arXiv subjects

Christoph Bobeth

Publications and source records attributed to Christoph Bobeth.

At least 19 recordsLinked to original sources

arXiv2022

Power-enhanced leading-logarithmic QED corrections to $B_q \to μ^+μ^-$

We provide a systematic treatment of the previously discovered power-enhanced QED corrections to the leptonic decay $B_q\to μ^+μ^-$ ($q = d, s$) in the framework of soft-collinear effective theory (SCET). Employing two-step matching on SCET$_\text{I}$ and SCET$_\text{II}$, and the respective renormalization group equations, we sum the leading-logarithmic QED corrections and the mixed QED-QCD corrections to all orders in the couplings for the matrix element of the semileptonic weak effective operator $\sim Q_9$. We propose a treatment of the $B$-meson decay constant and light-cone distribution amplitude in the presence of process-specific QED corrections. Finally we include ultrasoft photon radiation and provide updated values of the non-radiative and radiative branching fractions of $B_q \to μ^+μ^-$ decay that include the double-logarithmic QED and QCD corrections.

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arXiv2021

General non-leptonic $ΔF=1$ WET at the NLO in QCD

We reconsider the complete set of four-quark operators in the Weak Effective Theory (WET) for non-leptonic $ΔF=1$ decays that govern $s\to d$ and $b\to d, s$ transitions in the Standard Model (SM) and beyond, at the Next-to-Leading Order (NLO) in QCD. We discuss cases with different numbers $N_f$ of active flavours, intermediate threshold corrections, as well as the issue of transformations between operator bases beyond leading order to facilitate the matching to high-energy completions or the Standard Model Effective Field Theory (SMEFT) at the electroweak scale. As a first step towards a SMEFT NLO analysis of $K\toππ$ and non-leptonic $B$-meson decays, we calculate the relevant WET Wilson coefficients including two-loop contributions to their renormalization group running, and express them in terms of the Wilson coefficients in a particular operator basis for which the one-loop matching to SMEFT is already known.

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arXiv2021

EOS -- A Software for Flavor Physics Phenomenology

EOS is an open-source software for a variety of computational tasks in flavor physics. Its use cases include theory predictions within and beyond the Standard Model of particle physics, Bayesian inference of theory parameters from experimental and theoretical likelihoods, and simulation of pseudo events for a number of signal processes. EOS ensures high-performance computations through a C++ back-end and ease of usability through a Python front-end. To achieve this flexibility, EOS enables the user to select from a variety of implementations of the relevant decay processes and hadronic matrix elements at run time. In this article, we describe the general structure of the software framework and provide basic examples. Further details and in-depth interactive examples are provided as part of the EOS online documentation.

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arXiv2021

Searching for New Physics with $\overline{\mathcal{B}}(B_{s,d}\toμ\barμ)/ΔM_{s,d}$

We reemphasize that the ratio $R_{sμ} \equiv \overline{\mathcal{B}}(B_s\toμ\barμ)/ΔM_s$ is a measure of the tension of the Standard Model (SM) with latest measurements of $\overline{\mathcal{B}}(B_s\toμ\barμ)$ that does not suffer from the persistent puzzle on the $|V_{cb}|$ determinations from inclusive versus exclusive $b\to c\ell\barν$ decays and which affects the value of the CKM element $|V_{ts}|$ that is crucial for the SM predictions of both $\overline{\mathcal{B}}(B_s\toμ\barμ)$ and $ΔM_s$, but cancels out in the ratio $R_{sμ}$. In our analysis we include higher order electroweak and QED corrections und adapt the latest hadronic input to find a tension of about $2σ$ for $R_{sμ}$ measurements with the SM independently of $|V_{ts}|$. We also discuss the ratio $R_{dμ}$ which could turn out, in particular in correlation with $R_{sμ}$, to be useful for the search for New Physics, when the data on both ratios improves. Also $R_{dμ}$ is independent of $|V_{cb}|$ or more precisely $|V_{td}|$.

