B→D* and Bs→Ds* vector, axial-vector and tensor form …

We compute the complete set of Standard Model (SM) and tensor <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>D</a:mi><a:mo>*</a:mo></a:msup><a:mo>ℓ</a:mo><a:mover accent="true"><a:mi>ν</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> and <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:mo stretchy="false">→</f:mo><f:msubsup><f:mi>D</f:mi><f:mi>s</f:mi><f:mo>*</f:mo></f:msubsup><f:mo>ℓ</f:mo><f:mover accent="true"><f:mi>ν</f:mi><f:mo stretchy="false">¯</f:mo></f:mover></f:math> semileptonic form factors across the full kinematic range of the decays using second generation MILC <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>n</k:mi><k:mi>f</k:mi></k:msub><k:mo>=</k:mo><k:mn>2</k:mn><k:mo>+</k:mo><k:mn>1</k:mn><k:mo>+</k:mo><k:mn>1</k:mn></k:math> highly improved staggered quark (HISQ) gluon field configurations and HISQ valence quarks, with the method. Lattice spacings range from 0.09 to 0.044 fm with pion masses from <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mo>≈</m:mo><m:mn>300</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>MeV</m:mi></m:math> down to the physical value and heavy quark masses ranging between <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo>≈</o:mo><o:mn>1.5</o:mn><o:msub><o:mi>m</o:mi><o:mi>c</o:mi></o:msub></o:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mn>4.1</q:mn><q:msub><q:mi>m</q:mi><q:mi>c</q:mi></q:msub><q:mo>≈</q:mo><q:mn>0.9</q:mn><q:msub><q:mi>m</q:mi><q:mi>b</q:mi></q:msub></q:math>; currents are normalized nonperturbatively. Using the recent untagged <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>B</s:mi><s:mo stretchy="false">→</s:mo><s:msup><s:mi>D</s:mi><s:mo>*</s:mo></s:msup><s:mo>ℓ</s:mo><s:msub><s:mover accent="true"><s:mi>ν</s:mi><s:mo stretchy="false">¯</s:mo></s:mover><s:mo>ℓ</s:mo></s:msub></s:math> data from Belle and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msub><x:mi>B</x:mi><x:mi>s</x:mi></x:msub><x:mo stretchy="false">→</x:mo><x:msubsup><x:mi>D</x:mi><x:mi>s</x:mi><x:mo>*</x:mo></x:msubsup><x:mi>μ</x:mi><x:msub><x:mover accent="true"><x:mi>ν</x:mi><x:mo stretchy="false">¯</x:mo></x:mover><x:mi>μ</x:mi></x:msub></x:math> from LHCb together with our form factors, we determine a model independent value of <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>V</cb:mi><cb:mrow><cb:mi>c</cb:mi><cb:mi>b</cb:mi></cb:mrow></cb:msub><cb:mo>=</cb:mo><cb:mn>39.03</cb:mn><cb:mo stretchy="false">(</cb:mo><cb:mn>56</cb:mn><cb:msub><cb:mo stretchy="false">)</cb:mo><cb:mi>exp</cb:mi></cb:msub><cb:mo stretchy="false">(</cb:mo><cb:mn>67</cb:mn><cb:msub><cb:mo stretchy="false">)</cb:mo><cb:mrow><cb:mi>latt</cb:mi></cb:mrow></cb:msub><cb:mo>×</cb:mo><cb:msup><cb:mn>10</cb:mn><cb:mrow><cb:mo>−</cb:mo><cb:mn>3</cb:mn></cb:mrow></cb:msup></cb:math>, in agreement with previous exclusive determinations and in tension with the most recent inclusive result at the level of <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mn>3.6</ib:mn><ib:mi>σ</ib:mi></ib:math>. We also observe a <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mo>≈</kb:mo><kb:mn>1</kb:mn><kb:mi>σ</kb:mi></kb:math> tension between the shape of the differential decay rates computed using our form factors and those measured