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Stefan Schacht

Publications and source records attributed to Stefan Schacht.

At least 19 recordsLinked to original sources
arXiv2026

$CP$ violation in neutral kaon mixing in $D^0\rightarrow K_SK_S$

We study CP violation induced by neutral kaon mixing in $a_{CP}(D^0 \rightarrow K_S K_S)$. We show that the contribution from neutral kaon mixing arises only in connection with second-order weak interactions in $D$ decays. We estimate this effect to be at the $10^{-6}$ level, and thus negligible compared to current experimental sensitivity and to the expected contribution from CP violation in the charm sector. Similar reasoning can be applied to other systems.

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arXiv2026

$\bar B\to D^{(*)}\ell\bar ν$ Branching Ratios and Evidence for Isospin Breaking in $Υ(4S)$ Decays

We introduce a new method for the determination of the ratio of production fractions $R^{\pm0}=\mathcal B(Υ(4S)\to B^+B^-)/\mathcal B(Υ(4S)\to B^0\bar B^0)$ based on $\bar B\to D^{(*)}\ell\bar ν$ decays. Given the importance of these modes, we perform a comprehensive analysis of the available data, extracting the information on their branching fractions and $R^{\pm0}$ in parallel and providing their correlations in order to avoid double-use of this information in phenomenological analyses. We obtain the most precise value for $R^{\pm0}$ from a single channel so far, about 2$σ$ from unity. The combination with previously available determinations from other channels yields $R^{\pm0}=1.062(19)$, constituting evidence for isospin violation in $Υ(4S)$ decays. This demonstrates the necessity to take this effect into account in experimental and phenomenological analyses. The results for the $\bar B\to D^{(*)}\ell\bar ν$ branching fractions are up to $1.6σ$ larger compared to averages available in the literature, owing to the removal of overlooked inconsistencies in the treatment of older analyses and correcting for d'Agostini bias where possible, thereby reducing the $V_{cb}$ puzzle.

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arXiv2026

One Sum To Rule Them All: A Second Order Master Rate Sum Rule for Charm Decays

We show that within the Standard Model any system of hadronic weak charm decays related by $U$-spin satisfies the following rate sum rule: (sum of CF and DCS CKM-free rates) divided by (sum of SCS CKM-free rates) = 1, which holds up to second order in $U$-spin breaking. We test this sum rule against available data and find that it is well satisfied in all cases. For systems in which some decay rates have not yet been measured, we use this sum rule to predict the missing rates.

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arXiv2026

CP Violation in Charmed Meson Decays into Final States with $η'$

We derive Standard Model predictions for the CP asymmetries of singly-Cabibbo suppressed $D\rightarrow Pη'$ decays, where $P=K,π,η$. Our predictions are based on the approximate SU(3)$_F$ symmetry of QCD and include first-order symmetry-breaking effects in a systematic way. The underlying symmetry leads to correlations between different decay modes. To this end we predict the correlations between $ a_{\rm CP}^{\rm dir}(D^+\to π^+ η')$ and $a_{\rm CP}^{\rm dir}(D_s^+ \to K^+ η')$ as well as $a_{\rm CP}^{\rm dir}(D^0\to π^0 η')$ and $ a_{\rm CP}^{\rm dir}(D^0\to ηη')$. Our results can be used to probe the Standard Model with future measurements by LHCb, Belle II and BESIII. At the same time, such future measurements permit the extraction of the key theory parameter related to the ratio of color-suppressed to color-favoured contributions to the decay amplitudes. Future data on both branching ratios and CP asymmetries will automatically improve our predictions and thereby also their sensitivity to physics beyond the Standard Model.

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arXiv2026

Unbinned extraction of $γ$ from $B\to DK$ with normalizing flows

We introduce an unbinned method for extracting the CKM angle $γ$ from the decay chain $B^\pm \to (D \to K_S π^+ π^-) K^\pm$ using normalizing flows (NFs). The NFs, trained on $D$ decay data, learn a faithful continuous representation of the amplitude and strong phase variation over the $D\to K_Sπ^+π^-$ Dalitz plot whose fidelity improves with increased data sample sizes. With this input, the $B$ decay data can be used to extract the parameters $r_B$, $δ_B$, and $γ$. We test the method on Monte Carlo generated data, where it successfully recovers the injected value of $γ$ within uncertainties. The present implementation propagates statistical uncertainties from finite training data via an ensemble of independently trained flows, and does not attempt to capture the effects of systematic experimental errors. We explore two versions of the method that differ in how the trigonometric constraint on phase variation is encoded, and comment on the possible extension to Bayesian NFs, which would provide direct uncertainty estimates on the learned densities without requiring ensemble training.

