Paul B. Mackenzie
Lattice QCD plays an essential role in testing and determining the parameters of the CKM theory of flavor mixing and CP violation. Very high precisions are required for lattice calculations analysing CKM data; I discuss the prospects for achieving them. Lattice calculations will also play a role in investigating flavor mixing and CP violation beyond the Standard Model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
I discuss the lattice calculations relevant to recent advances in CKM phenomenology, focusing on those relevant to new experimental results reported at this workshop.
CKM matrix element Vcb in a QCD Potential model
在QCD势模型中研究重轻介子的Isgur-Wise函数，并用于计算B⁰半轻子衰变，得到CKM矩阵元|Vcb|=0.040，与实验数据吻合。
Although the two-body charmed decays $B_{(s)} \to \bar D_{(s)}^{(*)}P$ and $\bar D_{(s)}^{(*)}V$, where $P$($V$) denotes a light pseudoscalar(vector) meson, are CKM suppressed comparing with the $B_{(s)} \to D_{(s)}^{(*)}P$ and $ D_{(s)}^{(*)}V$ decays, they are important in the CKM angle $γ=ϕ_3$ extraction method. We investigated these decays in the perturbative QCD approach to the leading order of $m_D/m_B$ and $Λ_{\rm{QCD}}/m_D$ expansion. We find that the nonfactorizable emission diagrams and the annihilation diagrams are not negligible in many of these channels. The numerical results show…
These lectures (given at TASI 2000) provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1 (Ch. 2) is a very vanilla introduction to lattice QCD. Lecture 2 (Ch. 3) describes examples of recent lattice calculations relevant to fixing the parameters of the CKM matrix.
A full determination of the CKM matrix using recent results from lattice QCD is presented. To extract the CKM matrix in a uniform fashion, I exclusively use results from unquenched lattice QCD as the theory input for nonperturbative QCD effects. All 9 CKM matrix elements and all 4 Wolfenstein parameters are obtained from results for gold-plated quantities, which include semileptonic decay form factors and leptonic decay constants of B, D and K mesons, and B^0-\bar{B}^0 and K^0-\bar{K}^0 mixing amplitudes.
I discuss the role of lattice QCD in testing the Standard Model and searching for physics beyond the Standard Model in the quark flavor sector. I first review the Standard Model CKM framework. I then present the current status of the CKM matrix, focusing on determinations of CKM matrix elements and constraints on the CKM unitarity triangle that rely on lattice QCD calculations of weak matrix elements. I also show the potential impact of improved lattice QCD calculations on the global CKM unitarity triangle fit. I then describe several hints of new physics in the quark flavor sector that rely o…
We review the current status of |V(cb)|, |V(ub)| and |V(tb)|, the absolute values of the matrix elements in the CKM third column.
The magnitudes of the CKM matrix elements $V_{td}$, $V_{ts}$, and $V_{tb}$ are determined for the first time without any assumptions of unitarity. The implications for the unitarity of the CKM matrix as a whole are discussed.
We review the present status of the CKM matrix and we offer some visions of its future. After a brief presentation of the theoretical framework for weak decays we discuss the following topics: i) CKM matrix from tree level decays, ii) Standard analysis of the unitarity triangle, iii) CKM matrix from rare and CP violating K- and B-decays, iv) CKM matrix from CP violation in two-body B-decays. In particular we compare the CKM potentials of the standard analysis of the unitarity triangle, of the very clean K --> πν\barνdecays and of CP asymmetries in B-decays.
Lattice QCD is an important tool for theoretical input for flavor physics. There have been four reviews by the Flavour Lattice Averaging Group (FLAG). This talk will review the current status of the magnitude of eight of the nine CKM matrix elements, borrowing heavily from the most recent FLAG review (co-authored by the speaker). Future prospects for improving the determination of the CKM matrix will be discussed.
