Unitarity Triangle Research Articles

Recent Developments in Chiral Unitary Theory and Triangle Singularities Involving Baryons

We report on several reactions involving baryons that develop triangle singularities. The combination of elements of chiral unitary theory with the triangle mechanisms explain different features of reactions and shed light on some decay modes of several resonances. We address the role of a triangle singularity in the $$\pi N(1535)$$ contribution to $$\gamma p \rightarrow p \pi ^0 \eta $$ , another singularity, producing a peak in the $$\gamma p\rightarrow K^+ \varLambda (1405)$$ reaction which was previously unexplained, the role of a singularity in the $$\pi \varDelta $$ decay of the N(1700), and also discuss the $$N^*(1875)$$ resonance from this perspective.

Connecting Majorana phases to the geometric parameters of the Majorana unitarity triangle in a neutrino mass matrix model

We have investigated a possible connection between the Majorana phases and geometric parameters of Majorana unitarity triangle (MT) in two-texture zero neutrino mass matrix. Such analytical relations can, also, be obtained for other theoretical models viz. hybrid textures, neutrino mass matrix with vanishing minors and have profound implications for geometric description of $CP$ violation. As an example, we have considered the two-texture zero neutrino mass model to obtain a relation between Majorana phases and MT parameters that may be probed in various lepton number violating processes. In particular, we find that Majorana phases depend on only one of the three interior angles of the MT in each class of two-texture zero neutrino mass matrix. We have also constructed the MT for class $A$, $B$, and $C$ neutrino mass matrices. Nonvanishing areas and nontrivial orientations of these Majorana unitarity triangles indicate nonzero $CP$ violation as a generic feature of this class of mass models.

Renormalization-group equations of neutrino masses and flavor mixing parameters in matter

We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter aequiv 2sqrt{2}kern0.5em {G}_{mathrm{F}}{N}_eE to be an arbitrary scale-like variable with Ne being the net electron number density and E being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix V and the effective neutrino masses {tilde{m}}_i (for i = 1, 2, 3). Given the standard parametrization of V , the RGEs for left{{tilde{theta}}_{12},kern0.5em {tilde{theta}}_{13},kern0.5em {tilde{theta}}_{23},kern0.5em tilde{delta}right} in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial μ-τ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of V are also obtained as a by-product.

6a-J-2 第1象限のunitarity triangleとNNI型クォーク質量行列

6a-J-2 第1象限のunitarity triangleとNNI型クォーク質量行列

Optimizing sensitivity to γ with B0→DK+π− , D→KS0π+π− double Dalitz plot analysis

Two of the most powerful methods currently used to determine the angle $\gamma$ of the CKM Unitarity Triangle exploit $B^+ \to DK^+$, $D \to K_{\rm S}^0\pi^+\pi^-$ decays and $B^0 \to DK^+\pi^-$, $D \to K^+K^-$, $\pi^+\pi^-$ decays. It is possible to combine the strengths of both approaches in a "double Dalitz plot" analysis of $B^0 \to DK^+\pi^-$, $D \to K_{\rm S}^0\pi^+\pi^-$ decays. The potential sensitivity of such an analysis is investigated in the light of recently published experimental information on the $B^0 \to DK^+\pi^-$ decay. The formalism is also expanded, compared to previous discussions in the literature, to allow $B^0 \to DK^+\pi^-$ with any subsequent $D$ decay to be included.

Unbinned model-independent measurements with coherent admixtures of multibody neutral D meson decays

Various studies of Standard Model parameters involve measuring the properties of a coherent admixture of {D} ^0 and {overline{D}{}} {}^0 states. A typical example is the determination of the Unitarity Triangle angle gamma in the decays Brightarrow DK, Drightarrow {{K} ^0_mathrm{scriptscriptstyle S}} {{pi } ^+} {{pi } ^-} . A model-independent approach to perform this measurement is proposed that has superior statistical sensitivity than the well-established method involving binning of the Drightarrow {{K} ^0_mathrm{scriptscriptstyle S}} {{pi } ^+} {{pi } ^-} decay phase space. The technique employs Fourier analysis of the complex phase difference between {D} ^0 and {overline{D}{}} {}^0 decay amplitudes and can easily be generalised to other similar measurements, such as studies of charm mixing or determination of the angle beta from {{B} ^0} rightarrow D h^0 decays.