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arXiv2025

CP violation in $K\toμ^+μ^-$ with and without time dependence through a tagged analysis

We point out that using current knowledge of ${\cal B}(K^0_L\toμ^+μ^-)$ and $ {\cal B}(K^0_L\to γγ)$, one can extract short-distance information from the combined measurement of the time-integrated CP asymmetry, $A_{\rm CP}(K^0\toμ^+μ^-)$, and of ${\cal B}(K^0_S\toμ^+μ^-)$. We discuss the interplay between this set of observables, and demonstrate that determining ${\rm sign}[A_{\rm CP}(K^0\toμ^+μ^-)]$ would eliminate the discrete ambiguity in the Standard Model prediction for ${\cal B}(K^0_L\toμ^+μ^-)$. We then move on to feasibility studies within an LHCb-like setup, using both time-integrated and time-dependent information, employing $K^0$ and $\overline K{}^0$ tagging methods. We find that, within an optimistic scenario, the short-distance amplitude, proportional to the CKM parameter combination $|A^2λ^5\barη|$, could be constrained by LHCb at the level of about $35\%$ of its Standard Model value, and the discrete ambiguity in ${\cal B}(K^0_L\toμ^+μ^-)_{\rm SM}$ could be resolved at more than $3σ$ by the end of the high luminosity LHC.

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arXiv2025

Anatomy of Non-Leptonic Two-Body Decays of Charmed Mesons into Final States with $η'$

We show that $D\rightarrow Pη^\prime$ decay amplitudes, where $P=K,π,η$, cannot be simply related to their $D\rightarrow Pη$ counterparts with a single $η_0$--$η_8$ mixing angle. We propose a novel, consistent treatment of $η_0$--$η_8$ mixing for application in $D\to Pη$ and $D\to Pη^\prime$ decays. Using this framework, we perform a global analysis of $D\rightarrow Pη^\prime$ decays employing SU(3)$_F$ symmetry including linear SU(3)$_F$ breaking. We find that the assumption of 30\% SU(3)$_F$ breaking is in slight tension ($2.5σ$) with the data when compared to a fit that allows for 50\% SU(3)$_F$ breaking, the latter giving a perfect description of the data. In order to allow for further scrutinization of SU(3)$_F$-breaking effects in the future, we give branching ratio predictions for all $D\rightarrow Pη'$ modes. Our predictions deviate from the current data in case of the branching ratios $\mathcal{B}(D_s^+\rightarrow K^+η^\prime)$ and $\mathcal{B}(D^+\rightarrow K^+η')$. Future more precise measurements of these channels are therefore highly important in order to clarify the quality of the SU(3)$_F$ expansion in nonleptonic $D\rightarrow Pη^\prime$ decays.

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arXiv2025

$\bar{B}\rightarrow \bar{D} D$ Decays and the Extraction of $f_d/f_u$ at Hadron Colliders

We perform a detailed model-independent phenomenological analysis of $\bar B\to \bar D D$ decays. Employing an SU(3)$_F$ analysis including symmetry-breaking contributions together with a conservative power counting for various suppression effects, we obtain updated Standard Model predictions for all branching fractions and CP asymmetries from a fit to the available experimental data, testable at Belle II and the LHC experiments. These results include all relevant suppressed contributions, thereby providing upper limits on subleading Standard Model (SM) effects like "penguin pollution", enabling searches for physics beyond the SM. Importantly, allowing in the same fit for the production fractions of charged and neutral $B$ mesons to be different, we find $f_d/f_u = 0.86\pm0.05$, which is $2.5σ$ away from unity, which, if confirmed, would have important phenomenological consequences.

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arXiv2024

Systematics of U-Spin Sum Rules for Systems with Direct Sums

A rich mathematical structure underlying flavor sum rules has been discovered recently. In this work, we extend these findings to systems with a direct sum of representations. We prove several results for the general case. We derive an algorithm that enables the determination of all $U$-spin amplitude sum rules at arbitrary order of the symmetry breaking for any system containing a direct sum of the representations $0 \oplus 1$. Potential applications are numerous and include, for example, higher order sum rules for CP-violating charm decays with an arbitrary number of final states.

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arXiv2024

Reappraisal of SU(3)-flavor breaking in $B\rightarrow DP$

In light of recently found deviations of the experimental data from predictions from QCD factorization for $B_{(s)}\rightarrow D_{(s)}P$ decays, where $P=\{π,K\}$, we systematically probe the current status of the SU(3)$_F$ expansion from a fit to experimental branching ratio data without any further theory input. We find that the current data are in agreement with the power counting of the SU(3)$_F$ expansion. While the SU(3)$_F$ limit is excluded at $>5σ$, amplitude-level SU(3)$_F$-breaking contributions of $\sim 20\%$ suffice for an excellent description of the data. SU(3)$_F$ breaking is needed in tree ($>5σ$) and color-suppressed tree ($2.4σ$) diagrams. We are not yet sensitive to SU(3)$_F$ breaking in exchange diagrams. From the underlying SU(3)$_F$ parametrization we predict the unmeasured branching ratios $\mathcal{B}(\overline{B}_s^0\rightarrow π^- D^+) = 2 \mathcal{B}(\overline{B}_s^0\rightarrow π^0 D^0) = [0.3, 7.2] \times 10^{-6}$ of suppressed decays that can be searched for at the LHCb experiment.

