Open-flavour meson studies are the necessary completion to any comprehensive investigation of quarkonia. We extend recent studies of quarkonia in the Dyson-Schwinger-Bethe-Salpeter equation approach to explore their results for all possible flavour combinations. Within the inherent limitations of the setup, we present the most comprehensive results for meson masses and leptonic decay constants currently available and put them in perspective with respect to experiment and other approaches.

We consider threshold pion electroproduction on a proton target for photon virtualities in the region 1 − 10 GeV. The S-wave multipoles at threshold, E0+ and L0+, are calculated using light-cone sum rules.

Updated predictions for the decay constants of the D, Ds, B and Bs mesons obtained from Borel QCD sum rules for heavy-light currents are presented and compared with the recent lattice averages performed by the Flavor Lattice Averaging Group. An excellent agreement is obtained in the charm sector, while some tension is observed in the bottom sector. Moreover, available lattice and QCD sum-rule calculations of the decay constants of the vector D*, Ds*, B* and Bs* mesons are compared. Again some tension in the bottom sector is observed.

We revisit F π(Q 2) and F Pγ(Q 2), P = π, η, η′, making use of the local-duality (LD) version of QCD sum rules. We give arguments that the LD sum rule provides reliable predictions for these form factors at Q 2 ≥ 5–6 GeV2, the accuracy of the method increasing with Q 2 in this region. For the pion elastic form factor, the well-measured data at small Q 2 give a hint that the LD limit may be reached already at relatively low values of momentum transfers, Q 2 ≈ 4–8 GeV2; we therefore conclude that large deviations from LD in the region Q 2 = 20–50 GeV2 seem very unlikely. The data on the (η, η′) → γγ* form factors meet the expectations from the LD model. However, the BaBar results for the π 0 → γγ* form factor imply a violation of LD growing with Q 2 even at Q 2 ≈ 40 GeV2, at odds with the η, η′ case and with the general properties expected for the LD sum rule.

We study the $\gamma^* \gamma^*\to\eta_c$ transition form factor, $F_{\eta_c\gamma\gamma}(Q_1^2,Q_2^2),$ with the local-duality (LD) version of QCD sum rules. We analyse the extraction of this quantity from two different correlators, $ $ and $ ,$ with $P,$ $A,$ and $V$ being the pseudoscalar, axial-vector, and vector currents, respectively. The QCD factorization theorem for $F_{\eta_c\gamma\gamma}(Q_1^2,Q_2^2)$ allows us to fix the effective continuum thresholds for the $ $ and $ $ correlators at large values of $Q^2=Q_2^2$ and some fixed value of $\beta\equiv Q_1^2/Q_2^2$. We give arguments that, in the region $Q^2\ge10$--$15 GeV^2$, the effective threshold should be close to its asymptotic value such that the LD sum rule provides reliable predictions for $F_{\eta_c\gamma\gamma}(Q_1^2,Q_2^2).$ We show that, for the experimentally relevant kinematics of one real and one virtual photon, the result of the LD sum rule for $F_{\eta_c\gamma}(Q^2)\equiv F_{\eta_c\gamma\gamma}(0,Q^2)$ may be well approximated by the simple monopole formula $F_{\eta_c\gamma}(Q^2)={2e_c^2N_cf_P}(M_V^2+Q^2)^{-1},$ where $f_P$ is the $\eta_c$ decay constant, $e^2_c$ is the $c$-quark charge, and the parameter $M_V$ lies in the mass range of the lowest $\bar cc$ vector states.

