons with different spin-parities and different quark contents are investigated in the framework of the QCD sum rule method. The mass and current coupling of these states are calculated by taking into account the quark, gluon and mixed vacuum condensates up to dimension 10. The obtained results are compared with the existing QCD Laplace sum rule predictions. The results of mass and current coupling for all the considered channels are obtained to be stable and reliable. Our results can be useful for future experimental searches as well as theoretical studies of different parameters related to the hybrid mesons and their decays and interactions with other particles.

Rare radiative Ξb−→ Ξ−γ decay in the relativistic quark model

Recently, the LHCb collaboration put the upper limit on the [Formula: see text] decay branching ratio [Formula: see text]. The measured value is below the light-cone sum rule prediction. In this paper, the rare radiative decay of the [Formula: see text] baryon is studied in the framework of the relativistic quark model based on the quasipotential approach and QCD. The decay form factors are calculated with the comprehensive account of the relativistic effects. The obtained result for the branching ratio is found to be below the upper limit set by LHCb and is consistent with theoretical predictions based on the SU(3) flavor-symmetry, light-front quark model and light-cone QCD sum rules in full theory within theoretical uncertainties.

Charm meson couplings in Hard-Wall holographic QCD

In phenomenology of quantum chromodynamics (QCD), charmed meson vertices are useful tools to study the final-state re-scattering effects in the hadronic B decays. The strong couplings of charm mesons vertices, are related to the basic parameters in the heavy quark effective Lagrangian. Here, the four-flavor Hard-Wall holographic QCD is illustrated to evaluate the couplings of (D^{_{-(*-)}}, {bar{D}}^{_0}, a_{1}^{_-}), (D^{_{-(*-)}}, {bar{D}}^{_0}, b_{1}^{_-}), (D_{s}^{_{-(*-)}},{bar{D}}^{_{0}}, K_{1A}^{_-}), (D_{s}^{_{-(*-)}}, {bar{D}}^{_{0}}, K_{1B}^{_{-(*-)}}), (D_{s}^{_{+(*+)}}, {D}^{_+}, K_{1A}^{_0}), (D_{s}^{_{+(*+)}}, {D}^{_+}, K_{1B}^{_0}), (D^{_{-(*-)}}, {bar{D}}^{_{0(*0)}}, rho ^{_-}), (D_{s}^{_{-(*-)}}, {bar{D}}^{_{0(*0)}}, K^{_{*-}}), ({D}^{_{0(*0)}}, {bar{D}}^{_{0(*0)}}, psi ), (D_{1}^{_-}, {bar{D}}_{1}^{_0}, pi ^{_-}), (D_{s1}^{_-}, {bar{D}}_{1}^{_0}, K^{_{-}}), ({D}_{1}^{_0}, {bar{D}}_{1}^{_0}, eta _{c}), (psi , D^{_{0(*0)}}, D^{_{+}}, pi ^{_-}), (psi , D^{_{0(*0)}}, {bar{D}}^{_0}, pi ^{_0}), (psi , D_{s}^{_{+(*+)}}, D^{_{-}}, K^{_{0}}), (psi , D^{_{0(*0)}}, D^{_{+}}, a_{1}^{_-}), (psi , D^{_{0(*0)}}, D^{_{+}}, b_{1}^{_-}), (psi , D_{s}^{_{+(*+)}}, D^{_{-}}, K_{1B}^{_{0}}) and (psi , D_{s}^{_{+(*+)}}, D^{_{-}}, K_{1B}^{_{0}}) vertices. Moreover, the values of the masses of D^{_{0(*0)}}, D_{s}^{_{-(*-)}}, omega , psi , D_{1}^{_{0}}, D_{1}^{_{-}}, K^{0}, eta _{c}, D_{s1}^{_{-}} and chi _{_{c1}} as well as the decay constant of pi ^{-}, D^{_{-(*-)}}, K^{-}, rho ^{-}, D_{1}^{_{-}}, a_{1}^{-} and D_{s}^{_{-(*-)}} are estimated in this study. A comparison is also made between our results and the experimental values of the masses and decay constants. Our results for strong couplings are also compared with the three point sum rule (3PSR) and light-cone QCD sum rule (LCSR) predictions.

