Unitarity Constraints on the B and B^* Form Factors from QCD Analyticity and Heavy Meson Spin Symmetry

A method of deriving bounds on the weak meson form factors, based on perturbative QCD, analyticity and unitarity, is generalized in order to fully exploit heavy quark spin symmetry in the ground state $(L=0)$ doublet of pseudoscalar $(B)$ and vector $(B^*)$ mesons. All the relevant form factors of these mesons are taken into account in the unitarity sum. They are treated as independent functions along the timelike axis, being related by spin symmetry only near the zero recoil point. Heavy quark vacuum polarisation up to three loops in perturbative QCD and the experimental cross sections $\sigma(e^+e^- \rightarrow \Upsilon)$ are used as input. We obtain bounds on the charge radius of the elastic form factor of the $B$ meson, which considerably improve previous results derived in the same framework.Comment: 13 pages LaTex, 1 figure as a separate ps fil

Analytic structure in the coupling constant plane in perturbative QCD

We investigate the analytic structure of the Borel-summed perturbative QCD amplitudes in the complex plane of the coupling constant. Using the method of inverse Mellin transform, we show that the prescription dependent Borel-Laplace integral can be cast, under some conditions, into the form of a dispersion relation in the a-plane. We also discuss some recent works relating resummation prescriptions, renormalons and nonperturbative effects, and show that a method proposed recently for obtaining QCD nonperturbative condensates from perturbation theory is based on special assumptions about the analytic structure in the coupling plane that are not valid in QCD.Comment: 14 pages, revtex4, 1 eps-figur

Determination of the strong coupling from hadronic tau decays using renormalization group summed perturbation theory

We determine the strong coupling constant \alpha_s from the \tau hadroni width using a renormalization group summed (RGS) expansion of the QCD Adler function. The main theoretical uncertainty in the extraction of \alpha_s is due to the manner in which renormalization group invariance is implemented, and the as yet uncalculated higher order terms in the QCD perturbative series. We show that new expansion exhibits good renormalization group improvement and the behaviour of the series is similar to that of the standard CIPT expansion. The value of the strong coupling in {\bar{\rm MS}} scheme obtained with the RGS expansion is \alpha_s(M_\tau^2)= 0.338 \pm 0.010. The convergence properties of the new expansion can be improved by Borel transformation and analytic continuation in the Borel plane. This is discussed elsewhere in these proceedings.Comment: Contribution to the proceedings of the workshop "Determination of the Fundamental Parameters of QCD", Nanyang Technological University, Singapore, 18-22 March 2013, to be published in Mod. Phys. Lett. A, version 2 contains an extra footnote and a reference compared to version

Parametrization-free determination of the shape parameters for the pion electromagnetic form factor

Recent data from high statistics experiments that have measured the modulus of the pion electromagnetic form factor from threshold to relatively high energies are used as input in a suitable mathematical framework of analytic continuation to find stringent constraints on the shape parameters of the form factor at $t=0$. The method uses also as input a precise description of the phase of the form factor in the elastic region based on Fermi-Watson theorem and the analysis of the $\pi\pi$ scattering amplitude with dispersive Roy equations, and some information on the spacelike region coming from recent high precision experiments. Our analysis confirms the inconsistencies of several data on the modulus, especially from low energies, with analyticity and the input phase, noted in our earlier work. Using the data on the modulus from energies above $0.65 \,{\rm GeV}$, we obtain, with no specific parametrization, the prediction for the charge radius. The same formalism leads also to very narrow allowed ranges for the higher-order shape parameters at $t=0$, with a strong correlation among them.Comment: v2 is 11 pages long using EPJ style files, and has 8 figures; Compared to v1, number of figures has been reduced, discussion has been improved significantly, minor errors have been corrected, references have added, and the manuscript has been significantly revised; this version has been accepted for publication in EPJ

Bounds on the spacelike pion electromagnetic form factor from analyticity and unitarity

We use the recently measured accurate BaBaR data on the modulus of the pion electromagnetic form factor, $F_\pi(t)$, up to an energy of 3 GeV, the I=1 $P$-wave phase of the $\pi\pi$ scattering amplitude up to the $\omega-\pi$ threshold, the pion charge radius known from Chiral Perturbation Theory, and the recently measured JLAB value of $F_\pi$ in the spacelike region at $t=-2.45 {\rm GeV}^2$ as inputs in a formalism that leads to bounds on $F_\pi$ in the intermediate spacelike region. We compare our constraints with experimental data and with perturbative QCD along with the results of several theoretical models for the non-perturbative contributions proposed in the literature.Comment: 6 pages, using PoS style files, 2 figures; talk given at QNP 2012, Palaiseau, France, April 16-20, 201

Theory of unitarity bounds and low energy form factors

We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarity. The values resulting from the symmetries of QCD at low energies or from lattice calculations at special points inside the analyticity domain can beincluded in an exact way. We write down the general solution of the corresponding Meiman problem for an arbitrary number of interior constraints and the integral equations that allow one to include the phase of the form factor along a part of the unitarity cut. A formalism that includes the phase and some information on the modulus along a part of the cut is also given. For illustration we present constraints on the slope and curvature of the K_l3 scalar form factor and discuss our findings in some detail. The techniques are useful for checking the consistency of various inputs and for controlling the parameterizations of the form factors entering precision predictions in flavor physics.Comment: 11 pages latex using EPJ style files, 5 figures; v2 is version accepted by EPJA in Tools section; sentences and figures improve