arXiv subjects

Stefan Schacht

Publications and source records attributed to Stefan Schacht.

At least 37 records · Page 2Linked to original sources

arXiv2023

A $U$-Spin Anomaly in Charm CP Violation

Recent LHCb data shows that the direct CP asymmetries of the decay modes $D^0\rightarrow π^+π^-$ and $D^0\rightarrow K^+K^-$ have the same sign, violating an improved $U$-spin limit sum rule in an unexpected way at $2.1σ$. From the new data, we determine for the first time the imaginary part of the CKM-subleading, $U$-spin breaking $ΔU=1$ correction to the $U$-spin limit $ΔU=0$ amplitude. The imaginary part of the $ΔU=0$ amplitude is determined by $Δa_{CP}^{\mathrm{dir}}$. The corresponding strong phases are yet unknown and could be extracted in the future from time-dependent measurements. Assuming $\mathcal{O}(1)$ strong phases due to non-perturbative rescattering, we find the ratio of $U$-spin breaking to $U$-spin limit contributions to the CKM-subleading amplitudes to be $(173^{+85}_{-74})\%$. This highly exceeds the Standard Model (SM) expectation of $\sim 30\%$ $U$-spin breaking, with a significance of $1.95σ$. If this puzzle is confirmed with more data in the future, in the SM it would imply the breakdown of the $U$-spin expansion in CKM-subleading amplitudes of charm decays. The other solution are new physics models that generate an additional $ΔU=1$ operator, leaving the $U$-spin power expansion intact. Examples for the latter option are an extended scalar sector or flavorful $Z'$ models.

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arXiv2022

CP violation in $b$ and $c$ quark decays

Generically, non-Standard-Model particles contribute to processes with order-one charge-parity (CP) violating phases, as CP is not a fundamental symmetry of nature. The exploration of CP violation becomes therefore a sensitive search for non-Standard-Model physics. We briefly review the current status of CP-violation studies in bottom- and charm-quark transitions focusing on those quantities that are most sensitive to non-Standard-Model contributions and discuss opportunities and challenges for the next decade and beyond.

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arXiv2022

The Mathematical Structure of $U$-Spin Amplitude Sum Rules

We perform a systematic study of $SU(2)$ flavor amplitude sum rules with particular emphasis on $U$-spin. This study reveals a rich mathematical structure underlying the sum rules that allows us to formulate an algorithm for deriving all $U$-spin amplitude sum rules to any order of the symmetry breaking. This novel approach to deriving the sum rules does not require one to explicitly compute the Clebsch-Gordan tables, and allows for simple diagrammatic interpretation. Several examples that demonstrate the application of our novel method to systems that can be probed experimentally are provided.

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arXiv2021

Enhancement of charm CP violation due to nearby resonances

Quantitative understanding of CP violation is extremely important as naturalness reasoning strongly suggests that new physics should be accompanied by beyond the Standard Model CP-odd phases. In 2019 LHCb made the first $5 σ$ discovery of CP violation in the charm system, leading to the new world average $Δa_{CP}^{\mathrm{dir}} = -0.00161 \pm 0.00028$. While some calculations have found this observation as requiring new physics, we suggest that scalar resonances nearby to $m_{D^0}$, in particular, $f_0(1710)$ and/or $f_0(1790)$ cause enhancements for CP violation within the SM. Thereby, our calculations based on the Standard Model suggest compatibility with the LHCb observations for now. However, experimental information especially on $f_0(1790)$ is rather sparse limiting our accuracy and further data on these resonances is strongly advocated.

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arXiv2021

$K\to μ^{+} μ^{-}$ as a clean probe of short-distance physics

The $K\toμ^+μ^-$ decay is often considered to be uninformative of fundamental theory parameters since the decay is polluted by long-distance hadronic effects. We demonstrate that, using very mild assumptions and utilizing time-dependent interference effects, ${\cal B}(K_S\toμ^+μ^-)_{\ell=0}$ can be experimentally determined without the need to separate the $\ell=0$ and $\ell=1$ final states. This quantity is very clean theoretically and can be used to test the Standard Model. In particular, it can be used to extract the CKM matrix element combination $\left|V_{ts}V_{td}\sin(β+β_s)\right|\approx |A^2 λ^5 \bar η|$ with hadronic uncertainties below $1\%$.