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arXiv2021

BSM Master Formula for $\varepsilon'/\varepsilon$ in the WET Basis at NLO in QCD

As an important step towards a complete next-to-leading order (NLO) QCD analysis of the ratio $\varepsilon'/\varepsilon$ within the Standard Model Effective Field Theory (SMEFT), we present for the first time the NLO master formula for the BSM part of this ratio expressed in terms of the Wilson coefficients of all contributing operators evaluated at the electroweak scale. To this end we use the common Weak Effective Theory (WET) basis (the so-called JMS basis) for which tree-level and one-loop matching to the SMEFT are already known. The relevant hadronic matrix elements of BSM operators at the electroweak scale are taken from Dual QCD approach and the SM ones from lattice QCD. It includes the renormalization group evolution and quark-flavour threshold effects at NLO in QCD from hadronic scales, at which these matrix elements have been calculated, to the electroweak scale.

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arXiv2021

Lepton-flavour non-universality of $\bar{B}\to D^*\ell \barν$ angular distributions in and beyond the Standard Model

We analyze in detail the angular distributions in $\bar{B}\to D^*\ell \barν$ decays, with a focus on lepton-flavour non-universality. We investigate the minimal number of angular observables that fully describes current and upcoming datasets, and explore their sensitivity to physics beyond the Standard Model (BSM) in the most general weak effective theory. We apply our findings to the current datasets, extract the non-redundant set of angular observables from the data, and compare to precise SM predictions that include lepton-flavour universality violating mass effects. Our analysis shows that the current presentation of the experimental data is not ideal and prohibits the extraction of the full set of relevant BSM parameters, since the number of independent angular observables that can be inferred from data is limited to only four. We uncover a $\sim4σ$ tension between data and predictions that is hidden in the redundant presentation of the Belle 2018 data on $\bar{B}\to D^*\ell \barν$ decays. This tension specifically involves observables that probe $e-μ$ lepton-flavour universality. However, we find inconsistencies in these data, which renders results based on it suspicious. Nevertheless, we discuss which generic BSM scenarios could explain the tension, in the case that the inconsistencies do not affect the data materially. Our findings highlight that $e-μ$ non-universality in the SM, introduced by the finite muon mass, is already significant in a subset of angular observables with respect to the experimental precision.

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arXiv2021

$B_{d,s}\toγ\ell\bar{\ell}$ decay with an energetic photon

We calculate the differential branching fraction, lepton forward-backward asymmetry and direct CP asymmetry for $B_{d,s}\toγ\ell\bar{\ell}$ decays with an energetic photon. We employ factorization methods, which result in rigorous next-to-leading order predictions in the strong coupling at leading power in the large-energy/heavy-quark expansion, together with estimates of power corrections and a resonance parameterization of sub-leading power form factors in the region of small lepton invariant mass $q^2$. The $B_{d,s}\toγ\ell\bar{\ell}$ decay shares features of the charged-current decay $B_u \to γ\ell\barν_\ell$, and the FCNC decays $B\to K^{(*)}\ell\bar\ell$. As in the former, the leading-power decay rates can be expressed in terms of the $B$-meson light-cone distribution amplitude and short-distance factors. However, similar to $B\to K^{(*)}\ell\bar\ell$, four-quark and dipole operators contribute to the $B_{d,s}\toγ\ell\bar{\ell}$ decay in an essential way, limiting the calculation to $q^2\lesssim 6\,$GeV$^2$ below the charmonium resonances in the lepton invariant mass spectrum. A detailed analysis of the main observables and theoretical uncertainties is presented.

