Model-independent extraction of form factors and |Vcb| in B¯→</mml…

Using the entire <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">ϒ</a:mi><a:mo stretchy="false">(</a:mo><a:mn>4</a:mn><a:mi>S</a:mi><a:mo stretchy="false">)</a:mo></a:math> dataset, the first two-dimensional unbinned angular analysis of the semileptonic decay <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mover accent="true"><f:mi>B</f:mi><f:mo stretchy="false">¯</f:mo></f:mover><f:mo stretchy="false">→</f:mo><f:mi>D</f:mi><f:msup><f:mo>ℓ</f:mo><f:mo>−</f:mo></f:msup><f:msub><f:mover accent="true"><f:mi>ν</f:mi><f:mo stretchy="false">¯</f:mo></f:mover><f:mo>ℓ</f:mo></f:msub></f:math> is performed, employing hadronic reconstruction of the tag-side <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>B</m:mi></m:math> meson from <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi mathvariant="normal">ϒ</o:mi><o:mo stretchy="false">(</o:mo><o:mn>4</o:mn><o:mi>S</o:mi><o:mo stretchy="false">)</o:mo><o:mo stretchy="false">→</o:mo><o:mrow><o:mi>B</o:mi><o:mover accent="true"><o:mi>B</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:mrow></o:math>. Here, <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mo>ℓ</w:mo></w:math> denotes the light charged leptons <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>e</y:mi></y:math> and <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>μ</ab:mi></ab:math>. A novel data-driven signal-background separation procedure with minimal dependence on simulation is developed. This procedure preserves all multidimensional correlations present in the data. The expected <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msup><cb:mi>sin</cb:mi><cb:mn>2</cb:mn></cb:msup><cb:msub><cb:mi>θ</cb:mi><cb:mo>ℓ</cb:mo></cb:msub></cb:math> dependence of the differential decay rate in the Standard Model is demonstrated, where <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi>θ</eb:mi><eb:mo>ℓ</eb:mo></eb:msub></eb:math> is the lepton helicity angle. Including input from the latest lattice QCD calculations and previously available experimental data, the underlying form factors are extracted using both model-independent (BGL) and dependent (CLN) methods. Comparisons with lattice calculations show flavor SU(3) symmetry to be a good approximation in the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>B</gb:mi><gb:mrow><gb:mo stretchy="false">(</gb:mo><gb:mi>s</gb:mi><gb:mo stretchy="false">)</gb:mo></gb:mrow></gb:msub><gb:mo stretchy="false">→</gb:mo><gb:msub><gb:mi>D</gb:mi><gb:mrow><gb:mo stretchy="false">(</gb:mo><gb:mi>s</gb:mi><gb:mo stretchy="false">)</gb:mo></gb:mrow></gb:msub></gb:math> sector. Using the BGL results, the CKM matrix element <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:mo>=</nb:mo><nb:mo stretchy="false">(</nb:mo><nb:mn>41.09</nb:mn><nb:mo>±</nb:mo><nb:mn>1.16</nb:mn><nb:mo stretchy="false">)</nb:mo><nb:mo>×</nb:mo><nb:msup><nb:mn>10</nb:mn><nb:mrow><nb:mo>−</nb:mo><nb:mn>3</nb:mn></nb:mrow></nb:msup></nb:math> and the Standard Model prediction of the lepton-flavor universality violation variable <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:mi mathvariant="script">R</tb:mi><tb:mo stretchy="false">(</tb:mo><tb:mi>D</tb:mi><tb:mo stretchy="false">)</tb:mo><tb:mo>=</tb:mo><tb:mn>0.300</tb:mn><tb:mo>±</tb:mo><tb:mn>0.004</tb:mn></tb:math>, are extracted. The value of <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mo stretchy="false">|</yb:mo><yb:msub><yb:mi>V</yb:mi><yb:mrow><yb:mi>c</yb:mi><yb:mi>b</yb:mi></yb:mrow></yb:msub><yb:mo stretchy="false">|</yb:mo></yb:math> from <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:mover accent="true"><cc:mi>B</cc:mi><cc:mo stretchy="false">¯</cc:mo></cc:mover><cc:mo stretchy="false">→</cc:mo><cc:mi>D</cc:mi><cc:msup><cc:mo>ℓ</cc:mo><cc:mo>−</cc:mo></cc:msup><cc:msub><cc:mover accent="true"><cc:mi>ν</cc:mi><cc:mo stretchy="false">¯</cc:mo></cc:mover><cc:mo>ℓ</cc:mo></cc:msub></cc:math> tends to be higher than that extracted using <jc:math xmlns:jc="http://www.w3.org/1998/Math/MathML" display="inline"><jc:mover accent="true"><jc:mi>B</jc:mi><jc:mo stretchy="false">¯</jc:mo></jc:mover><jc:mo stretchy="false">→</jc:mo><jc:msup><jc:mi>D</jc:mi><jc:mo>*</jc:mo></jc:msup><jc:msup><jc:mo>ℓ</jc:mo><jc:mo>−</jc:mo></jc:msup><jc:msub><jc:mover accent="true"><jc:mi>ν</jc:mi><jc:mo stretchy="false">¯</jc:mo></jc:mover><jc:mo>ℓ</jc:mo></jc:msub></jc:math>. The Standard Model <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:mi mathvariant="script">R</qc:mi><qc:mo stretchy="false">(</qc:mo><qc:mi>D</qc:mi><qc:mo stretchy="false">)</qc:mo></qc:math> calculation is at a <vc:math xmlns:vc="http://www.w3.org/1998/Math/MathML" display="inline"><vc:mn>1.97</vc:mn><vc:mi>σ</vc:mi></vc:math> tension with the latest HFLAV experimental average. Published by the American Physical Society 2024