Precise lattice QCD results for hadronic matrix elements, decay constants and form factors play a crucial role in the determination of CKM matrix elements and in the identification of possible new physics contributions to flavour violating observables. This article reviews the implications of recent lattice QCD results on the phenomenology of flavour and CP violating meson decays, and highlights some future directions for lattice QCD calculations which would have a major impact on flavour phenomenology.
This manuscript has been withdrawn due to some default.
We investigate a scenario in which the CKM matrix arises from leptoquark--down quark mixing in a particular standard--like superstring model. We find that for some choices of F and D flat directions realistic quark mixing can be obtained without any phenomenological problems. This scenario predicts a symmetric (in absolute value) CKM matrix.
I discuss the combination and extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements under the Standard Model (SM) framework from a global fit. The analysis shown here relies on the CKMfitter package, consisting in a frequentist approach that employs the Range fit (Rfit) scheme to handle theoretical uncertainties.
The experimental status and theoretical uncertainties of the Cabibbo--Kobayashi--Maskawa (CKM) matrix describing the charge-changing weak transitions between quarks with charges -1/3 ($d, s, b$) and 2/3 ($u, c, t$) are reviewed. Some recent methods of obtaining phases of CKM elements are described.
We show that all CP violation in the MSSM could originate in the supersymmetry breaking sector rather than the CKM matrix, and discuss the important consequences for $B$-physics.
A general discussion of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is given and the importance stressed of determining the matrix elements as an essential part of understanding CP violation in and beyond the Standard Model. The status of knowledge of the matrix elements connecting the first and second generation quarks is reviewed. A perspective on determinations of the full CKM matrix is presented as an introduction to the separate contributions to the panel discussion that follows.
We identified a set of four rephasing invariant parameters of the CKM matrix. They are found to exhibit hierarchies in powers of $λ^2$, from $λ^2$ to $λ^8$. It is shown that, at the present level of accuracy, only the first three parameters are needed to fit all available data on flavor physics.
The aim of the paper is to propose a new type of fits in terms of invariant quantities for finding the entries of the CKM matrix from the quark sector, by using the mathematical solution to the reconstruction problem of 3 x 3 unitary matrices from experimental data, recently found. The necessity of this type of fit comes from the compatibility conditions between the data and the theoretical model formalised by the CKM matrix, which imply many strong nonlinear conditions on moduli which all have to be satisfied in order to obtain a unitary matrix.
We use lattice QCD to fully determine the CKM matrix. |V_{cd}|, |V_{cs}|, |V_{ub}|, |V_{cb}| and |V_{us}| are, respectively, directly determined with recent lattice results for form factors of semileptonic D->pi l nu, D->K l nu, B->pi l nu, B->D l nu and K->pi l nu decays obtained by the Fermilab Lattice, MILC, and HPQCD Collaborations. In addition, |V_{ud}|, |V_{tb}|, |V_{ts}| and |V_{td}| are determined by using unitarity of the CKM matrix and the experimental result for sin(2beta).
We propose a phenomenological formula relating the Cabibbo--Kobayashi--Masukawa matrix $V_{CKM}$ and quark masses in the form $(\sqrt{m_d} \, \sqrt{m_s} \, \sqrt{m_b}) \propto (\sqrt{m_u} \, \sqrt{m_c} \, \sqrt{m_t})V_{CKM}$. The results of the proposed formula are in agreement with experimental data. Under the constraint of the formula, we show that the invariant amplitude of the charged current weak interactions is maximized.
I report on developments in the experimental and phenomenological understanding of the rare decays of mesons containing b and c quarks, especially as they pertain to the understanding of the CKM matrix and the testing of the standard model. Some related measurements are also discussed.
The difference between induced by box diagram value of \tilde εand experimentally measured value of εis estimated. It appeared to be around 5 - 10 %, depending on the values of hadronic matrix elements. With this result, the fit of CKM marix parameters within the SM is performed.