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arXiv2021

Leptoquarks meet $\varepsilon'/\varepsilon$ and rare Kaon processes

We analyse for the first time the CP violating ratio $\varepsilon'/\varepsilon$ in $K\to ππ$ decays in leptoquark (LQ) models. Assuming a mass gap to the electroweak (EW) scale, the main mechanism for LQs to contribute to $\varepsilon'/\varepsilon$ is EW gauge-mixing of semi-leptonic into non-leptonic operators, which we treat in the Standard Model effective theory (SMEFT). We perform also the one-loop decoupling for scalar LQs, finding that in all models with both left-handed and right-handed LQ couplings box-diagrams generate numerically strongly enhanced EW-penguin operators $Q_{8,8'}$ already at the LQ scale. We then investigate correlations of $\varepsilon'/\varepsilon$ with rare Kaon processes ($K_L\toπ^0ν\barν$, $K^+\toπ^+ν\barν$, $K_L\toπ^0\ell\bar\ell$, $K_S\toμ\barμ$, $ΔM_K$ and $\varepsilon_K$) and find that even imposing only a moderate enhancement of $(\varepsilon'/\varepsilon)_{\rm NP} = 5 \times 10^{-4}$ to explain the current anomaly hinted by the Dual QCD approach and RBC-UKQCD lattice QCD calculations leads to conflicts with experimental upper bounds on rare Kaon processes. They exclude all LQ models with only a single coupling as an explanation of the $\varepsilon'/\varepsilon$ anomaly and put strong-to-serious constraints on parameter spaces of the remaining models. Future results on $K^+\toπ^+ν\barν$ from the NA62 collaboration, $K_L\toπ^0ν\barν$ from the KOTO experiment and $K_S\toμ\barμ$ from LHCb will even stronger exhibit the difficulty of LQ models in explaining the measured $\varepsilon'/\varepsilon$, in case the $\varepsilon'/\varepsilon$ anomaly will be confirmed by improved lattice QCD calculations. Hopefully also improved measurements of $K_L\toπ^0\ell\bar\ell$ decays will one day help in this context.

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arXiv2020

SMEFT ATLAS of $ΔF=2$ Transitions

We present a model-independent anatomy of the $ΔF=2$ transitions $K^0-\bar K^0$, $B_{s,d}-\bar B_{s,d}$ and $D^0-\bar D^0$ in the context of the Standard Model Effective Field Theory (SMEFT). We present two master formulae for the mixing amplitude $\big[M_{12} \big]_\text{BSM}$. One in terms of the Wilson coefficients (WCs) of the Low-Energy Effective Theory (LEFT) operators evaluated at the electroweak scale $μ_\text{ew}$ and one in terms of the WCs of the SMEFT operators evaluated at the BSM scale $Λ$. The coefficients $P_a^{ij}$ entering these formulae contain all the information below the scales $μ_\text{ew}$ and $Λ$, respectively. Renormalization group effects from the top-quark Yukawa coupling play the most important role. The collection of the individual contributions of the SMEFT operators to $\big[M_{12}\big]_\text{BSM}$ can be considered as the SMEFT ATLAS of $ΔF=2$ transitions and constitutes a travel guide to such transitions far beyond the scales explored by the LHC. We emphasize that this ATLAS depends on whether the down-basis or the up-basis for SMEFT operators is considered. We illustrate this technology with tree-level exchanges of heavy gauge bosons ($Z^\prime$, $G^\prime$) and corresponding heavy scalars.