Semileptonic decays and |Vxb| determinations

We briefly summarize up-to-date results on the determination of the parameters of the Cabibbo-Kobayashi-Maskawa matrix |Vcb| and |Vub|, which play an important role in the unitarity triangle and in testing the Standard Model, and recent results on semileptonic B meson decays involving a τ lepton.

CP Violation Sensitivity at the Belle II Experiment

The sensitivity on the measurements of the angles of the CKM unitarity triangle, i.e. [Formula: see text], [Formula: see text] and [Formula: see text], for Belle II experiment is presented in this letter, the CKM mechanism is expected to be tested at 1% level on Belle II.

CP Violation in b- and c-hadron decays at LHCb

Testing the Standard Model of particle physics by precision measurements of CP violating observables in the decays of b and c hadrons has been one of the design goals of the LHCb experiment. World-leading measurements have been performed of the semileptonic asymmetry, , and of the mixing-induced CP-violating phase ϕs in the system. The CKM angle γ is still the least known angle of the Unitarity Triangle, and the only one easily accessible using tree-level decays. A recent combination of LHCb measurements in various B → DK decay modes has yielded the most precise determination of γ from a single experiment to date. The LHCb experiment is collecting unprecedented samples of beauty baryons, allowing for the first time to study CP violating observables in their decays. A recent analysis provided the first evidence for CP violation in the beauty baryon sector. Finally, LHCb has the largest samples of charmed hadron decays collected by any experiment to date. These samples yield some of the world’s most sensitive searches for direct and indirect CP violation in the charm sector.

Belle achievements and Belle II prospects for CP violation

The Belle experiment has accomplished various CP violation measurements, in order to constrain the CKM Unitarity Triangle and to search for New Physics signatures, using a data sample of 772 million B-meson pairs. The Belle II experiment will extend research capabilities in this field, thanks to the 50 times larger integrated luminosity expected to be delivered by the SuperKEKB e+e− collider. The results from Belle and future prospects at Belle II are presented.

Connecting the leptonic unitarity triangle to neutrino oscillation with CP violation in the vacuum and in matter

Leptonic unitarity triangle (LUT) provides fundamental means to geometrically describe CP violation in neutrino oscillation. In this work, we use LUT to present a new geometrical interpretation of the vacuum oscillation probability, and derive a compact new oscillation formula in terms of only 3 independent parameters of the corresponding LUT. Then, we systematically study matter effects in the geometrical formulation of neutrino oscillation with CP violation. Including nontrivial matter effects, we derive a very compact new oscillation formula by using the LUT formulation. We further demonstrate that this geometrical formula holds well for applications to neutrino oscillations in matter, including the long baseline experiments T2K, MINOS, NOvA, and DUNE.

New strategy to explore CP violation with Bs0→K−K+

The $U$-spin symmetry provides a powerful tool to extract the angle $\gamma$ of the Unitarity Triangle and the $B_s^0$-$\bar{B}_s^0$ mixing phase $\phi_s$ from CP violation in the $B^0_s\to K^-K^+$, $B^0_d\to\pi^-\pi^+$ system. LHCb has obtained first results with uncertainties at the $7^\circ$ level. Due to $U$-spin-breaking corrections, it will be challenging to reduce the uncertainty below ${\cal O}(5^\circ)$ at Belle II and the LHCb upgrade. We propose a new strategy, using $\gamma$ as input and utilizing $B^0_s\to K^-\ell^+\nu_\ell$, $B^0_d\to \pi^-\ell^+\nu_\ell$ decays, which allows an extraction of $\phi_s$ with a future theoretical precision of up to ${\cal O}(0.5^\circ)$, thereby matching the experimental prospects. Since $B^0_s\to K^-K^+$ is dominated by penguin topologies, new sources of CP violation may be revealed.

Erratum: Constraints on the unitarity triangle angleγfrom Dalitz plot analysis ofB0→DK+π−decays [Phys. Rev. D93, 112018 (2016)

The first study is presented of CP violation with an amplitude analysis of the Dalitz plot of $B^0 \to D K^+ \pi^-$ decays, with $D \to K^+ \pi^-$, $K^+ K^-$ and $\pi^+ \pi^-$. The analysis is based on a data sample corresponding to $3.0\,{\rm fb}^{-1}$ of $pp$ collisions collected with the LHCb detector. No significant CP violation effect is seen, and constraints are placed on the angle $\gamma$ of the unitarity triangle formed from elements of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. Hadronic parameters associated with the $B^0 \to D K^*(892)^0$ decay are determined for the first time. These measurements can be used to improve the sensitivity to $\gamma$ of existing and future studies of the $B^0 \to D K^*(892)^0$ decay.