The aim of the paper is to propose one paradigm change of CKM global fits on experimental data from electroweak sector. The change refers to using in fits the exact unitarity constraints expressed in terms of four invariant parameters, such as moduli of the CKM matrix, and to take into account an important set of the available experimental data. In the paper we use data from nuclear beta decays, and from leptonic and semileptonic decays, in order to find the most probable numerical form of the CKM matrix, as well as the determination of decay constants, $f_{P}$, and of various form factors $f_…
An updated determination of the parameters of the Cabibbo-Kobayashi-Maskawa matrix is presented.
To extract sum rules of CKM matrix elements, eigenvalue problems for quasi-democratic mass matrices are solved in the first order perturbation approximation with respect to small deviations from the democratic limit. Mass spectra of up and down quark sectors and the CKM matrix are shown to have clear and distinctive hierarchical structures. Numerical analysis shows that the absolute values of calculated CKM matrix elements fit the experimental data quite well. The order of the magnitude of the Jarlskog parameter is estimated by the relation $|J| \approx \sqrt{2}(m_c/m_t + m_s/m_b)|V_{us}|^2|V_…
The Jarlskog rephasing invariant parameter $|J|$ is evaluated using one of the six Unitarity Triangles involving well known CKM matrix elements \vud, \vus,~\rub, ~\vcd, ~\vcs~ and ~\vcb. With PDG2000 values of \vud~ etc. as input, we obtain $|J|=(2.71 \pm 1.12) \times 10^{-5}$, which in the PDG representation of CKM matrix leads to the range $21^o~to~159^o$ for the CP violating phase $δ$. The CKM matrix elements evaluated using this range of $δ$ are in agreement with the PDG CKM matrix. The implications of refinements in the input on $|J|$, $δ$ and CKM matrix elements have also been studied.
I give a brief overview of recent results from lattice QCD calculations which are relevant for the phenomenology of the Standard Model. I discuss, in particular, the lattice determination of light quark masses and the calculation of those hadronic quantities, such as semileptonic form factors, decay constants and B-parameters, which are of particular interest for the analysis of the CKM mixing matrix and the origin of CP violation.
The hypothesis of a real Cabibbo-Kobayashi-Maskawa matrix has been considered and found to be disfavoured by present measurements even when neglecting results from CP violation in neutral Kaon decay. This result contradicts statements reported in hep-ph/9810333.
An analysis of the CKM matrix parameters within the {\it R}fit approach is presented using updated input values with special emphasis on the recent $\sin{2β}$ measurements from BABAR and Belle. The QCD Factorisation Approach describing $B \to ππ,Kπ$ decays has been implemented in the software package CKMfitter. Fits using branching ratios and CP asymmetries are discussed.
Hierarchy of CKM matrix elements and implications of unitarity
本文在幺正性约束下重新审视CKM矩阵元素的层级结构，并比较9种等价参数化方案对CP破坏参数ε_k的计算，发现并非所有方案都能重现该参数值，揭示了层级结构对参数化选择的影响。
Schemes for fermion masses should predict elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. We review the freedom allowed by present experiments and how the parameter space will shrink in the next few years. In addition to experiments which directly affect CKM parameters, we discuss constraints arising from precise electroweak tests.
