arXiv subjects

Bastian Kubis

Publications and source records attributed to Bastian Kubis.

At least 37 records · Page 2Linked to original sources

arXiv2024

Correlations of $C$ and $CP$ violation in $η\to π^0\ell^+\ell^-$ and $η'\to η\ell^+\ell^-$

Based on recent progress in the systematic analysis of $C$ and $CP$ violation in the light-meson sector, we calculate the $C$-odd transition amplitudes $η\toπ^0\ell^+\ell^-$ and $η'\toη\ell^+\ell^-$. Focusing on long-distance contributions driven by the lowest-lying hadronic intermediate states, we work out the correlations between these beyond-the-Standard-Model signals and the Dalitz-plot asymmetries in $η\rightarrow π^0 π^+ π^-$ and $η' \rightarrow ηπ^+ π^- $, using dispersion theory.

hep-ph↗

arXiv2023

The semileptonic decays $η^{(\prime)} \to π^0 \ell^+ \ell^-$ and $η' \to η\ell^+ \ell^-$ in the standard model

We perform a theoretical analysis of the semileptonic decays $η^{(\prime)} \to π^0 \ell^+ \ell^-$ and $η' \to η\ell^+ \ell^-$, where $\ell = e, μ$, via a charge-conjugation-conserving two-photon mechanism. The underlying form factors are modeled using vector-meson dominance, phenomenological input, and $\mathrm{U}(3)$ flavor symmetry. We consider both a monopole and a dipole model, the latter tailored such that the expected high-energy behavior is ensured. Furthermore, we benchmark the effect of $S$-wave rescattering contributions to the decays. We infer significant effects of the form factors neglected in the literature so far, still finding branching ratios of the various decays well below the current experimental upper limits.

hep-ph↗

arXiv2023

A phenomenological estimate of isospin breaking in hadronic vacuum polarization

Puzzles in the determination of the hadronic-vacuum-polarization contribution currently impede a conclusive interpretation of the precision measurement of the anomalous magnetic moment of the muon at the Fermilab experiment. One such puzzle concerns tensions between evaluations in lattice QCD and using $e^+e^-\to\text{hadrons}$ cross-section data. In lattice QCD, the dominant isospin-symmetric part and isospin-breaking (IB) corrections are calculated separately, with very different systematic effects. Identifying these two pieces in a data-driven approach provides an opportunity to compare them individually and trace back the source of the discrepancy. Here, we estimate the IB component of the lattice-QCD calculations from phenomenology, based on a comprehensive study of exclusive contributions that can be enhanced via infrared singularities, threshold effects, or hadronic resonances, including, for the first time, in the $e^+e^-\to3π$ channel. We observe sizable cancellations among different channels, with a sum that even suggests a slightly larger result for the QED correction than obtained in lattice QCD. We conclude that the tensions between lattice QCD and $e^+e^-$ data therefore cannot be explained by the IB contributions in the lattice-QCD calculations.

hep-ph↗

arXiv2023

Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization

Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the $e^+e^-\toπ^+π^-$ channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for $e^+e^-\to 3π$ by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and $ρ$-$ω$ mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor $η_{3π}$ that generalizes the analog treatment of virtual and final-state photons in the $2π$ case. The global fit to the $e^+e^-\to 3π$ data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives $a_μ^{3π}|_{\leq 1.8\,\text{GeV}}=45.91(53)\times 10^{-10}$ for the total $3π$ contribution to the anomalous magnetic moment of the muon, of which $a_μ^\text{FSR}[3π]=0.51(1)\times 10^{-10}$ and $a_μ^{ρ\text{-}ω}[3π]=-2.68(70)\times 10^{-10}$ can be ascribed to IB. We argue that the resulting cancellation with $ρ$-$ω$ mixing in $e^+e^-\to 2π$ can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters $M_ω=782.70(3)\,\text{MeV}$, $M_ϕ=1019.21(2)\,\text{MeV}$, $Γ_ω=8.71(3)\,\text{MeV}$, and $Γ_ϕ=4.27(1)\,\text{MeV}$.

