New constraints on the pion EM form factor using $ \Pi^{{ \prime}}_{}$ (- Q2)

Abstract

We study the constraints arising on the expansion parameters c and d of the Pion electromagnetic form factor from the inclusion of pure space-like data and the phase of time-like data along with one space-like datum, using as input the first derivative of the QCD polarization amplitude Π ′ (−Q 2 ). These constraints when combined with other analyses, provide a valuable check on a determination of c due to Guo et al. and on our previous work where pionic contribution to the (g − 2) of the muon was used as the input. This work further illustrates the power of analyticity techniques in form factor analysis.

A new parameterization for the pion vector form factor

“…For the curvature we find c V = 3.9 GeV −4 , in line with Refs. [14,37]. The effect of the higher resonances is quantitatively in line with expectations from dimensional analysis that predicts an effect on the mean square radius of order of the square of the inverse resonance mass ∼ 0.02 fm 2 .…”

Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region

“…Of special interest is the issue of the zeros of the form factor, investigated by means of dispersive sum-rules [18,[43][44][45]52] or by the more powerful techniques of analytic optimization theory [42,47,48]. In [61][62][63]66] similar functional-analytic techniques were applied for deriving bounds on the expansion coefficients at t = 0, from an weighted integral of the modulus squared along the cut, known from unitarity and dispersion relations for a related QCD correlator.…”

Implications of unitarity and analyticity for the Dπ form factors

“…The condition (21) is expressed in a straightforward way in terms of the values f k (t p ) of the form factors at t p = t(z p , t 0 ) and the derivatives at t = 0, using eqns. (14) and (16). The generalization to complex points z p can be found in [20,25].…”

“…Employing standard mathematical techniques, one can then correlate the values of the form factor and its derivatives at different points inside the analyticity domain. Various versions of the method were applied to the pion electromagnetic form factor [13,14,15,16,17], the Kπ form factors [18,19,20,21,22,23,24,25,26], as well as to the heavy-heavy [27,28,29,30,31,32] and heavy-light form factors [33,34,35]. A review of the method was presented recently in [25].…”