We study the possible existence of a real Cabibbo-Kobayashi-Maskawa (CKM) matrix, with CP violation originating from physics beyond the standard model (SM). We show that present experimental data allow for a real CKM matrix provided that new physics also contributes to Delta m_{B_d} by at least 20% of the SM contribution (for rho > 0), besides generating CP violation in the kaon sector. The naturalness of a real CKM matrix is studied within the framework of general multi-Higgs-doublet models with spontaneous CP violation. As an example, we discuss a specific two-Higgs-doublet model and its imp…
We analyze the two loop renormalization group equations in the standard model and its extensions for the coupling constants and the quark Yukawa couplings. The key point of our analysis is the observed hierarchy of the quark masses and the CKM matrix. For the one loop evolution we find the explicit solution for the evolution of the Yukawa couplings and show the following: 1. the CKM matrix depends on the energy on only one function of energy; 2. the ratios of the down quark masses depend on the energy through the same function as the CKM matrix; 3. the diagonalizing matrices of the biunitary t…
Based on the present data, the three CKM angles may construct a spherical surface triangle whose area automatically provides a "holonomy" phase. By assuming this geometrical phase to be that in the CKM matrix determined by an unknown hidden symmetry, we compare the theoretical prediction on $ε$ with data and find they are consistent within error range. We also suggest restrictions for the Wolfenstein parameters explicitly, the agreement will be tested by more precise measurements in the future. At least we can claim that such geometrical phase should be part of the weak phase appearing in the …
An up-to-date profile of the CKM matrix is presented, with emphasis on the interpretation of recent CP-violation results from the $B$ factories. The apex of the Unitarity Triangle is determined by a global CKM fit. A study is performed to probe the dynamics of B decays into $ππ$, $Kπ$, $ρπ$ and $ρρ$ within two theoretical frameworks. A model-independent investigation of New Physics effects in $\Bz\Bzb$ mixing is given.
We explore the unitarity violation of the CKM matrix in the model in which the third generation fermions are subjected to the separate SU(2)$_L$ gauge interaction. With the recent LEP and SLC data at $Z$-pole and low-energy neutral current interaction data, the analysis on the parameter space of the model is updated, and the unitary violation is predicted under the constraint.
In the context of the supersymmetric unification model in which the massless sector contains extra particles beyond those in the minimal supersymmetric standard model, we obtain mixings between quarks (leptons) and the extra particles which are closely intertwined with Yukawa hierarchies. With the assumption that the unification gauge group $G$ includes $SU(2)_R$, it is shown that the non-trivial texture of the CKM matrix originates from the extra-particle mixings. The CKM matrix of quarks emerges as a consequence of the mixings between the down-type quarks and colored Higgses, both of which a…
The paper is devoted to a discussion of general properties of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. First we propose a general method of a recursive construction of the CKM matrix for any number of generations. This allows to set up a parameterization with desired properties. As an application we generalize the Wolfenstein parameterization to the case of 4 generations and obtain restrictions on the CKM suppression of the fourth generation. Motivated by the rephasing invariance of the CKM observables we next consider the general phase invariant monomials built out of the CKM matrix elemen…
This paper has been withdrawn by the authors, and instead we have replaced hep-ph/9807214 by this new version.
The maximal CP violation hypothesis depends on the phase convention of the Cabibbo-Kobayashi-Maskawa matrix. A phase convention which leads to successful prediction under the maximal CP violation hypothesis is searched, and thereby, possible structures of the quark mass matrices are speculated.