Optimized determination of the polarized Bjorken sum rule in pQCD

We present the method of numerical optimization for the perturbative series using the renormalization group in quantum chromodynamics. We apply our approach to the perturbation series in $\alpha_s$ for the coefficient function $C_\text{Bjp}(\alpha_s)$ of the Bjorken sum rule for the polarized deep inelastic lepton-hadron scattering. We optimize the Bjorken sum rule value, $\Gamma_1^\text{p-n}$, at the COMPASS, SLAC and JLab kinematics and compare the obtained results with the experimental measurements and also with the truncated Bjorken sum rule predictions.

Semileptonic decays of the scalar tetraquark Z_{bc;overline{u}overline{d}}^{0}

We study semileptonic decays of the scalar tetraquark Z_{bc;overline{u} overline{d}}^{0} to final states T_{bs;overline{u}overline{d} }^{-}e^{+}nu _{e} and T_{bs;overline{u}overline{d}}^{-}mu ^{+}nu _{mu } , which run through the weak transitions crightarrow se^{+}nu _{e} and crightarrow smu ^{+}nu _{mu }, respectively. To this end, we calculate the mass and coupling of the final-state scalar tetraquark T_{bs;overline{u}overline{d} }^{-} by means of the QCD two-point sum rule method: these spectroscopic parameters are used in our following investigations. In calculations we take into account the vacuum expectation values of the quark, gluon, and mixed operators up to dimension ten. We use also three-point sum rules to evaluate the weak form factors G_{i}(q^2) (i=1,~2) that describe these decays. The sum rule predictions for G_{i}(q^2) are employed to construct fit functions F_{i}(q^2), which allow us to extrapolate the form factors to the whole region of kinematically accessible q^2. These functions are required to get partial widths of the semileptonic decays Gamma left( Z_{bc}^{0}rightarrow Te^{+}nu _{e}right) and Gamma left( Z_{bc}^{0}rightarrow Tmu ^{+}nu _{mu }right) by integrating corresponding differential rates. We analyze also the two-body nonleptonic decays Z_{bc;overline{u}overline{d}}^{0} rightarrow T_{bs;overline{u}overline{d }}^{-}pi ^{+} and Z_{bc;overline{u}overline{d}}^{0} rightarrow T_{bs;overline{u }overline{d}}^{-}K^{+}, which are necessary to evaluate the full width of the Z_{bc;overline{u}overline{d}}^{0}. The obtained results for Gamma _{mathrm {full}}=(3.18pm 0.39)times 10^{-11}~{mathrm {MeV}} and mean lifetime 20.7_{-2.3}^{+2.9}~{mathrm {ps}} of the tetraquark Z_{bc;overline{u} overline{d}}^{0} can be used in experimental investigations of this exotic state.

Heavy-to-light scalar form factors from Muskhelishvili\u2013Omn\xe8s dispersion relations

By solving the Muskhelishvili–Omnès integral equations, the scalar form factors of the semileptonic heavy meson decays Drightarrow pi bar{ell }nu _ell , Drightarrow {bar{K}} bar{ell }nu _ell , {bar{B}}rightarrow pi ell bar{nu }_ell and {bar{B}}_srightarrow K ell bar{nu }_ell are simultaneously studied. As input, we employ unitarized heavy meson–Goldstone boson chiral coupled-channel amplitudes for the energy regions not far from thresholds, while, at high energies, adequate asymptotic conditions are imposed. The scalar form factors are expressed in terms of Omnès matrices multiplied by vector polynomials, which contain some undetermined dispersive subtraction constants. We make use of heavy quark and chiral symmetries to constrain these constants, which are fitted to lattice QCD results both in the charm and the bottom sectors, and in this latter sector to the light-cone sum rule predictions close to q^2=0 as well. We find a good simultaneous description of the scalar form factors for the four semileptonic decay reactions. From this combined fit, and taking advantage that scalar and vector form factors are equal at q^2=0, we obtain |V_{cd}|=0.244pm 0.022, |V_{cs}|=0.945pm 0.041 and |V_{ub}|=(4.3pm 0.7)times 10^{-3} for the involved Cabibbo–Kobayashi–Maskawa (CKM) matrix elements. In addition, we predict the following vector form factors at q^2=0: |f_+^{Drightarrow eta }(0)|=0.01pm 0.05, |f_+^{D_srightarrow K}(0)|=0.50 pm 0.08, |f_+^{D_srightarrow eta }(0)|=0.73pm 0.03 and |f_+^{{bar{B}}rightarrow eta }(0)|=0.82 pm 0.08, which might serve as alternatives to determine the CKM elements when experimental measurements of the corresponding differential decay rates become available. Finally, we predict the different form factors above the q^2-regions accessible in the semileptonic decays, up to moderate energies amenable to be described using the unitarized coupled-channel chiral approach.

