[論文レビュー] $B ightarrow D^*$ 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 studies被引用数 9

ひとこと要約

B→D*（および B_s→D_s*）の全 SM およびテンソル形状因子の格子 QCD 計算を、全 q^2 範囲にわたって実施し、モデル非依存の V_cb の決定と R(D*) および関連観測量の予測を可能にする。

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.

研究の動機と目的

• B→D^{*}および B_s→D_s^{*}の全運動学範囲にわたるSMおよびテンソル形状因子の完全なセットを計算する。
• 格子形状因子を最新の実験データと組み合わせてモデル非依存のV_{cb}を決定する。
• R(D^{*})およびD^{*}の縦偏 polarization など関連観測量のSM予測を提供し、実験データとの乖離を評価する。

提案手法

• 2nd-generation MILC $n_f=2+1+1$ HISQ グルーオン構成と重-HISQ 法を用いて全運動学範囲へアクセス。
• 電流の非摂動的再標準化と重-HISQ 外挿を用いて重クォーク質量を近似 Charm から物理的 bottom までの範囲で適用。
• Charm 慣性モーメントのために staggered spin-taste 演算子と twist boundary conditions を用いた2点・3点の相関関数から行列要素を抽出。
• 格子の行列要素をHQETに基づく形状因子 $h_V$、$h_{A1}$、$h_{A2}$、$h_{A3}$ およびテンソル形状因子 $h_{T1}$、$h_{T2}$、$h_{T3}$ の定義された運動学的結合を用いて結ぶ。
• 重-クォーク質量依存性と離散化効果を含むカイラ・連続外挿を実施。

実験結果

リサーチクエスチョン

• RQ1 $B\to D^{*}$ および $B_s\to D_s^{*}$ の全ての $q^2$ にわたる SM およびテンソル形状因子は何か？
• RQ2 格子形状因子を現在の実験データと組み合わせて得られるモデル非依存の $V_{cb}$ はいくらか？
• RQ3 $R(D^{*})$ および $F_L^{D^{*}}$ の格子結果は実験測定値および SM 期待値とどう比較されるか？
• RQ4 $B\to D^{*}$ と $B_s\to D_s^{*}$ 形状因子間の $SU(3)_{flav}$ breaking 効果はどの程度か？

主な発見

• $V_{cb}=39.03(56)_{exp}(67)_{latt}\times 10^{-3}$, 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 $B\to D^{*}\ell\nu$.