Precision calculations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:math> form factors from SCET sum r

We construct light cone sum rules (LCSR) for the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>B</a:mi><a:mo stretchy="false">→</a:mo><a:msup><a:mi>K</a:mi><a:mo>*</a:mo></a:msup></a:math> form factors in the large recoil region using vacuum-to-<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>B</d:mi></d:math>-meson correlation functions, and systematically calculate subleading-power corrections to these form factors at tree level, including next-to-leading power contributions from the hard-collinear propagator, the subleading effective current <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mover accent="true"><f:mi>q</f:mi><f:mo stretchy="false">¯</f:mo></f:mover><f:mi mathvariant="normal">Γ</f:mi><f:mo stretchy="false">[</f:mo><f:mi>i</f:mi><f:msub><f:menclose notation="updiagonalstrike" other="updiag5"><f:mi>D</f:mi></f:menclose><f:mo>⊥</f:mo></f:msub><f:mo>/</f:mo><f:mo stretchy="false">(</f:mo><f:mn>2</f:mn><f:msub><f:mi>m</f:mi><f:mi>b</f:mi></f:msub><f:mo stretchy="false">)</f:mo><f:mo stretchy="false">]</f:mo><f:msub><f:mi>h</f:mi><f:mi>v</f:mi></f:msub></f:math>, and twist-five/six four-particle higher-twist effects. By incorporating the available leading-power results at <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi mathvariant="script">O</q:mi><q:mo stretchy="false">(</q:mo><q:msub><q:mi>α</q:mi><q:mi>s</q:mi></q:msub><q:mo stretchy="false">)</q:mo></q:math> and the corrections to higher-twist <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>B</v:mi></v:math>-meson light cone distribution amplitudes from our previous work, we improve the precision of theoretical predictions for <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi>B</x:mi><x:mo stretchy="false">→</x:mo><x:msup><x:mi>K</x:mi><x:mo>*</x:mo></x:msup></x:math> form factors and find that the subleading-power contributions amount to 30% of the corresponding leading-power results. Employing the Bourrely-Caprini-Lellouch parametrization, we determine the numerical results for <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>B</ab:mi><ab:mo stretchy="false">→</ab:mo><ab:msup><ab:mi>K</ab:mi><ab:mo>*</ab:mo></ab:msup></ab:math> form factors across the full kinematic range through a combined fit of LCSR predictions in the large recoil region and lattice QCD results in the small recoil region. Using the newly obtained <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>B</db:mi><db:mo stretchy="false">→</db:mo><db:msup><db:mi>K</db:mi><db:mo>*</db:mo></db:msup></db:math> form factors, we compute the branching fractions for the rare decays <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi>B</gb:mi><gb:mo stretchy="false">→</gb:mo><gb:msup><gb:mi>K</gb:mi><gb:mo>*</gb:mo></gb:msup><gb:msub><gb:mi>ν</gb:mi><gb:mo>ℓ</gb:mo></gb:msub><gb:msub><gb:mover accent="true"><gb:mi>ν</gb:mi><gb:mo stretchy="false">¯</gb:mo></gb:mover><gb:mo>ℓ</gb:mo></gb:msub></gb:math> in the Standard Model, obtaining <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:mrow><lb:mrow><lb:mi mathvariant="script">B</lb:mi><lb:mi mathvariant="script">R</lb:mi></lb:mrow><lb:mo stretchy="false">(</lb:mo><lb:msup><lb:mrow><lb:mover accent="true"><lb:mrow><lb:mi>B</lb:mi></lb:mrow><lb:mrow><lb:mo stretchy="false">¯</lb:mo></lb:mrow></lb:mover></lb:mrow><lb:mn>0</lb:mn></lb:msup><lb:mo stretchy="false">→</lb:mo><lb:msup><lb:mrow><lb:mover accent="true"><lb:mrow><lb:mi>K</lb:mi></lb:mrow><lb:mrow><lb:mo stretchy="false">¯</lb:mo></lb:mrow></lb:mover></lb:mrow><lb:mrow><lb:mo>*</lb:mo><lb:mn>0</lb:mn></lb:mrow></lb:msup><lb:msub><lb:mrow><lb:mi>ν</lb:mi></lb:mrow><lb:mrow><lb:mo>ℓ</lb:mo></lb:mrow></lb:msub><lb:msub><lb:mrow><lb:mover accent="true"><lb:mrow><lb:mi>ν</lb:mi></lb:mrow><lb:mrow><lb:mo stretchy="false">¯</lb:mo></lb:mrow></lb:mover></lb:mrow><lb:mrow><lb:mo>ℓ</lb:mo></lb:mrow></lb:msub><lb:mo stretchy="false">)</lb:mo><lb:mo>=</lb:mo><lb:mn>8.09</lb:mn><lb:mo stretchy="false">(</lb:mo><lb:mn>96</lb:mn><lb:mo stretchy="false">)</lb:mo><lb:mo>×</lb:mo><lb:msup><lb:mn>10</lb:mn><lb:mrow><lb:mo>−</lb:mo><lb:mn>6</lb:mn></lb:mrow></lb:msup></lb:mrow></lb:math> and <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mrow><ac:mi mathvariant="script">B</ac:mi><ac:mi mathvariant="script">R</ac:mi></ac:mrow><ac:mo stretchy="false">(</ac:mo><ac:msup><ac:mover accent="true"><ac:mi>B</ac:mi><ac:mo stretchy="false">¯</ac:mo></ac:mover><ac:mo>+</ac:mo></ac:msup><ac:mo stretchy="false">→</ac:mo><ac:msup><ac:mover accent="true"><ac:mi>K</ac:mi><ac:mo stretchy="false">¯</ac:mo></ac:mover><ac:mrow><ac:mo>*</ac:mo><ac:mo>+</ac:mo></ac:mrow></ac:msup><ac:msub><ac:mi>ν</ac:mi><ac:mo>ℓ</ac:mo></ac:msub><ac:msub><ac:mover accent="true"><ac:mi>ν</ac:mi><ac:mo stretchy="false">¯</ac:mo></ac:mover><ac:mo>ℓ</ac:mo></ac:msub><ac:mo stretchy="false">)</ac:mo><ac:mo>=</ac:mo><ac:mn>9.95</ac:mn><ac:mo stretchy="false">(</ac:mo><ac:mn>1.05</ac:mn><ac:mo stretchy="false">)</ac:mo><ac:mo>×</ac:mo><ac:msup><ac:mn>10</ac:mn><ac:mrow><ac:mo>−</ac:mo><ac:mn>6</ac:mn></ac:mrow></ac:msup></ac:math>. Additionally, we predict that the longitudinal <pc:math xmlns:pc="http://www.w3.org/1998/Math/MathML" display="inline"><pc:msup><pc:mi>K</pc:mi><pc:mo>*</pc:mo></pc:msup></pc:math> polarization fraction is <rc:math xmlns:rc="http://www.w3.org/1998/Math/MathML" display="inline"><rc:msub><rc:mi>F</rc:mi><rc:mi>L</rc:mi></rc:msub><rc:mo>=</rc:mo><rc:mn>0.44</rc:mn><rc:mo stretchy="false">(</rc:mo><rc:mn>4</rc:mn><rc:mo stretchy="false">)</rc:mo></rc:math>.