Endpoint Logarithms in the NLO Mueller-Navelet Jet Vertex: Threshold Matching and BLM/MOM Prescription Sensitivity

Abstract

The endpoint region $\zeta\to1$ of the NLO forward jet vertex has not been systematically separated from BFKL energy-scale terms in Mueller-Navelet phenomenology. Starting from the small-cone NLO vertex, we isolate the quark and gluon plus distributions and construct a BFKL-aware threshold matching scheme that preserves exact NLO accuracy. The conservative Scheme-II exponent resums only the ordinary endpoint logarithms and leaves the $\chi(n,\gamma)\ln\bar N$ term in the fixed-order coefficient, avoiding an uncontrolled tower of mixed endpoint-BFKL logarithms. In fixed-baseline CMS tests, this matched vertex is a controlled deformation of an optimized-NLL pointwise BLM/MOM calculation: it moves $R_{21}=C_2/C_1$ in the high-$\Delta Y$ direction favored by CMS, but it does not improve $C_1/C_0$ or $R_{32}=C_3/C_2$ in the same prescription. A coefficient-projected table-BLM diagnostic improves the absolute moments but lowers $R_{21}$ and is sensitive to the large-$|\nu|$ tail. Thus the endpoint matching is internally consistent and phenomenologically informative, while the present setup does not provide a simultaneous description of all five CMS azimuthal observables.