TY - JOUR

T1 - Matter dependence of the four-loop QCD cusp anomalous dimension

T2 - from small angles to all angles

AU - Brüser, Robin

AU - Grozin, Andrey

AU - Henn, Johannes M.

AU - Stahlhofen, Maximilian

PY - 2019/5/1

Y1 - 2019/5/1

N2 - We compute the fermionic contributions to the cusp anomalous dimension in QCD at four loops as an expansion for small cusp angle. As a byproduct we also obtain the respective terms of the four-loop HQET wave function anomalous dimension. Our new results at small angles provide stringent tests of a recent conjecture for the exact angle dependence of the matter terms in the four-loop cusp anomalous dimension. We find that the conjecture does not hold for two of the seven fermionic color structures, but passes all tests for the remaining terms. This provides strong support for the validity of the corresponding conjectured expressions with full angle dependence. Taking the limit of large Minkowskian angle, we extract novel analytic results for certain terms of the light-like cusp anomalous dimension. They agree with the known numerical results. Finally, we study the anti-parallel lines limit of the cusp anomalous dimension. In a conformal theory, the latter is proportional to the static quark-antiquark potential. We use the new four-loop results to determine parts of the conformal anomaly term.

AB - We compute the fermionic contributions to the cusp anomalous dimension in QCD at four loops as an expansion for small cusp angle. As a byproduct we also obtain the respective terms of the four-loop HQET wave function anomalous dimension. Our new results at small angles provide stringent tests of a recent conjecture for the exact angle dependence of the matter terms in the four-loop cusp anomalous dimension. We find that the conjecture does not hold for two of the seven fermionic color structures, but passes all tests for the remaining terms. This provides strong support for the validity of the corresponding conjectured expressions with full angle dependence. Taking the limit of large Minkowskian angle, we extract novel analytic results for certain terms of the light-like cusp anomalous dimension. They agree with the known numerical results. Finally, we study the anti-parallel lines limit of the cusp anomalous dimension. In a conformal theory, the latter is proportional to the static quark-antiquark potential. We use the new four-loop results to determine parts of the conformal anomaly term.

KW - Effective Field Theories

KW - Perturbative QCD

KW - Scattering Amplitudes

KW - Wilson, ’t Hooft and Polyakov loops

KW - WILSON LOOPS

KW - ANNIHILATION

KW - Wilson

KW - 3-LOOP SPLITTING FUNCTIONS

KW - IMPLEMENTATION

KW - QUARK EFFECTIVE THEORY

KW - INFRARED ASYMPTOTIC-BEHAVIOR

KW - 't Hooft and Polyakov loops

KW - RENORMALIZATION

UR - http://www.scopus.com/inward/record.url?scp=85066501007&partnerID=8YFLogxK

U2 - 10.1007/JHEP05(2019)186

DO - 10.1007/JHEP05(2019)186

M3 - Article

AN - SCOPUS:85066501007

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1029-8479

IS - 5

M1 - 186

ER -