C$_{20}$ ( t ) form factors. Similarly to the pion case we have tried to deduce some information from the high-energy region, t ∼ − 1 . 2 GeV $^{2}$, by attempting the Regge form Unfortunately, again the large errors in the data do not allow to fix the b parameter unambiguously, and it is compatible with b = 2. Thus we stick to the simple monopole form, Since most of the lattice data are accumulated at pion masses significantly above the physical value, extrapola- tion to the physical point is necessary. At low values of the pion mass and t the chiral corrections are expected to be significant. 4 Not entering these intricacies, we assume, following many lattice studies, the simple dependence of m$_{σ}$ on m$_{π}$ : Hence m$_{σ}$ (without an argument) denotes the value at the physical point. Similarly, 〈 x 〉 N u + $_{d}$( m$_{π}$ ) = 〈 x 〉 N u + d + d ( m 2 π − m 2 π, phys ) . (82) m 2 $_{σ}$( m$_{π}$ ) = m 2 σ + c ( m 2 π − m 2 π, phys ) . (81) We use simultaneously the form factors (77) for the six pion masses from LHPC [73]. There are several ways one can perform the fit, all leading to similar but not identical results. Our procedure is as follows: We first normalize the form factors to unity at t = 0, by dividing a data set at a particular m$_{π}$ by the value of the point at t = 0. That way we get rid of the dependence on 〈 x 〉 N u + d and can carry out a two-parameter fit, with the parameters of Eq. (81). The χ 2 method yields with χ $^{2}$/ DOF = 5 . 2 / (87 − 2). The resulting correlation plot is shown in Fig. 6 One may perform separately the fit to the normalized form factors at each value of m$_{π}$ . An example for the two lowest pion masses, 356 and 352 MeV, is shown in Fig. 5. The band indicates the uncertainty in m$_{σ}$ obtained with the χ 2 method. The result of the procedure at all values of m$_{π}$ is shown in Fig. 7, together with the best fit curve with parameters (83). The point at the physical value of 11 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 1.0 m Π GLYPH<LBracket1> GeV GLYPH<RBracket1> m Σ GLYPH<LBracket1> GeV GLYPH<RBracket1> FIG. 7: (Color online) Dependence of the σ mass on m$_{π}$ in- ferred from the LHPC data [73]. The line shows the best fit of Eq. (83). The point at physical m$_{π}$ indicates the result of the extrapolation. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 m Π GLYPH<LBracket1> GeV GLYPH<RBracket1> m Σ GLYPH<LBracket1> GeV GLYPH<RBracket1> FIG. 8: (Color online) Dependence of the σ mass on m$_{π}$ in- ferred from the QCDSF data [72]. The line indicates the best fit of Eq. (85). m$_{π}$ indicates the resulting extrapolation for the physical value of m$_{σ}$ , Eq. (83). Taking the values of the unnormalized form factors at t = 0 we may compute the momentum fraction carried by the quarks as a function of m$_{π}$ . The result of the χ 2 fit is In the case of the lattice calculations of the QCDSF Collaboration [72], five points have been provided at val- ues ranging between 0 ≤ − t ≤ 3 GeV 2 for the pion masses m$_{π}$ = 930, 760, and 550 MeV, then extrapolated to the physical pion mass. The corresponding nucleon masses are M$_{N}$ = 1724, 1519, and 1308 MeV. The A , B , and C form factors have been parametrized in Ref. [72] 〈 x 〉 N u + d = 0 . 447(14) , d = − 0 . 13(3) . (84) m$_{σ}$ = 550 +180 − $_{200}$MeV , c = 0 . 95 +0 . 80 − 0 $_{75}$, (83) Θ q $_{N}$( t ) = M$_{N}$ 〈 x 〉 N u + d m 2 σ m 2 σ − t . (80) Θ$_{N}$( t ) = M$_{N}$ B ( b − 1 , M $^{2}$− t a/ 2 ) B ( b − 1 , M 2 a/ $_{2}$) . (79) 4 Experience with the vector form factor shows that the low mo- mentum region is quite sensitive to chiral corrections, whereas the intermediate energy region is better described by the large- N$_{c}$ dynamics.