CKM Elements Research Articles

Measurement of CKM element |Vcb| from W boson decays at the future Higgs factories

This study investigates the precision measurement of the CKM matrix element |Vcb| through semileptonic WW events at future Higgs factories, i.e., FCC-ee, ILC, C3, and CEPC. We use full detector simulation to generate the WW → ℓνcb signal events and various backgrounds at s = 240 GeV with unpolarized beams. The relative statistical uncertainties of |Vcb| are projected to be 0.91% for the muon channel and 1.2% for the electron channel, assuming a baseline integrated luminosity of 5 ab−1. The sensitivities at other Higgs factory scenarios are also projected. Possible contributors to systematic uncertainties are discussed, with the most prominent one being the systematics of flavor-tagging and mistagging rates. Combining with WW threshold runs, the relative systematic uncertainty can be further reduced.

Direct CKM determination from W decays at future lepton colliders

We project the reach of future lepton colliders for measuring CKM elements from direct observations of W decays. We focus our attention to |Vcs| and |Vcb| determinations, using FCC-ee as case study. We employ state-of-the-art jet flavor taggers to obtain the projected sensitivity, and scan over tagger performances to show their effect. We conclude that future lepton collider can sizeably improve the sensitivity on |Vcs| and |Vcb|, albeit the achievable reach will strongly depend on the level of systematic uncertainties on tagger parameters.

SMEFT restrictions on exclusive b → uℓν decays

Exclusive semileptonic b hadron decays (b → uℓν) serve as a sandbox for probing strong and electroweak interactions and for extracting the CKM element Vub. Instead, this work investigates their underexplored potential to reveal new short-distance physics. Utilizing SMEFT as a conduit to chart territory beyond the SM, we demonstrate that substantive new physics contributions in b → uℓν are necessarily linked to correlated effects in rare neutral-current b decays, neutral B meson mixing or high-mass Drell-Yan tails. We find that measurements of the latter processes strongly restrict the allowed deviations in the former. A complete set of tree-level mediators, originating from a perturbative ultraviolet model and matching at dimension 6, is thoroughly explored to support this assertion. As a showcase application, we examine the feasibility of a new physics interpretation of the recent tension in exclusive |Vub| extraction from B → Vℓν where V = (ρ, ω).

A detailed investigation of W+c-jet at the LHC

State-of-the-art analyses of W+c-jet production at the LHC require precise predictions. In the present work, we study in detail the impact of off-diagonal CKM elements up to next-to-next-to leading order in QCD, the influence of flavored jet algorithms, and the size of electroweak corrections. In addition, we also investigate phenomenological aspects related to the exact definition of the process. We find that all these effects can be of the order of several per cent for both the fiducial cross section and differential distributions. They are, therefore, very relevant for the interpretation of current and upcoming measurements.

New physics contributions to moments of inclusive b → c semileptonic decays

Inclusive semileptonic B → {X}_cell {overline{nu}}_{ell } decays, where ℓ = μ, e, are by now standard candles in the determination of the CKM element |Vcb|. These determinations rely on the heavy-quark expansion and use moments of decay spectra to extract the non-perturbative parameters directly from data under the standard model assumption.At the same time, new physics could influence the moments of the inclusive decay. In this paper, we compute power-corrections and next-to-leading order corrections in the strong coupling constant using the full basis of dimension-six new physics operators for the inclusive B → {X}_cell overline{nu} decay. We provide predictions for lepton energy, hadronic and leptonic invariant mass moments, and perform a phenomenological study to show the possible impact of new physics. Our results could be used to perform a global fit including new physics contributions.

New extraction of CP violation in b-baryon decays

We study CP violation in b-baryon decays of Ξb−→Ξ−D with D=D0,D¯0 and Di(i=1,2). We find that these baryonic decay processes provide an ideal opportunity to measure the weak phase due to the absence of the relative strong phase. Explicitly, we relate ρ¯ and η¯ the CKM elements with the decay rate ratios of Ri=Γ(Ξb−→Ξ−Di)/Γ(Ξb−→Ξ−D0) without the charge conjugate states. As a complementary, we also examine the decay distributions of Λb→Λ(→pπ−)D. There are in total 32 decay observables, which can be parameterized by 9 real parameters, allowing the experiments to extract the angle γ≡arg⁡(−VudVub⁎/VcdVcb⁎) in the CKM unitarity triangle. In addition, the feasibilities of the experimental measurements are discussed. We find that ρ¯ and η¯ can be extracted at LHCb Run3 from Ξb−→Ξ−D, and a full analysis of Λb→Λ(→pπ−)D is available at LHCb Run4.

