Cabibbo-Kobayashi-Maskawa Unitarity Research Articles

Ratio of kaon and pion leptonic decay constants with Nf=2+1+1 Wilson-clover twisted-mass fermions

We present a determination of the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (isoQCD), $f_K / f_\pi$, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks, including configurations close to the physical point for all dynamical flavors. The simulations are carried out at three values of the lattice spacing ranging from $\sim 0.068$ to $\sim 0.092$ fm with linear lattice size up to $L \sim 5.5$~fm. The scale is set by the PDG value of the pion decay constant, $f_\pi^{isoQCD} = 130.4~(2)$ MeV, at the isoQCD pion point, $M_\pi^{isoQCD} = 135.0~(2)$ MeV, obtaining for the gradient-flow (GF) scales the values $w_0 = 0.17383~(63)$ fm, $\sqrt{t_0} = 0.14436~(61)$ fm and $t_0 / w_0 = 0.11969~(62)$ fm. The data are analyzed within the framework of SU(2) Chiral Perturbation Theory (ChPT) without resorting to the use of renormalized quark masses. At the isoQCD kaon point $M_K^{isoQCD} = 494.2~(4)$ MeV we get $(f_K / f_\pi)^{isoQCD} = 1.1995~(44)$, where the error includes both statistical and systematic uncertainties. Implications for the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{us}|$ and for the first-row CKM unitarity are discussed.

Measurement of CKM matrix elements in single top quark t-channel production in proton-proton collisions at [formula omitted

The first direct, model-independent measurement is presented of the modulus of the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements |η|Vtb, |η|Vtd, and |η|Vts, in final states enriched in single top quark t-channel events. The analysis uses proton-proton collision data from the LHC, collected during 2016 by the CMS experiment, at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb−1. Processes directly sensitive to these matrix elements are considered at both the production and decay vertices of the top quark. In the standard model hypothesis of CKM unitarity, a lower limit of |η|Vtb>0.970 is measured at the 95% confidence level. Several theories beyond the standard model are considered, and by releasing all constraints among the involved parameters, the values |η|Vtb=0.988±0.024, and |η|Vtd2+|η|Vts2=0.06±0.06, where the uncertainties include both statistical and systematic components, are measured.

On the statistical treatment of the Cabibbo angle anomaly

We point out that testing the equality of the Cabibbo angle as extracted from Γ(K → πlν), the ratio Γ(K → lν)/Γ(π → lν) and nuclear β decays is not identical to a test of first row unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. The reason is that a CKM unitarity test involves only two parameters, while the degrees of freedom for the assessment of the goodness-of-fit of the universality of the Cabibbo angle entailed by the Standard Model (SM) is equal to the number of measurements minus one. Beyond the SM all different processes could in principle give different Cabibbo angles. Consequently, the difference between the two tests becomes relevant starting from three observables giving results for the Cabibbo angle that are in tension with each other. With current data, depending on the treatment of the nuclear β decays, we find that New Physics is favored over the SM at 5.1 σ or 3.6 σ while CKM unitarity is rejected at 4.8σ or 3.0σ, respectively. We argue that the best method to test the SM is to test the equality of the Cabibbo angle, because CKM unitarity is only one aspect of the SM.

Vector-like quark interpretation for the CKM unitarity violation, excess in Higgs signal strength, and bottom quark forward-backward asymmetry

Due to a recent more precise evaluation of Vud and Vus, the unitarity condition of the first row in the Cabibbo-Kobayashi-Maskawa (CKM) matrix: |Vud|2 +|Vus|2 +|Vub|2 = 0.99798 ± 0.00038 now stands at a deviation more than 4σ from unity. Furthermore, a mild excess in the overall Higgs signal strength appears at about 2σ above the standard model (SM) prediction, as well as the long-lasting discrepancy in the forward-backward asymmetry {mathcal{A}}_{mathrm{FB}}^b in Zto boverline{b} at LEP. Motivated from the above three anomalies we investigate an extension of the SM with vector-like quarks (VLQs) associated with the down-quark sector, with the goal of alleviating the tension among these datasets. We perform global fits of the model under the constraints coming from the unitarity condition of the first row of the CKM matrix, the Z -pole observables {mathcal{A}}_{mathrm{FB}}^b , Rb and Γhad, Electro-Weak precision observables ∆S and ∆T , B-meson observables {B}_d^0-{overline{B}}_d^0 mixing, B+→ π+ℓ+ℓ− and B0→ μ+μ− and direct searches for VLQs at the Large Hadron Collider (LHC). Our results suggest that adding VLQs to the SM provides better agreement than the SM.

