On the analysis of the pion--nucleon $σ$--term: The size of the remainder at the Cheng--Dashen point

Details On the analysis of the pion--nucleon $σ$--term: The size of the remainder at the Cheng--Dashen point On the analysis of the pion--nucleon $σ$--term: The size of the remainder at the Cheng--Dashen point

1996-07-05

arxiv.org/abs/hep-ph/9607245v1

Phys.Lett. B389 (1996) 144-148

Physics

High Energy Physics

High Energy Physics - Phenomenology

7 pp, LaTeX, uses epsf, 1 figure in separate PS file

Scientific paper

10.1016/S0370-2693(96)01243-9

We calculate the one--loop contributions of order $M_\pi^4$ to the difference $\Delta_R$ between the on--shell pion--nucleon scattering amplitude $\bar{D}^+(0,2M_\pi^2)$ at the Cheng--Dashen point $\nu =0$, $t=2M_\pi^2$ and the scalar form factor $\sigma (2M_\pi^2)$ in the framework of heavy baryon chiral perturbation theory. We proof that to this order $\Delta_R$ contains $no$ chiral logarithms and therefore it vanishes simply as $M_\pi^4$ in the chiral limit. Numerically, we find as an upper limit $\Delta_R \simeq 2\,$MeV.

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