Theory of unitarity bounds and low energy form factors

Abstract

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.

11 pages latex using EPJ style files, 5 figures; v2 is version accepted by EPJA in Tools section; sentences and figures improved

References in corpus (6)

• Constraints on the form factors for K --> pi l nu and implications for V_us
• Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems
• Constraining the low energy pion electromagnetic form factor with space-like data
• Constraining the low energy Pion electromagnetic form factor with space-like and phase of time-like data
• Improved bounds on the radius and curvature of the K pi scalar form factor and implications to low-energy theorems
• New constraints on the Pion EM form factor using Pi'(-Q^2)

Cited by in corpus (17)

• Extrapolation and unitarity bounds for the $B\to \pi$ form factor
• Electromagnetic charge radius of the pion at high precision
• Precise determination of the low-energy hadronic contribution to the muon $g-2$ from analyticity and unitarity: An improved analysis
• Two-pion low-energy contribution to the muon $g-2$ with improved precision from analyticity and unitarity
• Constraints on the $\omega \pi$ form factor from analyticity and unitarity
• Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region
• Spacelike pion form factor from analytic continuation and the onset of perturbative QCD
• Parametrization-free determination of the shape parameters for the pion electromagnetic form factor
• Implications of unitarity and analyticity for the Dπform factors
• Improving the phenomenology of K_{l3} form factors with analyticity and unitarity
• Test of analyticity and unitarity for the pion form-factor data around the $\rho$ resonance
• Model independent bounds on the modulus of the pion form factor on the unitarity cut below the $\omega \pi$ threshold
• Model-independent constraints on hadronic form factors with above-threshold poles
• Model-independent constraint on the pion scalar form factor and light quark masses
• Constraining Form Factors with the Method of Unitarity Bounds
• The $K\pi$ form factors from Analyticity and Unitarity
• The $D\pi$ form factors from analyticity and unitarity