by Belle. We compute a purely theoretical Standard Model value for the ratio of semitauonic and semimuonic decay rates, <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>R</mb:mi><mb:mo stretchy="false">(</mb:mo><mb:msup><mb:mi>D</mb:mi><mb:mo>*</mb:mo></mb:msup><mb:mo stretchy="false">)</mb:mo><mb:mo>=</mb:mo><mb:mn>0.273</mb:mn><mb:mo stretchy="false">(</mb:mo><mb:mn>15</mb:mn><mb:mo stretchy="false">)</mb:mo></mb:math>, which we find to be closer to the recent Belle measurement and heavy flavor averaging group average than theory predictions using fits to experimental differential rate data for <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mi>B</sb:mi><sb:mo stretchy="false">→</sb:mo><sb:msup><sb:mi>D</sb:mi><sb:mo>*</sb:mo></sb:msup><sb:mo>ℓ</sb:mo><sb:msub><sb:mover accent="true"><sb:mi>ν</sb:mi><sb:mo stretchy="false">¯</sb:mo></sb:mover><sb:mo>ℓ</sb:mo></sb:msub></sb:math>. Determining <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:msub><xb:mi>V</xb:mi><xb:mrow><xb:mi>c</xb:mi><xb:mi>b</xb:mi></xb:mrow></xb:msub></xb:math> from our form factors and the experimental total rate for <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:mi>B</zb:mi><zb:mo stretchy="false">→</zb:mo><zb:msup><zb:mi>D</zb:mi><zb:mo>*</zb:mo></zb:msup><zb:mo>ℓ</zb:mo><zb:mi>ν</zb:mi></zb:math> also gives a value in agreement with inclusive results. We also compute the longitudinal polarization fraction for the semitauonic mode, <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:msubsup><cc:mi>F</cc:mi><cc:mi>L</cc:mi><cc:msup><cc:mi>D</cc:mi><cc:mo>*</cc:mo></cc:msup></cc:msubsup><cc:mo>=</cc:mo><cc:mn>0.395</cc:mn><cc:mo stretchy="false">(</cc:mo><cc:mn>24</cc:mn><cc:mo stretchy="false">)</cc:mo></cc:math>, which is in tension at the level of <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"><gc:mn>2.2</gc:mn><gc:mi>σ</gc:mi></gc:math> with the recent Belle measurement. Our calculation combines <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:mi>B</ic:mi><ic:mo stretchy="false">→</ic:mo><ic:msup><ic:mi>D</ic:mi><ic:mo>*</ic:mo></ic:msup></ic:math> and <lc:math xmlns:lc="http://www.w3.org/1998/Math/MathML" display="inline"><lc:msub><lc:mi>B</lc:mi><lc:mi>s</lc:mi></lc:msub><lc:mo stretchy="false">→</lc:mo><lc:msubsup><lc:mi>D</lc:mi><lc:mi>s</lc:mi><lc:mo>*</lc:mo></lc:msubsup></lc:math> lattice results in a simultaneous chiral continuum extrapolation, maintaining correlations between both modes. We then give results for both <oc:math xmlns:oc="http://www.w3.org/1998/Math/MathML" display="inline"><oc:mi>B</oc:mi><oc:mo stretchy="false">→</oc:mo><oc:msup><oc:mi>D</oc:mi><oc:mo>*</oc:mo></oc:msup></oc:math> and <rc:math xmlns:rc="http://www.w3.org/1998/Math/MathML" display="inline"><rc:msub><rc:mi>B</rc:mi><rc:mi>s</rc:mi></rc:msub><rc:mo stretchy="false">→</rc:mo><rc:msubsup><rc:mi>D</rc:mi><rc:mi>s</rc:mi><rc:mo>*</rc:mo></rc:msubsup></rc:math>, with the <uc:math xmlns:uc="http://www.w3.org/1998/Math/MathML" display="inline"><uc:msub><uc:mi>B</uc:mi><uc:mi>s</uc:mi></uc:msub><uc:mo stretchy="false">→</uc:mo><uc:msubsup><uc:mi>D</uc:mi><uc:mi>s</uc:mi><uc:mo>*</uc:mo></uc:msubsup></uc:math> results superseding our previous lattice computation. We also give the chiral perturbation theory needed to analyze the tensor form factors.