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.

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.

Superallowed0+→0+nuclearβdecays: 2014 critical survey, with precise results forVudand CKM unitarity

A new critical survey is presented of all half-life, decay-energy and branching-ratio measurements related to 20 superallowed 0+ --> 0+ beta decays. Included are 222 individual measurements of comparable precision obtained from 177 published references. Compared with our last review in 2008, we have added results from 24 new publications and eliminated 9 references, the results from which having been superseded by much more precise modern data. We obtain world-average ft-values for each of the eighteen transitions that have a complete set of data, then apply radiative and isospin-symmetry-breaking corrections to extract corrected Ft values. Fourteen of these Ft values now have a precision of order 0.1% or better. In the process of obtaining these results we carefully evaluate the available calculations of the isospin-symmetry-breaking corrections by testing the extent to which they lead to Ft values consistent with conservation of the vector current (CVC). Only one set of calculations satisfactorily meets this condition. The resultant average Ft value, when combined with the muon liftime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, Vud = 0.97417 +/- 0.00021. The unitarity test on the top row of the matrix becomes |Vud|^2 + |Vus|^2 + |Vub|^2 = 0.99978 +/- 0.00055 if the Particle Data Group recommended value for Vus is used. However, recent lattice QCD calculations, not included yet in the PDG evaluation, have introduced some inconsistency into kaon-decay measurements of Vus and Vus/Vud. We examine the impact of these new results on the unitarity test and conclude that there is no evidence of any statistically significant violation of unitarity. Finally, from the Ft-value data we also set limits on the possible existence of scalar interactions.

Testing CVC and CKM Unitarity via superallowed nuclear beta decay

Currently, the most restrictive test of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is anchored by nuclear beta decay. Precise measurements of the ft-values for superallowed beta transitions between analog 0+ states are used to determine GV, the vector coupling constant; this, in turn, yields Vud, the up-down quark-mixing element of the CKM matrix. The determination of a transition’s ft-value requires the measurement of three quantities: its Q value, branching ratio and parent half-life. To achieve 0.1% precision on the final result, each of these quantities must be measured to substantially better precision, for which special techniques have had to be developed. A new survey and analysis of world data reveals that there are now fourteen such transitions with ft-values known to ∼ 0.1% precision or better, and that they span a wide range of nuclear masses, from 10C, the lightest parent, to 74Rb, the heaviest. Of particular interest is the recent completion of the first mirror pair of 0+ → 0+ transitions, 38Ca → 38mK and 38mK → 38Ar, which provides a valuable constraint on the calculated isospin-symmetry-breaking corrections needed to derive GV from the experimental data. As anticipated by the Conserved Vector Current hypothesis, CVC, all fourteen transitions yield consistent values for GV. The value of Vud derived from their average makes it by far the most precisely known element of the CKM matrix, which, when combined with the other top-row elements, Vus and Vub, leads to the most demanding test available of the unitarity of that matrix. Since CKM unitarity is a key pillar of the Electroweak Standard Model, this test is of fundamental significance.

βDecay ofCa38: Sensitive test of Isospin Symmetry-Breaking Corrections from Mirror Superallowed0+→0+Transitions

We report the first branching-ratio measurement of the superallowed 0+→0+β transition from Ca38. The result, 0.7728(16), leads to an ft value of 3062.3(68)s with a relative precision of ±0.2%. This makes possible a high-precision comparison of the ft values for the mirror superallowed transitions, Ca38→38mK and K38m→Ar38, which sensitively tests the isospin symmetry-breaking corrections required to extract Vud, the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, from superallowed β decay. The result supports the corrections currently used and points the way to even tighter constraints on CKM unitarity.

CKM unitarity normalization tests, present and future

The Cabibbo‐Kobayashi‐Maskawa (CKM) quark‐mixing matrix is a central pillar of the Electroweak Standard Model. The elements of the matrix must be determined from experiment, but the Model requires the matrix itself to be unitary. Any deviation from unitarity would signal the presence of “new physics” beyond the Standard Model, so tests of CKM unitarity have attracted considerable attention. Currently the most precise test is of the normalization of the top row, which has now reached a precision of 0.06% based on measurements of superallowed 0+ nuclear β decay and of kaon semileptonic and leptonic decays. This work overviews the status of the normalization tests and speculates on likely future improvements.