hep-ph↗

arXiv2023

Axial-vector transition form factors and $e^+ e^- \to f_1 π^+ π^-$

We study the transition form factors (TFFs) of axial-vector mesons in the context of currently available experimental data, including new constraints from $e^+ e^- \to f_1(1285) π^+ π^-$ that imply stringent limits on the high-energy behavior and, for the first time, allow us to provide an unambiguous determination of the couplings corresponding to the two antisymmetric TFFs. We discuss how these constraints can be implemented in a vector-meson-dominance picture, and, in combination with contributions from the light-cone expansion, construct TFFs as input for the evaluation of axial-vector contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

hep-ph↗

arXiv2023

$C$ and $CP$ violation in effective field theories

The quest for new sources of the simultaneous violation of $C$ and $CP$ symmetry was popular in the 1960s and has since been mostly neglected for more than half a century. In this work we revisit fundamental quark-level operators that break $C$ and $CP$ up to and including mass dimension 8 for flavor-conserving transitions, relying on the complete operator sets of the so-called Standard Model effective field theory and the low-energy effective field theory. With the formalism of chiral perturbation theory, we match these quark operators to light-meson physics, derive $C$- and $CP$-odd Lagrangians for several processes in the $η$, $η'$, and pion sectors, and furthermore, as a proof of principle, give estimates for the respective observables in explicit dependence of the underlying high-energy scale for new physics.

hep-ph↗

arXiv2023

On the role of isospin violation in the pion-nucleon $σ$-term

In recent years, a persistent tension between phenomenological and lattice QCD determinations of the pion-nucleon $σ$-term $σ_{πN}$ has developed. In particular, lattice-QCD calculations have matured to the point that isospin-violating effects need to be included. Here, we point out that the standard conventions adopted in both fields are incompatible, with the data-driven extraction based on the charged-pion mass, but lattice-QCD conventions relying on the mass of the neutral pion to define the isospin limit. The corresponding correction amounts to $Δσ_{πN}=3.1(5)\,\text{MeV}$ when evaluated in chiral perturbation theory with low-energy constants determined from a Roy-Steiner analysis of pion-nucleon scattering as well as $σ_{πN}$ itself. It reduces the tension with lattice QCD, and should be included in the comparison to phenomenological determinations. We also update the extraction from pionic atoms accounting for the latest measurement of the width of pionic hydrogen, $σ_{πN}=59.0(3.5)\,\text{MeV}$, and provide the corresponding set of scalar couplings of the nucleon.

hep-ph↗

arXiv2023

Dispersion relations for $B^- \to \ell^- \barν_\ell \ell^{\prime-} \ell^{\prime+}$ form factors

Using dispersive methods, we study the $B \to γ^*$ form factors underlying the decay $B^- \to \ell^- \barν_\ell \ell^{\prime-} \ell^{\prime+}$. We discuss the ambiguity that arises from a separation of the full $B^- \to \ell^- \barν_\ell \ell^{\prime-} \ell^{\prime+}$ amplitude into a hadronic tensor and a final-state-radiation piece, including effects from nonvanishing lepton masses. For the eligibility of a dispersive treatment, we propose a decomposition of the hadronic part that leads to four form factors that are free of kinematic singularities. By establishing a set of dispersion relations, we then relate the $B \to γ^*$ form factors to the well-known $B \to V$, $V=ω(782),ρ(770)$, analogues. Using the combination of a series expansion in a conformal variable and a vector-meson-dominance ansatz to parameterize the $B \to γ^*$ form factors, we infer the values of the associated unknown parameters from the available input on $B \to V$. The phenomenological application of our formalism includes the determination of the branching ratios and forward-backward asymmetries of the process $B^- \to \ell^- \barν_\ell \ell^{\prime-} \ell^{\prime+}$ for the two lightest leptons.

hep-ph↗

arXiv2023

Analysis of rescattering effects in $3π$ final states

Decays into three particles are often described in terms of two-body resonances and a non-interacting spectator particle. To go beyond this simplest isobar model, crossed-channel rescattering effects need to be accounted for. We quantify the importance of these rescattering effects in three-pion systems for different decay masses and angular-momentum quantum numbers. We provide the amplitude decompositions for four decay processes with total $J^{PC} = 0^{--}$, $1^{--}$, $1^{-+}$, and $2^{++}$, all of which decay predominantly as $ρπ$ states. Two-pion rescattering is described in terms of an Omnès function, which incorporates the $ρ$ resonance. Inclusion of crossed-channel effects is achieved by solving the Khuri-Treiman integral equations. The unbinned log-likelihood estimator is used to determine the significance of the rescattering effects beyond two-body resonances; we compute the minimum number of events necessary to unambiguously find these in future Dalitz-plot analyses. Kinematic effects that enhance or dilute the rescattering are identified for the selected set of quantum numbers and various masses.