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arXiv2021

Probing the $ΔU=0$ Rule in Three Body Charm Decays

CP violation in charm decay was observed in the decays $D^0\rightarrow P^{\pm}P^{\mp}$ of a $D^0$ meson to two pseudoscalars. When interpreted within the SM, the results imply that the ratio of the relevant rescattering amplitudes has a magnitude and phase that are both of $O(1)$. We discuss ways to probe similar ratios in $D^0\rightarrow V^{\pm}P^{\mp}$ decays, where $V$ is a vector that decays to two pseudoscalars, from the Dalitz-plot analysis of time-integrated three-body decays. Compared to two-body decays, three-body decays have the advantage that the complete system can be solved without the need for time-dependent CP violation measurements or use of correlated $D^0$--$\overline{D}^0$ production. We discuss the decays $D^0\rightarrow π^+π^-π^0$ and $D^0\rightarrow K^+K^-π^0$ as examples by considering a toy model of only two overlapping charged resonances, treating the underlying pseudo two-body decays in full generality.

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arXiv2020

Relations between $b\rightarrow cτν$ Decay Modes in Scalar Models

As a consequence of the Ward identity for hadronic matrix elements, we find relations between the differential decay rates of semileptonic decay modes with the underlying quark-level transition $b\rightarrow cτν$, which are valid in scalar models. The decay-mode dependent scalar form factor is the only necessary theoretical ingredient for the relations. Otherwise, they combine measurable decay rates as a function of the invariant mass-squared of the lepton pair $q^2$ in such a way that a universal decay-mode independent function is found for decays to vector and pseudoscalar mesons, respectively. This can be applied to the decays $B\rightarrow D^{*}τν$, $B_s\rightarrow D_s^*τν$, $B_c\rightarrow J/ψτν$ and $B\rightarrow Dτν$, $B_s\rightarrow D_sτν$, $B_c\rightarrow η_cτν$, with implications for $R(D^{(*)})$, $R(D_s^{(*)})$, $R(J/ψ)$, $R(η_c)$, and $\mathcal{B}(B_c\rightarrow τν)$. The slope and curvature of the characteristic $q^2$-dependence is proportional to scalar new physics parameters, facilitating their straight forward extraction, complementary to global fits.

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arXiv2020

On the Statistical Treatment of the Cabibbo Angle Anomaly

We point out that testing the equality of the Cabibbo angle as extracted from $Γ(K\rightarrow πlν)$, the ratio $Γ(K\rightarrow lν)/Γ(π\rightarrow lν)$ and nuclear $β$ 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 $β$ decays, we find that New Physics is favored over the SM at $5.1\,σ$ or $3.6\,σ$ while CKM unitarity is rejected at $4.8σ$ or $3.0σ$, 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.

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arXiv2020

SU(3)$_F$ Analysis for Beauty Baryon Decays

We perform a general SU(3)$_F$ analysis of $b\rightarrow c\bar{c}s(d)$ decays of members of the beauty baryon antitriplet to a member of the light baryon octet and a singlet. Under several reasonable assumptions we found $\left\vert \mathcal{A}(Ξ_b^0\rightarrow ΛS)/ \mathcal{A}(Ξ_b^0\rightarrow Ξ^0 S)\right\vert\approx 1/\sqrt{6}\, \left\vert V_{cb}^* V_{cd} / (V_{cb}^* V_{cs})\right\vert$ and $\left\vert\mathcal{A}(Λ_b\rightarrow Σ^0 S)/\mathcal{A}(Λ_b\rightarrow ΛS)\right\vert \sim 0.02$. These two relations have been recently probed by LHCb for the case of $S=J/ψ$. The former agrees with the measurement, while for the latter our prediction lies close to the upper bound set by LHCb.

