Determination of m¯b/m¯c and

Abstract

We extend HPQCD's earlier n f = 4 lattice-QCD analysis of the ratio of MS masses of the b and c quark to include results from finer lattices (down to 0.03 fm) and a new calculation of QED contributions to the mass ratio. We find that m b (µ)/mc(µ) = 4.586( 12) at renormalization scale µ = 3 GeV. This result is nonperturbative. Combining it with HPQCD's recent lattice QCD+QED determination of mc(3 GeV) gives a new value for the b-quark mass: m b (3 GeV) = 4.513(26) GeV. The b-mass corresponds to m b (m b , n f = 5) = 4.202(21) GeV. These results are the first based on simulations that include QED.

$m_c$ (and $m_b$) from lattice QCD

“…At this level of precision one may expect QED effects to become relevant. These were quantified in [25] and [26], and found to be small ( 0.2% for charm).…”

“…framework by extending [20] in [25] and [26] for and respectively. In this approximation the QED field is simply multiplied into the SU(3) gauge field.…”

“…The results entering this average are shown in Fig. 5, plus the new result published since the FLAG review from HPQCD [26]. The HPQCD result comes from a determination of the mass ratio / , including the effects of (quenched) QED, multiplied by the determination of via RI/SMOM described in Sec.…”

Precision bottomonium properties and b quark mass from lattice QCD

“…The ratio of quark masses is scheme and scale independent in pure QCD, but not in QCD+QED if the quarks have different electric charges. We calculate the ratio of 𝑏 and 𝑐 masses at 3 GeV in the MS scheme using a 3 step procedure (for full details see [3]). The first step is to fit results for 𝑚 ℎ /𝑚 𝑐 as a function of the 𝜙 ℎ mass and lattice spacing in pure QCD.…”

“…Accurate masses for heavy quarks are important for high-precision searches for new physics in Higgs decay [2]. We give here a new determination of the ratio of the masses for 𝑏 and 𝑐 quarks that is completely nonperturbative in lattice QCD and includes the calculation of QED effects for the first time [3]. This allows an accurate determination of the 𝑏 quark mass using our earlier accurate results for 𝑚 𝑐 in QCD+QED [4].…”