15.3 Luescher analysis
The phase shift can be computed from the formula
cotδ=Z00(1,q2)π3/2γq where γ=E/ECM, q=kL/2π with k the scattering momentum k2=E2CM4−m2=E2−→P24−m2. The Energy in the center of mass is related to the one in a generic frame with total momentum →P via E2CM=E2imp−→P2. Eimp is the energy measured in the lattice E=Emeasured−Efree−latt+Efree−cont Efree−latt=cosh−1(cosh(m)+12(3∑i=14sin(p1i2)2))+cosh−1(cosh(m)+12(3∑i=14sin(p2i2)2)).
For the Z function we use the rzeta package. The fit function for the phase shift is
kmcotδ=1a0m+r0m2k2m2
P[0]=am , P[1]=r0m
χ2/d.o.f.=4.58739P[0]=−0.151619±(0.0011)P[1]=−3.02208±(0.1) {C=(1.12e−060.5590.5590.0102)}