hep-ph↗

arXiv2023

Patterns of $C$- and $CP$-violation in hadronic $η$ and $η'$ three-body decays

We construct hadronic amplitudes for the three-body decays $η^{(\prime)}\toπ^+π^-π^0$ and $η'\toηπ^+π^-$ in a non-perturbative fashion, allowing for $C$- and $CP$-violating asymmetries in the $π^+π^-$ distributions. These amplitudes are consistent with the constraints of analyticity and unitarity. We find that the currently most accurate Dalitz-plot distributions taken by the KLOE-2 and BESIII collaborations confine the patterns of these asymmetries to a relative per mille level. Our dispersive representation allows us to extract the individual coupling strengths of the $C$- and $CP$-violating contributions arising from effective isoscalar and isotensor operators in $η^{(\prime)}\toπ^+π^-π^0$ and an effective isovector operator in $η'\toηπ^+π^-$, while the strongly different sensitivities to these operators can be understood from chiral power counting arguments.

hep-ph↗

arXiv2022

A dispersive analysis of $η'\toπ^+π^-γ$ and $η'\to \ell^+\ell^-γ$

We present a dispersive representation of the $η'$ transition form factor that allows one to account, in a consistent way, for the effects of $ρ$-$ω$ mixing in both the isoscalar and the isovector contributions. Using this formalism, we analyze recent data on $η'\to π^+π^-γ$ to constrain the isovector part of the form factor, individually and in combination with data for the pion vector form factor. As a first application, we use our results, in combination with the most recent input for the isoscalar part of the form factor, to predict the corresponding spectrum of $η'\to\ell^+\ell^-γ$, in particular we find the slope parameter $b_{η'}=1.431(23)\, \text{GeV}^{-2}$. With forthcoming data on the latter process, our results establish the necessary framework to improve the evaluation of the $η'$-pole contribution to the anomalous magnetic moment of the muon using experimental input from both $η'$ decay channels.

hep-ph↗

arXiv2022

$CP$ violation in $η^{(\prime)}\toπ^+π^-μ^+μ^-$ decays

It has been pointed out recently that a certain set of dimension-6 scalar $P$- and $CP$-violating light-quark-muon operators may be tested in $η$ and $η'$ decays to various final states involving $μ^+μ^-$ pairs, at a level not yet excluded by constraints from electric dipole moments. We here work out the hadronic matrix elements required for the predictions for the decays $η, η' \toπ^+π^-μ^+μ^-$. We relate a new asymmetry in the angular distribution between the dipion and dimuon decay planes to the corresponding Wilson coefficients. Despite the advantage of not requiring the measurement of muon polarization, the projected sensitivities are shown to be moderate due to a combination of small phase space and chiral suppression. Such sensitivity studies are most timely in view of upcoming or planned high-statistics $η^{(\prime)}$ experiments such as the JLab eta factory or REDTOP.

hep-ph↗

arXiv2022

Chiral extrapolation of hadronic vacuum polarization and isospin-breaking corrections

By far the biggest contribution to hadronic vacuum polarization (HVP) arises from the two-pion channel. Its quark-mass dependence can be evaluated by combining dispersion relations with chiral perturbation theory, providing guidance on the functional form of chiral extrapolations, or even interpolations around the physical point. In addition, the approach allows one to estimate in a controlled way the isospin-breaking (IB) corrections that arise from the pion mass difference. As an application, we present an updated estimate of phenomenological expectations for electromagnetic and strong IB corrections to the HVP contribution to the anomalous magnetic moment of the muon. In particular, we include IB effects in the $\bar K K$ channel, which are enhanced due to the proximity of the $\bar K K$ threshold and the $ϕ$ resonance. The resulting estimates make it unlikely that the current tension between lattice-QCD and data-driven evaluations of the HVP contribution is caused by IB corrections.

hep-ph↗

arXiv2022

Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization

Isospin-breaking (IB) effects in the two-pion contribution to hadronic vacuum polarization (HVP) can be resonantly enhanced, if related to the interference of the $ρ(770)$ and $ω(782)$ resonances. This particular IB contribution to the pion vector form factor and thus the line shape in $e^+e^-\to π^+π^-$ can be described by the residue at the $ω$ pole - the $ρ$-$ω$ mixing parameter $ε_ω$. Here, we argue that while in general analyticity requires this parameter to be real, the radiative channels $π^0γ$, $ππγ$, $ηγ$ can induce a small phase, whose size we estimate as $δ_ε=3.5(1.0)^\circ$ by using a narrow-width approximation for the intermediate-state vector mesons. We then perform fits to the $e^+e^-\to π^+π^-$ data base and study the consequences for the two-pion HVP contribution to the anomalous magnetic moment of the muon, its IB part due to $ρ$-$ω$ mixing, and the mass of the $ω$ resonance. We find that the global fit does prefer a non-vanishing value of $δ_ε=4.5(1.2)^\circ$, close to the narrow-resonance expectation, but with a large spread among the data sets, indicating systematic differences in the $ρ$-$ω$ region.

