CKM Matrix Element Research Articles

B→πℓνandBs→Kℓνform factors and|Vub|from2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks

We calculate the $B \to\pi\ell\nu$ and $B_s \to K \ell\nu$ form factors in dynamical lattice QCD. We use the (2+1)-flavor RBC-UKQCD gauge-field ensembles generated with the domain-wall fermion and Iwasaki gauge actions. For the $b$ quarks we use the anisotropic clover action with a relativistic heavy-quark interpretation. We analyze two lattice spacings $a \approx 0.11, 0.086$ fm and unitary pion masses as light as $M_\pi \approx 290$ MeV. We simultaneously extrapolate our numerical results to the physical light-quark masses and to the continuum and interpolate in the pion/kaon energy using SU(2) "hard-pion" chiral perturbation theory. We provide complete error budgets for the form factors $f_+(q^2)$ and $f_0(q^2)$ at three momenta that span the $q^2$ range accessible in our numerical simulations. We extrapolate these results to $q^2 = 0$ using a model-independent $z$-parametrization and present our final form factors as the $z$-coefficients and the matrix of correlations between them. Our results agree with other lattice determinations using staggered light quarks and provide important independent cross-checks. Both $B \to\pi\ell\nu$ and $B_s \to K \ell\nu$ decays enable a determination of the CKM matrix element $|V_{ub}|$. To illustrate this, we perform a combined $z$-fit of our numerical $B\to\pi\ell\nu$ form-factor data with the experimental branching-fraction measurements leaving the relative normalization as a free parameter; we obtain $|V_{ub}| = 3.61(32) \times 10^{-3}$, where the error includes statistical and systematic uncertainties. This approach can be applied to $B_s\to K \ell\nu$ decay to determine $|V_{ub}|$ once the process has been measured experimentally. Finally, in anticipation of future measurements, we make predictions for $B \to \pi\ell\nu$ and $B_s\to K \ell\nu$ Standard-Model differential branching fractions and forward-backward asymmetries.

Inclusive semileptonic B decays and |Vcb|: In memoriam Kolya Uraltsev

The CKM matrix elements |Vcb| can be extracted from inclusive semileptonic B decays in a model independent way pioneered by Kolya Uraltsev and collaborators. I review here the present status and latest developments in this field.

Leptonic decay constantsfK,fD, andfDswithNf=2+1+1twisted-mass lattice QCD

We present a lattice QCD calculation of the pseudoscalar decay constants fK, fD and fDs performed using the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their values in the real world. The simulations are based on a unitary setup for the two light mass-degenerate quarks and on a mixed action approach for the strange and charm quarks. We use data simulated at three different values of the lattice spacing in the range 0.06 - 0.09 fm and at pion masses in the range 210 - 450 MeV. Our main results are: fK+ / fpi+ = 1.184 (16), fK+ = 154.4 (2.0) MeV, which incorporate the leading strong isospin breaking correction due to the up- and down-quark mass difference, and fK = 155.0 (1.9) MeV, fD = 207.4 (3.8) MeV, fDs = 247.2 (4.1) MeV, fDs / fD = 1.192 (22) and (fDs / fD) / (fK / fpi) = 1.003 (14) obtained in the isospin symmetric limit of QCD. Combined with the experimental measurements of the leptonic decay rates of kaon, pion, D- and Ds-mesons our results lead to the following determination of the CKM matrix elements: |Vus| = 0.2269 (29), |Vcd| = 0.2221 (67) and |Vcs| = 1.014 (24). Using the latest value of |Vud| from superallowed nuclear beta decays the unitarity of the first row of the CKM matrix is fulfilled at the permille level.

Precision Determination of the Cabibbo-Kobayashi-Maskawa ElementVcb

We extract the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element V(c)} and the most relevant parameters of the heavy quark expansion from data of inclusive semileptonic B decays. Our calculation includes the recently computed O(α(s)Λ(QCD)(2)/m(b)(2)) corrections and a careful estimate of the residual theoretical uncertainty. Using a recent determination of the charm quark mass, we obtain |V(cb)|=(42.21±0.78)×10(-3) and m(b)(kin)(1 GeV)=(4.553±0.020) GeV.

$$S_3$$ S 3 discrete group as a source of the quark mass and mixing pattern in $$331$$ 331 models

