Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks

We present a computation of B-meson decay constants from lattice QCD simulations within the framework of Heavy Quark Effective Theory for the b-quark. The next-to-leading order corrections in the HQET expansion are included non-perturbatively. Based on <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><mo>=</mo><mn>2</mn></math> gauge field ensembles, covering three lattice spacings <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≈</mo><mo stretchy="false">(</mo><mn>0.08</mn><mtext>–</mtext><mn>0.05</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>fm</mtext></math> and pion masses down to <math altimg="si3.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mn>190</mn><mtext> </mtext><mtext>MeV</mtext></math> , a variational method for extracting hadronic matrix elements is used to keep systematic errors under control. In addition we perform a careful autocorrelation analysis in the extrapolation to the continuum and to the physical pion mass limits. Our final results read <math altimg="si4.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub><mo>=</mo><mn>186</mn><mo stretchy="false">(</mo><mn>13</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>MeV</mtext></math> , <math altimg="si5.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>f</mi></mrow><mrow><msub><mrow><mi mathvariant="normal">B</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></msub><mo>=</mo><mn>224</mn><mo stretchy="false">(</mo><mn>14</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>MeV</mtext></math> and <math altimg="si6.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>f</mi></mrow><mrow><msub><mrow><mi mathvariant="normal">B</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></msub><mo stretchy="false">/</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub><mo>=</mo><mn>1.203</mn><mo stretchy="false">(</mo><mn>65</mn><mo stretchy="false">)</mo></math> . A comparison with other results in the literature does not reveal a dependence on the number of dynamical quarks, and effects from truncating HQET appear to be negligible