Determination of off-shell ambiguities in correlation functions: Strategies to minimize them

We face here the problem of uncertainties in correlation functions due to the freedom in the off-shell dependence of the wave functions or, equivalently, off-shell ambiguities in the scattering matrices. We make the study for the case of meson baryon interaction, choosing the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>K</a:mi> <a:mi mathvariant="normal">Λ</a:mi> </a:math> , <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>K</d:mi> <d:mi mathvariant="normal">Σ</d:mi> </d:math> , and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>η</g:mi> <g:mi>N</g:mi> </g:math> coupled channels, which are related to the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mi>N</i:mi> <i:mo>*</i:mo> </i:msup> <i:mo stretchy="false">(</i:mo> <i:mn>1535</i:mn> <i:mo stretchy="false">)</i:mo> </i:math> resonance, and the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msup> <m:mi>K</m:mi> <m:mo>+</m:mo> </m:msup> <m:msup> <m:mover accent="true"> <m:mi>K</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> <m:mn>0</m:mn> </m:msup> </m:math> channel related to the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>a</q:mi> <q:mn>0</q:mn> </q:msub> <q:mo stretchy="false">(</q:mo> <q:mn>980</q:mn> <q:mo stretchy="false">)</q:mo> </q:math> resonance. We find that, by using realistic interactions based on chiral dynamics, the uncertainties are small, of the order of 2–3%, but could be much bigger if other methods are used. However, our study shows the way to optimally overcome these uncertainties in the analysis of correlation functions, and we provide a series of recommendations for any general analysis.