Weak Matrix Elements on the Lattice --- Circa 1995

Abstract

Status of weak matrix elements is reviewed. In particular, $\epspeps$, $\bkastg$, $B_K$, $B_B$ and $B_{B_s}$ are discussed and the overall situation with respect to the lattice effort and some of its phenomenological implications are summarized. For $\epspeps$ the need for the relevant matrix elements is stressed in view of the forthcoming improved experiments. For some of the operators, (e.g.\ $O_6$), even bounds on their matrix elements would be very helpful. On $\bkastg$, a constant behavior of $T_2$ appears disfavored although dependence of $T_2$ could, of course, be milder than a simple pole. Improved data is badly needed to settle this important issue firmly, especially in view of its ramification for extractions of $V_{td}$ from $B\to \rho \gamma$. On $B_K$, the preliminary result from JLQCD appears to contradict Sharpe \etal\ JLQCD data seems to fit very well to linear $a$ dependence and leads to an appreciably lower value of $B_K$. Four studies of $B_K$ in the ``full'' ($n_f=2$) theory indicate very little quenching effects on $B_K$; the full theory value seems to be just a little less than the quenched result. Based on expectations from HQET, analysis of the $B$-parameter ($B_{h\ell }$) for the heavy-light mesons via $B_{h\ell }=$constant$+$constants${}^{\prime }/m_{h\ell }$ is suggested. A summary of an illustrative sample of hadron matrix elements is given and constraints on CKM parameters (e.g.\ $V_{td}/V_{ts}$), on the unitarity triangle and on $x_s/x_d$, emerging from the lattice calculations along with experimental results are briefly discussed. In quite a few cases, for the first time, some indication of quenching errors on weak matrix elements are now becoming available.

References in corpus (13)

• Heavy Quark Symmetry
• Progress in Electroweak Baryogenesis
• On the Viability of Lattice Perturbation Theory
• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Two--Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays II: $\mathcal{O}({\alpha }_e{\alpha }_s)$
• ${\epsilon }^{\prime }/\epsilon$ at the next-to-leading order in QCD and QED
• $b\to s\gamma$ AND $b\to sg$: A THEORETICAL REAPPRAISAL
• A Lattice Computation of the Decay Constants of $B$ and $D$ Mesons
• Quark Masses from Lattice QCD at the Next-to-Leading Order
• Quenched Heavy-Light Decay Constants
• Uncertainties from Long Range Effects in $B \to K^* γ
• $B\to K^{\ast }+\gamma$ and $B_s\to \varphi +\gamma$ on the Lattice
• $B\to K^{\ast }\gamma$: Penguins on the Lattice

Cited by in corpus (12)

• Lattice QCD with two dynamical flavors of domain wall quarks
• Recent results from lattice calculations
• Measurements of the $\rho$ and $\eta$ parameters of the $V_{CKM}$ matrix and perspectives
• Present knowledge of the Cabibbo-Kobayashi-Maskawa matrix
• Novel CP-violating Effects in B decays from Charged-Higgs in a Two-Higgs Doublet Model for the Top Quark
• Renormalization of the ΔB=2 four-quark operators in lattice NRQCD
• Status of Heavy Quark Physics on the Lattice
• Sea quark effects in B_K from N_f=2 clover-improved Wilson fermions
• B Mixing
• Lattice Matrix Elements and CP Violation in B and K Physics: Status and Outlook
• Comments on the Sign of CP Asymmetries
• Sea quark effects in B_K from N_f=2 clover-improved Wilson fermions