Ground State Mass Predictions of Heavy-Light Hybrids from QCD Sum-Rule Analysis (JP = {0±,1±})

We present QCD Laplace sum-rule predictions of ground state masses of heavy-light open-flavour hybrid mesons. Having computed leading-order diagonal correlation functions, including up to dimension six gluon condensate contributions, we extract hybrid mass predictions for all JP∈{0±,1±}, and explore possible mixing effects with conventional meson states. Similarities are found in the mass hierarchy in both charm and bottom systems with some exceptions that are discussed.

Investigation of the light four-quark states with exotic JPC=0−−

We study the exotic $J^{PC}=0^{--}$ four-quark states in Laplace sum rules (LSR) and finite energy sum rules (FESR). We use the vector tetraquark-like currents as interpolating currents in the correlator, from which the $1^{+-}$ states are also studied. In the mass extraction, we use the standard stability criterion with respect to the Borel parameters and the QCD continuum thresholds and consider the effect of the violation of factorization in estimating the high dimensional condensates as a source of uncertainties. The obtained mass prediction $1.66\pm0.14$ GeV is much lower than the previous sum rule predictions obtained using the scalar currents. Our result favours the four-quark interpretation of the possible $\rho\pi$ dominance in the $D^0$ decay. We also discuss the possible decay patterns of these exotic four-quark states.

Renormalisation group corrections to neutrino mixing sum rules

Neutrino mixing sum rules are common to a large class of models based on the (discrete) symmetry approach to lepton flavour. In this approach the neutrino mixing matrix $U$ is assumed to have an underlying approximate symmetry form $\tilde{U}_{\nu}$, which is dictated by, or associated with, the employed (discrete) symmetry. In such a setup the cosine of the Dirac CP-violating phase $\delta$ can be related to the three neutrino mixing angles in terms of a sum rule which depends on the symmetry form of $\tilde{U}_{\nu}$. We consider five extensively discussed possible symmetry forms of $\tilde{U}_{\nu}$: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding to iii) golden ratio type A (GRA) mixing, iv) golden ratio type B (GRB) mixing, and v) hexagonal (HG) mixing. For each of these forms we investigate the renormalisation group corrections to the sum rule predictions for $\delta$ in the cases of neutrino Majorana mass term generated by the Weinberg (dimension 5) operator added to i) the Standard Model, and ii) the minimal SUSY extension of the Standard Model.

Evaluation of the forward Compton scattering off protons. II. Spin-dependent amplitude and observables

The forward Compton scattering off the proton is determined by substituting the empirical total photoabsorption cross sections into dispersive sum rules. In addition to the spin-independent amplitude evaluated previously [Phys. Rev. D 92, 074031 (2015)], we obtain the spin-dependent amplitude over a broad energy range. The two amplitudes contain all the information about this process, and we, hence, can reconstruct the nonvanishing observables of the proton Compton scattering in the forward kinematics. The results are compared with predictions of chiral perturbation theory where available. The low-energy expansion of the spin-dependent Compton scattering amplitude yields the Gerasimov-Drell-Hearn (GDH) sum rule and relations for the forward spin polarizabilities (FSPs) of the proton. Our evaluation provides an empirical verification of the GDH sum rule for the proton, and yields empirical values of the proton FSPs. For the GDH integral, we obtain $204.5(21.4)$ $\mu$b, in agreement with the sum rule prediction: $204.784481(4)$ $\mu$b. For the FSPs, we obtain: $\gamma_0=-92.9(10.5) \times 10^{-6}$ fm$^4$, and $\bar{\gamma_0}=48.4(8.2) \times 10^{-6}$ fm$^6$, improving on the accuracy of previous evaluations.