We propose a model based on the $SU(3)_{C}\otimes SU(3)_{L}\otimes U(1)_{X}$ gauge symmetry with an extra $S_{3}\otimes Z_{2}\otimes Z_{4}\otimes Z_{12}$ discrete group, which successfully accounts for the SM quark mass and mixing pattern. The observed hierarchy of the SM quark masses and quark mixing matrix elements arises from the $Z_{4}$ and $Z_{12}$ symmetries, which are broken at very high scale by the $SU(3)_{L}$ scalar singlets ($\sigma$,$\zeta$) and $\tau $, charged under these symmetries, respectively. The Cabbibo mixing arises from the down type quark sector whereas the up quark sector generates the remaining quark mixing angles. The obtained magnitudes of the CKM matrix elements, the CP violating phase and the Jarlskog invariant are in agreement with the experimental data.

Top quark studies with the ATLAS detector

The latest top quark studies in proton-proton collisions at a centre-of-mass energy of 7 and 8 TeV with the ATLAS detector are reported. We present recent results on the top pair production inclusive cross-sections, top pair production differential cross-section in the resolved and boosted regimes, single top-quark production cross-sections measured in the t-channel, s-channel and W-boson associated processes, as well as the determination of the CKM matrix element [Formula: see text]. The results are compared with theoretical expectations. Latest ATLAS results on top properties will be also shown in terms of direct and pole mass, spin correlations and charge asymmetry.

Off-diagonal Yukawa couplings in the s-channel charged Higgs production at LHC

The search for the heavy charged Higgs (mH±>mtop) has been mainly based on the off-shell top pair production process. However, resonance production in s-channel single top events is an important channel to search for this particle. In a previous work, it was shown that this process, i.e., qq′→H+→tb¯+h.c., can lead to comparable results to what is already obtained from LHC searches. What was obtained was, however, based on diagonal Yukawa couplings between incoming quarks assuming cs¯ as the main incoming pair due to the CKM matrix element being close to unity. The aim of this paper is to show that off-diagonal couplings, like cb¯, may lead to substantial contributions to the cross section, even if the corresponding CKM matrix element is two orders of magnitude smaller. For this reason, the cross section is calculated for each initial state including all diagonal and off-diagonal terms, and all is finally added together to get the total cross section which is observed to be ∼2.7 times larger than what is obtained from cs¯ initial state. Results are eventually reflected into 95% C.L. exclusion and 5σ discovery contours at different integrated luminosities of LHC. A reasonable coverage of the parameter space is obtained by the 95% C.L. exclusion contour.

Comprehensive measurements oft-channel single top-quark production cross sections ats=7 TeVwith the ATLAS detector

This article presents measurements of the $t$-channel single top-quark ($t$) and top-antiquark ($\bar{t}$) total production cross sections $\sigma(tq)$ and $\sigma(\bar{t}q)$, their ratio $R_{t}=\sigma(tq)/\sigma(\bar{t}q)$, and a measurement of the inclusive production cross section $\sigma(tq + \bar{t}q)$ in proton--proton collisions at $\sqrt{s} = 7$ TeV at the LHC. Differential cross sections for the $tq$ and $\bar{t}q$ processes are measured as a function of the transverse momentum and the absolute value of the rapidity of $t$ and $\bar{t}$, respectively. The analyzed data set was recorded with the ATLAS detector and corresponds to an integrated luminosity of 4.59 fb$^{-1}$. Selected events contain one charged lepton, large missing transverse momentum, and two or three jets. The cross sections are measured by performing a binned maximum-likelihood fit to the output distributions of neural networks. The resulting measurements are $\sigma(tq)= 46\pm 6\; \mathrm{pb}$, $\sigma(\bar{t}q)= 23 \pm 4\; \mathrm{pb}$, $R_{t}=2.04\pm 0.18$, and $\sigma(tq + \bar{t}q)= 68 \pm 8\; \mathrm{pb}$, consistent with the Standard Model expectation. The uncertainty on the measured cross sections is dominated by systematic uncertainties, while the uncertainty on $R_{t}$ is mainly statistical. Using the ratio of $\sigma(tq + \bar{t}q)$ to its theoretical prediction, and assuming that the top-quark-related CKM matrix elements obey the relation $|V_{tb}|\gg |V_{ts}|, |V_{td}|$, we determine $|V_{tb}|=1.02 \pm 0.07$.

