[Paper Review] $B ightarrow D^*$ vector, axial-vector and tensor form factors for the full $q^2$ range from lattice QCD

Judd Harrison, C. T. H. Davies|arXiv (Cornell University)|Apr 6, 2023

Particle physics theoretical and experimental studies9 citations

TL;DR

Lattice QCD calculation of the full set of SM and tensor form factors for B -> D* (and B_s -> D_s*) across the full q^2 range, enabling a model-independent V_cb determination and predictions for R(D*) and related observables.

ABSTRACT

We compute the complete set of SM and tensor $B_{(s)} o D_{(s)}^*\ell\barν$ semileptonic form factors across the full kinematic range of the decay using second generation MILC $n_f=2+1+1$ HISQ gluon field configurations and HISQ valence quarks, with the heavy-HISQ method. Lattice spacings range from $0.09\mathrm{fm}$ to $0.044\mathrm{fm}$ with pion masses from $\approx 300\mathrm{MeV}$ down to the physical value and heavy quark masses ranging between $\approx 1.5 m_c$ and $4.1 m_c \approx 0.9 m_b$; currents are normalised nonperturbatively. Using the recent $B_{(s)} o D^*_{(s)}\ell\barν_\ell$ data from Belle and LHCb together with our form factors we determine a model independent value of $V_{cb}=39.03(56)_\mathrm{exp}(67)_\mathrm{latt} imes 10^{-3}$, in agreement with previous exclusive determinations and in tension with the inclusive result at the level of $3.6σ$. We observe a $\approx 1σ$ tension between the shape of the differential decay rates computed using our form factors and those measured by Belle. We compute a lattice-only SM value for the ratio of semitauonic and semimuonic decay rates, $R(D^*)=0.273(15)$, which we find to be closer to the recent Belle measurement and HFLAV average than theory predictions using fits to experimental differential rate data for $B o D^*\ell\barν_\ell$. Determining $V_{cb}$ using the total rate for $B o D^*\ellν$ gives a value in agreement with inclusive results. We compute the longitudinal polarisation fraction for the semitauonic mode, $F_L^{D^*}=0.395(24)$, which is in tension at the level of $2.2σ$ with the recent Belle measurement. Our calculation combines $B o D^*$ and $B_s o D_s^*$ lattice results, and we provide an update which supersedes our previous lattice computation of the $B_s o D_s^*$ form factors. We also give the chiral perturbation theory needed to analyse the tensor form factors.

Motivation & Objective

• Compute the complete set of SM and tensor form factors for $B\to D^{*}$ and $B_s\to D_s^{*}$ across the full kinematic range.
• Determine a model-independent $V_{cb}$ by combining lattice form factors with latest experimental data.
• Provide SM predictions for $R(D^{*})$ and related observables such as the $D^{*}$ longitudinal polarization fraction, and assess tensions with experimental data.

Proposed method

• Use second-generation MILC $n_f=2+1+1$ HISQ gluon configurations and heavy-HISQ method to access the full kinematic range.
• Employ nonperturbative renormalisation of currents and heavy-HISQ extrapolation in heavy-quark mass from near charm to physical bottom.
• Extract matrix elements from 2-point and 3-point correlators with staggered spin-taste operators and twisted boundary conditions for charm momenta.
• Relate lattice matrix elements to HQET-based form factors $h_V$, $h_{A1}$, $h_{A2}$, $h_{A3}$ and tensor form factors $h_{T1}$, $h_{T2}$, $h_{T3}$ using defined kinematic combinations.
• Perform chiral-continuum extrapolations including heavy-quark mass dependence and discretisation effects.

Experimental results

Research questions

• RQ1 What are the full SM and tensor form factors for $B\to D^{*}$ and $B_s\to D_s^{*}$ across all $q^2$?
• RQ2 What is the model-independent value of $V_{cb}$ obtained from lattice form factors combined with current experimental data?
• RQ3 How do the lattice results for $R(D^{*})$ and $F_L^{D^{*}}$ compare with experimental measurements and SM expectations?
• RQ4 What are the $SU(3)_{flav}$-breaking effects between $B\to D^{*}$ and $B_s\to D_s^{*}$ form factors?

Key findings

• $V_{cb}=39.03(56)_{exp}(67)_{latt}\times 10^{-3}$, in agreement with previous exclusive determinations and in tension with the most recent inclusive result (~3.6σ).
• $R(D^{*})=0.273(15)$ in SM, closer to recent Belle measurements and HFLAV average than fits to differential rate data.
• $F_L^{D^{*}}=0.395(24)$ for the semitauonic mode, with a ~2.2σ tension with the Belle measurement.
• The analysis combines $B\to D^{*}$ and $B_s\to D_s^{*}$ lattice results to map spectator-quark mass dependence and study $SU(3)_{flav}$ breaking.
• The work updates and supersedes previous $B_s\to D_s^{*}$ form factor calculations and provides chiral perturbation theory needed for tensor form factors.
• The results are consistent with inclusive $V_{cb}$ when using their form factors and total rate for $B\to D^{*}\ell\nu$.