Kobayashi Maskawa Research Articles

Probing 4 × 4 quark mixing matrix

Without adhering to any specific model, we have presented 4 [Formula: see text] 4 quark mixing matrix as an extension of the 3 [Formula: see text] 3 Particle Data Group (PDG) parametrization of the Cabibbo–Kobayashi–Maskawa (CKM) matrix Using unitarity constraints as well as the hierarchy among the elements of the 3 [Formula: see text] 3 CKM matrix, we have found the hierarchy among the fourth row and fourth column elements of the 4 [Formula: see text] 4 quark mixing matrix. Further, for the fourth generation case, we have explicitly found the nine independent rephasing invariant parameters [Formula: see text]. Also, using phenomenological estimates of the fourth row and fourth column elements, we have numerically evaluated these nine parameters.

Revisiting Representations of Quark Mixing Matrix

Abstract Using unitarity, unlike the approaches available in the literature, we construct 9 independent representations of the Cabibbo–Kobayashi–Maskawa) CKM matrix starting with each of the 9 elements of the matrix. The relationship of these independently constructed representations with those already available in the literature is compared and discussed. Further, the implications of these representations are explored for some of the CKM parameters such as $\delta$, J and $\epsilon _k$. Interestingly, we find that the PDG representation which is equivalent to our first representation seems to be most appropriate to incorporate the hierarchy of the elements of the CKM matrix as well as to describe the related phenomenology.

Superallowed Nuclear Beta Decays and Precision Tests of the Standard Model

For many decades, the main source of information on the top-left corner element of the Cabibbo–Kobayashi–Maskawa quark mixing matrix, V ud , was superallowed nuclear β decays with an impressive 0.01% precision. This precision, apart from experimental data, relies on theoretical calculations in which nuclear structure–dependent effects and uncertainties play a prime role. This review is dedicated to a thorough reassessment of all ingredients that enter the extraction of the value of V ud from experimental data. We try to keep balance between historical retrospect and new developments, many of which occurred in just the past 5 years. They have not yet been reviewed in a complete manner, not least because new results are forthcoming. This review aims to fill this gap and offers an in-depth yet accessible summary of all recent developments.

Theory of CP angle measurements

Abstract In the early 1980s Sanda-san and collaborators wrote key papers on the direct and clean determination of the unitarity angle ϕ1(β). This motivated many of us to analogously come up with ways for direct and clean determinations of the other two unitarity angles, ϕ2(α) and ϕ3(γ). This paper describes the current status of these direct determinations as well as our expectations for when Belle-II has 50 ab−1 of luminosity and LHCb is upgraded. In particular, it is emphasized that, for direct determination of ϕ3, Belle-II should be able to handle final states in D0 or $\bar{D}^0$ Dalitz decays, which contain one π0 (which are difficult for LHCb); then they may make further inroads in improving the accuracy of the ϕ3 determination. Early lattice inputs for constraining the unitarity triangle (UT) are briefly recalled. Its crucial role in supporting the Kobayashi–Maskawa theory of CP violation is emphasized. Over the years significant progress has been made in lattice methods and the latest constraints from these for the UT will be discussed, as well as the compatibility with current direct determinations and some comments on the future outlook.

The Curious Early History of the Cabibbo–Kobayashi–Maskawa Matrix: Miracles Happen!

Abstract The 1973 Kobayashi–Maskawa paper proposed a compelling link between Cabibbo’s flavor mixing scheme and ${\mathcal {C}}$${\mathcal {P}}$ violation but, since it required the existence of six quarks at a time when the physics community was happy with only three, it received zero attention. However, two years after the paper appeared—at which time it had received a grand total of two citations—the charmed quark was discovered and it finally got some notice and acceptance. After this stumbling start, it subsequently emerged as the focal point of an enormous amount of experimental and theoretical research activity. In an invited talk at a KEK symposium to celebrate the 50th anniversary of the KM paper, I reviewed some of the less well known circumstances that occurred in the years preceding and following the paper’s appearance. Some spoilers: (i) Kobayashi and Maskawa (and a number of other Japanese physicists) were convinced about the existence of the charmed quark nearly three years before its “discovery” at Brookhaven and SLAC. (ii) The matrix provided in their seminal 1973 paper was mathematically incorrect. Another version that was in common use for the following 12 years was technically correct, but not really a rotation matrix. (iii) The CKM matrix ${\mathcal {C}}$${\mathcal {P}}$ phase was only measurable because of the very specific hierarchy of the flavor mixing angles and meson masses. (iv) Similarly, the neutrino mixing discovery, and the PMNS matrix measurability were only possible because of favorable values of the neutrino mass differences and mixing angles. In addition I include some speculations about what may be in store for the future.