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arXiv2024

Charm CP violation and searches

Charm CP violation is a unique gate to the physics of up-type quarks and allows searches for physics beyond the Standard Model in new and exciting ways, complementary to kaon and $b$ decays. We review recent advances, focusing on symmetry-based methods and providing an outlook on the next challenges at the intensity frontier of charm physics.

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arXiv2024

Determination of the $D\rightarrow ππ$ ratio of penguin over tree diagrams

We study the penguin over tree ratio in $D\rightarrow ππ$ decays. This ratio can serve as a probe for rescattering effects. Assuming the Standard Model and in the isospin limit, we derive expressions that relate both the magnitude and the phase of this ratio to direct CP asymmetries and branching fractions. We find that the current data suggest that rescattering is large. A dedicated experimental analysis with current and future data will be able to significantly reduce the errors on these determinations, and enable us to check if indeed there is significant rescattering in $D \to ππ$ decays.

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arXiv2023

Rare K decays off and on the lattice

The importance of rare $K$ decays especially in the context of a kaon unitarity triangle (KUT) is emphasized. The decay $K_L \to π^0 ν\bar ν$ is theoretically very clean but experimentally extremely challenging. The Standard Model prediction $\mathcal{B}\sim 3 \times 10^{-11}$ is still about two orders of magnitude away from the current experimental upper bound. One way to continue to make progress towards the construction of a KUT is by improving the accuracy in the calculation of $\varepsilon'$. Another way which is the primary focus here is via studies of $K^0 \to π^0 μ^+ μ^-$. LHCb, J-PARC, the proposed HIKE project, phenomenology, and in fact precision studies on the lattice can all play a very important role in this context.

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arXiv2023

Toward extracting $γ$ from $B \to DK$ without binning

$B^\pm \to DK^\pm$ transitions are known to provide theoretically clean information about the CKM angle $γ$, 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 $γ$, with improved choices of test statistic yielding higher sensitivity. While our current proof-of-principle implementation does not demonstrate optimal sensitivity to $γ$, its conceptually novel approach opens the door to new strategies for $γ$ extraction. More studies are required to see if these can be competitive with the existing methods.

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arXiv2023

A Precision Relation between $Γ(K\toμ^+μ^-)(t)$ and ${\cal B}(K_L\toμ^+μ^-)/{\cal B}(K_L\toγγ)$

We find that the phase appearing in the unitarity relation between $\mathcal{B}(K_L\rightarrow μ^+μ^-)$ and $\mathcal{B}(K_L\rightarrow γγ)$ is equal to the phase shift in the interference term of the time-dependent $K\rightarrow μ^+μ^-$ decay. A probe of this relation at future kaon facilities constitutes a Standard Model test with a theory precision of about $2\%$. The phase has further importance for sensitivity studies regarding the measurement of the time-dependent $K\rightarrow μ^+μ^-$ decay rate to extract the CKM matrix element combination $\vert V_{ts} V_{td} \sin(β+β_s)\vert\approx A^2λ^5\barη$. We find a model-independent theoretically clean prediction, $\cos^2φ_0 = 0.96 \pm 0.03$. The quoted error is a combination of the theoretical and experimental errors, and both of them are expected to shrink in the future. Using input from the large-$N_C$ limit within chiral perturbation theory, we find a theory preference towards solutions with negative $\cosφ_0$, reducing a four-fold ambiguity in the angle $φ_0$ to a two-fold one.

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arXiv2023

New Physics Searches at Kaon and Hyperon Factories

Rare meson decays are among the most sensitive probes of both heavy and light new physics. Among them, new physics searches using kaons benefit from their small total decay widths and the availability of very large datasets. On the other hand, useful complementary information is provided by hyperon decay measurements. We summarize the relevant phenomenological models and the status of the searches in a comprehensive list of kaon and hyperon decay channels. We identify new search strategies for under-explored signatures, and demonstrate that the improved sensitivities from current and next-generation experiments could lead to a qualitative leap in the exploration of light dark sectors.

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arXiv2023

Kaon Decays beyond the Standard Model

We review a new method in order to determine the parameter $\barη$ of the Cabibbo-Kobayashi-Maskawa matrix from $K\rightarrow μ^+μ^-$ decays, using interference effects in the time-dependent decay rate. Furthermore, we discuss a new precision relation for the phase-shift of the time-dependent oscillation. The new methodology enables the discovery potential of future time-dependent measurements of $K\rightarrow μ^+μ^-$ decays for physics beyond the Standard Model.

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