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arXiv2020

$\varepsilon'/\varepsilon$ in the Standard Model at the Dawn of the 2020s

We reanalyse the ratio $\varepsilon'/\varepsilon$ in the Standard Model (SM) using most recent hadronic matrix elements from the RBC-UKQCD collaboration in combination with most important NNLO QCD corrections to electroweak penguin contributions and the isospin-breaking corrections. We illustrate the importance of the latter by using their latest estimate from chiral perturbation theory (ChPT) based on the $octet$ approximation for lowest-lying mesons and a very recent estimate in the $nonet$ scheme that takes into account the contribution of $η_0$. We find $(\varepsilon'/\varepsilon)^{(8)}_\text{SM} = (17.4 \pm 6.1) \times 10^{-4}$ and $(\varepsilon'/\varepsilon)^{(9)}_\text{SM} = (13.9 \pm 5.2) \times 10^{-4}$, respectively. Despite a very good agreement with the measured value $(\varepsilon'/\varepsilon)_\text{exp} = (16.6 \pm 2.3) \times 10^{-4}$, the large error in $(\varepsilon'/\varepsilon)_\text{SM}$ still leaves room for significant new physics (BSM) contributions to this ratio. We update the 2018 master formula for $(\varepsilon'/\varepsilon)_\text{BSM}$ valid in any extension beyond the SM without additional light degrees of freedom. We provide new values of the penguin parameters $B_6^{(1/2)}(μ)$ and $B_8^{(3/2)}(μ)$ at the $μ$-scales used by the RBC-UKQCD collaboration and at lower scales $\mathcal{O}(1\,\text{GeV})$ used by ChPT and DQCD. We present semi-analytic formulae for $(\varepsilon'/\varepsilon)_\text{SM}$ in terms of these parameters and $\hatΩ_\text{eff}$ that summarizes isospin-breaking corrections to this ratio. We stress the importance of lattice calculations of the $\mathcal{O}(α_\text{em})$ contributions to the hadronic matrix elements necessary for the removal of renormalization scheme dependence at $\mathcal{O}(α_\text{em})$ in the present analyses of $\varepsilon'/\varepsilon$.

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arXiv2020

On the Importance of NNLO QCD and Isospin-breaking Corrections in $\varepsilon'/\varepsilon$

Following the 1999 analysis of Gambino, Haisch and one of us, we stress that all the recent NLO analyses of $\varepsilon'/\varepsilon$ in the Standard Model (SM) suffer from the renormalization scheme dependence present in the electroweak penguin contributions as well as from scale uncertainties in them related to the matching scale $μ_W$ and in particular to $μ_t$ in $m_t(μ_t)$. We also reemphasize the important role of isospin-breaking and QED effects in the evaluation of $\varepsilon'/\varepsilon$. Omitting all these effects, as done in the 2015 analysis by RBC-UKQCD collaboration, and choosing as an example the QCD penguin ($Q_6$) and electroweak penguin ($Q_8$) parameters $B_6^{(1/2)}$ and $B_8^{(3/2)}$ to be $B_6^{(1/2)} = 0.80 \pm 0.08$ and $B_8^{(3/2)} = 0.76 \pm 0.04$ at $μ= m_c = 1.3$ GeV, we find $(\varepsilon'/\varepsilon)_\text{SM} = (9.4 \pm 3.5) \times 10^{-4}$, whereas including them results in $(\varepsilon'/\varepsilon)_\text{SM} = (5.6\pm 2.4) \times 10^{-4}$. This is an example of an anomaly at the $3.3\,σ$ level, which would be missed without these corrections. NNLO QCD contributions to QCD penguins are expected to further enhance this anomaly. We provide a table for $\varepsilon'/\varepsilon$ for different values of $B_6^{(1/2)}$ and the isospin-breaking parameter $\hatΩ_\text{eff}$, that should facilitate monitoring the values of $\varepsilon'/\varepsilon$ in the SM when the RBC-UKQCD calculations of hadronic matrix elements including isospin-breaking corrections and QED effects will improve with time.

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arXiv2019

Master formula for $\varepsilon'/\varepsilon$ beyond the Standard Model

We present for the first time a master formula for $\varepsilon'/\varepsilon$, the ratio probing direct CP violation in $K \to ππ$ decays, valid in any theory beyond the Standard Model (BSM). The formula makes use of hadronic matrix elements of BSM operators calculated recently in the Dual QCD approach and the ones of the SM operators from lattice QCD. We emphasize the large impact of several scalar and tensor BSM operators in the context of the emerging $\varepsilon'/\varepsilon$ anomaly. We have implemented the results in the open source code flavio.

