Cabibbo-Kobayashi-Maskawa Elements Research Articles

Constraining new physics with possible dark matter signatures from a global CKM fit

We constrain the parameters of a representative new physics model with a possible dark matter (DM) signature from a global Cabibbo-Kobayashi-Maskawa (CKM) fit analysis. The model has neutral quark current interactions mediated by a scalar, impacting the semileptonic and purely leptonic meson decays at one loop. We take this opportunity to update the fit results for the Wolfenstein parameters and the CKM elements with and without a contribution from the new model using several other updated inputs. In addition, we analyze and include the $B\ensuremath{\rightarrow}{D}^{*}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ decay in the CKM fit. The newly available inputs on the relevant form factors from lattice calculations are included, and the possibility of new physics effects in $B\ensuremath{\rightarrow}{D}^{*}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ is considered. We obtain tight constraints on the relevant new physics parameters. We study the possible implications of this constraint on DM phenomenology. Apart from DM, the bounds are also applicable in other relevant phenomenological studies.

Precision measurement of the W boson decay branching fractions in proton-proton collisions at s=13 TeV

The leptonic and inclusive hadronic decay branching fractions of the W boson are measured using proton-proton collision data collected at s=13 TeV by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of 35.9 fb−1. Events characterized by the production of one or two W bosons are selected and categorized based on the multiplicity and flavor of reconstructed leptons, the number of jets, and the number of jets identified as originating from the hadronization of b quarks. A binned maximum likelihood estimate of the W boson branching fractions is performed simultaneously in each event category. The measured branching fractions of the W boson decaying into electron, muon, and tau lepton final states are (10.83±0.10)%, (10.94±0.08)%, and (10.77±0.21)%, respectively, consistent with lepton flavor universality for the weak interaction. The average leptonic and inclusive hadronic decay branching fractions are estimated to be (10.89±0.08)% and (67.32±0.23)%, respectively. Based on the hadronic branching fraction, three standard model quantities are subsequently derived: the sum of squared elements in the first two rows of the Cabibbo–Kobayashi–Maskawa (CKM) matrix ∑ij|Vij|2=1.984±0.021, the CKM element |Vcs|=0.967±0.011, and the strong coupling constant at the W boson mass scale, αS(mW2)=0.095±0.033.2 MoreReceived 19 January 2022Accepted 28 February 2022DOI:https://doi.org/10.1103/PhysRevD.105.072008Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.© 2022 CERN, for the CMS CollaborationPhysics Subject Headings (PhySH)Physical SystemsW & Z bosonsTechniquesHadron collidersParticles & Fields

Effective theory analysis for vector-like quark model

We study a model with a down-type SU(2) singlet vector-like quark (VLQ) as a minimal extension of the standard model (SM). In this model, flavor changing neutral currents (FCNCs) arise at tree level and the unitarity of the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM) matrix does not hold. In this paper, we constrain the FCNC coupling from $b\rightarrow s$ transitions, especially $B_s\rightarrow \mu^+\mu^-$ and $\bar{B}\rightarrow X_s\gamma$ processes. In order to analyze these processes, we derive an effective Lagrangian which is valid below the electroweak symmetry breaking scale. For this purpose, we first integrate out the VLQ field and derive an effective theory by matching Wilson coefficients up to one-loop level. Using the effective theory, we construct the effective Lagrangian for $b\rightarrow s\gamma^{(*)}$. It includes the effects of the SM quarks and the violation of the CKM unitarity. We show the constraints on the magnitude of the FCNC coupling and its phase by taking account of the current experimental data on $\Delta M_{B_s}$, $\mathrm{Br}[B_s\rightarrow\mu^+\mu^-]$, $\mathrm{Br}[\bar{B}\rightarrow X_s\gamma]$ and CKM matrix elements as well as theoretical uncertainties. We find that the constraint from the $\mathrm{Br}[B_s\rightarrow\mu^+\mu^-]$ is more stringent than that from the $\mathrm{Br}[\bar{B}\rightarrow X_s\gamma$]. We also obtain the bound for the mass of the VLQ and the strength of the Yukawa couplings related to the FCNC coupling of $b\rightarrow s$ transition. Using the CKM elements which satisfy above constraints, we show how the unitarity is violated on the complex plane.

