b¯c susceptibilities from fully relativistic lattice QCD

We compute the h¯c (pseudo)scalar, (axial-)vector and (axial-)tensor susceptibilities as a function of u=mc/mh between u=mc/mb and u=0.8 using fully relativistic lattice QCD, employing nonperturbative current renormalization and using the second generation 2+1+1 MILC HISQ gluon field configurations. We include ensembles with a≈0.09, 0.06, 0.045, and 0.033 fm and we are able to reach the physical b-quark on the two finest ensembles. At the physical mh=mb point we find m¯b2χ1+=0.720(34)×10−2, m¯b2χ1−=1.161(54)×10−2, χ0−=2.374(33)×10−2, and χ0+=0.609(14)×10−2. Our results for the (pseudo)scalar, vector, and axial vector are compatible with the expected small size of nonperturbative effects at u=mc/mb. We also give the first nonperturbative determination of the tensor susceptibilities, finding m¯b2χT=0.891(44)×10−2 and m¯b2χAT=0.441(33)×10−2. Our value of m¯b2χAT is in good agreement with the O(αs) perturbation theory, while our result for m¯b2χT is in tension with the O(αs) perturbation theory at the level of 2σ. These results will allow for dispersively bounded parametrizations to be employed using lattice inputs for the full set of h→c semileptonic form factors in future calculations, for heavy-quark masses in the range 1.25×mc≤mh≤mb. Published by the American Physical Society 2024