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arXiv2019

The Emergence of the $ΔU=0$ Rule in Charm Physics

We discuss the implications of the recent discovery of CP violation in two-body SCS $D$ decays by LHCb. We show that the result can be explained within the SM without the need for any large $SU(3)$ breaking effects. It further enables the determination of the imaginary part of the ratio of the $ΔU=0$ over $ΔU=1$ matrix elements in charm decays, which we find to be $(0.65\pm 0.12)$. Within the standard model, the result proves the non-perturbative nature of the penguin contraction of tree operators in charm decays, similar to the known non-perturbative enhancement of $ΔI=1/2$ over $ΔI=3/2$ matrix elements in kaon decays, that is, the $ΔI=1/2$ rule. As a guideline for future measurements, we show how to completely solve the most general parametrization of the $D \to P^+P^-$ system.

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arXiv2019

The $V_{cb}$ puzzle: an update

We discuss the impact of the recent untagged analysis of ${B}^0\rightarrow D^{*}l\barν_l$ decays by the Belle Collaboration on the extraction of the CKM element $|V_{cb}|$ and provide updated SM predictions for the $b\to cτν$ observables $R(D^*)$, $P_τ$, and $F_L^{D^*}$. The value of $|V_{cb}|$ that we find is about $2σ$ from the one from inclusive semileptonic $B$ decays, and is very sensitive to the slope of the form factor at zero recoil which should soon become available from lattice calculations.

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arXiv2019

Confronting SUSY SO(10) with updated Lattice and Neutrino Data

We present an updated fit of supersymmetric SO(10) models to quark and lepton masses and mixing parameters. Including latest results from lattice QCD determinations of quark masses and neutrino oscillation data, we show that fits neglecting supersymmetric threshold corrections are strongly disfavoured in our setup. Only when we include these corrections we find good fit points. We present $χ^2$-profiles for the threshold parameters, which show that in our setup the thresholds related to the third generation of fermions exhibit two rather narrow minima.

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arXiv2018

U-Spin Sum Rules for CP Asymmetries of Three-Body Charmed Baryon Decays

Triggered by a recent LHCb measurement and prospects for Belle II, we derive U-spin symmetry relations between integrated CP asymmetries of three-body $Λ_c^+$ and $Ξ_c^+$ decays. The sum rules read $A_{CP}(Λ_c^+\rightarrow p K^- K^+) + A_{CP}(Ξ_c^+\rightarrow Σ^+ π^- π^+) = 0$, $A_{CP}(Λ_c^+\rightarrow p π^- π^+) + A_{CP}(Ξ_c^+\rightarrow Σ^+ K^- K^+) = 0$, and $A_{CP}(Λ_c^+\rightarrow Σ^+ π^- K^+) + A_{CP}(Ξ_c^+\rightarrow pK^-π^+) = 0$. No such U-spin sum rule exists between $A_{CP}(Λ_c^+\rightarrow p K^- K^+)$ and $A_{CP}(Λ_c^+\rightarrow p π^- π^+)$. All of these sum rules are associated with a complete interchange of $d$ and $s$ quarks. Furthermore, there are no U-spin CP asymmetry sum rules which hold to first order U-spin breaking.

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arXiv2017

Neutral $D\rightarrow K K^*$ decays as discovery channels for charm CP violation

We point out that the CP asymmetries in the decays $D^0\rightarrow K_{S} K^{*0}$ and $D^0\rightarrow K_{S} \overline{K}{}^{*0}$ are potential discovery channels for charm CP violation in the Standard Model. We stress that no flavor tagging is necessary, the untagged CP asymmetry $a_{CP}^{\mathrm{dir}}(D \to K_S K^{*0})$ is essentially equal to the tagged one, so that the untagged measurement comes with a significant statistical gain. Depending on the relevant strong phase, $\vert a_{CP}^{\text{dir, untag}}\vert$ can be as large as $0.003$. The CP asymmetry is dominantly generated by exchange diagrams and does not require non-vanishing penguin amplitudes. While the CP asymmetry is smaller than in the case of $D^0\rightarrow K_SK_S$, the experimental analysis is more efficient due to the prompt decay $K^{*0}\rightarrow K^+π^-$. One may further search for favourable strong phases in the Dalitz plot in the vicinity of the $K^{*0}$ peak.

