arXiv subjects

Bastian Kubis

Publications and source records attributed to Bastian Kubis.

At least 55 records · Page 3Linked to original sources

arXiv2021

The $γπ\toππ$ anomaly from lattice QCD and dispersion relations

We propose a formalism to extract the $γπ\toππ$ chiral anomaly $F_{3π}$ from calculations in lattice QCD performed at larger-than-physical pion masses. To this end, we start from a dispersive representation of the $γ^{(*)}π\toππ$ amplitude, whose main quark-mass dependence arises from the $ππ$ scattering phase shift and can be derived from chiral perturbation theory via the inverse-amplitude method. With parameters constrained by lattice calculations of the $P$-wave phase shift, we use this combination of dispersion relations and effective field theory to extrapolate two recent $γ^{(*)}π\toππ$ calculations in lattice QCD to the physical point. Our formalism allows us to extract the radiative coupling of the $ρ(770)$ meson and, for the first time, the chiral anomaly $F_{3π}=38(16)(11)\,\text{GeV}^{-3}$. The result is consistent with the chiral prediction albeit within large uncertainties, which will improve in accordance with progress in future lattice-QCD computations.

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arXiv2021

On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^+e^-$

Estimating the contribution from axial-vector intermediate states to hadronic light-by-light scattering requires input on their transition form factors (TFFs). Due to the Landau-Yang theorem, any experiment sensitive to these TFFs needs to involve at least one virtual photon, which complicates their measurement. Phenomenologically, the situation is best for the $f_1(1285)$ resonance, for which information is available from $e^+e^-\to e^+e^- f_1$, $f_1\to 4π$, $f_1\to ργ$, $f_1\to ϕγ$, and $f_1\to e^+e^-$. We provide a comprehensive analysis of the $f_1$ TFFs in the framework of vector meson dominance, including short-distance constraints, to determine to which extent the three independent TFFs can be constrained from the available experimental input, a prerequisite for improved calculations of the axial-vector contribution to hadronic light-by-light scattering. In particular, we focus on the process $f_1\to e^+e^-$, evidence for which has been reported recently by SND for the first time, and discuss the impact that future improved measurements will have on the determination of the $f_1$ TFFs.

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arXiv2021

What can we learn about light-meson interactions at electron-positron colliders?

Precision studies at electron-positron colliders with center-of-mass energies in the charm-tau region and below have strongly contributed to our understanding of light-meson interactions at low energies. We focus on the processes involving two or three light mesons with invariant masses below nucleon-antinucleon threshold. A prominent role is given to the interactions of the nine lightest pseudoscalar mesons (pions, kaons, $η$, and $η'$) and the two narrow neutral isoscalar vector mesons $ω$ and $ϕ$. Experimental methods used to produce the mesons are reviewed as well as theory tools to extract properties of the meson-meson interactions. Examples of recent results from the DA$Φ$NE, BEPCII, and VEPP-2000 colliders are presented. In the outlook we briefly discuss prospects for further studies at future super-charm-tau factories.

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arXiv2021

On the scalar $πK$ form factor beyond the elastic region

Pion-kaon ($πK$) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of $πK$ scattering and production amplitudes over a wide energy range is therefore mandatory for multiple applications: in Standard Model tests; to describe crossed channels in the quest for exotic hadronic states; and for an improved spectroscopy of excited kaon resonances. In the elastic region, the phase shifts of $πK$ scattering in a given partial wave are related to the phases of the respective $πK$ form factors by Watson's theorem. Going beyond that, we here construct a representation of the scalar $πK$ form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from $πK$ scattering and maintaining the correct analytic structure. As a first application, we consider the decay ${τ\to K_Sπν_τ}$, in particular, we study to which extent the $S$-wave $K_0^*(1430)$ and the $P$-wave $K^*(1410)$ resonances can be differentiated and provide an improved estimate of the $CP$ asymmetry produced by a tensor operator. Finally, we extract the pole parameters of the $K_0^*(1430)$ and $K_0^*(1950)$ resonances via Padé approximants, $\sqrt{s_{K_0^*(1430)}}=[1408(48)-i\, 180(48)]$ MeV and $\sqrt{s_{K_0^*(1950)}}=[1863(12)-i\,136(20)]$ MeV, as well as the pole residues. A generalization of the method also allows us to formally define a branching fraction for ${τ\to K_0^*(1430) ν_τ}$ in terms of the corresponding residue, leading to the upper limit ${\text{BR}(τ\to K_0^*(1430) ν_τ)<1.6 \times 10^{-4}}$.