Measurement of the inclusive electron spectrum from B meson decays and determination of |Vub|

Based on the full BaBar data sample of 466.5 million BBbar pairs, we present measurements of the electron spectrum from semileptonic B meson decays. We fit the inclusive electron spectrum to distinguish Cabibbo-Kobayashi-Maskawa (CKM) suppressed B -> Xu e nu decays from the CKM-favored B -> Xc e nu decays, and from various other backgrounds, and determine the total semileptonic branching fraction BR(B -> X e nu) = (10.34 +- 0.04_stat +- 0.26_syst)%, averaged over B+- and B0 mesons. We determine the spectrum and branching fraction for charmless B -> Xu e nu decays and extract the CKM element |Vub|, by relying on four different QCD calculations based on the heavy quark expansion. While experimentally, the electron momentum region above 2.1GeV/c is favored, because the background is relatively low, the uncertainties for the theoretical predictions are largest in the region near the kinematic endpoint. Detailed studies to assess the impact of these four predictions on the measurements of the electron spectrum, the branching fraction, and the extraction of the CKM matrix element |Vub| are presented, with the lower limit on the electron momentum varied from 0.8GeV/c to the kinematic endpoint. We determine |Vub| using each of these different calculations and find, |Vub| = (3.794 +- 0.107_exp +0.292-0.219_SF +0.078-0.068_theory)*10^{-3} (De Fazio and Neubert), (4.563 +- 0.126_exp +0.230-0.208_SF +0.162-0.163_theory)*10^{-3} (Bosh, Lange, Neubert, and Paz), (3.959 +- 0.104_exp +0.164-0.154_SF +0.042-0.079_theory)*10^{-3} (Gambino, Giordano, Ossola, and Uraltsev), (3.848 +- 0.108_exp +0.084-0.070_theory)*10^{-3} (dressed gluon exponentiation), where the stated uncertainties refer to the experimental uncertainties of the partial branching fraction measurement, the shape function parameters, and the theoretical calculations.

αs and |Vcs| determination, and CKM unitarity test, from W decays at NNLO

The hadronic ($\Gamma^{\rm W}_{\rm had}$) and total ($\Gamma^{\rm W}_{\rm tot}$) widths of the W boson, computed at least at next-to-next-to-leading-order (NNLO) accuracy, are combined to derive a new precise prediction for the hadronic W branching ratio ${\cal B}^{\rm W}_{\rm had} \equiv \Gamma^{\rm W}_{\rm had}/\Gamma^{\rm W}_{\rm tot}$ = $0.682 \pm 0.011_{\rm par}$, using the experimental Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, or ${\cal B}^{\rm W}_{\rm had} = 0.6742 \pm 0.0002_{\rm th} \pm 0.0001_{\rm par}$ assuming CKM unitarity, with uncertainties dominated by the input parameters of the calculations. Comparing the theoretical predictions and experimental measurements for various W decay observables, the NNLO strong coupling constant at the Z pole, $\alpha_s(m_Z) = 0.117 \pm 0.042_{\rm exp} \pm 0.004_{\rm th} \pm 0.001_{\rm par}$, as well as the charm-strange CKM element, $\rm V_{cs}$ = 0.973 $\pm$ 0.004$_{\rm exp}$ $\pm$ 0.002$_{\rm par}$, can be extracted under different assumptions. We also show that W decays provide today the most precise test of CKM unitarity for the 5 quarks lighter than $m_{\rm W}$, $\sum_{ u,c,d,s,b} |V_{ ij}|^2 = 1.999 \pm 0.008_{\rm exp} \pm 0.001_{\rm th}$. Perspectives for $\alpha_s$ and $\rm V_{cs}$ extractions from W decays measurements at the LHC and future $e^+e^-$ colliders are presented.