Top quark couplings and polarization

Precise measurements of top quark couplings are presented. The measurements cover the single top tW cross section, the top-quark branching-fraction ratio R=B(t → Wb)/B(t → Wq) and the CKM matrix element Vtb from the single top cross sections. Top quark polarisation in the t-channel single-top quark production and dilepton tt, and W-helicity fraction measurements along with searches of top quark anomalous couplings in lepton plus jet channel are also presented. Finally measurements of top quark pair production in association with a W or Z boson or a photon are presented.

Semileptonic B decays at Belle

Recent results from the Belle experiment on semileptonic decays of B-mesons are reviewed, including their effect on the determination of the CKM matrix elements |Vcb| and |Vub|.

SUSY FLAVOR v2.5: A computational tool for FCNC and CP-violating processes in the MSSM

SUSY FLAVOR v2.5: A computational tool for FCNC and CP-violating processes in the MSSM

Experimental study of rare charged pion decays

The combination of simple dynamics, small number of available decay channels, and extremely well controlled radiative and loop corrections, make charged pion decays a sensitive means for testing the underlying symmetries and the universality of weak fermion couplings, as well as for improving our understanding of pion structure and chiral dynamics. This paper reviews the current state of experimental study of the allowed rare decays of charged pions: (a) leptonic, , or πe2, (b) radiative, , or , and , or πe2ee, and (c) semileptonic, , or πe3. Taken together, the combined data set presents an internally consistent picture that also agrees well with standard model predictions. The internal consistency is illustrated well by the value of the πe2 branching ratio of extracted in this work from the PIBETA measurement of the πe3 decay and the current best value for the CKM matrix element Vud. However, even after the great progress of the recent decades, experimental precision is lagging far behind that of the theoretical description for all above processes. We review the implications of the present state of knowledge and prospects for further improvement in the near term.

The semileptonic $$\bar{B}\rightarrow D\ell \bar{\nu }$$ B ¯ → D ℓ ν ¯ and $$\bar{B}_s \rightarrow D_s \ell \bar{\nu }$$ B ¯ s → D s ℓ ν ¯ decays in Isgur–Wise approach

We consider a combination of linear confining and Hulthén potentials in the Hamiltonian and, via the perturbation approach, report the corresponding Isgur–Wise function parameters. Next, we investigate the Isgur–Wise function for \(\bar{B}\rightarrow D\ell \bar{\nu }\) and \(\bar{B}_s \rightarrow D_s \ell \bar{\nu }\) semileptonic decays and report the decay width, branching ratio, and \(\vert V_{cb} \vert \)CKM matrix element. A comparison with other models and experimental values is included.

Review of lattice results concerning low-energy particle physics

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor f_+(0), arising in semileptonic K rightarrow pi transition at zero momentum transfer, as well as the decay-constant ratio f_K/f_pi of decay constants and its consequences for the CKM matrix elements V_{us} and V_{ud}. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of hbox {SU}(2)_Ltimes hbox {SU}(2)_R and hbox {SU}(3)_Ltimes hbox {SU}(3)_R Chiral Perturbation Theory and review the determination of the B_K parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on D- and B-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant alpha _mathrm{s}.

Progress on semi-leptonic B(s) decays

We report on the current status of semi-leptonic B(s) decays, including rare decays, and the extraction of the absolute values of the CKM matrix elements |Vcb| and |Vub|.

Measurement of the t-channel single-top-quark production cross section and of the |V tb| CKM matrix element in pp collisions at $ \sqrt{s} $ = 8 TeV

Measurements are presented of the t-channel single-top-quark production cross section in proton-proton collisions at sqrt(s) = 8 TeV. The results are based on a data sample corresponding to an integrated luminosity of 19.7 inverse femtobarns recorded with the CMS detector at the LHC. The cross section is measured inclusively, as well as separately for top (t) and antitop (t-bar), in final states with a muon or an electron. The measured inclusive t-channel cross section is sigma[t-ch] = 83.6 +/- 2.3 (stat.) +/- 7.4 (syst.) pb. The single t and t-bar cross sections are measured to be sigma[t-ch,t] = 53.8 +/- 1.5 (stat.) +/- 4.4 (syst.) pb and sigma[t-ch,t-bar] = 27.6 +/- 1.3 (stat.) +/- 3.7 (syst.) pb, respectively. The measured ratio of cross sections is R[t-ch] = sigma[t-ch,t]/sigma[t-ch,t-bar] = 1.95 +/- 0.10 (stat.) +/- 0.19 (syst.), in agreement with the standard model prediction. The modulus of the Cabibbo-Kobayashi-Maskawa matrix element Vtb is extracted and, in combination with a previous CMS result at sqrt(s) = 7 TeV, a value abs(Vtb) = 0.998 +/- 0.038 (exp.) +/- 0.016 (theo.) is obtained.