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arXiv2021

Where is the lightest charmed scalar meson?

The lightest charmed scalar meson is known as the $D_0^*(2300)$, which is one of the earliest new hadron resonances observed at modern $B$ factories. We show here that the parameters assigned to the lightest scalar $D$-meson are in conflict with the precise LHCb data of the decay $B^-\to D^+ π^- π^-$. On the contrary, these data can be well described by an unitarized chiral amplitude containing a much lighter charmed scalar meson, the $D_0^*(2100)$. We also extract the low-energy $S$-wave $Dπ$ phase of the decay $B^-\to D^+ π^- π^-$ from the data in a model-independent way, and show that its difference from the $Dπ$ scattering phase shift can be traced back to an intermediate $ρ^-$ exchange. Our work highlights that an analysis of data consistent with chiral symmetry, unitarity, and analyticity is mandatory in order to extract the properties of the ground-state scalar mesons in the singly heavy sector correctly, in analogy to the light scalar mesons $f_0(500)$ and $K_0^*(700)$.

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arXiv2021

Two-Meson Form Factors in Unitarized Chiral Perturbation Theory

We present a comprehensive analysis of form factors for two light pseudoscalar mesons induced by scalar, vector, and tensor quark operators. The theoretical framework is based on a combination of unitarized chiral perturbation theory and dispersion relations. The low-energy constants in chiral perturbation theory are fixed by a global fit to the available data of the two-meson scattering phase shifts. Each form factor derived from unitarized chiral perturbation theory is improved by iteratively applying a dispersion relation. This study updates the existing results in the literature and explores those that have not been systematically studied previously, in particular the two-meson tensor form factors within unitarized chiral perturbation theory. We also discuss the applications of these form factors as mandatory inputs for low-energy phenomena, such as the semi-leptonic decays $B_s\to π^+π^-\ell^+\ell^-$ and the $τ$ lepton decay $τ\rightarrowπ^{-}π^{0}ν_τ$, in searches for physics beyond the Standard Model.

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arXiv2021

Two-loop analysis of the pion-mass dependence of the $ρ$ meson

Analyzing the pion-mass dependence of $ππ$ scattering phase shifts beyond the low-energy region requires the unitarization of the amplitudes from chiral perturbation theory. In the two-flavor theory, unitarization via the inverse-amplitude method (IAM) can be justified from dispersion relations, which is therefore expected to provide reliable predictions for the pion-mass dependence of results from lattice QCD calculations. In this work, we provide compact analytic expression for the two-loop partial-wave amplitudes for $J=0,1,2$ required for the IAM at subleading order. To analyze the pion-mass dependence of recent lattice QCD results for the $P$-wave, we develop a fit strategy that for the first time allows us to perform stable two-loop IAM fits and assess the chiral convergence of the IAM approach. While the comparison of subsequent orders suggests a breakdown scale not much below the $ρ$ mass, a detailed understanding of the systematic uncertainties of lattice QCD data is critical to obtain acceptable fits, especially at larger pion masses.

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arXiv2021

Dispersive analysis of the Primakoff reaction $γK \to K π$

We provide a dispersion-theoretical representation of the reaction amplitudes $γK\to K π$ in all charge channels, based on modern pion-kaon $P$-wave phase shift input. Crossed-channel singularities are fixed from phenomenology as far as possible. We demonstrate how the subtraction constants can be matched to a low-energy theorem and radiative couplings of the $K^*(892)$ resonances, thereby providing a model-independent framework for future analyses of high-precision kaon Primakoff data.

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arXiv2020

Hadronic vacuum polarization and vector-meson resonance parameters from ${e^+e^-\toπ^0γ}$

We study the reaction $e^+e^-\toπ^0γ$ based on a dispersive representation of the underlying $π^0\toγγ^*$ transition form factor. As a first application, we evaluate the contribution of the $π^0γ$ channel to the hadronic-vacuum-polarization correction to the anomalous magnetic moment of the muon. We find $a_μ^{π^0γ}\big|_{\leq 1.35\,\text{GeV}}=43.8(6)\times 10^{-11}$, in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of $ω$ and $ϕ$. We observe good agreement with the $e^+e^-\to3π$ channel, explaining a previous tension in the $ω$ mass between $π^0γ$ and $3π$ by an unphysical phase in the fit function. Combining both channels we find $\bar M_ω=782.736(24)\,\text{MeV}$ and $\bar M_ϕ=1019.457(20)\,\text{MeV}$ for the masses including vacuum-polarization corrections. The $ϕ$ mass agrees perfectly with the PDG average, which is dominated by determinations from the $\bar K K$ channel, demonstrating consistency with $3π$ and $π^0γ$. For the $ω$ mass, our result is consistent but more precise, exacerbating tensions with the $ω$ mass extracted via isospin-breaking effects from the $2π$ channel.