Verification of T Invariance in the Total Interaction Cross Section of Neutrons with Unpolarized Nuclei Using the Polarization–Asymmetry Theorem

To date, the violation of T invariance (TI) has been experimentally established for the decays [J.H.Christenson et al., Phys. Rev. Lett.13, 138 (1964)] and oscillations [A. Angelopoulos et al., Phys. Lett. B444, 43 (1998)] of neutral kaons. Phenomenologically, TI violation in the system of neutral kaons is associated with the difference of the Kobayashi–Maskawa phase from zero (or from π) in the standard model of the electroweak interaction. For nucleon–nucleus interactions, this phase turns out to be very small [P.Herszeg, inSymmetries and Fundamental Interactions in Nuclei, World Scientific, Singapore (1995), p.89)]. Estimates of the nucleon–nucleon matrix element corresponding to TI violation in various models are given in [V. Gudkov, inFundamental Physics with Pulsed Neutron Beams, World Scientific, Singapore (2001), p. 117]. All these estimates are small and have a large spread. Therefore, the verification of TI in nuclear processes actually means a search for other mechanisms for its violation. Below is a description of the experimental methods for TI verification in the total interaction cross sections of low-energy resonance neutrons with unpolarized nuclei with the use of the polarization–asymmetry (PA) theorem.

The minimal flavor structure of quarks and leptons

A flavor structure with minimal parameters is proposed to address the fermion mass hierarchy and flavor mixing for quarks and leptons. Yukawa interaction is reconstructed in a new basis to show a common flat structure for up-type quarks, down-type quarks, charged leptons, and Dirac neutrinos. A flavor symmetry is found from the hierarchy masses of quarks and leptons, which dominated Cabibbo–Kobayashi–Maskawa (CKM) mixing for quarks and Pontecorvo–Maki–Nakagawa–Sakata mixing for leptons. It results that the minimal flavor structure successfully addresses flavor mixings of quarks and leptons even in the mass hierarchy limit, which means that mass hierarchy and flavor mixing are two independent questions. As a prediction, a sum rule on the mixing angles and CP violation phase (CPV) is suggested, which explains the smallness of s 13 as a natural result of the mass hierarchy. Generalizing the flat structure to quarks and leptons, a unified Yukawa interaction is also achieved for all fermions with only a single coupling.

Flavor physics at LHCb: 50 years of the Kobayashi–Maskawa paradigm

Abstract The LHCb experiment has been in operation since 2009 and has provided measurements of the Kobayashi–Maskawa matrix with unprecedented precision. 50 years after the original paper we are in the position to pin down the parameters of the theory, or possibly to show its limitations. In these proceedings the status of LHCb is shown from a historical perspective, along with some anecdotes.

Flavor physics beyond the Standard Model and the Kobayashi–Maskawa legacy

Abstract The Kobayashi–Maskawa (KM) hypothesis about the existence of a third generation of quarks represents a cornerstone of the Standard Model (SM). Fifty years after this seminal paper [M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973)], flavor physics continues to represent a privileged observatory on physics occurring at high energy scales. In this paper I first review this statement using general effective-theory arguments, highlighting some interesting modern lessons from the KM paper. I then discuss some novel extensions of the SM based on the concept of flavor deconstruction: the hypothesis that gauge interactions are manifestly flavor-non-universal in the ultraviolet. The phenomenological consequences of this class of models are also briefly illustrated.

The St. Benedict Facility: Probing Fundamental Symmetries through Mixed Mirror β-Decays

Precise measurements of nuclear beta decays provide a unique insight into the Standard Model due to their connection to the electroweak interaction. These decays help constrain the unitarity or non-unitarity of the Cabibbo–Kobayashi–Maskawa (CKM) quark mixing matrix, and can uniquely probe the existence of exotic scalar or tensor currents. Of these decays, superallowed mixed mirror transitions have been the least well-studied, in part due to the absence of data on their Fermi to Gamow-Teller mixing ratios (ρ). At the Nuclear Science Laboratory (NSL) at the University of Notre Dame, the Superallowed Transition Beta-Neutrino Decay Ion Coincidence Trap (St. Benedict) is being constructed to determine the ρ for various mirror decays via a measurement of the beta–neutrino angular correlation parameter (aβν) to a relative precision of 0.5%. In this work, we present an overview of the St. Benedict facility and the impact it will have on various Beyond the Standard Model studies, including an expanded sensitivity study of ρ for various mirror nuclei accessible to the facility. A feasibility evaluation is also presented that indicates the measurement goals for many mirror nuclei, which are currently attainable in a week of radioactive beam delivery at the NSL.