The procedure of extracting the ground-state parameters from vacuum-to-vacuum and vacuum-to-hadron correlators within the method of sum rules is considered. The emphasis is laid on the crucial ingredient of this method—the effective continuum threshold. A new algorithm to fix this quantity is proposed and tested. First, a quantum-mechanical potential model which provides the only possibility to probe the reliability and the actual accuracy of this method is used as a study case. In this model, our algorithm is shown to lead to a remarkable improvement of the accuracy of the extracted ground-state parameters compared to the standard procedures adopted in the method and used in all previous applications of dispersive sum rules in QCD. As a next step, it is demonstrated that the procedures of extracting the ground-state decay constant in the potential model and in QCD are quantitatively very close to each other. Therefore, the application of the proposed algorithm in QCD promises a considerable increase of the accuracy of the extracted hadron parameters.

We present the first systematic analysis of the off-light-cone effects in correlators relevant for the extraction of the heavy-to-light form factors within the method of light-cone sum rules. In a model with scalar constituents, the correlator is calculated in two different ways: (i) by performing the expansion of the Bethe-Salpeter amplitude of the light meson near the light cone x 2 = 0 and (ii) by adopting the known solution for the Bethe-Salpeter amplitude which allows one to calculate the correlator without invoking any expansion. We demonstrate that the contributions to the correlator from the off-light-cone terms x 2 ≠ 0 are not suppressed by any large parameter compared to the contribution of the light-cone term x 2 = 0. For decays of heavy particles of mass in the range 1.5–5 GeV, the light-cone correlator is shown to systematically overestimate the full correlator, numerically the difference being 10–20%.

The present report documents the results of Working Group 2: B, D and K decays, of the workshop on Flavor in the Era of the LHC, held at CERN from November 2005 through March 2007. With the advent of the LHC, we will be able to probe New Physics (NP) up to energy scales almost one order of magnitude larger than it has been possible with present accelerator facilities. While direct detection of new particles will be the main avenue to establish the presence of NP at the LHC, indirect searches will provide precious complementary information, since most probably it will not be possible to measure the full spectrum of new particles and their couplings through direct production. In particular, precision measurements and computations in the realm of flavor physics are expected to play a key role in constraining the unknown parameters of the Lagrangian of any NP model emerging from direct searches at the LHC. The aim of Working Group 2 was twofold: on the one hand, to provide a coherent up-to-date picture of the status of flavor physics before the start of the LHC; on the other hand, to initiate activities on the path towards integrating information on NP from high-p T and flavor data. This report is organized as follows: in Sect. 1, we give an overview of NP models, focusing on a few examples that have been discussed in some detail during the workshop, with a short description of the available computational tools for flavor observables in NP models. Section 2 contains a concise discussion of the main theoretical problem in flavor physics: the evaluation of the relevant hadronic matrix elements for weak decays. Section 3 contains a detailed discussion of NP effects in a set of flavor observables that we identified as "benchmark channels" for NP searches. The experimental prospects for flavor physics at future facilities are discussed in Sect. 4. Finally, Sect. 5 contains some assessments on the work done at the workshop and the prospects for future developments.

We study systematic errors of the ground-state parameters obtained from Shifman—Vainshtein—Zakharov sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator, which allows one to obtain both the OPE to any order and the parameters (masses and decay constants) of the bound states. We determine the parameters of the ground state making use of the standard procedures of the method of sum rules and compare the obtained results with the known exact values. We show that, in the situation when the continuum contribution to the polarization operator is not known and is modeled by an effective continuum, the method of sum rules does not allow one to control the systematic uncertainties of the extracted ground-state parameters.

We study the operator product expansion (OPE) and quark-hadron duality for two-and three-point correlators of the axial (A) and pseudoscalar (P) currents of the light quarks. In the chiral limit, these correlators are often dominated by nonperturbative power corrections leading to subtleties of quark-hadron duality relations and of the extraction of properties of light pseudoscalars. For the two-point correlators, we show the sum rule for 〈PP〉 to be sensitive to the excited light pseudoscalar. For the three-point correlators, we derive the Ward identities which provide the normalization of the pion electromagnetic form factor at zero momentum transfer. For large momentum transfer, we demonstrate the way the correct behavior of the pion form factor in agreement with perturbative QCD emerges from condensate terms in the OPE for the 〈PV P〉 and 〈AV P〉 correlators. The local-duality sum rule for 〈AV A〉 is shown to lead to the pion form factor with the required properties for all values of the momentum transfer.

