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A<sc>bstract</sc> We study the “three particle coupling”$$ {\Gamma}_{11}^1\left(\xi \right) $$ ${\Gamma }_{11}^1\left(\xi \right)$, in 2dIsing Field Theory in a magnetic field, as the function of the scaling parameterξ:=h/(−m)^15/8, wherem∼T_c−Tandh∼Hare scaled deviation from the critical temperature and scaled external field, respectively. The “φ³coupling”$$ {\Gamma}_{11}^1 $$ ${\Gamma }_{11}^1$is defined in terms of the residue of the 2 → 2 elastic scattering amplitude at its pole associated with the lightest particle itself. We limit attention to the High-Temperature domain, so thatmis negative. We suggest “standard analyticity”:$$ {\left({\Gamma}_{11}^1\right)}^2 $$ ${\left({\Gamma }_{11}^1\right)}^2$, as the function ofu:=ξ², is analytic in the whole complexu-plane except for the branch cut from – ∞ to –u₀≈ – 0.03585, the latter branching point –u₀being associated with the Yang-Lee edge singularity. Under this assumption, the values of$$ {\Gamma}_{11}^1 $$ ${\Gamma }_{11}^1$at any complexuare expressed through the discontinuity across the branch cut. We suggest approximation for this discontinuity which accounts for singular expansion of$$ {\Gamma}_{11}^1 $$ ${\Gamma }_{11}^1$near the Yang-Lee branching point, as well as its known asymptotic atu →+∞. The resulting dispersion relation agrees well with known exact data, and with numerics obtained via Truncated Free Fermion Space Approach. This work is part of extended project of studying the S-matrix of the Ising Field Theory in a magnetic field. 

A bstract We study Ising Field Theory (the scaling limit of Ising model near the Curie critical point) in pure imaginary external magnetic field. We put particular emphasis on the detailed structure of the Yang-Lee edge singularity. While the leading singular behavior is controlled by the Yang-Lee fixed point (= minimal CFT $$ \mathcal{M} $$ M 2 / 5 ), the fine structure of the subleading singular terms is determined by the effective action which involves a tower of irrelevant operators. We use numerical data obtained through the “Truncated Free Fermion Space Approach” to estimate the couplings associated with two least irrelevant operators. One is the operator $$ T\overline{T} $$ T T ¯ , and we use the universal properties of the $$ T\overline{T} $$ T T ¯ deformation to fix the contributions of higher orders in the corresponding coupling parameter α . Another irrelevant operator we deal with is the descendant L_ 4 $$ \overline{L} $$ L ¯ _ 4 ϕ of the relevant primary ϕ in $$ \mathcal{M} $$ M 2 / 5 . The significance of this operator is that it is the lowest dimension operator which breaks integrability of the effective theory. We also establish analytic properties of the particle mass M (= inverse correlation length) as the function of complex magnetic field.