Effective field theory approach to heavy quark fragmentation

TL;DR

This paper employs effective field theories, SCET and HQET, to precisely determine the $b$-quark fragmentation function from electron-positron data, achieving higher order accuracy and reduced theoretical errors.

Contribution

It advances the extraction of the $b$-quark fragmentation function by incorporating NNLO and resummation techniques within an effective field theory framework.

Findings

Higher order calculations reduce theoretical uncertainties.

The effective field theory approach systematically controls errors.

Data fits suggest potential need for higher order HQET corrections.

Abstract

Using an approach based on Soft Collinear Effective Theory (SCET) and Heavy Quark Effective Theory (HQET) we determine the $b$-quark fragmentation function from electron-positron annihilation data at the $Z$-boson peak at next-to-next-to leading order, with next-to-next-to leading log resummation of DGLAP logarithms, and next-to-next-to-next-to leading log resummation of endpoint logarithms. This analysis improves, by one order, the previous extraction of the $b$-quark fragmentation function. We find that while the addition of the next order in the calculation does not much shift the extracted form of the fragmentation function, it does reduce theoretical errors indicating that the expansion is converging. Using an approach based on effective field theory allows us to systematically control theoretical errors. While the fits of theory to data are generally good, the fits seem to be hinting that higher order correction from HQET may be needed to explain the $b$-quark fragmentation function at smaller values of momentum fraction.