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arXiv 0712.3741hep-lat
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HQET和QCD晶格中的重轻介子

Heavy-light mesons in lattice HQET and QCD

Damiano Guazzini

摘要:

我们提出了一个HQET和相对论QCD相结合的研究提取的b-夸克质量和BS介子衰变常数的晶格淬火模拟。我们从一个小体积开始,在那里人们可以直接模拟的b夸克,并计算连接到一个大体积,其中有限尺寸的影响是可以忽略不计的,通过有限尺寸的技术。后者由外推到连续极限的步骤组成,其中通过有效理论指导的插值达到b区域。用Sommer标度r 0给出晶格间距和实验Bs和K质量,我们得到最终结果:重整化群不变质量Mb = 6.88(10)GeV,在MSbar方案中转换为mb(mb)= 4.42(6)GeV,衰变常数fBs = 191(6)MeV.在重夸克质量展开的HQET中,色磁算符是介子重-轻束缚态中赝标和矢量通道质量分裂的主要原因,本文给出了色磁算符的重整化条件,该条件用格点关联函数表示,适合于大范围的重整化标度和无价夸克的非微扰计算.在薛定谔泛函(SF)计划中相应的反常尺寸的两个回路的表达式计算从文献中的结果开始,它需要一个非零背景场的SF计划中的单回路计算。截断效应影响的尺度演化的重整化因子的研究在一个循环的顺序,并确认由非微扰淬火计算是可以忽略不计的数值精度达到目前。

英文摘要:

We present a study of a combination of HQET and relativistic QCD to extract the b-quark mass and the Bs-meson decay constant from lattice quenched simulations. We start from a small volume, where one can directly simulate the b-quark, and compute the connection to a large volume, where finite size effects are negligible, through a finite size technique. The latter consists of steps extrapolated to the continuum limit, where the b-region is reached through interpolations guided by the effective theory. With the lattice spacing given in terms of the Sommer's scale r0 and the experimental Bs and K masses, we get the final results for the renormalization group invariant mass Mb = 6.88(10) GeV, translating into mb(mb) = 4.42(6) GeV in the MSbar scheme, and fBs = 191(6) MeV for the decay constant. A renormalization condition for the chromo-magnetic operator, responsible, at leading order in the heavy quark mass expansion of HQET, for the mass splitting between the pseudoscalar and the vector channel in mesonic heavy-light bound states, is provided in terms of lattice correlations functions which well suits a non-perturbative computation involving a large range of renormalization scales and no valence quarks. The two-loop expression of the corresponding anomalous dimension in the Schroedinger functional (SF) scheme is computed starting from results in the literature; it requires a one-loop calculation in the SF scheme with a non-vanishing background field. The cutoff effects affecting the scale evolution of the renormalization factors are studied at one-loop order, and confirmed by non-perturbative quenched computations to be negligible for the numerical precision achievable at present.

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