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arXiv2020

Extraction of $ND$ scattering lengths from the $Λ_b\rightarrowπ^-pD^0$ decay and properties of the $Σ_c(2800)^+$

The isovector and isoscalar $ND$ $s$-wave scattering lengths are extracted by fitting to the LHCb data of the $pD^0$ invariant-mass distribution in the decay $Λ_b\rightarrowπ^-pD^0$, making use of the cusp effect at the $nD^+$ threshold. The analysis is based on a coupled-channel nonrelativistic effective field theory. We find that the real part of the isovector $ND$ scattering length is unnaturally large due to the existence of a near-threshold state with a mass around 2.8 GeV. The state is consistent with the $Σ_c(2800)^+$ resonance observed at Belle. Our results suggest that it couples strongly to the $ND$ channel in an $s$-wave, and that its quantum numbers are $J^P=1/2^-$. The strong cusp behavior at the $nD^+$ threshold can be verified using updated LHCb data.

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arXiv2020

Nucleon matrix elements of the antisymmetric quark tensor

If physics beyond the Standard Model enters well above the electroweak scale, its low-energy effects are described by Standard Model Effective Field Theory. Already at dimension six many operators involve the antisymmetric quark tensor $\bar q σ^{μν} q$, whose matrix elements are difficult to constrain from experiment, Ward identities, or low-energy theorems, in contrast to the corresponding vector and axial-vector or even scalar and pseudoscalar currents. However, with normalizations determined from lattice QCD, analyticity and unitarity often allow one to predict the momentum dependence in a large kinematic range. Starting from recent results in the meson sector, we extend this method to the nucleon case and, in combination with pole dominance, provide a comprehensive assessment of the current status of the nucleon form factors of the quark tensor.

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arXiv2019

Light-quark components analysis and the nature of the $Y(4260)$

We study the processes $e^+ e^- \to Y(4260) \to J/ψππ(K\bar{K})$. The strong final-state interactions, especially the coupled-channel ($ππ$ and $K\bar{K}$) final-state interaction in the $S$-wave are taken into account in a model-independent way using dispersion theory. It is found that the light-quark SU(3) octet state plays a significant role in these transitions, implying that the $Y(4260)$ contains a large light-quark component. Our findings suggest that the $Y(4260)$ is neither a hybrid nor a conventional charmonium state. Furthermore, through an analysis of the ratio of the light-quark SU(3) octet and singlet components, we show that the $Y(4260)$ does not behave like a pure $\bar D D_1$ hadronic molecule as well.

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arXiv2019

Three-pion contribution to hadronic vacuum polarization

We address the contribution of the $3π$ channel to hadronic vacuum polarization (HVP) using a dispersive representation of the $e^+e^-\to 3π$ amplitude. This channel gives the second-largest individual contribution to the total HVP integral in the anomalous magnetic moment of the muon $(g-2)_μ$, both to its absolute value and uncertainty. It is largely dominated by the narrow resonances $ω$ and $ϕ$, but not to the extent that the off-peak regions were negligible, so that at the level of accuracy relevant for $(g-2)_μ$ an analysis of the available data as model independent as possible becomes critical. Here, we provide such an analysis based on a global fit function using analyticity and unitarity of the underlying $γ^*\to3π$ amplitude and its normalization from a chiral low-energy theorem, which, in particular, allows us to check the internal consistency of the various $e^+e^-\to 3π$ data sets. Overall, we obtain $a_μ^{3π}|_{\leq 1.8\,\text{GeV}}=46.2(6)(6)\times 10^{-10}$ as our best estimate for the total $3π$ contribution consistent with all (low-energy) constraints from QCD. In combination with a recent dispersive analysis imposing the same constraints on the $2π$ channel below $1\,\text{GeV}$, this covers nearly $80\%$ of the total HVP contribution, leading to $a_μ^\text{HVP}=692.3(3.3)\times 10^{-10}$ when the remainder is taken from the literature, and thus reaffirming the $(g-2)_μ$ anomaly at the level of at least $3.4σ$. As side products, we find for the vacuum-polarization-subtracted masses $M_ω=782.63(3)(1)\,\text{MeV}$ and $M_ϕ=1019.20(2)(1)\,\text{MeV}$, confirming the tension to the $ω$ mass as extracted from the $2π$ channel.