Radiative B to tensor meson decays at NLO in SCET

The radiative B to tensor meson decays are studied at next-to-leading order in soft-collinear effective theory (SCET). The SCET allows the systematic treatment of factorizable and non-factorizable contributions along with the resummation of large perturbative logarithms. We performed a two-step matching and determined the soft-overlap function and branching ratios for these B to tensor meson decays. In the case of , the numerical value of the branching ratio lies close to its experimental measurements. The estimated values of the branching ratios of Cabibbo–Kobayashi–Maskawa suppressed decays are significantly small compared to that of , but still could be measured in some ongoing and future B physics experiments.

NLO + parton-shower generator for varvec{Wc} production in the POWHEG BOX RES

We present the implementation of a next-to-leading-order plus parton-shower event generator for the hadronic production of a heavy charm quark accompanied by a leptonically-decaying W boson in the POWHEG BOX RES framework. We consider both signatures, i.e. pprightarrow c, ell ^- {bar{nu }}_{ell } and pprightarrow {bar{c}} ,ell ^+ {nu }_{ell }, and we include exactly off-shell and spin-correlation effects, as well as off-diagonal Cabibbo–Kobayashi–Maskawa contributions. We present particle-level results, obtained interfacing our code with the Herwig7.2 and Pythia8.3 shower Monte Carlo event generators, including hadronization and underlying-event effects, and compare them against the data collected by the CMS Collaboration at sqrt{s}=13 TeV.

Recent Progress in Leptonic and Semileptonic Decays of Charmed Hadrons

We present a comprehensive review of purely leptonic and semileptonic decays of D0(+), [Formula: see text], and charmed baryons (including [Formula: see text], Ξ c, and Ω c). The precise studies of these decays help deepen our understanding and knowledge of quantum chromodynamics via measuring decay constants and form factors, and test the Standard Model through examining the unitarity of the Cabibbo–Kobayashi–Maskawa matrix and lepton flavor universality. We give an overview of the theoretical and experimental tools before discussing the recent progress. The data sets collected by the Beijing Spectrometer III (BESIII) near the production thresholds of [Formula: see text], [Formula: see text], and [Formula: see text] offer important opportunities for studies of charm physics.

Construction of St. Benedict

The Superallowed Transition Beta-Neutrino Decay Ion Coincidence Trap (St. Benedict) is currently under construction at the University of Notre Dame Nuclear Science Laboratory. It is designed to measure the beta-neutrino angular correlation parameter in superallowed mixed beta-decay transitions between mirror nuclei in order to extract the Fermi-to-Gamow Teller mixing ratio and test theoretical corrections entering in the determination of the Vud element of the Cabibbo–Kobayashi–Maskawa quark mixing matrix. St. Benedict includes a large volume gas catcher to thermalize the radioactive ion beam from TwinSol, a differentially-pumped extraction system, a radiofrequency quadrupole ion cooler and buncher, and a Paul trap for the observation and detection of the β decay products. The status of each of these components will be presented.

BAU Production in the SN-Breaking Standard Model

The violation of charge-parity symmetry and the baryon asymmetry of the universe are two of the most significant unresolved problems in physics. This article presents further research on the CP violation problem in the Standard Model with 32 candidate sets of the 10 “natural” parameters that exhibit the same Cabibbo–Kobayashi–Maskawa performance. These parameters are considered “natural” because they consist solely of the Yukawa couplings and the vacuum expectation value of the unique Higgs doublet in the Standard Model. Then, the problems of CP violation and the baryon asymmetry of the universe are investigated by using the Jarlskog measure of CP violation, ΔCP=J(mt2−mc2)(mt2−mu2)(mc2−mu2)(mb2−ms2)(mb2−md2)(ms2−md2)/T12, given that CP symmetry is violated following the breakdown of SN symmetries. Subsequently, numerical tests are performed in a simplified scenario where eight of the ten parameters are assumed to be fixed by two assumptions, and the remaining two parameters are allowed to vary from the S2-symmetric point (x,y)=(−1,1) to their current values in all 32 parameter sets. To estimate the enhancement of CP violation in such processes, a ratio RΔ≡ΔCP/ΔCP(0) is proposed between the running ΔCP and its current value, denoted by ΔCP(0), which is approximately 10−20. In all 32 cases, the three-dimensional plots of RΔ exhibit many regions that stick out of the RΔ=1010 plane, especially in regions very close to (x,y)=(−1,1). These results demonstrate that the SN-breaking Standard Model is already sufficient to violate CP symmetry explicitly and generate a significant amount of baryon asymmetry of the universe. Furthermore, it solves existing problems without creating new ones, at least in the scenario presented in this article.