High-precision atomic mass measurements for a CKM unitarity test

The Cabibbo–Kobayashi–Maskawa (CKM) quark-mixing matrix describes the transformation of quarks from weak-force eigenstates to mass eigenstates. The most contributing element in this matrix is the up-down matrix element Vud, derived in most precise way from the nuclear beta decays and in particular, from decays having superallowed 0+→0+ decay branch. What high-precision mass spectrometry community can offer are decay energies of such decays derived from parent–daughter mass differences, which are ideally, and in almost all cases, determined with Penning trap mass spectrometry directly from parent–daughter cyclotron frequency ratio. Typically frequency (and thus mass) ratios are determined with 10−9 relative precision, which allows decay energies to be determined within 100eV-level.

Superallowed nuclear β decay: symmetry breaking, CVC and CKM unitarity

Currently, the most restrictive test of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is anchored by nuclear beta decay. Precise measurements of the ft-values for superallowed beta transitions between analog 0 + states are used to determine G V , the vector coupling constant; this, in turn, yields V u d , the up-down element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. When the value for V u d obtained from the latest survey of world data is combined with V u s and V u b , the other top-row elements, it leads to the most demanding test available of the unitarity of that matrix. Important ingredients required in the extraction of V u d from experiment are calculated radiative corrections as well as corrections to account for the isospin symmetry breaking that occurs between the analog parent and daughter states of each superallowed transition. The latter are well supported by comparison with experiment. The current value for the unitarity sum is 0.99995(61), a result that is in remarkable agreement with Standard Model expectations.

Update on angles and sides of the CKM unitarity triangle from BABAR

We report several recent updates from the BABAR Collaboration on the matrix elements | V c b | , | V u b | , and | V t d | of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix, and the angles β and α of the unitarity triangle. Most results presented here are using the full BABAR ϒ ( 4 S ) data set.

Superallowed0+→0+nuclearβdecays: A new survey with precision tests of the conserved vector current hypothesis and the standard model

A new critical survey is presented of all half-life, decay-energy, and branching-ratio measurements related to 20 superallowed ${0}^{+}\ensuremath{\rightarrow}{0}^{+}\ensuremath{\beta}$ decays. Compared with our last review, there are numerous improvements: First, we have added 27 recently published measurements and eliminated 9 references, either because they have been superseded by much more precise modern results or because there are now reasons to consider them fatally flawed; of particular importance, the new data include a number of high-precision Penning-trap measurements of decay energies. Second, we have used the recently improved isospin symmetry-breaking corrections, which were motivated by these new Penning-trap results. Third, our calculation of the statistical rate function $f$ now accounts for possible excitation in the daughter atom, a small effect but one that merits inclusion at the present level of experimental precision. Finally, we have re-examined the systematic uncertainty associated with the isospin symmetry-breaking corrections by evaluating the radial-overlap correction using Hartree-Fock radial wave functions and comparing the results with our earlier calculations, which used Saxon-Woods wave functions; the provision for systematic uncertainty has been changed as a consequence. The new ``corrected'' $\mathcal{F}t$ values are impressively constant and their average, when combined with the muon lifetime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, ${V}_{\mathit{ud}}=0.97425\ifmmode\pm\else\textpm\fi{}0.00022$. The unitarity test on the top row of the matrix becomes $|{V}_{\mathit{ud}}|{}^{2}+|{V}_{\mathit{us}}|{}^{2}+|{V}_{\mathit{ub}}|{}^{2}=0.99995\ifmmode\pm\else\textpm\fi{}0.00061$. Both ${V}_{\mathit{ud}}$ and the unitarity sum have significantly reduced uncertainties compared with our previous survey, although the new value of ${V}_{\mathit{ud}}$ is statistically consistent with the old one. From these data we also set limits on the possible existence of scalar interactions, right-hand currents, and extra $Z$ bosons. Finally, we discuss the priorities for future theoretical and experimental work with the goal of making the CKM unitarity test even more definitive.

Vector form factor inKl3semileptonic decay with two flavors of dynamical domain-wall quarks

