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

The 27-plet contributions to the CP-conserving K→πl+l−K\rightarrow \pi l^+l^- decays

We revisit the the rare kaon decays $K\to \pi l^+l^-$ which are of interest specially due to the recent measurements of the charged kaon decay spectra. We compute the contribution of the 27-plet to the decay amplitudes in one loop SU(3) Chiral Perturbation Theory. We estimate the resulting impact to be $\sim 10$ to the branching ratios of the charged kaon decays, and also noticeably influence the shape of the spectra. With current values of the constants $G_8$ associated with the octet and $G_{27}$ associated with the 27-plet, the contribution of the latter pushes the spectrum in the correct direction for the charged lepton spectra. We also discuss the impact for the neutral decay rates and spectra.Comment: 9 pages, plain latex, 5 figure

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

Extrapolation and unitarity bounds for the B→πB \to \pi form factor

We address the problem of extrapolating the vector form factor $f_{B\pi}^+$, which is relevant to $B\to \pi\ell \nu_\ell$ decays, from the region of small to the region of large momentum transfer. As input, we use the QCD light-cone sum rule at small momentum transfer. We carry out a comprehensive Bayesian uncertainty analysis and obtain correlated uncertainties for the normalization and shape parameters of the form factor. The $z$-series parametrization for $f_{B\pi}^+$ is employed to extrapolate our results to large momentum transfer, and to compare with the lattice QCD results. To test the validity of our extrapolation we use the upper and lower bounds from the unitarity and positivity of the two-point correlator of heavy-light quark currents. This correlator is updated by including the NNLO perturbative term and the NLO correction to the quark condensate contribution. We demonstrate that an additional input including the form factor, its first and second derivative calculated at one value of momentum transfer from the light-cone sum rules, considerably improves the bounds. This only holds when the correlations between the form factor parameters are taken into account. We further combine our results with the latest experimental measurements of $B\to \pi \ell \nu_\ell$ by the BaBar and Belle collaborations, and obtain $|V_{ub}|= (3.32^{+0.26}_{-0.22}) \cdot 10^{-3}$ from a Bayesian analysis.Comment: 26 pages, 4 figures; v2: as published (reference and zoomed plot added, conclusions and numerics unchanged

The DπD\pi form factors from analyticity and unitarity

We study the shape parameters of the $D\pi$ scalar and vector form factors using as input dispersion relations and unitarity for the moments of suitable heavy-light correlators evaluated with Operator Product Expansions, including $O(\alpha_s^2)$ terms in perturbative QCD. For the scalar form factor, a low energy theorem and phase information on the unitarity cut are implemented to further constrain the shape parameters. We finally determine points on the real axis and isolate regions in the complex energy plane where zeros of the form factors are excluded.Comment: 6 pages, 4 figures; Seminar given at DAE-BRNS Workshop on Hadron Physics Bhabha Atomic Research Centre, Mumbai, India, October 31-November 4, 2011, submitted to Proceeding

The KπK\pi form factors from Analyticity and Unitarity

Analyticity and unitarity techniques are employed to obtain bounds on the shape parameters of the scalar and vector form factors of semileptonic $K_{l3}$ decays. For this purpose we use vector and scalar correlators evaluated in pQCD, a low energy theorem for scalar form factor, lattice results for the ratio of kaon and pion decay constants, chiral perturbation theory calculations for the scalar form factor at the Callan-Treiman point and experimental information on the phase and modulus of $K\pi$ form factors up to an energy \tin=1 {\rm GeV}^2. We further derive regions on the real axis and in the complex-energy plane where the form factors cannot have zeros.Comment: 6 pages, 5 figures; Seminar given at DAE-BRNS Workshop on Hadron Physics Bhabha Atomic Research Centre, Mumbai, India October 31-November 4, 2011, submitted to Proceeding

Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems

We investigate the scalar K pi form factor at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using at input the values of the form factor at t=0 and the Callan-Treiman point, we obtain stringent constraints on the slope and curvature parameters of the Taylor expansion at the origin. Also, we predict a quite narrow range for the higher order ChPT corrections at the second Callan-Treiman point.Comment: 5 pages latex, uses EPJ style files, 3 figures, replaced with version accepted by EPJ