Abstract
We present a dispersive analysis of the double-virtual photon-photon scattering to two pions up to 1.5 GeV. Through unitarity, this process is very sensitive to hadronic final-state interaction. For the $s$-wave, we use a coupled-channel $\ensuremath{\pi}\ensuremath{\pi}$, $K\overline{K}$ analysis which allows for a simultaneous description of both ${f}_{0}(500)$ and ${f}_{0}(980)$ resonances. For higher energies, ${f}_{2}(1270)$ shows up as a dominant structure which we approximate by a single-channel $\ensuremath{\pi}\ensuremath{\pi}$ rescattering in the $d$-wave. In the dispersive approach, the latter requires taking into account $t$- and $u$-channel vector-meson exchange left-hand cuts which exhibit an anomalouslike behavior for large spacelike virtualities. We show how to readily incorporate such behavior using a contour deformation. Besides, we devote special attention to kinematic constraints of helicity amplitudes and show their correlations explicitly.
Highlights
It is still an open question whether a current ultraprecise ðg − 2Þμ measurement can probe the physics beyond the Standard Model
We emphasize that for the dispersion relation (DR) written in the form of Eq (15) only Disc hðλJ1λÞ;2VðsÞ is required as input, which is unique for the vector pole contribution
One transverse and one longitudinal (TL) photon polarization defined by dσTT d cos θ βππ 64πλ1=2ðs; −Q21;
Summary
It is still an open question whether a current ultraprecise ðg − 2Þμ measurement can probe the physics beyond the Standard Model. The remaining hadronic uncertainty results from HLBL, where, apart from the pseudoscalar pole contribution, a further nontrivial contribution comes from the two-particle intermediate states such as ππ, πη, and KK. Given the fact that it is relatively narrow, its contribution to ðg − 2Þμ can be accounted for in two ways: by using a pole contribution as it is given in [8] (updated in [9] using recent data from the Belle Collaboration [10]) or through fully dispersive formalisms [11] and with input from γÃγà → ππ [12]. The critical step in finding these constraints is the decomposition of the amplitude into Lorentz structures and invariant amplitudes [15]. The latter are expected to satisfy the Mandelstam dispersion-integral representation [16]. We will show an alternative way of taking this contribution into account using an appropriate contour deformation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
