Determination of the strong coupling constant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:mrow>

We demonstrate the feasibility of determining the strong coupling constant, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>α</a:mi> <a:mi>s</a:mi> </a:msub> </a:math> , from the inclusive semileptonic decay width of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>B</c:mi> </c:math> mesons. We express the semileptonic <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>B</e:mi> </e:math> decay width as a function of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>α</g:mi> <g:mi>s</g:mi> </g:msub> <g:mo stretchy="false">(</g:mo> <g:mn>5</g:mn> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>GeV</g:mi> <g:mo stretchy="false">)</g:mo> </g:math> , the Cabibbo-Kobayashi-Maskawa matrix element <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mo stretchy="false">|</k:mo> <k:msub> <k:mi>V</k:mi> <k:mrow> <k:mi>c</k:mi> <k:mi>b</k:mi> </k:mrow> </k:msub> <k:mo stretchy="false">|</k:mo> </k:math> , and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>b</o:mi> </o:math> - and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>c</q:mi> </q:math> -quark masses in the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mover accent="true"> <s:mi>MS</s:mi> <s:mo stretchy="true">¯</s:mo> </s:mover> </s:math> scheme. We fit <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>α</w:mi> <w:mi>s</w:mi> </w:msub> <w:mo stretchy="false">(</w:mo> <w:mn>5</w:mn> <w:mtext> </w:mtext> <w:mtext> </w:mtext> <w:mi>GeV</w:mi> <w:mo stretchy="false">)</w:mo> </w:math> to current world averages of the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msup> <ab:mi>B</ab:mi> <ab:mo>±</ab:mo> </ab:msup> </ab:math> and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msup> <cb:mi>B</cb:mi> <cb:mn>0</cb:mn> </cb:msup> </cb:math> semileptonic decay widths. This yields <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mi>α</eb:mi> <eb:mi>s</eb:mi> </eb:msub> <eb:mo stretchy="false">(</eb:mo> <eb:mn>5</eb:mn> <eb:mtext> </eb:mtext> <eb:mtext> </eb:mtext> <eb:mi>GeV</eb:mi> <eb:mo stretchy="false">)</eb:mo> <eb:mo>=</eb:mo> <eb:mn>0.245</eb:mn> <eb:mo>±</eb:mo> <eb:mn>0.009</eb:mn> </eb:math> , corresponding to a five-flavor extrapolation of <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:msub> <ib:mi>α</ib:mi> <ib:mi>s</ib:mi> </ib:msub> <ib:mo stretchy="false">(</ib:mo> <ib:msub> <ib:mi>m</ib:mi> <ib:mi>Z</ib:mi> </ib:msub> <ib:mo stretchy="false">)</ib:mo> <ib:mo>=</ib:mo> <ib:mn>0.1266</ib:mn> <ib:mo>±</ib:mo> <ib:mspace linebreak="goodbreak"/> <ib:mn>0.0023</ib:mn> </ib:math> . The primary uncertainty contributions arise from the uncertainty on the perturbative expansion and the value of <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"> <nb:mo stretchy="false">|</nb:mo> <nb:msub> <nb:mi>V</nb:mi> <nb:mrow> <nb:mi>c</nb:mi> <nb:mi>b</nb:mi> </nb:mrow> </nb:msub> <nb:mo stretchy="false">|</nb:mo> </nb:math> . Future advancements, including higher-order perturbative calculations and precise measurements of <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"> <rb:mo stretchy="false">|</rb:mo> <rb:msub> <rb:mi>V</rb:mi> <rb:mrow> <rb:mi>c</rb:mi> <rb:mi>b</rb:mi> </rb:mrow> </rb:msub> <rb:mo stretchy="false">|</rb:mo> </rb:math> and <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:mi>B</vb:mi> </vb:math> decay widths from upcoming <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"> <xb:mi>B</xb:mi> </xb:math> and <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"> <zb:mi>Z</zb:mi> </zb:math> factories, could enable this method to determine <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"> <bc:msub> <bc:mi>α</bc:mi> <bc:mi>s</bc:mi> </bc:msub> <bc:mo stretchy="false">(</bc:mo> <bc:msub> <bc:mi>m</bc:mi> <bc:mi>Z</bc:mi> </bc:msub> <bc:mo stretchy="false">)</bc:mo> </bc:math> with a competitive precision of <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"> <fc:mi mathvariant="normal">Δ</fc:mi> <fc:msub> <fc:mi>α</fc:mi> <fc:mi>s</fc:mi> </fc:msub> <fc:mo stretchy="false">(</fc:mo> <fc:msub> <fc:mi>m</fc:mi> <fc:mi>Z</fc:mi> </fc:msub> <fc:mo stretchy="false">)</fc:mo> <fc:mo>∼</fc:mo> <fc:mn>0.0018</fc:mn> </fc:math> . This precision is comparable to the current accuracy of <kc:math xmlns:kc="http://www.w3.org/1998/Math/MathML" display="inline"> <kc:msub> <kc:mi>α</kc:mi> <kc:mi>s</kc:mi> </kc:msub> <kc:mo stretchy="false">(</kc:mo> <kc:msub> <kc:mi>m</kc:mi> <kc:mi>Z</kc:mi> </kc:msub> <kc:mo stretchy="false">)</kc:mo> </kc:math> measurements from <oc:math xmlns:oc="http://www.w3.org/1998/Math/MathML" display="inline"> <oc:mi>τ</oc:mi> </oc:math> -lepton decays, which is regarded as the most precise experimental approach.