Abstract
We calculate all contributions ∝TF to the polarized three–loop anomalous dimensions in the M–scheme using massive operator matrix elements and compare to results in the literature. This includes the complete anomalous dimensions γqq(2),PS and γqg(2). We also obtain the complete two–loop polarized anomalous dimensions in an independent calculation. While for most of the anomalous dimensions the usual direct computation methods in Mellin N–space can be applied since all recurrences factorize at first order, this is not the case for γqg(2). Due to the necessity of deeper expansions of the master integrals in the dimensional parameter ε=D−4, we had to use the method of arbitrary high moments to eliminate elliptic contributions in intermediate steps. 4000 moments were generated to determine this anomalous dimension and 2640 moments turned out to be sufficient. As an aside, we also recalculate the contributions ∝TF to the three–loop QCD β–function.
Highlights
The polarized three–loop anomalous dimensions γi(j2)(N ) and splitting functions Pi(j2)(z) govern the scale-evolution of the polarized parton distribution functions in Quantum Chromodynamics (QCD) at next-to-next-to-leading order (NNLO) and are of importance for precision predictions at ep- and hadron colliders, for the analysis of the different fixed target experiments, for the planned electron-ion collider EIC [1] and for RHIC
In the unpolarized case the three–loop splitting functions were calculated in Refs. [9,12] and all contributions ∝ TF were confirmed in independent massive calculations in Refs. [10,13,14,15,16]
We note that the use of the projectors (9, 11) for the massive operator matrix elements (OMEs) allow to extract the contributions to the anomalous dimensions in the Larin–scheme6 from all pole terms of O(ε−k), k = 3, 2, 1
Summary
The polarized three–loop anomalous dimensions γi(j2)(N ) and splitting functions Pi(j2)(z) govern the scale-evolution of the polarized parton distribution functions in Quantum Chromodynamics (QCD) at next-to-next-to-leading order (NNLO) and are of importance for precision predictions at ep- and hadron colliders, for the analysis of the different fixed target experiments, for the planned electron-ion collider EIC [1] and for RHIC. A first computation of the polarized three–loop splitting functions in the M–scheme was performed in Ref. In the present paper we compute the polarized three–loop splitting functions Pq(q2),PS and Pq(g2) and the parts ∝ TF of the three–loop splitting functions Pg(q2) and Pg(g2) from massive three–loop operator matrix elements (OMEs). They are necessary for the computation of the heavy flavor contributions to deep–inelastic scattering in the region of virtualities Q2 much larger than the heavy quark mass squared m2. Appendix B contains the splitting functions in z-space calculated in the present paper
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