Analytical approximations for matter effects on CP violation in the accelerator-based neutrino oscillations with E ≲ 1 GeV

Given an accelerator-based neutrino experiment with the beam energy E \lesssim 1 GeV, we expand the probabilities of \nu_\mu \to \nu_e and \overline {\nu}_\mu \to \overline {\nu}_e oscillations in matter in terms of two small quantities \Delta_{21}/\Delta_{31} and A/\Delta_{31}, where \Delta_{21} \equiv m^2_2 - m^2_1 and \Delta_{31} \equiv m^2_3 - m^2_1 are the neutrino mass-squared differences, and A measures the strength of terrestrial matter effects. Our analytical approximations are numerically more accurate than those made by Freund in this energy region, and thus they are particularly applicable for the study of leptonic CP violation in the low-energy MOMENT, ESS\nuSM and T2K oscillation experiments. As a by-product, the new analytical approximations help us to easily understand why the matter-corrected Jarlskog parameter \widetilde{\cal J} peaks at the resonance energy E_* \simeq 0.14 GeV (or 0.12 GeV) for the normal (or inverted) neutrino mass hierarchy, and how the three Dirac unitarity triangles are deformed due to the terrestrial matter contamination. We also affirm that a medium-baseline neutrino oscillation experiment with the beam energy E lying in the E_* \lesssim E \lesssim 2 E_* range is capable of exploring leptonic CP violation with little matter-induced suppression.

Constraints on the unitarity triangle angleγfrom Dalitz plot analysis ofB0→DK+π−decays

The first study is presented of CP violation with an amplitude analysis of the Dalitz plot of B0→DK+π- decays, with D→K+π-, K+K-, and π+π-. The analysis is based on a data sample corresponding to 3.0 fb-1 of pp collisions collected with the LHCb detector. No significant CP violation effect is seen, and constraints are placed on the angle γ of the unitarity triangle formed from elements of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. Hadronic parameters associated with the B0→DK∗(892)0 decay are determined for the first time. These measurements can be used to improve the sensitivity to γ of existing and future studies of the B0→DK∗(892)0 decay.

B(s)0-mixing matrix elements from lattice QCD for the Standard Model and beyond

We calculate---for the first time in three-flavor lattice QCD---the hadronic matrix elements of all five local operators that contribute to neutral $B^0$- and $B_s$-meson mixing in and beyond the Standard Model. We present a complete error budget for each matrix element and also provide the full set of correlations among the matrix elements. We also present the corresponding bag parameters and their correlations, as well as specific combinations of the mixing matrix elements that enter the expression for the neutral $B$-meson width difference. We obtain the most precise determination to date of the SU(3)-breaking ratio $\xi = 1.206(18)(6)$, where the second error stems from the omission of charm sea quarks, while the first encompasses all other uncertainties. The threefold reduction in total uncertainty, relative to the 2013 Flavor Lattice Averaging Group results, tightens the constraint from $B$ mixing on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle. Our calculation employs gauge-field ensembles generated by the MILC Collaboration with four lattice spacings and pion masses close to the physical value. We use the asqtad-improved staggered action for the light valence quarks, and the Fermilab method for the bottom quark. We use heavy-light meson chiral perturbation theory modified to include lattice-spacing effects to extrapolate the five matrix elements to the physical point. We combine our results with experimental measurements of the neutral $B$-meson oscillation frequencies to determine the CKM matrix elements $|V_{td}| = 8.00(34)(8) \times 10^{-3}$, $|V_{ts}| = 39.0(1.2)(0.4) \times 10^{-3}$, and $|V_{td}/V_{ts}| = 0.2052(31)(10)$, which differ from CKM-unitarity expectations by about 2$\sigma$. These results and others from flavor-changing-neutral currents point towards an emerging tension between weak processes that are mediated at the loop and tree levels.