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arXiv2019

Anatomy of $\varepsilon'/\varepsilon$ beyond the Standard Model

We present for the first time a model-independent anatomy of the ratio $\varepsilon'/\varepsilon$ in the context of the $ΔS = 1$ effective theory with operators invariant under QCD and QED and in the context of the Standard Model Effective Field Theory (SMEFT) with the operators invariant under the full SM gauge group. Our goal is to identify the new physics scenarios that are probed by this ratio and which could help to explain a possible deviation from the SM that is hinted by the data. To this end we derive a master formula for $\varepsilon'/\varepsilon$, which can be applied to any theory beyond the Standard Model (BSM) in which the Wilson coefficients of all contributing operators have been calculated at the electroweak scale. The relevant hadronic matrix elements of BSM operators are from the Dual QCD approach and the SM ones from lattice QCD. Within SMEFT, the constraints from $K^0$ and $D^0$ mixing as well as electric dipole moments limit significantly potential new physics contributions to $\varepsilon'/\varepsilon$. Correlations of $\varepsilon'/\varepsilon$ with $K\toπν\barν$ decays are briefly discussed. Building on our EFT analysis and the model-independent constraints, we discuss implications of a possible deviation from the SM in $\varepsilon'/\varepsilon$ for model building, highlighting the role of the new scalar and tensor matrix elements in models with scalar mediators.

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arXiv2017

Enhanced electromagnetic correction to the rare $B$-meson decay $B_{s,d} \to μ^+ μ^-$

We investigate electromagnetic corrections to the rare $B$-meson leptonic decay $B_{s,d} \to μ^+μ^-$ from scales below the bottom-quark mass $m_b$. Contrary to QCD effects, which are entirely contained in the $B$-meson decay constant, we find that virtual photon exchange can probe the $B$-meson structure, resulting in a "non-local annihilation" effect. We find that this effect gives rise to a dynamical enhancement by a power of $m_b/Λ_{\rm QCD}$ and by large logarithms. The impact of this novel effect on the branching ratio of $B_{s,d}\toμ^+μ^-$ is about $1\%$, of the order of the previously estimated non-parametric theoretical uncertainty, and four times the size of previous estimates of next-to-leading order QED effects due to residual scale dependence. We update the Standard Model prediction to $\overline{\cal B}(B_s \to μ^+μ^-)_{\rm SM} = (3.57 \pm 0.17) \cdot 10^{-9}$.

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arXiv2017

Long-distance effects in $B\to K^*\ell\ell$ from Analyticity

We discuss a novel approach to systematically determine the long-distance contribution to $B\to K^*\ell\ell$ decays in the kinematic region where the dilepton invariant mass is below the open charm threshold. This approach provides the most consistent and reliable determination to date and can be used to compute Standard Model predictions for all observables of interest, including the kinematic region where the dilepton invariant mass lies between the $J/ψ$ and the $ψ(2S)$ resonances. We illustrate the power of our results by performing a New Physics fit to the Wilson coefficient $C_9$. This approach is systematically improvable from theoretical and experimental sides, and applies to other decay modes of the type $B\to V\ell\ell$, $B\to P\ell\ell$ and $B\to Vγ$.

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arXiv2017

Yukawa enhancement of $Z$-mediated New Physics in $ΔS = 2$ and $ΔB = 2$ Processes

