2021/01/31 by Jochen Heitger, Fabian Joswig, Simon Kuberski · 11 citations
Physics and Astronomy · #Bottom quark #Charm quark #Down quark #High-Energy Particle Collisions Research #Lattice QCD #Lattice field theory #Lattice gauge theory #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quark #Up quark #hep-lat
paper · pdf · doi:10.1007/jhep05(2021)288
published in Journal of High Energy Physics 2021(5) (Springer Nature) · 40 pages, 5 figures; added figure, results unchanged, matches published version
openalex created_date 2021/01/18 · openalex publication_date 2021/05/01 · arxiv created 2021/06/04 · arxiv updated 2021/06/07 · openalex updated_date 2026/08/05
A bstract We present a determination of the charm quark mass in lattice QCD with three active quark flavours. The calculation is based on PCAC masses extracted from N f = 2 + 1 flavour gauge field ensembles at five different lattice spacings in a range from 0.087 fm down to 0.039 fm. The lattice action consists of the O( a ) improved Wilson-clover action and a tree-level improved Symanzik gauge action. Quark masses are non-perturbatively O( a ) improved employing the Symanzik-counterterms available for this discretisation of QCD. To relate the bare mass at a specified low-energy scale with the renormalisation group invariant mass in the continuum limit, we use the non-pertubatively known factors that account for the running of the quark masses as well as for their renormalisation at hadronic scales. We obtain the renormalisation group invariant charm quark mass at the physical point of the three-flavour theory to be M c = 1486(21) MeV. Combining this result with five-loop perturbation theory and the corresponding decoupling relations in the MS <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>MS</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> scheme, one arrives at a result for the renormalisation group invariant charm quark mass in the four-flavour theory of M c ( N f = 4) = 1548(23) MeV, where effects associated with the absence of a charmed, sea quark in the non-perturbative evaluation of the QCD path integral are not accounted for. In the MS <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>MS</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> scheme, and at finite energy scales conventional in phenomenology, we quote mc^MS <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>m</mml:mi><mml:mi>c</mml:mi><mml:mover><mml:mi>MS</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:msubsup></mml:math> ( mc^MS <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>m</mml:mi><mml:mi>c</mml:mi><mml:mover><mml:mi>MS</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:msubsup></mml:math> ; N f = 4) = 1296(19) MeV and mc^MS <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>m</mml:mi><mml:mi>c</mml:mi><mml:mover><mml:mi>MS</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:msubsup></mml:math> (3 GeV; N f = 4) = 1007(16) MeV for the renormalised charm quark mass.