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arXiv2019

Nature of the $Y(4260)$: A light-quark perspective

The $Y(4260)$ has been one of the most puzzling pieces among the so-called $XYZ$ states. In this paper, we try to gain insights into the structure of the $Y(4260)$ from the light-quark perspective. We study the dipion invariant mass spectrum of the $e^+ e^- \to Y(4260) \to J/ψπ^+π^-$ process and the ratio of the cross sections ${σ(e^+e^- \to J/ψK^+ K^-)}/{σ(e^+e^- \to J/ψπ^+π^-)}$. In particular, we consider the effects of different light-quark SU(3) eigenstates inside the $Y(4260)$. The strong pion-pion final-state interactions as well as the $K\bar{K}$ coupled channel in the $S$-wave are taken into account in a model-independent way using dispersion theory. We find that the SU(3) octet state plays a significant role in these transitions, implying that the $Y(4260)$ contains a large light-quark component. Our findings suggest that the $Y(4260)$ is neither a hybrid nor a conventional charmonium state, and they are consistent with the $Y(4260)$ having a sizeable $\bar D D_1$ component which, however, is not completely dominant.

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arXiv2019

Quark mass dependence of $γ^{*}π\rightarrowππ$

Usually the simulation of scattering processes in lattice QCD is carried out at unphysically high values of the quark masses. Hence, a method to extrapolate data obtained in lattice calculations to physical masses is needed to allow for comparison between theory and experiment. To obtain a sound extrapolation, dispersion relations and chiral perturbation theory can be invoked. While a simple combined approach known as the inverse amplitude method allows for a successful extrapolation of $ππ\toππ$ data, a more complicated framework is needed for inelastic processes such as $γ^{*}π\toππ$. By employing a well-established dispersive description, the extrapolation can be performed for $γ^{*}π\toππ$ both for on-shell as well as virtual photons, the decay $γ^*\rightarrowπππ$ is also within the range of applicability. This particular process is interesting due to both its contribution to the anomalous magnetic moment of the muon and its connection to the axial anomaly.

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arXiv2018

A new parametrization for the scalar pion form factors

We derive a new parametrization for the scalar pion form factors that allows us to analyze data over a large energy range via the inclusion of resonances, and at the same time to ensure consistency with the high-accuracy dispersive representations available at low energies. As an application the formalism is used to extract resonance properties of excited scalar mesons from data for $\bar B^0_s\to J/ψππ$. In particular we find for the pole positions of $f_0(1500)$ and $f_0(2020)$ $1465\pm 18 - i (50\pm 9)\,\text{MeV}$ and $1910\pm 50 - i(199\pm 40)\,\text{MeV}$, respectively. In addition, from their residues we calculate the respective branching ratios into $ππ$ to be $(58\pm31)\%$ and $(1.3\pm1.8)\%$.

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arXiv2018

Quark-mass dependence in $ω\to3π$ decays

We study the quark-mass dependence of $ω\to3π$ decays, based on a dispersion-theoretical framework. We rely on the quark-mass-dependent scattering phase shift for the pion-pion $P$-wave extracted from unitarized chiral perturbation theory. The dispersive representation then takes into account the final-state rescattering among all three pions. The described formalism may be used as an extrapolation tool for lattice QCD calculations of three-pion decays, for which $ω\to3π$ can serve as a paradigm case.

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arXiv2018

Dispersion relation for hadronic light-by-light scattering: pion pole

The pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon $(g-2)_μ$ is fully determined by the doubly-virtual pion transition form factor. Although this crucial input quantity is, in principle, directly accessible in experiment, a complete measurement covering all kinematic regions relevant for $(g-2)_μ$ is not realistic in the foreseeable future. Here, we report in detail on a reconstruction from available data, both space- and time-like, using a dispersive representation that accounts for all the low-lying singularities, reproduces the correct high- and low-energy limits, and proves convenient for the evaluation of the $(g-2)_μ$ loop integral. We concentrate on the systematics of the fit to $e^+e^-\to 3π$ data, which are key in constraining the isoscalar dependence, as well as the matching to the asymptotic limits. In particular, we provide a detailed account of the pion transition form factor at low energies in the time- and space-like region, including the error estimates underlying our final result for the pion-pole contribution, $a_μ^{π^0\text{-pole}}=62.6^{+3.0}_{-2.5}\times 10^{-11}$, and demonstrate how forthcoming singly-virtual measurements will further reduce its uncertainty.

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