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Measurement of the CKM angle $\gamma $ in the ${{{B} ^0} \rightarrow {D} {{K} ^{*0}}}$ channel using self-conjugate ${D} \rightarrow {{K} ^0_{\textrm{S}}} h^+ h^-$ decays

A model-independent study of $C\!P$ violation in ${{B} ^0} \rightarrow {D} {{K} ^{*0}}$ decays is presented using data corresponding to an integrated luminosity of 9 fb -1 collected by the LHCb experiment at centre-of-mass energies of $\sqrt{s}=7, \, 8$ and 13 TeV. The CKM angle $\gamma$ is determined by examining the distributions of signal decays in phase-space bins of the self-conjugate ${D} \rightarrow {{K} ^0_{\textrm{S}}} h^+ h^-$ decays, where $h = \pi , K$. Observables related to $C\!P$ violation are measured and the angle $\gamma$ is determined to be $\gamma =(49^{+ 22}_{-19})^\circ$. Measurements of the amplitude ratio and strong-phase difference between the favoured and suppressed ${B} ^0$ decays are also presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Toward extracting $$\gamma $$ from $$B\rightarrow DK$$ without binning

Abstract $$B^\pm \rightarrow DK^\pm $$ B ± → D K ± transitions are known to provide theoretically clean information about the CKM angle $$\gamma $$ γ , with the most precise available methods exploiting the cascade decay of the neutral D into CP self-conjugate states. Such analyses currently require binning in the D decay Dalitz plot, while a recently proposed method replaces this binning with the truncation of a Fourier series expansion. In this paper, we present a proof of principle of a novel alternative to these two methods, in which no approximations at the level of the data representation are required. In particular, our new strategy makes no assumptions about the amplitude and strong phase variation over the Dalitz plot. This comes at the cost of a degree of ambiguity in the choice of test statistic quantifying the compatibility of the data with a given value of $$\gamma $$ γ , with improved choices of test statistic yielding higher sensitivity. While our current proof-of-principle implementation does not demonstrate optimal sensitivity to $$\gamma $$ γ , its conceptually novel approach opens the door to new strategies for $$\gamma $$ γ extraction. More studies are required to see if these can be competitive with the existing methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Measurement of the CKM angle γ in B ± → DK ± and B ± → Dπ ± decays with D → $ {K}_{\mathrm{S}}^0 $h + h -

A measurement of CP -violating observables is performed using the decays B ± → DK ± and B ± → Dπ ± , where the D meson is reconstructed in one of the self-conjugate three-body final states \( {K}_{\mathrm{S}}^0 \) π + π - and \( {K}_{\mathrm{S}}^0 \) K + K - (commonly denoted \( {K}_{\mathrm{S}}^0 \) h + h - ). The decays are analysed in bins of the D -decay phase space, leading to a measurement that is independent of the modelling of the D -decay amplitude. The observables are inter- preted in terms of the CKM angle γ . Using a data sample corresponding to an integrated luminosity of 9 fb - 1 collected in proton-proton collisions at centre-of mass energies of 7, 8, and 13 TeV with the LHCb experiment, γ is measured to be \( \left({68.7}_{-5.1}^{+5.2}\right){}^{\circ} \) . The hadronic parameters \( {r}_B^{D K},{r}_B^{D\pi},{\delta}_B^{D K},\kern0.5em \mathrm{and}\kern0.5em {\delta}_B^{D\pi} \) , which are the ratios and strong-phase differences of the suppressed and favoured B ± decays, are also reported.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Combined analysis of Belle and Belle II data to determine the CKM angle φ 3 using B + → D($ {K}_S^0 $h + h – )h + decays

We present a measurement of the Cabibbo-Kobayashi-Maskawa unitarity triangle angle φ 3 (also known as γ) using a model-independent Dalitz plot analysis of B + → D($ {K}_S^0 $h + h – )h + , where D is either a D o or D o ¯ meson and h is either a π or K. This is the first measurement that simultaneously uses Belle and Belle II data, combining samples corresponding to integrated luminosities of 711 fb –1 and 128 fb –1 , respectively. All data were accumulated from energy-asymmetric e + e – collisions at a centre-of-mass energy corresponding to the mass of the Υ(4S) resonance. We measure φ 3 = (78.4 ± 11.4 ± 0.5 ± 1.0)°, where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is from the uncertainties on external measurements of the D-decay strong-phase parameters.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Measurement of CP observables in B ± → D (*) K ± and B ± → D (*) π ± decays using two-body D final states