Spectroscopy and decay properties of Σb, Λb baryons in quark–diquark model

Properties of single beauty baryons (Σb, Λb) are studied based on the quark–diquark structure. The confinement potential is assumed as two body color coulomb plus power potential with exponent ν. We find a strong correlation between the choice of the heavy quark mass parameter (mb), strong coupling constant (αs) and the potential exponent (ν) for getting the experimental mass spilt of mΣb*−mΣb=21.2±2.0 MeV. The resultant spectroscopic parameters are used for computing magnetic moments, the electromagnetic radiative decay and strong hadronic decay of Σb, Λb systems. Our predictions on the radiative decay width correspond to Σb*0→Λbγ are in agreement with the QCD sum rule prediction.

Spectroscopy and flavor changing decays ofB,Bsmesons in a Dirac formalism

In the framework of the relativistic independent quark model, the mass spectra and decay properties of $B$ and ${B}_{s}$ mesons are obtained using a Martin-like potential for the quark confinement. The predicted excited states are in good agreement with the experimental results as well as with the lattice QCD and other theoretical predictions. For instance, the ${B}_{2}(5747)$ as $1{^{3}P}_{2}$, ${B}_{1}(5721)$ as $1{^{3}P}_{1}$, and ${B}_{0}(5732)$ as $1{^{3}P}_{0}$ are identified. The spectroscopic parameters are used to calculate the electromagnetic transitions, pseudoscalar decay constants, hadronic decay widths, and leptonic decay widths. The present result for the decay constant, ${f}_{B}(1S)=188.56\text{ }\text{ }\mathrm{MeV}$, is in good agreement with recent lattice results (UKQCD Collaboration, Fermilab) and comparable with the experimental value of $(206.7\ifmmode\pm\else\textpm\fi{}8.9)$. The pseudoscalar decay constant for the ${B}_{s}$ meson obtained here, ${f}_{{B}_{s}}(1S)=240.21\text{ }\text{ }\mathrm{MeV}$, is in very good agreement with recent lattice QCD and QCD sum rule predictions. The predicted branching ratio for ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ ($1.354\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$) is in accordance with the value, $(1.65\ifmmode\pm\else\textpm\fi{}0.34)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ reported by the Particle Data Group (PDG). The branching ratios of the rare decays ${B}_{s}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ ($(3.1\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$) and ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ ($l6.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$) as observed by the CMS and LHCb Collaborations very recently are in accordance with our predictions of $3.602\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ and $1.018\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, respectively. The Cabibbo-favored hadronic branching ratios of ${B}^{0}\ensuremath{\rightarrow}{D}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ ($3.724\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$), ${B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\pi}}^{+}$ ($3.475\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$), and ${B}_{s}\ensuremath{\rightarrow}{D}_{s}^{\ensuremath{-}}{\ensuremath{\rho}}^{+}$ ($3.800\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$) are in good agreement with the respective PDG values. The mixing parameters ${x}_{q}$, ${\ensuremath{\chi}}_{q}$ for ${B}^{0}\ensuremath{-}{\overline{B}}^{0}$ (${x}_{d}=0.769$, ${\ensuremath{\chi}}_{d}=0.1859$) and ${B}_{s}\ensuremath{-}{\overline{B}}_{s}$ (${x}_{s}=26.41$, ${\ensuremath{\chi}}_{s}=0.49929$) are also found to be in excellent agreement with the PDG values of ($0.770\ifmmode\pm\else\textpm\fi{}0.008$, $0.1862\ifmmode\pm\else\textpm\fi{}0.0023$) and ($26.49\ifmmode\pm\else\textpm\fi{}0.29$, $0.499292\ifmmode\pm\else\textpm\fi{}0.000016$), respectively.

