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Dressing phase in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>Bethe ansatz
In this paper we study the function $\ensuremath{\chi}({x}_{1},{x}_{2},g)$ that determines the dressing phase that appears in the all-loop Bethe ansatz equations for the $SL(2)$ sector of $\mathcal{N}=4$ super Yang-Mills theory. First, we consider the coefficients ${c}_{r,s}(g)$ of the expansion of $\ensuremath{\chi}({x}_{1},{x}_{2},g)$ in inverse powers of ${x}_{1,2}$. We obtain an expression …