We discuss Yukawa-enhanced contributions from $Z$-mediated new physics to down-type quark $ΔF=2$ processes in the framework of the standard model gauge-invariant effective theory (SMEFT). Besides the renormalization group (RG) mixing of the $Z$-mediating $ψ^2 H^2 D$ operators into $ΔF = 2$ operators, we include at the electroweak scale one-loop (NLO) matching corrections consistently, necessary for the removal of the matching scale dependence. We point out that the right-handed $Z$-mediated interactions generate through Yukawa RG mixing $ΔF=2$ left-right operators, which are further enhanced through QCD RG effects and chirally enhanced hadronic matrix elements. We investigate the impact of these new effects on the known correlations between $ΔF=2$ and $ΔF=1$ transitions in the SMEFT framework and point out qualitative differences to previous parameterizations of $Z$-mediated new physics that arise for the left-handed case. We illustrate how specific models fit into our model-independent framework by using four models with vector-like quarks. We carry out model-independent analyses of scenarios with purely left-handed and purely right-handed new-physics $Z$ couplings for each of the three sectors $s\to d$, $b\to s$ and $b\to d$. Specifically we discuss the correlations between $\varepsilon'/\varepsilon$, $\varepsilon_K$, $K_L\to μ^+μ^-$ $K^+\to π^+ν\barν$ and $K_L\toπ^0ν\barν$ in the Kaon sector, and $ϕ_s$, $B_s\toμ^+μ^-$ and $B\to K^{(*)} (μ^+μ^-, ν\barν)$ in the $b\to s$ sector and $B_d\toμ^+μ^-$ in the $b\to d$ sector.

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arXiv2017

Patterns of Flavour Violation in Models with Vector-Like Quarks

We study the patterns of flavour violation in renormalisable extensions of the Standard Model (SM) that contain vector-like quarks (VLQs) in a single complex representation of either the SM gauge group $G_{SM}$ or $G_{SM}' = G_{SM} \times U(1)_{L_μ- L_τ}$. We first decouple VLQs in the $M=(1-10)$ TeV range and then at the electroweak scale also $Z, Z'$ gauge bosons and additional scalars to study the resulting phenomenology that depends on the relative size of $Z$- and $Z'$-induced flavour-changing neutral currents, as well as the size of $ΔF=2$ contributions including the effects of renormalisation group Yukawa evolution from $M$ to the electroweak scale that turn out to be very important for models with right-handed currents through the generation of left-right operators. In addition to rare decays like $P\to \ell\bar\ell$, $P\to P' \ell\bar\ell$, $P\to P'ν\barν$ with $P=K, B_s, B_d$ and $ΔF=2$ observables we analyze the ratio $\varepsilon'/\varepsilon$ which appears in the SM to be significantly below the data. We study patterns and correlations between these observables which taken together should in the future allow for differentiating between VLQ models. In particular the patterns in models with left-handed and right-handed currents are markedly different from each other. Among the highlights are large $Z$-mediated new physics effects in Kaon observables in some of the models and significant effects in $B_{s,d}$-observables. $\varepsilon'/\varepsilon$ can easily be made consistent with the data, implying then uniquely the suppression of $K_L\to π^0 ν\barν$. Significant enhancements of $Br(K^+\to π^+ ν\barν)$ are still possible. We point out that the combination of $ΔF=2$ and $ΔF=1$ observables in a given meson system generally allows to determine the masses of VLQs independently of the size of VLQ couplings.

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arXiv2016

General Analysis of B -> K^(*) l^+ l^- Decays at Low Recoil

We analyze the angular distributions of B -> K^* (-> K pi) l^+ l^- and B -> K l^+ l^- decays in the region of low hadronic recoil in a model-independent way by taking into account the complete set of dimension-six operators [sbar Gamma b][lbar Gamma' l]. We obtain several novel low-recoil observables with high sensitivity to non-standard-model Dirac structures, including CP-asymmetries which do not require flavor tagging. The transversity observables H_T^(1,3,4,5) are found to be insensitive to hadronic matrix elements and their uncertainties even when considering the complete set of operators. In the most general scenario we show that the low recoil operator product expansion can be probed at the few-percent level using the angular observable J_7. Higher sensitivities are possible assuming no tensor contributions, specifically by testing the low-recoil relation |H_T^(1)|=1. We explicitly demonstrate the gain in reach of the low-recoil observables in accessing the ratio |C_9/C_10| compared to the forward-backward asymmetry, and probing CP-violating right-handed currents Im C_10'. We give updated Standard Model predictions for key observables in B -> K^(*) l^+ l^- decays.

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