hep-ph↗

arXiv2022

Kaon electromagnetic form factors in dispersion theory

The electromagnetic form factors of charged and neutral kaons are strongly constrained by their low-energy singularities, in the isovector part from two-pion intermediate states and in the isoscalar contribution in terms of $ω$ and $ϕ$ residues. The former can be predicted using the respective $ππ\to\bar K K$ partial-wave amplitude and the pion electromagnetic form factor, while the latter parameters need to be determined from electromagnetic reactions involving kaons. We present a global analysis of time- and spacelike data that implements all of these constraints. The results enable manifold applications: kaon charge radii, elastic contributions to the kaon electromagnetic self energies and corrections to Dashen's theorem, kaon boxes in hadronic light-by-light (HLbL) scattering, and the $ϕ$ region in hadronic vacuum polarization (HVP). Our main results are: $\langle r^2\rangle_\text{c}=0.359(3)\,\text{fm}^2$, $\langle r^2\rangle_\text{n}=-0.060(4)\,\text{fm}^2$ for the charged and neutral radii, $ε=0.63(40)$ for the elastic contribution to the violation of Dashen's theorem, $a_μ^{K\text{-box}}=-0.48(1)\times 10^{-11}$ for the charged kaon box in HLbL scattering, and $a_μ^\text{HVP}[K^+K^-, \leq 1.05\,\text{GeV}]=184.5(2.0)\times 10^{-11}$, $a_μ^\text{HVP}[K_SK_L, \leq 1.05\,\text{GeV}]=118.3(1.5)\times 10^{-11}$ for the HVP integrals around the $ϕ$ resonance. The global fit to $\bar K K$ gives $\bar M_ϕ=1019.479(5)\,\text{MeV}$, $\bar Γ_ϕ=4.207(8)\,\text{MeV}$ for the $ϕ$ resonance parameters including vacuum-polarization effects.

hep-ph↗

arXiv2022

Improved Standard-Model prediction for $π^0\to e^+e^-$

We present an improved Standard-Model (SM) prediction for the dilepton decay of the neutral pion. The loop amplitude is determined by the pion transition form factor for $π^0\toγ^*γ^*$, for which we employ a dispersive representation that incorporates both space-like and time-like data as well as short-distance constraints. The resulting SM branching fraction, $\text{BR}[π^0\to e^+e^-]=6.25(3)\times 10^{-8}$ , sharpens constraints on physics beyond the SM, including pseudoscalar and axial-vector mediators.

hep-ph↗

arXiv2022

Chiral extrapolation of hadronic vacuum polarization

We study the pion-mass dependence of the two-pion channel in the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon $a_μ^\text{HVP}$, by using an Omnès representation for the pion vector form factor with the phase shift derived from the inverse-amplitude method (IAM). Our results constrain the dominant isospin-$1$ part of the isospin-symmetric light-quark contribution, and should thus allow one to better control the chiral extrapolation of $a_μ^\text{HVP}$, required for lattice-QCD calculations performed at larger-than-physical pion masses. In particular, the comparison of the one- and two-loop IAM allows us to estimate the associated systematic uncertainties and show that these are under good control.

hep-ph↗

arXiv2022

Precision tests of fundamental physics with $η$ and $η^\prime$ mesons

Decays of the neutral and long-lived $η$ and $η'$ mesons provide a unique, flavor-conserving laboratory to test low-energy Quantum Chromodynamics and search for new physics beyond the Standard Model. They have drawn world-wide attention in recent years and have inspired broad experimental programs in different high-intensity-frontier centers. New experimental data will offer critical inputs to precisely determine the light quark mass ratios, $η$-$η'$ mixing parameters, and hadronic contributions to the anomalous magnetic moment of the muon. At the same time, it will provide a sensitive probe to test potential new physics. This includes searches for hidden photons, light Higgs scalars, and axion-like particles that are complementary to worldwide efforts to detect new light particles below the GeV mass scale, as well as tests of discrete symmetry violation. In this review, we give an update on theoretical developments, discuss the experimental opportunities, and identify future research needed in this field.

hep-ph↗