Formula omitted] from the semileptonic decay [formula omitted] and the properties of the D-meson distribution amplitude

The improved QCD light-cone sum rule (LCSR) provides an effective way to deal with the heavy-to-light transition form factors (TFFs). Firstly, we adopt the improved LCSR approach to deal with the B→D TFF f+(q2) up to twist-4 accuracy. Due to the elimination of the most uncertain twist-3 contribution and the large suppression of the twist-4 contribution, the obtained LCSR shall provide us a good platform for testing the D-meson leading-twist DA. For the purpose, we suggest a new model for the D-meson leading-twist DA (ϕ3D), whose longitudinal behavior is dominantly determined by a parameter B. Moreover, we find its second Gegenbauer moment a2D∼B. Varying B within certain region, one can conveniently mimic the D-meson DA behavior suggested in the literature. Inversely, by comparing the estimations with the experimental data on the D-meson involved processes, one can get a possible range for the parameter B and a determined behavior for the D-meson DA. Secondly, we discuss the B→D TFF at the maximum recoil region and present a detailed comparison of it with the pQCD estimation and the experimental measurements. Thirdly, by applying the LCSR on f+(q2), we study the CKM matrix element |Vcb| together with its uncertainties by adopting two types of processes, i.e. the B0/B¯0-type and the B±-type. It is noted that a smaller B≾0.20 shows a better agreement with the experimental value on |Vcb|. For example, for the case of B=0.00, we obtain |Vcb|(B0/B¯0−type)=(41.28−4.82+5.68−1.16+1.13)×10−3 and |Vcb|(B±−type)=(40.44−4.72+5.56 −1.00+0.98)×10−3, whose first (second) uncertainty comes from the squared average of the mentioned theoretical (experimental) uncertainties.

On the bounds of CKM matrix element Vcb in a potential model

Considering the allowed range of slope ρ2 and curvature C of Isgur–Wise function for B meson, we obtain an allowed range of strong coupling constant αs as well as the QCD scale parameter Λ in a specific prescription. The allowed range of Λ is then used to obtain the theoretical bounds on Vcb in a potential model. The recent available data of Vcb are found to lie within this computed range 0.0375 ≤|Vcb|≤0.0410.

Cabibbo–Kobayashi–Maskawa matrix: rephasing invariants and parameterizations

In this work we study two topics: the first one considers the general phase invariant monomials built out of the CKM matrix elements and their conjugates. We show, that there exist 30 fundamental phase invariant monomials and 18 of them are a product of 4 CKM matrix elements and 12 are a product of 6 CKM matrix elements. In our main result we show that all rephasing invariant monomials can be expressed as a product of at most 5 factors with positive powers. Next, we propose a general method of a recursive construction of the CKM matrix for any number of generations. This allows to construct 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.

General 4–zero texture mass matrix parametrizations

It is performed the diagonalization of a non–Hermitian four–zero texture Yukawa matrix with a general formalism. This procedure leads to 3 possibilities to parametrize the relation between the fermion masses and the elements of the corresponding Yukawa matrix. Then, the matrices that diagonalize each Yukawa mass matrix are combined in order to obtain 9 different theoretical CKM or PMNS mixing matrices [1]. Through a χ2 analysis, we have constrained the values of the remaining free parameters such as the theoretical mixing matrix matches the latest experimental measurements of the mixing matrices. This analysis was done without assuming any approximations. In the case of the quark sector, it is found that only four different theoretical mixing matrices are compatible with the actual high precision experimental measurement of the CKM matrix elements. For the lepton sector, where the masses of neutrinos are not known, we found that independently of the parametrization that have been chosen, the updated experimental measurements of the mixing angles in the PMNS matrix, imply a mass for the heaviest left–handed neutrino to be ~ 0.05eV.