Masses of tetraquarks with two heavy quarks and open charm and bottom are calculated in the framework of the diquark-antidiquark picture in the relativistic quark model. All model parameters were regarded as fixed by previous considerations of various properties of mesons and baryons. The light quarks and diquarks are treated completely relativistically. The c quark is assumed to be heavy enough to make the diquark configurations dominating. The diquarks are considered not to be point-like but to have an internal structure which is taken into account by the calculated diquark form factor entering the diquark-gluon interaction. It is found that all the (cc)(\bar q\bar q') tetraquarks have masses above the thresholds for decays into open charm mesons. Only the I(J^P)=0(1^+) state of (bb)(\bar u\bar d) lies below the BB* threshold and is predicted to be narrow.

We study the operator product expansion (OPE) and quark-hadron duality for 2- and 3-point correlators of the axial (A) and pseudoscalar (P) currents of the light quarks. In the chiral limit these correlators are often dominated by nonperturbative power corrections leading to subtleties of quark-hadron duality relations and of the extraction of properties of light pseudoscalars. For the 2-point correlators, we show the sum rule for < PP > to be sensitive to the excited light pseudoscalar. For the 3-point correlators, we derive the Ward identities which provide the normalization of the pion electromagnetic form factor at zero momentum transfer. For large momentum transfer, we demonstrate the way the correct behavior of the pion form factor in agreement with perturbative QCD emerges from condensate terms in the OPE for the < PVP > and < AVP > correlators. The local-duality sum rule for < AVA > is shown to lead to the pion form factor with the required properties for all values of the momentum transfer.

Consequent application of the instantaneous approximation to both the interaction and all propagators of the bound-state constituents allows us to forge, within the framework of the Bethe-Salpeter formalism for the description of bound states, an instantaneous form of the Bethe-Salpeter equation with exact (i.e., full) propagators of the bound-state constituents. This instantaneous equation generalizes the well-known Salpeter equation the derivation of which needs the additional assumption of free propagation of the bound-state constituents.

Several techniques for deriving semianalytical bounds on the energy eigenvalues of the spinless Salpeter equation and for estimating the quality of the corresponding approximate eigenstates are reviewed.

We study the semirelativistic Hamiltonian operator composed of the relativistic kinetic energy and a static harmonic-oscillator potential in three spatial dimensions and construct, for bound states with vanishing orbital angular momentum, its eigenfunctions in compact form, i. e., as power series, with expansion coefficients determined by an explicitly given recurrence relation. The corresponding eigenvalues are fixed by the requirement of normalizability of the solutions.

Problems posed by semirelativistic Hamiltonians of the form H = sqrt{m^2+p^2} + V(r) are studied. It is shown that energy upper bounds can be constructed in terms of certain related Schroedinger operators; these bounds include free parameters which can be chosen optimally.

We study the lowest energy E of a relativistic system of N identical bosons bound by pair potentials of the form V(r(ij))=g(r(ij)(2)) in three spatial dimensions. In natural units (h) over bar =c=1 the system has the semirelativistic "spinless-Salpeter" Hamiltonian H=Sigma(i=1)(N)rootm(2)+p(i)(2)+Sigma(j>i=1)(N)g(\r(i)-r(j\)(2)), where g is monotone increasing and has convexity g"greater than or equal to0. We use "envelope theory" to derive formulas for general lower energy bounds and we use a variational method to find complementary upper bounds valid for all Ngreater than or equal to2. In particular, we determine the energy of the N-body oscillator g(r(2))=cr(2) with error less than 0.15% for all mgreater than or equal to0, Ngreater than or equal to2, and c>0. (C) 2004 American Institute of Physics.