The exclusive vision of rare K and B decays and of the quark mixing in the standard model

The most common predictions for rare K and B decay branching ratios in the Standard Model in the literature are based on the CKM elements |V_{cb}| and |V_{ub}| resulting from global fits, that are in the ballpark of their inclusive and exclusive determinations, respectively. In the present paper we follow another route, which to our knowledge has not been explored for Delta M_{s,d} and rare K and B decays by anybody to date. We assume, in contrast to the prevailing inclusive expectations for |V_{cb}|, that the future true values of |V_{cb}| and |V_{ub}| will be both from exclusive determinations; in practice we use the most recent averages from FLAG. With the precisely known |V_{us}| the resulting rare decay branching ratios, varepsilon _K, Delta M_d, Delta M_s and S_{psi K_S} depend then only on the angles beta and gamma in the unitarity triangle that moreover are correlated through the CKM unitarity. An unusual pattern of SM predictions results from this study with some existing tensions being dwarfed and new tensions being born. In particular using HPQCD B^0_{s,d}-{{bar{B}}}^0_{s,d} hadronic matrix elements a 3.1sigma tension in Delta M_s independently of gamma is found. For 60^circ le gamma le 75^circ the tension in Delta M_d between 4.0sigma and 1.1sigma is found and in the case of varepsilon _K between 5.2sigma and 2.1sigma . Moreover, the room for new physics in K^+rightarrow pi ^+nu {bar{nu }}, K_Lrightarrow pi ^0nu {bar{nu }} and Brightarrow K(K^*)nu {bar{nu }} decays is significantly increased. We compare the results in this EXCLUSIVE scenario with the HYBRID one in which |V_{cb}| in the former scenario is replaced by the most recent inclusive |V_{cb}| and present the dependence of all observables considered by us in both scenarios as functions of gamma . As a byproduct we compare the determination of |V_{cb}| from Delta M_s, Delta M_d, varepsilon _K and S_{psi K_S} using B^0_{s,d}-{{bar{B}}}^0_{s,d} hadronic matrix elements from LQCD with 2+1+1 flavours, 2+1 flavours and their average. Only for the 2+1+1 case values for beta and gamma exist for which the same value of |V_{cb}| is found: |V_{cb}|=42.6(4)times 10^{-3}, gamma =64.6(16)^circ and beta =22.2(7)^circ . This in turn implies a 2.7sigma anomaly in B_srightarrow mu ^+mu ^-.

CKM substructure from the weak to the Planck scale

We look for relations among CKM matrix elements that are not consequences of the Wolfenstein parametrization. In particular, we search for products of CKM elements raised to integer powers that approximately equal 1. We study the running of the CKM matrix elements and resolve an apparent discrepancy in the literature. To a good approximation only A runs, among the Wolfenstein parameters. Using the Standard Model renormalization group we look for CKM relations at energy scales ranging from the electroweak scale to the Planck scale, and we find 19 such relations. These relations could point to structure in the UV, or be numerical accidents. For example, we find that |VtdVus| = | {V}_{cb}^2 |, within 2% accuracy, in the 109–1015 GeV range. We discuss the implications of this CKM relation for a Yukawa texture in the UV.

Frac{left|{V}_{ub}right|}{left|{V}_{cb}right|} and quest for new physics

Charged current semi-leptonic decays of B-meson are important for a precise determination of the CKM elements. The CKM elements |Vub| and |Vcb| show a discrepancy between the exclusive and inclusive determinations. These determinations are however masked with hadronic and other uncertainties, and thus can’t be unambiguously taken as implying new physics. In the present study, we propose a new observable: the ratio of these two CKM elements, {R}_Vequiv frac{left|{V}_{ub}right|}{left|{V}_{cb}right|} , which is found to receive negligible corrections due to hadronic as well as QED effects. Interestingly, RV as constructed from exclusive determinations of |Vub| and |Vcb| agrees quite well with that constructed from the inclusive determinations of these CKM elements. Hence, we propose that RV is a better and cleaner observable, and can serve as an excellent tool for the test of the Standard Model. We also provide an example of its probing power.