Unitarity and the three flavor neutrino mixing matrix

Unitarity is a fundamental property of any theory required to ensure we work in a theoretically consistent framework. In comparison with the quark sector, experimental tests of unitarity for the 3x3 neutrino mixing matrix are considerably weaker. It must be remembered that the vast majority of our information on the neutrino mixing angles originates from $\overline{\nu}_e$ and $\nu_\mu$ disappearance experiments, with the assumption of unitarity being invoked to constrain the remaining elements. New physics can invalidate this assumption for the 3x3 subset and thus modify our precision measurements. We perform a reanalysis to see how global knowledge is altered when one refits oscillation results without assuming unitarity, and present $3 \sigma$ ranges for allowed $U_\text{PMNS}$ elements consistent with all observed phenomena. We calculate the bounds on the closure of the six neutrino unitarity triangles, with the closure of the $\nu_e \nu_\mu$ triangle being constrained to be $\leq$ 0.03, while the remaining triangles are significantly less constrained to be $\leq$ 0.1 - 0.2. Similarly for the row and column normalization, we find their deviation from unity is constrained to be $\leq$ 0.2 - 0.4, for four out of six such normalisations, while for the $\nu_\mu$ and $\nu_e$ row normalisation the deviations are constrained to be $\leq$ 0.07, all at the $3\sigma$ CL. We emphasise that there is significant room for new low energy physics, especially in the $\nu_\tau$ sector which very few current experiments constrain directly.

Improved determination of the D → K − π + π + π − coherence factor and associated hadronic parameters from a combination ofe+e−→ψ(3770)→cc¯andpp→cc¯Xdata

Measurements of the coherence factor $R_{K3\pi}$, the average strong-phase difference $\delta^{K3\pi}_D$ and mean amplitude ratio $r_D^{K3\pi}$ for the decay $D \to K^-\pi^+\pi^+\pi^-$ are presented. These parameters are important inputs to the determination of the unitarity triangle angle $\gamma$ in $B^- \to DK^-$ decays, where $D$ designates a superposition of $D^0$ and $\bar{D}{}^0$ mesons decaying to a common final state. The results are based on a combined fit to observables obtained from a re-analysis of the CLEO-c $\psi(3770)$ data set and those measured in a $D^0\bar{D}^0$ mixing study performed by the LHCb collaboration.

Emerging lattice approach to the K-unitarity triangle

It has been clear for past many years that in low energy observables new physics can only appear as a perturbation. Therefore precise theoretical predictions and precise experimental measurements have become mandatory. Here we draw attention to the significant advances that have been made on the lattice in recent years in $K\to \pi \pi$, $\Delta M_K$, the long-distance part of $\varepsilon$ and rare K-decays. Thus, in conjunction with experiments, the construction of a unitarity triangle purely from Kaon physics should soon become feasible. Along with the B-unitarity triangle, this should allow for more stringent tests of the Standard Model and tighter constraints on new physics.

Universal Unitarity Triangle 2016 and the tension between [Formula: see text] and [Formula: see text] in CMFV models.

Motivated by the recently improved results from the Fermilab Lattice and MILC Collaborations on the hadronic matrix elements entering Delta M_{s,d} in B_{s,d}^0–bar{B}_{s,d}^0 mixing, we determine the universal unitarity triangle (UUT) in models with constrained minimal flavour violation (CMFV). Of particular importance are the very precise determinations of the ratio |V_{ub}|/|V_{cb}|=0.0864pm 0.0025 and of the angle gamma =(62.7pm 2.1)^circ . They follow in this framework from the experimental values of Delta M_{d}/Delta M_s and of the CP-asymmetry S_{psi K_S}. As in CMFV models the new contributions to meson mixings can be described by a single flavour-universal variable S(v), we next determine the CKM matrix elements |V_{ts}|, |V_{td}|, |V_{cb}| and |V_{ub}| as functions of S(v) using the experimental value of Delta M_s as input. The lower bound on S(v) in these models, derived by us in 2006, implies then upper bounds on these four CKM elements and on the CP-violating parameter varepsilon _K, which turns out to be significantly below its experimental value. This strategy avoids the use of tree-level determinations of |V_{ub}| and |V_{cb}|, which are presently subject to considerable uncertainties. On the other hand, if varepsilon _K is used instead of Delta M_s as input, Delta M_{s,d} are found to be significantly above the data. In this manner we point out that the new lattice data have significantly sharpened the tension between Delta M_{s,d} and varepsilon _K within the CMFV framework. This implies the presence of new physics contributions beyond this framework that are responsible for the breakdown of the flavour universality of the function S(v). We also present the implications of these results for K^+rightarrow pi ^+nu bar{nu }, K_{L}rightarrow pi ^0nu bar{nu } and B_{s,d}rightarrow mu ^+mu ^- within the Standard Model.