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arXiv2017

The role of theory input for exclusive $V_{cb}$ determinations

Available form factor parametrizations for $B\rightarrow D^*lν$ imply different theoretical assumptions and different treatments of theoretical uncertainties. They give results for $\vert V_{cb}\vert$ whose central values are apart by up to $8\%$. The way the Caprini Lellouch Neubert (CLN) parametrization has been used in experimental analyses sets theoretical uncertainties of the Heavy Quark Effective Theory (HQET) results on slope and curvature of the form factor ratios $R_1$ and $R_2$ to zero. Furthermore, the relation of curvature and slope of the axial form factor $A_1$ is fixed to the HQET central value. In view of the current experimental precision these uncertainties cannot be neglected any more. Using the Boyd Grinstein Lebed (BGL) parametrization and taking into account theoretical uncertainties in a conservative way, we extract $\vert V_{cb}\vert$ from recent preliminary Belle data and the world average of the total branching ratio. We include an $\mathcal{O}(10\%-20\%)$ theoretical uncertainty of HQET input due to unknown corrections beyond NLO which were neglected in all previous analyses. This is important for reliable extractions of $\vert V_{cb}\vert$ as well as precision tests of the Standard Model with robust predictions of the lepton flavor nonuniversality observable $R(D^*)$ and the $τ$ polarization asymmetry $P_τ$. Including input from Light Cone Sum Rules (LCSRs) we find $\vert V_{cb}\vert = 40.6\left(^{+1.2}_{-1.3}\right)\cdot 10^{-3}$, $R(D^*) = 0.260(8)$ and $P_τ=-0.47(4)$. Without LCSRs we find $\vert V_{cb}\vert = 41.5(1.3)\cdot 10^{-3}$ and the same results for $R(D^*)$ and $P_τ$. The $R(D^*)$ anomaly is persistent, but its statistical significance is slightly reduced to 2.6$σ$.

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arXiv2017

$R(D^*)$, $|V_{cb}|$, and the Heavy Quark Symmetry relations between form factors

Stringent relations between the $B^{(*)} \to D^{(*)} $ form factors exist in the heavy quark limit and the leading symmetry breaking corrections are known. We reconsider their uncertainty and role in the analysis of recent Belle data for $B\to D^{(*)}\ellν$ with model-independent parametrizations and in the related prediction of $R(D^{(*)})$. We find $|V_{cb}|=41.5(1.3) \ 10^{-3}$ and $|V_{cb}|=40.6(^{+1.2}_{-1.3}) \ 10^{-3}$ using input from Light Cone Sum Rules, and $R(D^{*})=0.260(8)$.

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arXiv2017

A fresh look at the determination of |V_cb| from B-> D^* l nu

We use recent Belle results on $\bar{B}^0\rightarrow D^{*+}l^-\barν_l$ decays to extract the CKM element $|V_{cb}|$ with two different but well-founded parameterizations of the form factors. We show that the CLN and BGL parameterizations lead to quite different results for $|V_{cb}|$ and provide a simple explanation of this unexpected behaviour. A long lasting discrepancy between the inclusive and exclusive determinations of $|V_{cb}|$ may have to be thoroughly reconsidered.

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arXiv2017

CP asymmetries in $D\to PP^\prime$ decays

This talk addresses two topics related to CP asymmetries in $D$ meson decays to two pseudoscalar mesons. First I discuss how new physics can be distinguished from the Standard Model through two sum rules relating three direct CP asymmetries each, using the sum rule correlating $D^0\to K^+K^-$, $D^0\to π^+ π^-$, and $D^0\to π^0 π^0$ for illustration. The other sum rule involves $a_{CP}^{\mathrm{dir}}(D^+\rightarrow \bar{K}^0K^+)$, $a_{CP}^{\mathrm{dir}}(D_s^+\rightarrow K^0π^+)$, and $a_{CP}^{\mathrm{dir}}(D_s^+\to K^+ π^0)$. The second topic is the direct CP asymmetry in the decay $D^0 \to K_S K_S$, which is expected to be large in the Standard Model for two reasons: Flavor-SU(3) symmetry suppresses the tree amplitude which enhances the crucial "penguin-to-tree" ratio and the "penguin" amplitude is dominated by the tree-level $W$ boson exchange between $c$ and $u$ quarks. We find that $|a_{CP}^{\mathrm{dir}} (D^0 \to K_S K_S)|$ can be as large as $1.1 \%$ in the Standard Model. We advocate $D^0 \to K_S K_S$ as a discovery channel for charm CP violation.

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