Duhr Claude, Mistlberger Bernhard, Vita Gherardo
Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn, Germany.
SLAC National Accelerator Laboratory, Stanford University, Menlo Park, California 94025, USA.
Phys Rev Lett. 2022 Oct 14;129(16):162001. doi: 10.1103/PhysRevLett.129.162001.
We obtain the quark and gluon rapidity anomalous dimension to fourth order in QCD. We calculate the N^{3}LO rapidity anomalous dimensions to higher order in the dimensional regulator and make use of the soft and rapidity anomalous dimension correspondence in conjunction with the recent determination of the N^{4}LO threshold anomalous dimensions to achieve our result. We show that the results for the quark and gluon rapidity anomalous dimensions at four loops are related by generalized Casimir scaling. Using the N^{4}LO rapidity anomalous dimension, we perform the resummation of the energy-energy correlation in the back-to-back limit at N^{4}LL, achieving for the first time the resummation of an event shape at this logarithmic order. We present numerical results and observe a reduction of perturbative uncertainties on the resummed cross section to below 1%.
我们在量子色动力学（QCD）中得到了夸克和胶子快度反常维度至四阶的结果。我们在维数正规化中计算了至更高阶的(N^{3}LO)快度反常维度，并结合近期对(N^{4}LO)阈反常维度的确定，利用软和快度反常维度对应关系来得到我们的结果。我们表明，四圈时夸克和胶子快度反常维度的结果通过广义卡西米尔标度相关联。利用(N^{4}LO)快度反常维度，我们在(N^{4}LL)的背对背极限下对能量-能量关联进行了重整化，首次在这个对数阶实现了对一个事件形状的重整化。我们给出了数值结果，并观察到重整化截面的微扰不确定性降低到了1%以下。