Study ofB¯→Xuℓν¯decays inBB¯events tagged by a fully reconstructedB-meson decay and determination of|Vub|

We report measurements of partial branching fractions for inclusive charmless semileptonic B decays B¯→Xuℓν¯ and the determination of the Cabibbo–Kobayashi–Maskawa (CKM) matrix element |Vub|. The analysis is based on a sample of 467×106 Υ(4S)→BB¯ decays recorded with the BABAR detector at the PEP-II e+e− storage rings. We select events in which the decay of one of the B mesons is fully reconstructed and an electron or a muon signals the semileptonic decay of the other B meson. We measure partial branching fractions ΔB in several restricted regions of phase space and determine the CKM element |Vub| based on different QCD predictions. For decays with a charged lepton momentum pℓ*>1.0 GeV in the B meson rest frame, we obtain ΔB=(1.80±0.13stat±0.15sys±0.02theo)×10−3 from a fit to the two-dimensional MX−q2 distribution. Here, MX refers to the invariant mass of the final state hadron X and q2 is the invariant mass squared of the charged lepton and neutrino. From this measurement we extract |Vub|=(4.33±0.24exp±0.15theo)×10−3 as the arithmetic average of four results obtained from four different QCD predictions of the partial rate. We separately determine partial branching fractions for B¯0 and B− decays and derive a limit on the isospin breaking in B¯→Xuℓν¯ decays.2 MoreReceived 5 December 2011DOI:https://doi.org/10.1103/PhysRevD.86.032004© 2012 American Physical Society

Supersymmetric renormalization of the CKM matrix and new constraints on the squark mass matrices

We compute the finite renormalisation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix induced by gluino-squark diagrams in the MSSM with non-minimal sources of flavour violation. Subsequently we derive bounds on the flavour-off-diagonal elements of the squark mass matrices by requiring that the radiative corrections to the CKM elements do not exceed the experimental values. Our constraints on the associated dimensionless quantities delta^{d LR}_{ij}, j>i, are stronger than the bounds from flavour-changing neutral current (FCNC) processes if gluino and squarks are heavier than 500 GeV. Our bound on |delta^{u LR}_{12}| is stronger than the FCNC bound from D-D-bar mixing for superpartner masses above 900 GeV. We further find a useful bound on |delta_{13}^{u LR}|, for which no FCNC constraint is known. Our results imply that it is still possible to generate all observed flavour violation from the soft supersymmetry-breaking terms without conflicting with present-day data on FCNC processes. We suggest that a flavour symmetry renders the Yukawa sector flavour-diagonal and the trilinear supersymmetry-breaking terms are the spurion fields breaking this flavour symmetry. We further derive the dominant supersymmetric radiative corrections to the couplings of charged Higgs bosons and charginos to quarks and squarks.

CP violation due to multi-Froggatt–Nielsen fields

We study how to incorporate CP violation in the Froggatt–Nielsen (FN) mechanism. To this end, we introduce non-renormalizable interactions with a flavor democratic structure to the fermion mass generation sector. It is found that at least two iso-singlet scalar fields with a discrete symmetry imposed are necessary to generate CP violation due to the appearance of the relative phase between their vacuum expectation values. In the simplest model, the ratios of quark masses and the Cabibbo–Kobayashi–Maskawa (CKM) matrix including the CP violating phase are determined by the CKM element |Vus| and the ratio of two vacuum expectation values of FN fields, R=|R|eiα (a magnitude and a phase). It is demonstrated how the angles φi (i=1,...,3) of the unitarity triangle and the CKM off-diagonal elements |Vub| and |Vcb| are predicted as a function of |Vus|, |R| and α. Although the predicted value of the CP violating phase does not agree with the experimental data within the simplest model, the basic idea of our scenario would be promising if one wants to construct a more realistic model of flavor and CP violation.