Exploring the Origin of CP Violation in the Standard Model

In this article, we present a very general but not ultimate solution of CPV problem in the standard model. Our study starts from a naturally Hermitian ${\bf M^2}\equiv M^q \cdot M^{q\dagger}$ rather than the previously assumed Hermitian $M^q$. The only assumption employed here is that the real part and imaginary part of $\bf M^2$ can be, respectively, diagonalized by a common $\bf U^q$ matrix. Such an assumption leads to a $\bf M^2$ pattern which depends on only five parameters and can be diagonalized analytically by a $\bf U^q$ matrix which depends on only two of the parameters. Two of the derived mass eigenvalues are predicted degenerate if one of the parameters $\bf C ~(C')$ in up- (down-) quark sector is zero. As the $\bf U^q$ patterns are obtained, thirty-six $V_{CKM}$ candidates are yielded and only eight of them, classified into two groups, fit empirical data within the order of $O(\lambda)$. One of the groups is further excluded in a numerical test, and the surviving group predicts that the degenerate pair in a quark type are the lightest and the heaviest generations rather than the lighter two generations assumed in previous researches. However, there is still one unsatisfactory prediction in this research, a quadruple equality in which four CKM elements of very different values are predicted to be equal. It indicates the $\bf M^2$ pattern studied here is still oversimplified by that employed assumption and the ultimate solution can only be obtained by diagonalizing the unsimplified $\bf M^2$ matrix containing nine parameters directly. The $V_{CKM}$ presented here is already very close to such an ultimate CPV solution.

Time-reversal asymmetries and angular distributions in \u039bb \u2192 \u039bV

We study the spin correlations to probe time-reversal (T) asymmetries in the decays of Λb→ ΛV (V = ϕ, ρ0, ω, K∗0). The eigenstates of the T-odd operators are obtained along with definite angular momenta. We obtain the T-odd spin correlations from the complex phases among the helicity amplitudes. We give the angular distributions of Λb→ Λ(→ pπ−)V (→ PP′) and show the corresponding spin correlations, where P(′) are the pseudoscalar mesons. Due to the helicity conservation of the s quark in Λ, we deduce that the polarization asymmetries of Λ are close to −1. Since the decay of Λb→ Λϕ in the standard model (SM) is dictated by the single weak phase from the product of CKM elements, {V}_{tb}{V}_{ts}^{ast } , the true T and CP asymmetries are suppressed, providing a clean background to test the SM and search for new physics. In the factorization approach, as the helicity amplitudes in the SM share the same complex phase, T-violating effects are absent. Nonetheless, the experimental branching ratio of Br(Λb→ Λϕ) = (5.18 ± 1.29) × 10−6 suggests that the nonfactorizable effects or some new physics play an important role. By parametrizing the nonfactorizable contributions with the effective color number, we calculate the branching ratios and direct CP asymmetries. We also explore the possible T-violating effects from new physics.

Implications of precision measurements and unitarity on CKM paradigm

In the context of precise measurements in some of the CKM elements and angles of the unitarity triangle coupled with latest theoretical improvements of lattice QCD calculations of “hadronic factors,” we have explored the implication of these and unitarity on some of the CKM parameters which are ridden with ambiguities. In particular, we have undertaken a thorough scrutiny of the implications of the precise measurements of the angles of the unitarity triangle along with the element [Formula: see text], on the [Formula: see text], [Formula: see text], [Formula: see text], as well as the CP violating parameter [Formula: see text]. Interestingly, we find a unitarity-based analysis while unambiguously favoring [Formula: see text] exclusive-over-inclusive value which is also in agreement with the present data pertaining to [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], etc. The present analysis also shows that the presence of NP in [Formula: see text] and [Formula: see text] systems, if any, would be less than a few percent only.

