Dispersive approach to QCD and hadronic contributions to electroweak observables

Abstract

Abstract. The dispersive approach to QCD is briefly overviewed and its application to the assessment of hadronic contributions to electroweak observables is discussed.Various strong interaction processes, as well as the hadronic contributions to electroweak observables, are governed by the hadronic vacuum polarization function Π(q 2 ), related Adler function D(Q 2 ) [1], and the function R(s), which is identified with the R-ratio of electron-positron annihilation into hadrons. The hadronic vacuum polarization function constitutes the scalar part of the hadronic vacuum polarization tensorwhereas the definition of functions R(s) and D(Q 2 ) is given in Eqs. (3) and (4), respectively. The QCD asymptotic freedom makes it possible to study the high-energy behavior of the functions Π(q 2 ) and D(Q 2 ) directly within perturbation theory. At the same time, the description of the function R(s) additionally requires the use of pertinent dispersion relations, see papers [2-6] and references therein. As for the low-energy hadron dynamics, it can only be accessed within nonperturbative approaches, for instance, analytic gauge-invariant QCD [7][8][9][10] A certain nonperturbative hint about the strong interactions in the infrared domain is provided by the relevant dispersion relations. The latter are widely employed in a variety of issues of contemporary theoretical particle physics, such as, for example, the extension of applicability range of chiral perturbation theory [34,35], the precise determination of parameters of resonances [36], the assessment of the hadronic light-by-light scattering [37], and many others (see, e.g., papers [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] and references therein).Basically, the dispersion relations render the kinematic restrictions on pertinent physical processes into the mathematical form and thereby impose stringent intrinsically nonperturbative constraints on the relevant quantities. In particular, the complete set of dispersion relations (see 55,56] a

The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD

“…The estimate for a hvp µ which enters the Standard Model prediction is typically obtained from dispersion theory using the experimentally determined cross section e + e − → hadrons as input [2][3][4][5][6][7]. Recently it was proposed to extract the photon vacuum polarization in the spacelike region from Bhabha and µe scattering data [8,9], which would allow for a direct comparison with lattice results.…”

Electron–positron annihilation into hadrons at the higher-loop levels

“…For this purpose the effects due to the masses of the involved particles can be safely neglected (a discussion of the impact of such effects 1 on the low-energy behavior of the functions Π(q 2 ), R(s), and D(Q 2 ) can be found in, e.g., Refs. [31][32][33][34][45][46][47][48][49][50][51][52][53]). Additionally, for the schemedependent perturbative coefficients β j and d j the MS-scheme will be assumed and for the uncalculated yet five-loop coefficient d 5 its numerical estimation [42] will be employed.…”

Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

“…which constitutes an update of the assessment performed in Refs. [71,80,81]. As one can infer from the right plot of Fig.…”

“…3.1. First of all, it is worthwhile to note that the DPT has proved to be capable of describing the hadronic vacuum polarization contribution to the muon anomalous magnetic moment [71,80,81]. Specifically, the hadronic vacuum polarization function (22a), being applicable in the entire energy range, can be directly used in the representation (8a) for a HVP µ .…”