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Physics Letters B
Article . 2005
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https://dx.doi.org/10.48550/ar...
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The scalar radius of the pion

Authors: Felix Yndurain;

The scalar radius of the pion

Abstract

The pion scalar radius is given by $=(6/��)\int_{4M^2_��}^\infty{\rm d}s ��_S(s)/s^2$, with $��_S$ the phase of the scalar form factor. Below $\bar{K}K$ threshold, $��_S=��_��$, $��_��$ being the isoscalar, S-wave $����$ phase shift. At high energy, $s>2 {\rm GeV}^2$, $��_S$ is given by perturbative QCD. In between I argued, in a previous letter, that one can interpolate $��_S\sim��_��$, 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 $��_S\simeq��_��-��$; then $=0.61\pm0.04 {\rm fm}^2$. Here I show that the ACCGL phase $��_S$ 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 $��_��(4m^2_K)$ different from what experiment indicates. If one uses the value for $��_��(4m^2_K)$ favoured by experiment, the ensuing phase $��_S$ is continuous, agrees with perturbative QCD expectations, and satisfies $��_S\simeq��_��$, thus confirming the correctness of my previous estimate, $=0.75\pm0.07 {\rm fm}^2$.

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

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Keywords

Nuclear and High Energy Physics, High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), FOS: Physical sciences

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
26
Average
Top 10%
Top 10%
Green
gold