New UTfit analysis of the unitarity triangle in the Cabibbo–Kobayashi–Maskawa scheme

Flavour mixing and CP violation as measured in weak decays and mixing of neutral mesons are a fundamental tool to test the Standard Model and to search for new physics. New analyses performed at the LHC experiment open an unprecedented insight into the Cabibbo–Kobayashi–Maskawa metrology and new evidence for rare decays. Important progress has also been achieved in theoretical calculations of several hadronic quantities with a remarkable reduction of the uncertainties. This improvement is essential since previous studies of the Unitarity Triangle did show that possible contributions from new physics, if any, must be tiny and could easily be hidden by theoretical and experimental errors. Thanks to the experimental and theoretical advances, the Cabibbo–Kobayashi–Maskawa picture provides very precise Standard Model predictions through global analyses. We present here the results of the latest global Standard Model analysis performed by the UTfit collaboration including all the most updated inputs from experiments, lattice Quantum Chromo-Dynamics and phenomenological calculations.

Scrutinizing CKM unitarity with a new measurement of the Kμ3/Kμ2 branching fraction

Precision tests of first-row unitarity of the Cabibbo–Kobayashi–Maskawa matrix currently display two intriguing tensions, both at the 3σ level. First, combining determinations of Vud from superallowed β decays with Vus from kaon decays suggests a deficit in the unitarity relation. At the same time, a tension of similar significance has emerged between Kℓ2 and Kℓ3 decays. In this Letter, we point out that a measurement of the Kμ3/Kμ2 branching fraction at the level of 0.2% would have considerable impact on clarifying the experimental situation in the kaon sector, especially in view of tensions in the global fit to kaon data as well as the fact that the Kμ2 channel is currently dominated by a single experiment. Such a measurement, as possible for example at NA62, would further provide important constraints on physics beyond the Standard Model, most notably on the role of right-handed vector currents.

Standard model and predictions for the Higgs boson

This article describes the electroweak interactions of the Standard Model (SM) with Brout-Englert-Higgs (BEH) mechanism, the appearance and properties of the Higgs boson. Braut-Engler-Higgs mechanism plays an important role in the Standard Model, which introduce a scalar Higgs field with a non-zero vacuum expectation results from spontaneous symmetry breaking. So, due to the interaction with this field, elementary particles become massive. Here arise electrically neutral quanta associated with the Higgs field, so called Higgs boson, in the same way that there is a quanta associated with the electromagnetic field, i.e. photons. The strong part of the Standard Model, Quantum Chromodynamics, quark mixing Cabibbo–Kobayashi–Maskawa matrix, physics of the neutrino and many other issues were not mentioned in the article. Brout-Englert-Higgs mechanism and associated Higgs boson are important parts of the Standard Model of elementary particles. In this paper we present the full Lagrangian of the Standard Model and a set of theoretical predictions about the Higgs boson before its detection, as well as the current state of the Higgs boson problem. Keywords: Standard Model, High Energy, Large Hadron Collider, Higgs boson, Higgs mechanism, Spontaneous symmetry breaking.

Quark unitarity triangles

The angles and the lengths of the sides of all unitarity triangles of the Cabibbo–Kobayashi–Maskawa (CKM) matrix are determined with very high precision from the experimental data. Our analysis is independent of parameterization of the CKM matrix and it is based on the predictions of the unitarity for the angles and the areas of the unitarity triangles. We note that the lengths of the sides of the three unitarity triangles determined from the experimental data do not form a triangle. We resolve this incompatibility by performing a constrained fit, assuming the equality of the area of the unitarity triangles. We demonstrate that the measured data are compatible with the predictions of the unitarity of the CKM matrix. We show that the angles of the unitarity triangles obtained by the multiplication of the rows of the CKM matrix can be obtained from the angles obtained by the multiplication of the columns. The equality of those two types of angles is a simple, but a very powerful test of the general structure of the Standard Model.

Testing Lepton Flavor Universality with Pion, Kaon, Tau, and Beta Decays

We present an overview of searches for violation of lepton flavor universality with a focus on low energy precision probes using π, K, τ, and nuclear beta decays. We review the current experimental results, summarize the theoretical status within the context of the Standard Model, and discuss future prospects (both experimental and theoretical). We review the implications of these measurements for physics beyond the Standard Model by performing a global model-independent fit to modified W couplings to leptons and four-fermion operators. We also discuss new physics in the context of simplified models and review Standard Model extensions with a focus on those that can explain a possible deviation from unitarity of the Cabibbo–Kobayashi–Maskawa quark mixing matrix.