Measurements of CP observables in B ± → D (*) K ± and B ± → D (*) π ± decays are presented, where D (∗) indicates a neutral D or D ∗ meson that is an admixture of meson and anti-meson states. Decays of the D (∗) meson to the Dπ 0 and Dγ final states are partially reconstructed without inclusion of the neutral pion or photon. Decays of the D meson are reconstructed in the K ± π ∓ , K + K - , and π + π - final states. The analysis uses a sample of charged B mesons produced in proton-proton collisions and collected with the LHCb experiment, corresponding to integrated luminosities of 2.0, 1.0, and 5.7 fb -1 taken at centre-of-mass energies of 7, 8, and 13 TeV, respectively. The measurements of partially reconstructed B ± → D (*) K ± and B ± → D (∗) π ± with D → K ∓ π ± decays are the first of their kind, and a first observation of the B ± → (Dπ 0 ) D ∗ π ± decay is made with a significance of 6.1 standard deviations. All CP observables are measured with world-best precision, and in combination with other LHCb results will provide strong constraints on the CKM angle γ.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measurement of the D → K - π + π + π- and D → K - π + π 0 coherence factors and average strong-phase differences in quantum-correlated $ D\overline{D} $ decays

The decays D → K - π + π + π - and D → K - π + π 0 are studied in a sample of quantum-correlated \( D\overline{D} \) pairs produced through the process e + e - → ψ (3770) → \( D\overline{D} \) , exploiting a data set collected by the BESIII experiment that corresponds to an integrated luminosity of 2.93 fb - 1 . Here D indicates a quantum superposition of a D 0 and a \( {\overline{D}}^0 \) meson. By reconstructing one neutral charm meson in a signal decay, and the other in the same or a different final state, observables are measured that contain information on the coherence factors and average strong-phase differences of each of the signal modes. These parameters are critical inputs in the measurement of the angle γ of the Unitarity Triangle in B - → DK - decays at the LHCb and Belle II experiments. The coherence factors are determined to be R K 3 π = \( {0.52}_{-0.10}^{+0.12} \) and \( {R}_{K{\pi \pi}^0} \) = 0 . 78 ± 0 . 04, with values for the average strong-phase differences that are \( {\delta}_D^{K3\pi }=\left({167}_{-19}^{+31}\right){}^{\circ} \) and \( {\delta}_D^{K{\pi \pi}^0}=\left({196}_{-15}^{+14}\right){}^{\circ} \) , where the uncertainties include both statistical and systematic contributions. The analysis is re-performed in four bins of the phase-space of the D → K - π + π + π - to yield results that will allow for a more sensitive measurement of γ with this mode, to which the BESIII inputs will contribute an uncertainty of around 6°.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Constraints on the CKM angle γ from B ± → Dh ± decays using D → h ± h' ∓ π 0 final states

A data sample collected with the LHCb detector corresponding to an integrated luminosity of 9 fb –1 is used to measure eleven CP violation observables in B ± → Dh ± decays, where h is either a kaon or a pion. The neutral D meson decay is reconstructed in the three-body final states: K ± π ∓ π o ; π + π – π o ; K + K – π o and the suppressed π ± K ∓ π o combination. The mode where a large CP asymmetry is expected, B ± → [π ± K ∓ π o ] D K ± , is observed with a significance greater than seven standard deviations. The ratio of the partial width of this mode relative to that of the favoured mode, B ± → [K ± π ∓ π o ] D K ± , is R ADS(K) = (1.27 ± 0.16 ± 0.02) × 10 –2 . Evidence for a large CP asymmetry is also seen: A ADS(K) = –0.38 ± 0.12 ± 0.02. Constraints on the CKM angle γ are calculated from the eleven reported observables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simultaneous determination of CKM angle γ and charm mixing parameters

A combination of measurements sensitive to the CP violation angle γ of the Cabibbo-Kobayashi-Maskawa unitarity triangle and to the charm mixing parameters that describe oscillations between D 0 and $ \overline{D} $ 0 mesons is performed. Results from the charm and beauty sectors, based on data collected with the LHCb detector at CERN’s Large Hadron Collider, are combined for the first time. This method provides an improvement on the precision of the charm mixing parameter y by a factor of two with respect to the current world average. The charm mixing parameters are determined to be $ x=\left({0.400}_{-0.053}^{+0.052}\right)\% $ and y = $ \left({0.630}_{-0.030}^{+0.033}\right)\% $. The angle γ is found to be γ = ($ 65.4_{-4.2}^{+3.8} $)° and is the most precise determination from a single experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Measurement of the CKM angle γ with B ± → D[K ∓ π ± π ± π ∓ ]h ± decays using a binned phase-space approach