Impact of background effects on the inclusive Vcb determination

The determination of the CKM element Vcb from inclusive semileptonic b → cℓ overline{nu} decays has reached a high precision thanks to a combination of theoretical and experimental efforts. Aiming towards even higher precision, we discuss two processes that contaminate the inclusive Vcb determination; the b → u background and the contribution of the tauonic mode: b → c(τ → μν overline{nu} ) overline{nu} . Both of these contributions are dealt with at the experimental side, using Monte-Carlo methods and momentum cuts. However, these contributions can be calculated with high precision within the Heavy-Quark Expansion. In this note, we calculate the theoretical predictions for these two processes. We compare our b → u results qualitatively with generator-level Monte-Carlo data used at Belle and Belle II. Finally, we suggest to change the strategy for the extraction of Vcb by comparing the data on B → Xℓ directly with the theoretical expressions, to which our paper facilitates.

Global electroweak fit and vector-like leptons in light of the Cabibbo angle anomaly

The “Cabibbo Angle Anomaly” (CAA) originates from the disagreement between the CKM elements Vud and Vus extracted from superallowed beta and kaon decays, respectively, once compared via CKM unitarity. It points towards new physics with a significance of up to 4 σ, depending on the theoretical input used, and can be explained through modified W couplings to leptons. In this context, vector-like leptons (VLLs) are prime candidates for a corresponding UV completion since they can affect Wℓν couplings at tree-level, such that this modification can have the dominant phenomenological impact. In order to consistently assess agreement data, a global fit is necessary which we perform for gauge-invariant dimension-6 operators and all patterns obtained for the six possible representations (under the SM gauge group) of VLLs. We find that even in the lepton flavour universal case, including the measurements of the CKM elements Vus and Vud into the electroweak fit has a relevant impact, shifting the best fit point significantly. Concerning the VLLs we discuss the bounds from charged lepton flavour violating processes and observe that a single representation cannot describe experimental data significantly better than the SM hypothesis. However, allowing for several representations of VLLs at the same time, we find that the simple scenario in which N couples to electrons via the Higgs and Σ1 couples to muons not only explains the CAA but also improves the rest of the electroweak fit in such a way that its best fit point is preferred by more than 4 σ with respect to the begin.

β Decays as Sensitive Probes of Lepton Flavor Universality

Nuclear β decays as well as the decay of the neutron are well-established low-energy probes of physics beyond the standard model (SM). In particular, with the axial-vector coupling of the nucleon g_{A} determined from lattice QCD, the comparison between experiment and SM prediction is commonly used to derive constraints on right-handed currents. Further, in addition to the CKM element V_{us} from kaon decays, V_{ud} from β decays is a critical input for the test of CKM unitarity. Here, we point out that the available information on β decays can be reinterpreted as a stringent test of lepton flavor universality (LFU). In fact, we find that the ratio of V_{us} from kaon decays over V_{us} from β decays (assuming CKM unitarity) is extremely sensitive to LFU violation (LFUV) in W-μ-ν couplings thanks to a CKM enhancement by (V_{ud}/V_{us})^{2}∼20. From this perspective, recent hints for the violation of CKM unitarity can be viewed as further evidence for LFUV, fitting into the existing picture exhibited by semileptonic B decays and the anomalous magnetic moments of muon and electron. Finally, we comment on the future sensitivity that can be reached with this LFU violating observable and discuss complementary probes of LFU that may reach a similar level of precision, such as Γ(π→μν)/Γ(π→eν) at the PEN and PiENu experiments or even direct measurements of W→μν at an FCC-ee.

CP violation in beauty and charm at LHCb

Precision measurements of CP violating observables in the decays of b and c hadrons are powerful probes to search for physics beyond the Standard Model. The most recent results on CP violation in the decay, mixing and interference of both b and c hadrons obtained by the LHCb Collaboration with Run I and years 2015-2016 of Run II are presented, including the first observation of CP violation in the charm system. In particular world best constraints and world first measurements are provided for CKM elements, unitarity angles and charm parameters. Prospects for future sensitivities are also discussed.