We argue that a Tau-Charm factory (TCF) could improve our knowledge of CKM matrix elements since it is an incomparable tool to check the models and methods applied to extract $V_{bu}$ from $B$ decay partial widths. We report on some recent proposals to improve on parton model. Turning to exclusive decays, we compare the predictions from quark models, QCD sum rules, effective Lagrangians and lattice QCD. Quark models have anticipated on heavy quark symmetry. Their difficutly to account for the $q^2$ dependence might be partly cured by relativistic corrections. QCD sum rules and lattice seem to …
We estimate the CKM matrix elements in the recently proposed minimal model, anti-SU(7) GUT for the family unification, $[\,3\,]+2\,[\,2\,]+8\,[\,\bar{1}\,]$+\,(singlets). It is shown that the real angles of the right-handed unitary matrix diagonalizing the mass matrix can be determined to fit the Particle Data Group data. However, the phase in the right-handed unitary matrix is not constrained very much. We also includes an argument about allocating the Jarlskog phase in the CKM matrix. Phenomenologically, there are three classes of possible parametrizations, $\delq=α,β,$ or $γ$ of the unitari…
The unitarity of the CKM matrix is examined in the light of the latest available accurate data. The analysis shows that for the elements in the first row, there are two types of experimental measurements leading to different results for the violation of unitarity. A conclusive result cannot be derived at present. Only more precise data can determine whether the CKM matrix opens new vistas beyond the standard model or not. The experimental data for the elements in the second row are not as precise as for those in the first row, and within the measured uncertainty, the unitarity is not violated.…
We report on a new method to a global fit of the CKM matrix by using the necessary and sufficient condition the data have to satisfy in order to find a unitary matrix compatible with them. This condition writes as $-1\le \cosϕ\le 1$ where $ϕ$ is the phase that accounts for CP violation. By using it we get that the experimental data are to a high degree compatible to unitarity and that $ϕ$ takes values around $90^0$, in contrast to the previous determinations. Numerical results are provided for the CKM matrix entries, the mixing angles between generations and all the angles of the standard unit…
The unitarity triangles of the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM) matrix are studied in a systematic way. We show that the phases of the nine CKM rephasing invariants are indeed the outer angles of the six unitarity triangles and measurable in the $CP$-violating decay modes of $B_{d}$ and $B_{s}$ mesons. An economical notation system is introduced for describing properties of the unitarity triangles. To test unitarity of the CKM matrix we present some approximate but useful relations among the sides and angles of the unitarity triangles, which can be confronted with the accessible exp…
These lectures give an introduction and the current status of flavour physics in the quark sector, with special attention to the CKM matrix and CP violation. We describe the measurements which contribute to the determination of the CKM matrix elements and how, together with important theoretical developments, they have significantly improved our knowledge on the flavour sector of the Standard Model. These lectures are complemented by the seminar of U. Mallik (see these proceedings) which describes in more details the most recent CP-violating related measurements by the B-factories. The results…
A shape of the unitary triangle versus a CP violating parameter δdepends on the phase conventions of the CKM matrix, because the CP violating parameter δcannot directly be observed, so that it is not rephasing-invariant. In order to seek for a clue to the quark mass matrix structure and the origin of the CP violation, the dependence of the unitary triangle shape on the parameter δis systematically investigated.
We derive the two-loop evolution equations for the Cabibbo-Kobayashi-Maskawa matrix. We show that to leading order in the mass and CKM hierarchies the scaling of the mixings $|V_{ub}|^2$, $|V_{cb}|^2$, $|V_{td}|^2$, $|V_{ts}|^2$ and of the rephase-invariant CP-violating parameter $J$ is universal to all orders in perturbation theory. In leading order the other CKM elements do not scale. Imposing the constraint $λ_b=λ_τ$ at the GUT scale determines the CKM scaling factor to be $\simeq 0.58$ in the MSSM.
We compute the renormalization of the complete CKM matrix in the MSbar scheme and perform a renormalization group analysis of the CKM parameters. The calculation is simplified by studying only the Higgs sector, which for the β-function of the CKM matrix is at one loop the same as in the full Standard Model. The renormalization group flow including QCD corrections can be computed analytically using the hierarchy of the CKM parameters and the large mass differences between the quarks. While the evolution of the Cabibbo angle is tiny V_{ub} and V_{cb} increase sizably. We compare our results with…