The CKM angle γ is determined from CP-violating observables measured in B ± → D[K ∓ π ± π ± π ∓ ]h ± , (h = K, π) decays, where the measurements are performed in bins of the decay phase-space of the D meson. Using proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to a total integrated luminosity of 9 fb –1 , γ is determined to be $\gamma ={\left(54.8\begin{array}{c}+6.0\\ {}-5.8\end{array}\begin{array}{c}+0.6\\ {}-0.6\end{array}\begin{array}{c}+6.7\\ {}-4.3\end{array}\right)}^{\circ },$ where the first uncertainty is statistical, the second systematic and the third from the external inputs on the coherence factors and strong phases of the D-meson decays.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

On the statistical treatment of the Cabibbo angle anomaly

We point out that testing the equality of the Cabibbo angle as extracted from $\Gamma(K\rightarrow \pi l\nu)$, the ratio $\Gamma(K\rightarrow l\nu)/\Gamma(\pi\rightarrow l\nu)$ and nuclear $\beta$ 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 $\beta$ decays, we find that New Physics is favored over the SM at $5.1\,\sigma$ or $3.6\,\sigma$ while CKM unitarity is rejected at $4.8\sigma$ or $3.0\sigma$, 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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Testing Lepton Flavor Universality and CKM Unitarity with Rare Pion Decays in the PIONEER experiment

The physics motivation and the conceptual design of the PIONEER experiment, a next-generation rare pion decay experiment testing lepton flavor universality and CKM unitarity, are described. Phase I of the PIONEER experiment, which was proposed and approved at Paul Scherrer Institut, aims at measuring the charged-pion branching ratio to electrons vs. muons, $R_{e/\mu}$, 15 times more precisely than the current experimental result, reaching the precision of the Standard Model (SM) prediction at 1 part in $10^4$. Considering several inconsistencies between the SM predictions and data pointing towards the potential violation of lepton flavor universality, the PIONEER experiment will probe non-SM explanations of these anomalies through sensitivity to quantum effects of new particles up to the PeV mass scale. The later phases of the PIONEER experiment aim at improving the experimental precision of the branching ratio of pion beta decay (BRPB), $\pi^+\to \pi^0 e^+ \nu (\gamma)$, currently at $1.036(6)\times10^{-8}$, by a factor of three (Phase II) and an order of magnitude (Phase III). Such precise measurements of BRPB will allow for tests of CKM unitarity in light of the Cabibbo Angle Anomaly and the theoretically cleanest extraction of $|V_{ud}|$ at the 0.02% level, comparable to the deduction from superallowed beta decays.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

PIONEER: Studies of Rare Pion Decays

A next-generation rare pion decay experiment, PIONEER, is strongly motivated by several inconsistencies between Standard Model (SM) predictions and data pointing towards the potential violation of lepton flavor universality. It will probe non-SM explanations of these anomalies through sensitivity to quantum effects of new particles even if their masses are at very high scales. Measurement of the charged-pion branching ratio to electrons vs. muons $R_{e/\mu}$ is extremely sensitive to new physics effects. At present, the SM prediction for $R_{e/\mu}$ is known to 1 part in $10^4$, which is 15 times more precise than the current experimental result. An experiment reaching the theoretical accuracy will test lepton flavor universality at an unprecedented level, probing mass scales up to the PeV range. Measurement of pion beta decay, $\pi^+\to \pi^0 e^+ \nu (\gamma)$, with 3 to 10-fold improvement in sensitivity, will determine $V_{ud}$ in a theoretically pristine manner and test CKM unitarity, which is very important in light of the recently emerged tensions. In addition, various exotic rare decays involving sterile neutrinos and axions will be searched for with unprecedented sensitivity. The experiment design benefits from experience with the recent PIENU and PEN experiments at TRIUMF and the Paul Scherrer Institut (PSI). Excellent energy and time resolutions, greatly increased calorimeter depth, high-speed detector and electronics response, large solid angle coverage, and complete event reconstruction are all critical aspects of the approach. The PIONEER experiment design includes a 3$\pi$ sr 25 radiation length calorimeter, a segmented low gain avalanche detector stopping target, a positron tracker, and other detectors. Using intense pion beams, and state-of-the-art instrumentation and computational resources, the experiments can be performed at the PSI ring cyclotron.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