<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>B</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>μ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>μ</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>γ</mml:mi></mml:math> decay rate at large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>q</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math> from lattice QCD
R. Frezzotti, Nazario Tantalo, G. Gagliardi, Francesco Sanfilippo, Silvano Simula, V. Lubicz, G. Martinelli, Christopher Sachrajda
Abstract
We determine, by means of lattice QCD calculations, the local form factors describing the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>B</a:mi><a:mi>s</a:mi></a:msub><a:mo stretchy="false">→</a:mo><a:msup><a:mi>μ</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>μ</a:mi><a:mo>−</a:mo></a:msup><a:mi>γ</a:mi></a:math> decay, in the so-called electroquenched approximation. For this analysis we make use of the gauge configurations produced by the ETM Collaboration with <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi>N</d:mi><d:mi>f</d:mi></d:msub><d:mo>=</d:mo><d:mn>2</d:mn><d:mo>+</d:mo><d:mn>1</d:mn><d:mo>+</d:mo><d:mn>1</d:mn></d:math> flavor of Wilson-Clover twisted-mass fermions at maximal twist. To obtain the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>B</f:mi><f:mi>s</f:mi></f:msub></f:math> meson form factors, we perform simulations for several heavy-strange meson masses <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>m</h:mi><h:msub><h:mi>H</h:mi><h:mi>s</h:mi></h:msub></h:msub></h:math> in the range <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi>m</j:mi><j:msub><j:mi>H</j:mi><j:mi>s</j:mi></j:msub></j:msub><j:mo>∈</j:mo><j:mo stretchy="false">[</j:mo><j:msub><j:mi>m</j:mi><j:msub><j:mi>D</j:mi><j:mi>s</j:mi></j:msub></j:msub><j:mo>,</j:mo><j:mn>2</j:mn><j:msub><j:mi>m</j:mi><j:msub><j:mi>D</j:mi><j:mi>s</j:mi></j:msub></j:msub><j:mo stretchy="false">]</j:mo></j:math>, and extrapolate to the physical <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>B</n:mi><n:mi>s</n:mi></n:msub></n:math> meson point <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>m</p:mi><p:msub><p:mi>B</p:mi><p:mi>s</p:mi></p:msub></p:msub><p:mo>≃</p:mo><p:mn>5.367</p:mn><p:mtext> </p:mtext><p:mtext> </p:mtext><p:mi>GeV</p:mi></p:math> making use of the HQET scaling laws. We cover the region of large dimuon invariant masses <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msqrt><r:msup><r:mi>q</r:mi><r:mn>2</r:mn></r:msup></r:msqrt><r:mo>></r:mo><r:mn>4.16</r:mn><r:mtext> </r:mtext><r:mtext> </r:mtext><r:mi>GeV</r:mi></r:math>, and use our results to determine the branching fraction for <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msub><t:mi>B</t:mi><t:mi>s</t:mi></t:msub><t:mo stretchy="false">→</t:mo><t:msup><t:mi>μ</t:mi><t:mo>+</t:mo></t:msup><t:msup><t:mi>μ</t:mi><t:mo>−</t:mo></t:msup><t:mi>γ</t:mi></t:math>, which has been recently measured by LHCb in the region <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msqrt><w:msup><w:mi>q</w:mi><w:mn>2</w:mn></w:msup></w:msqrt><w:mo>></w:mo><w:mn>4.9</w:mn><w:mtext> </w:mtext><w:mtext> </w:mtext><w:mi>GeV</w:mi></w:math>. The largest contribution to the uncertainty in the partial branching fractions at values of <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msqrt><y:msup><y:mi>q</y:mi><y:mn>2</y:mn></y:msup></y:msqrt><y:mo><</y:mo><y:mn>4.8</y:mn><y:mtext> </y:mtext><y:mtext> </y:mtext><y:mi>GeV</y:mi></y:math> is now due to resonance and other long-distance effects, including those from “charming penguins,” which we estimate by summing over the contributions from the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msup><ab:mi>J</ab:mi><ab:mi>P</ab:mi></ab:msup><ab:mo>=</ab:mo><ab:msup><ab:mn>1</ab:mn><ab:mo>−</ab:mo></ab:msup></ab:math> charmonium resonances. Published by the American Physical Society 2024