%0 Journal Article %1 Broadhurst1994Matching %A Broadhurst, D. J. %A Grozin, A. G. %D 1994 %J Physical Review D %K vector %N 7 %P 4082--4098 %R 10.1103/physrevd.52.4082 %T Matching QCD and HQET heavy&\#45;&\#45;light currents at two loops and beyond %U http://dx.doi.org/10.1103/physrevd.52.4082 %V 52 %X Heavy--light QCD currents are matched with HQET currents at two loops and leading order in \$1/m\$. A single formula applies to all current matchings. As a by--product, a master formula for the two--loop anomalous dimension of the QCD current \$q\gamma^\mu\_1łdots\gamma^\mu\_nq\$ is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on \$\gamma\_5\$ prescriptions is elucidated. Ratios of QCD matrix elements are obtained, independently of the three--loop anomalous dimension of HQET currents. The two--loop coefficient in \$f\_B^*/f\_B =1-2\alpha\_\rm s(m\_b)/3\pi-K\_b\alpha\_s^2/\pi^2 +O(\alpha\_s^3,1/m\_b)\$ is \K\_b=8312+481\pi^2+227\pi^2łog2-\frac19\zeta(3) -1954N\_l+\Delta\_c=6.37+\Delta\_c\ with \$N\_l=4\$ light flavours, and a correction, \$\Delta\_c=0.18\pm0.01\$, that takes account of the non--zero ratio \$m\_c/m\_b=0.28\pm0.03\$. Fastest apparent convergence would entail \$\alpha\_\rm s(\mu)\$ at \$\mu=370\$\~MeV. ``Naive non--abelianization'' of large--\$N\_l\$ results, via \$N\_lN\_l-332\$, gives reasonable approximations to exact two--loop results. All--order results for anomalous dimensions and matching coefficients are obtained at large \$\beta\_0=11-\frac23N\_l\$. Consistent cancellation between infrared-- and ultraviolet--renormalon ambiguities is demonstrated.

@article{Broadhurst1994Matching, abstract = {Heavy--light QCD currents are matched with HQET currents at two loops and leading order in \$1/m\$. A single formula applies to all current matchings. As a by--product, a master formula for the two--loop anomalous dimension of the QCD current \$\bar{q}\gamma^{[\mu\_1}\ldots\gamma^{\mu\_n]}q\$ is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on \$\gamma\_5\$ prescriptions is elucidated. Ratios of QCD matrix elements are obtained, independently of the three--loop anomalous dimension of HQET currents. The two--loop coefficient in \$f\_{{\rm B}^*}/f\_{\rm B} =1-2\alpha\_{\rm s}(m\_b)/3\pi-K\_b\alpha\_{\rm s}^2/\pi^2 +{\rm O}(\alpha\_{\rm s}^3,1/m\_b)\$ is \[K\_b=\frac{83}{12}+\frac{4}{81}\pi^2+\frac{2}{27}\pi^2\log2-\frac19\zeta(3) -\frac{19}{54}N\_l+\Delta\_c=6.37+\Delta\_c\] with \$N\_l=4\$ light flavours, and a correction, \$\Delta\_c=0.18\pm0.01\$, that takes account of the non--zero ratio \$m\_c/m\_b=0.28\pm0.03\$. Fastest apparent convergence would entail \$\alpha\_{\rm s}(\mu)\$ at \$\mu=370\$\~{}MeV. ``Naive non--abelianization'' of large--\$N\_l\$ results, via \$N\_l\to N\_l-\frac{33}{2}\$, gives reasonable approximations to exact two--loop results. All--order results for anomalous dimensions and matching coefficients are obtained at large \$\beta\_0=11-\frac23N\_l\$. Consistent cancellation between infrared-- and ultraviolet--renormalon ambiguities is demonstrated.}, added-at = {2019-02-23T22:09:48.000+0100}, archiveprefix = {arXiv}, author = {Broadhurst, D. J. and Grozin, A. G.}, biburl = {https://www.bibsonomy.org/bibtex/25cfd642556cc7fb5e268149a8fe4c908/cmcneile}, citeulike-article-id = {7229521}, citeulike-linkout-0 = {http://arxiv.org/abs/hep-ph/9410240}, citeulike-linkout-1 = {http://arxiv.org/pdf/hep-ph/9410240}, citeulike-linkout-2 = {http://dx.doi.org/10.1103/physrevd.52.4082}, day = 7, doi = {10.1103/physrevd.52.4082}, eprint = {hep-ph/9410240}, interhash = {717543664c61684bc0a18c35502ce0aa}, intrahash = {5cfd642556cc7fb5e268149a8fe4c908}, issn = {0556-2821}, journal = {Physical Review D}, keywords = {vector}, month = oct, number = 7, pages = {4082--4098}, posted-at = {2013-05-10 16:38:25}, priority = {2}, timestamp = {2019-02-23T22:15:27.000+0100}, title = {{Matching QCD and HQET heavy\&\#45;\&\#45;light currents at two loops and beyond}}, url = {http://dx.doi.org/10.1103/physrevd.52.4082}, volume = 52, year = 1994 }