The scalar radius of the pion

Details The scalar radius of the pion The scalar radius of the pion

2005-01-13

arxiv.org/abs/hep-ph/0501104v2

Phys.Lett. B612 (2005) 245-257

Physics

High Energy Physics

High Energy Physics - Phenomenology

Version to be published in Phys. Letters. A few typos corrected. Plain YeX file. 5 figures

Scientific paper

10.1016/j.physletb.2005.03.014

The pion scalar radius is given by $=(6/\pi)\int_{4M^2_\pi}^\infty{\rm d}s \delta_S(s)/s^2$, with $\delta_S$ the phase of the scalar form factor. Below $\bar{K}K$ threshold, $\delta_S=\delta_\pi$, $\delta_\pi$ being the isoscalar, S-wave $\pi\pi$ phase shift. At high energy, $s>2 {\rm GeV}^2$, $\delta_S$ is given by perturbative QCD. In between I argued, in a previous letter, that one can interpolate $\delta_S\sim\delta_\pi$, because inelasticity is small, compared with the errors. This gives $=0.75\pm0.07 {\rm fm}^2$. Recently, Ananthanarayan, Caprini, Colangelo, Gasser and Leutwyler (ACCGL) have claimed that this is incorrect and one should have instead $\delta_S\simeq\delta_\pi-\pi$; then $=0.61\pm0.04 {\rm fm}^2$. Here I show that the ACCGL phase $\delta_S$ is pathological in that it is discontinuous for small inelasticity, does not coincide with what perturbative QCD suggests at high energy, and only occurs because these authors take a value for $\delta_\pi(4m^2_K)$ different from what experiment indicates. If one uses the value for $\delta_\pi(4m^2_K)$ favoured by experiment, the ensuing phase $\delta_S$ is continuous, agrees with perturbative QCD expectations, and satisfies $\delta_S\simeq\delta_\pi$, thus confirming the correctness of my previous estimate, $=0.75\pm0.07 {\rm fm}^2$.

Affiliated with

Also associated with

No associations

Rating

The scalar radius of the pion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The scalar radius of the pion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The scalar radius of the pion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-274223