We calculate the vector form factor in K{yields}{pi}l{nu} semileptonic decays at zero momentum transfer f{sub +}(0) from numerical simulations of two-flavor QCD on the lattice. Our simulations are carried out on 16{sup 3}x32 at a lattice spacing of a{approx_equal}0.12 fm using a combination of the DBW2 gauge and the domain-wall quark actions, which possesses excellent chiral symmetry even at finite lattice spacings. The size of fifth dimension is set to L{sub s}=12, which leads to a residual quark mass of a few MeV. Through a set of double ratios of correlation functions, the form factor calculated on the lattice is accurately interpolated to zero momentum transfer, and then is extrapolated to the physical quark mass. We obtain f{sub +}(0)=0.968(9)(6), where the first error is statistical and the second is the systematic error due to the chiral extrapolation. Previous estimates based on a phenomenological model and chiral perturbation theory are consistent with our result. Combining with an average of the decay rate from recent experiments, our estimate of f{sub +}(0) leads to the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |V{sub us}|=0.2245(27), which is consistent with CKM unitarity. These estimates of f{sub +}(0) and |V{sub us}| are subject to systematic uncertainties due to themore » finite lattice spacing and quenching of strange quarks, though nice consistency in f{sub +}(0) with previous lattice calculations suggests that these errors are not large.« less

CVC tests and CKM unitarity

The study of superallowed nuclear β -decay currently provides the most precise and convincing confirmation of the conservation of the vector current (CVC) and is a key component of the most demanding available test of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, a basic pillar of the Electroweak Standard Model. The status of these fundamental studies is summarized and recent work described.

New Limits on Fundamental Weak-Interaction Parameters from SuperallowedβDecay

A new survey of all world data on superallowed beta decays provides demanding tests of, and tight constraints on, the weak interaction. In confirmation of the conserved vector current hypothesis, the vector coupling constant G(V) is demonstrated to be constant to better than three parts in 10(4), and any induced scalar current is limited to f(S)</=0.0013 in electron rest-mass units. Any possible fundamental scalar current is similarly limited to /C(S)/C(V)/</=0.0013. The superallowed data also determine the up-down element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix to be V(ud)=0.9738(4). With Particle Data Group values for V(us) and V(ub), the top-row test of CKM unitarity yields /V(ud)/(2)+/V(us)/(2)+/V(ub)/(2)=0.9966(14); if V(us) comes instead from two recent results on K(e3) decay, this sum becomes 0.9996(11). Either unitarity result can be used to constrain the possible existence of right-hand currents.

Rare top decays t→cγ, t→cg and CKM unitarity

Top flavour-changing neutral decays are extremely suppressed within the Standard Model (SM) by the GIM mechanism, but can reach observable rates in some of its extensions. We compute the branching ratios for t→cγ and t→cg in minimal SM extensions where the addition of a vector-like up or down quark singlet breaks the unitarity of the 3×3 Cabibbo–Kobayashi–Maskawa (CKM) matrix. The maximum rates obtained indicate to what extent present experimental data allow 3×3 CKM unitarity to be broken in these models, and are too small to be observed in the near future. As a by-product, we reproduce the calculation of these branching ratios in the SM, and with an improved set of parameters we obtain values one order of magnitude smaller than the ones usually quoted in the literature. We study the CP asymmetries between the decay rates of the top quark and antiquark, which can be much larger than in the SM, also as a consequence of the partial breaking of 3×3 CKM unitarity.

CKM update, B 0- [formula omitted] mixings and rare B decays-a review

We review the current status of the Cabibbo-Kobayashi-Maskawa (CKM) matrix for quark mixing. The updated matrix is used to obtain a profile of the CKM unitarity triangle and estimates of the CP violating phases sin 2α, sin 2β and sin 2 γ that will be measured in neutral B meson decays. Measurements of the aforementioned CP asymetries, B s 0- B s 0 mixing and rare B decays will overconstrain the CKM unitarity triangle, thereby determining the mixing matrix precisely and possibly providing hints of physics beyond the standard model. The role of the B 0- B 0 mixing ratio x s x d (equivalently the mass difference ratio δM s δM d ) and the CKM-suppressed rare B decays in restricting the unitarity triangle is emphasized. The potential of rare B decays in searching for new physics involving flavour changing neutral current transitions, in particular B → X sℓ +ℓ − and B s → ℓ +ℓ −, is also briefly discussed.

Testing the symmetric Cabibbo-Kobayashi-Maskawa (CKM) matrix with lattice QCD calculations

We examine quantitatively the expectation of a symmetric quark mixing using recent lattice QCD calculations on the various hadronic matrix elements. We present a general parametrization of the symmetric CKM matrix which has directly measurable parameters. The direct measurements of the CKM matrix elements, unitarity and CP violation are used to constrain the parameters. The symmetric CKM matrix is also confronted with e in the kaon system,xd of\(B_d^0 - \bar B_d^0 \) mixing, and e′/e of ΔS=1 CP-violation in the kaon system. Our analyses reveal that the symmetric CKM matrix is consistent with the present experiments, providedmt>130 GeV. The factorfBd2BBd plays an important role in reaching the conclusions.