<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup><mml:mo>ℓ</mml:mo><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mo>ℓ</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math> semileptonic form factors from lattice QCD with Möbius domain-wall quarks

Abstract

We calculate the form factors for the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>B</a:mi><a:mo stretchy="false">→</a:mo><a:msup><a:mrow><a:mi>D</a:mi></a:mrow><a:mrow><a:mo>*</a:mo></a:mrow></a:msup><a:mo>ℓ</a:mo><a:msub><a:mrow><a:mi>ν</a:mi></a:mrow><a:mrow><a:mo>ℓ</a:mo></a:mrow></a:msub></a:mrow></a:math> decay in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mrow><d:mn>2</d:mn><d:mo>+</d:mo><d:mn>1</d:mn></d:mrow></d:math> flavor lattice QCD. For all quark flavors, we employ the Möbius domain-wall action, which preserves chiral symmetry to a good precision. Our gauge ensembles are generated at three lattice cutoffs <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:msup><f:mrow><f:mi>a</f:mi></f:mrow><f:mrow><f:mo>−</f:mo><f:mn>1</f:mn></f:mrow></f:msup><f:mo>∼</f:mo><f:mn>2.5</f:mn></f:mrow></f:math>, 3.6, and 4.5 GeV with pion masses as low as <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:msub><h:mrow><h:mi>M</h:mi></h:mrow><h:mrow><h:mi>π</h:mi></h:mrow></h:msub><h:mo>∼</h:mo><h:mn>230</h:mn><h:mtext> </h:mtext><h:mtext> </h:mtext><h:mi>MeV</h:mi></h:mrow></h:math>. The physical lattice size <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:mi>L</j:mi></j:mrow></j:math> satisfies the condition <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mrow><l:msub><l:mrow><l:mi>M</l:mi></l:mrow><l:mrow><l:mi>π</l:mi></l:mrow></l:msub><l:mi>L</l:mi><l:mo>≥</l:mo><l:mn>4</l:mn></l:mrow></l:math> to control finite volume effects (FVEs), while we simulate a smaller size at the smallest <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>M</n:mi><n:mi>π</n:mi></n:msub></n:math> to directly examine FVEs. The bottom quark masses are chosen in a range from the physical charm quark mass to <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:mn>0.7</p:mn><p:msup><p:mrow><p:mi>a</p:mi></p:mrow><p:mrow><p:mo>−</p:mo><p:mn>1</p:mn></p:mrow></p:msup></p:mrow></p:math> to control discretization effects. We extrapolate the form factors to the continuum limit and physical quark masses based on heavy meson chiral perturbation theory at next-to-leading order. Then the recoil parameter dependence is parametrized using a model independent form leading to our estimate of the decay rate ratio between the tau (<r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mo>ℓ</r:mo><r:mo>=</r:mo><r:mi>τ</r:mi></r:math>) and light lepton (<t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mo>ℓ</t:mo><t:mo>=</t:mo><t:mi>e</t:mi></t:math>, <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mrow><v:mi>μ</v:mi></v:mrow></v:math>) channels <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mrow><x:mi>R</x:mi><x:mo stretchy="false">(</x:mo><x:msup><x:mrow><x:mi>D</x:mi></x:mrow><x:mrow><x:mo>*</x:mo></x:mrow></x:msup><x:mo stretchy="false">)</x:mo><x:mo>=</x:mo><x:mn>0.252</x:mn><x:mo stretchy="false">(</x:mo><x:mn>22</x:mn><x:mo stretchy="false">)</x:mo></x:mrow></x:math> in the Standard Model. A simultaneous fit with recent data from the Belle experiment yields <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mrow><db:mo stretchy="false">|</db:mo><db:msub><db:mrow><db:mi>V</db:mi></db:mrow><db:mrow><db:mi>c</db:mi><db:mi>b</db:mi></db:mrow></db:msub><db:mo stretchy="false">|</db:mo><db:mo>=</db:mo><db:mn>39.19</db:mn><db:mo stretchy="false">(</db:mo><db:mn>91</db:mn><db:mo stretchy="false">)</db:mo><db:mo>×</db:mo><db:msup><db:mrow><db:mn>10</db:mn></db:mrow><db:mrow><db:mo>−</db:mo><db:mn>3</db:mn></db:mrow></db:msup></db:mrow></db:math>, which is consistent with previous exclusive determinations, and shows good consistency in the kinematical distribution of the differential decay rate between the lattice and experimental data. Published by the American Physical Society 2024

Topics & Concepts