Neutral B -meson mixing from full lattice QCD at the physical point

We calculate the bag parameters for neutral $B$-meson mixing in and beyond the Standard Model, in full four-flavour lattice QCD for the first time. We work on gluon field configurations that include the effect of $u$, $d$, $s$ and $c$ sea quarks with the Highly Improved Staggered Quark (HISQ) action at three values of the lattice spacing and with three $u/d$ quark masses going down to the physical value. The valence $b$ quarks use the improved NRQCD action and the valence light quarks, the HISQ action. Our analysis was blinded. Our results for the bag parameters for all five operators are the most accurate to date. For the Standard Model operator between $B_s$ and $B_d$ mesons we find: $\hat{B}_{B_s}=1.232(53)$, $\hat{B}_{B_d}=1.222(61)$. Combining our results with lattice QCD calculations of the decay constants using HISQ quarks from the Fermilab/MILC collaboration and with experimental values for $B_s$ and $B_d$ oscillation frequencies allows determination of the CKM elements $V_{ts}$ and $V_{td}$. We find $V_{ts} = 0.04189(93)$, $V_{td} = 0.00867(23)$ and $V_{ts}/V_{td} = 0.2071(27)$. Our results agree well (within $2\sigma$) with values determined from CKM unitarity constraints based on tree-level processes (only). Using a ratio to $\Delta M$ in which CKM elements cancel in the Standard Model, we determine the branching fractions ${\text{Br}}(B_s\rightarrow \mu^+\mu^-) = 3.81(18) \times 10^{-9}$ and ${\text{Br}}(B_d\rightarrow \mu^+\mu^-) = 1.031(54) \times 10^{-10}$. We also give results for matrix elements of the operators $R_0$, $R_1$ and $\tilde{R}_1$ that contribute to neutral $B$-meson width differences.

The Vcb puzzle: An update

We discuss the impact of the recent untagged analysis of B0→D⁎lν¯l decays by the Belle Collaboration on the extraction of the CKM element |Vcb| and provide updated SM predictions for the b→cτν observables R(D⁎), Pτ, and FLD⁎. The value of |Vcb| that we find is about 2σ from the one from inclusive semileptonic B decays, and is very sensitive to the slope of the form factor at zero recoil which should soon become available from lattice calculations.

Natural quark mixing and inverse seesaw in a left-right model with an axion

We consider a minimal left-right model with a Peccei-Quinn symmetry, where generalised charge conjugation plays the role of the left-right symmetry. We show how the spontaneous breaking of the Peccei-Quinn symmetry by a scalar singlet can provide us with solutions not only to the strong CP and dark matter problems but can also help to generate naturally suppressed off-diagonal CKM elements and small neutrino masses via the inverse seesaw mechanism. For this, we make use of an economical scalar sector composed of a bi-doublet, two doublets and a singlet only. As a result of the new gauge bosons and neutrinos, the neutrinoless double beta decay, as well as lepton flavour violating processes, receives new contributions which can, in principle, become relevant due to the low-scale nature of the inverse seesaw mechanism. The model can easily accommodate all the current data on fermion masses and mixing even if the left-right scale is only high enough to evade the current experimental constraints.

Bs mixing observables and |Vtd/Vts| from sum rules

We consider the effects of a non-vanishing strange-quark mass in the determination of the full basis of dimension six matrix elements for Bs mixing, in particular we get for the ratio of the V − A Bag parameter in the Bs and Bd system: {overline{B}}_{Q_1}^s/{overline{B}}_{Q_1}^d={0.987}_{-0.009}^{+0.007} . Combining these results with the most recent lattice values for the ratio of decay constants {f}_{B_s}/{f}_{B_d} we obtain the most precise determination of the ratio xi ={f}_{B_s}sqrt{{overline{B}}_{Q_1}^s}/{f}_{B_d}sqrt{{overline{B}}_{Q_1}^d}={1.2014}_{-0.0072}^{+0.0065} in agreement with recent lattice determinations. We find ΔMs = (18.5− 1.5+ 1.2)ps− 1 and ΔMd = (0.547− 0.046+ 0.035)ps− 1 to be consistent with experiments at below one sigma. Assuming the validity of the SM, our calculation can be used to directly determine the ratio of CKM elements |Vtd/Vts| = 0.2045− 0.0013+ 0.0012, which is compatible with the results from the CKM fitting groups, but again more precise.