A simple inspection of the one loop quark self-energy suggests a prescription of the CKM matrix renormalization in the standard model. It leads to a CKM matrix counterterm which is gauge parameter independent and satisfies the unitarity constraint, and renormalized physical amplitudes which are gauge parameter independent and smooth in quark mass difference. We make a point that caution should be practiced when interpreting the CKM martix counterterm in terms of those of parameters in a given representation due to rephasing effects from renormalization. We show how this can be done using the d…
We argue that in dynamical models of fermion masses, which explain the three mass scales of the generations of fermions with three separate heavy scales above the electroweak symmetry breaking scale, the off diagonal CKM matrix elements must be generated at a fourth scale. The simplest form for the additional mass generation is a mechanism that has an $SU(3)_L \otimes SU(3)_R$ family symmetry. We show that such an ansatz can produce the up down mass inversion and the observed Cabibbo angle. If the mass terms for the third family quarks are enhanced by additional interactions the full CKM matri…
The CKM matrix is not generic. The Wolfenstein parametrization encodes structure by having one small parameter, $λ\approx 0.22$. We pose the question: is there substructure in the CKM matrix that goes beyond the single small parameter of the Wolfenstein parameterization? We find two relations that are approximately satisfied: $|V_{td}|^2 = |V_{cb}|^3$ and $|V_{ub}|^2 |V_{us}| = |V_{cb}|^4$. We discuss the statistical significance of these relations and find that they may indicate deeper structure in the CKM matrix. The current precision, however, cannot exclude an $\mathcal{O}(10 \%)$ accident…
We discuss the problem of theoretical uncertainties in the combination of observables related to the CKM matrix elements and propose a statistically sensible method for combining them. The overall fit is performed on present data, and constraints on the matrix elements are presented as well as on fB*sqrt(Bb). We then explore the implications of recent measurements and developments: jpsi-KS CP asymmetry, epsilon_prime/epsilon and B -> K pi branching fractions. Finally, we extract from the overall fit the Standard Model expectations for the rare kaon decays K -> pi nu anti-nu.
We show that it is now possible to fully determine the CKM matrix, for the first time, using lattice QCD. |V_{cd}|, |V_{cs}|, |V_{ub}|, |V_{cb}| and |V_{us}| are, respectively, directly determined with our lattice results for form factors of semileptonic D->pi l nu, D->K l nu, B->pi l nu, B->D l nu, and K->pi l nu decays. The error from the quenched approximation is removed by using the MILC unquenched lattice gauge configurations, where the effect of u,d and s quarks is included. The error from the ``chiral'' extrapolation (m_l->m_{ud}) is greatly reduced by using improved staggered quarks. T…
I review the current status of our knowledge of CP violation and flavor physics. I discuss where one should look for future improvements, and outline the experimental and theoretical priorities of the field.
I shall present a pedagogical discussion of hyperon semileptonic decays, covering some of the historical background, the basics notions of hyperon semileptonic decays, deeply inelastic scattering and the CKM matrix, and the description of SU(2) and SU(3) breaking. I shall also present a prediction for a process under current experimental study.
Parity nonconservation led Lee and Yang (1956) to the hypothesis of additional fermions with properties that mirror those of usual particles. It is shown here that the well-known observed qualitative structure of the quark mixing matrix (CKM matrix) is precisely reproduced when usual quark mass hierarchies result from mass hierarchies of heavy mirror generations. The last ones are of the Lee--Yang type only. The usual quark spectrum is formed likewise the see--saw spectrum of the neutrino physics. The lightest mirror quark is closely related with the t quark and might be available even in a re…
We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix. When considering the prescription which is formulated with reference to the case of zero mixing we find it doesn't satisfy the unitary condition of the bare CKM matrix. After added a delicate patch this problem can be solved at one-loop level. In this paper We generalize this prescription to all loop levels and keep the unitarity of the bare CKM matrix, simultaneously make the amplitude of an arbitrary physical process involving quark mixing convergent and gauge independent. We also find t…
We evaluate the finite 1-loop threshold corrections, proportional to $tanβ$, to the down quark mass matrix. These result in corrections to down quark masses and to Cabibbo-Kobayashi-Maskawa [CKM] matrix elements. The corrections to CKM matrix elements are the novel feature of this paper. For grand unified theories with large $\tanβ$ these corrections may significantly alter the low energy predictions of four of the CKM matrix elements and the Jarlskog parameter J, a measure of CP violation. The angles $α,\: β$ and $γ$ of the unitarity triangle and the ratio $|{V_{ub} \over V_{cb}}|$, however, …
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。