QUARK MIXING AND CP VIOLATION — THE CKM MATRIX

I summarize the theoretical progress in the determination of the CKM elements since Lepton-Photon 2003 and present the status of the elements and parameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. One finds |Vus| = 0.2227 ± 0.0017 from K and τ decays and |Vcb| = (41.6 ± 0.5) · 10-3 from inclusive semileptonic B decays. The unitarity triangle can now be determined from tree-level quantities alone and the result agrees well with the global fit including flavour-changing neutral current (FCNC) processes, which are sensitive to new physics. From the global fit one finds the three CKM angles θ12 = 12.9° ± 0.1°, θ23 = 2.38° ± 0.03° and θ13 = 0.223° ± 0.007° in the standard PDG convention. The CP phase equals [Formula: see text] at 1σ CL and [Formula: see text] at 2σ CL. A major progress are first results from fully unquenched lattice QCD computations for the hadronic quantities entering the UT fit. I further present the calculation of three-loop QCD corrections to the charm contribution in [Formula: see text] decays, which removes the last relevant theoretical uncertainty from the [Formula: see text] system. Finally I discuss mixing-induced CP asymmetries in [Formula: see text] penguin decays, whose naive average is below its Standard Model value by 3σ.

Solving the supersymmetricCPproblem with flavor breakingFterms

Supersymmetric flavor models for the radiative generation of fermion masses offer an alternative way to solve the SUSY-$CP$ problem. We assume that the supersymmetric theory is flavor and $CP$ conserving. $CP$ violating phases are associated to the vacuum expectation values of flavor violating SUSY-breaking fields. As a consequence, phases appear at tree level only in the soft supersymmetry-breaking matrices. Using a U(2) flavor model as an example we show that it is possible to generate radiatively the first and second generation of quark masses and mixings as well as the Cabibbo-Kobayashi-Maskawa (CKM) $CP$ phase. The one-loop supersymmetric contributions to electric dipole moments are automatically zero since all the relevant parameters in the Lagrangian are flavor conserving and as a consequence real. The size of the flavor and $CP$ mixing in the SUSY-breaking sector is mostly determined by the fermion mass ratios and CKM elements. We calculate the contributions to $ϵ$, ${ϵ}^{\ensuremath{'}}$ and to the $CP$ asymmetries in the $B$ decays to $\ensuremath{\psi}{K}_{s}$, $\ensuremath{\phi}{K}_{s}$, ${\ensuremath{\eta}}^{\ensuremath{'}}{K}_{s}$ and ${X}_{s}\ensuremath{\gamma}$. We analyze a case study with maximal predictivity in the fermion sector. For this worst case scenario the measurements of $\ensuremath{\Delta}{m}_{K}$, $\ensuremath{\Delta}{m}_{B}$ and $ϵ$ constrain the model requiring extremely heavy squark spectra.

Comments on CKM elements

The sensitivity of determination of elements of the Cabibbo–Kobayashi–Maskawa (CKM) matrix to experimental inputs (particularly | V cb|) is discussed and caution in assigning probable errors is urged.

Present knowledge of the Cabibbo-Kobayashi-Maskawa matrix

A complete review of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and of the experimental methods for their determination is presented. A critical analysis of the relevant experimental results, and in particular of the most recent ones, allows to improve the accuracies of all the matrix elements. A chi-square minimization with the three-family unitarity constraint on the CKM matrix is performed to test the current interpretation of the CP violating phenomena inside the Standard Model. A complete and unambiguous solution satisfying all the imposed constraints is found. As a by-product of the fit, the precision on the values of the matrix elements is further increased and it is possible to obtain estimates for the important CP violation observables $sin 2\beta$, $sin 2\alpha$ and $\gamma$. Finally, an independent estimation of the CKM elements based on a Bayesian approach is performed. This complementary method constitutes a check of the results obtained, providing also the probability functions of the CKM elements and of the related quantities.

B physics – a theoretical review

This overview of what we can hope to learn from high-statistics experiments in B physics in the next few years includes (a) a review of parameters of the Cabibbo–Kobayashi–Maskawa (CKM) matrix; (b) direct determination of magnitudes of CKM elements; (c) forthcoming information from studies of kaons; (d) CP violation in B decays; (e) aspects of rate measurements; (f) the role of charm–anticharm annihilation; (g) remarks on tagging; and (h) effects beyond the standard model.