Perturbative corrections to Λ b → Λ form factors from QCD light-cone sum rules

We compute radiative corrections to $\Lambda_b \to \Lambda$ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with $\Lambda_b$-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-$\Lambda_b$-baryon correlation function is justified at leading power in $\Lambda/m_b$, with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to-$B$-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at ${\cal O}(\alpha_s)$ shift the $\Lambda_b \to \Lambda$ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the $\Lambda_b \to \Lambda$ from factors we further investigate several decay observables in the electro-weak penguin $\Lambda_b \to \Lambda \, \ell^{+} \ell^{-}$ transitions in the factorization limit (i.e., ignoring the "non-factorizable" hadronic effects which cannot be expressed in terms of the $\Lambda_b \to \Lambda$ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.

Thermal behaviors of light unflavored tensor mesons in the framework of QCD sum rule

In this paper, we investigated the sensitivity of the masses and decay constants of f2(1270) and a2(1320) tensor mesons to the temperature using OCD sum rule approach. In our calculations, we take into account new additional operators appearing in operator product expansion (OPE). At the end of numerical analyses we show that at deconfinement temperature the decay constants and masses decreased by 6% and 96% of their vacuum values, respectively. Our results on the masses and decay constants at zero temperature of the tensor mesons are consistent with the experimental data as well as the vacuum sum rules predictions.

B→K*form factors from flavor data to QCD and back

Sufficient control of transition form factors is a vital ingredient for the precision flavor programs including the nearer term searches at the Large Hadron Collider and the forthcoming Belle II experiment. We improve on existing methods to extract $B\ensuremath{\rightarrow}{K}^{*}$ form factor ratios at low hadronic recoil from $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ data on the angular observables ${F}_{L}$, ${A}_{T}^{(2)}$ and ${P}_{4}^{\ensuremath{'}}$ by adding heavy quark symmetry-based constraints and by investigating the cross talk between low and large recoil. The data-extracted form factor ratios (i) provide benchmarks for the lattice and light-cone sum rule predictions, the latter of which have been updated including improved uncertainty estimations, and (ii) allow us to improve the predictions for benchmark observables. We find that present data on the forward-backward asymmetry ${A}_{\mathrm{FB}}$ and the angular observable ${P}_{5}^{\ensuremath{'}}$ at low recoil are in good agreement with the Standard Model.

Decay Constants of Beauty Mesons from QCD Sum Rules

Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i) For the input value of the bottom-quark mass in the $\overline{\rm MS}$ scheme $\overline{m}_b(\overline{m}_b)\approx4.18\;\mbox{GeV},$ the sum-rule result $f_B\approx210$-$220\;\mbox{MeV}$ for the $B$ meson decay constant is substantially larger than the recent lattice-QCD finding $f_B\approx190\;\mbox{MeV}.$ Requiring QCD sum rules to reproduce the lattice-QCD value of $f_B$ yields a significantly larger $b$-quark mass: $\overline{m}_b(\overline{m}_b)=4.247\;\mbox{GeV}.$ (ii) Whereas QCD sum-rule predictions for the charmed-meson decay constants $f_D,$ $f_{D_s},$ $f_{D^*}$ and $f_{D_s^*}$ are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants - and especially for the ratio $f_{B^*}/f_B$ - prove to be very sensitive to the specific scale setting.

Longitudinal spin physics results from COMPASS

The COMPASS experiment at the CERN SPS has a broad physics program focused on the nucleon spin structure and hadron spectroscopy, using muon and hadron beams, respectively. Results from the COMPASS on the inclusive longitudinal double spin asymmetries A1d,p measured in deep-inelastic polarized muon scattering off the polarized 6LiD and NH3 targets are presented. The new proton data cover the range Q2>1(GeV2/c), 0.004<x<0.7 and improve the statistical precision of g1p(x) by factor of two at x<0.02 compared to previous measurements. The spin-dependent non-singlet function g1NS(x,Q2) extracted from the data allows to evaluate the isovector quark density Δq3(x,Q2) and check the Bjorken sum rule prediction. The helicity distributions for the three lightest quark and antiquark flavours extracted from the measured double spin asymmetries for production of charged pions and kaons in semi-inclusive deep-inelastic scattering are also presented and discussed. The gluon polarization in the nucleon was determined using open charm production or high transverse-momentum hadron pairs production in polarized muon scattering off longitudinally polarized target.