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Peter Stoffer

Publications and source records attributed to Peter Stoffer.

At least 37 records · Page 2Linked to original sources
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

One-loop matching of $CP$-odd four-quark operators to the gradient-flow scheme

The translation of experimental limits on the neutron electric dipole moment into constraints on heavy $CP$-violating physics beyond the Standard Model requires knowledge about non-perturbative matrix elements of effective operators, which ideally should be computed in lattice QCD. However, this necessitates a matching calculation as an interface to the effective field theory framework, which is based on dimensional regularization and renormalization by minimal subtraction. We calculate the one-loop matching between the gradient-flow and minimal-subtraction schemes for the $CP$-violating four-quark operators contributing to the neutron electric dipole moment. The gradient flow is a modern regularization-independent scheme amenable to lattice computations that promises, e.g., better control over power divergences than traditional momentum-subtraction schemes. Our results extend previous work on dimension-five operators and provide a necessary ingredient for future lattice-QCD computations of the contribution of four-quark operators to the neutron electric dipole moment.

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arXiv2023

Puzzles in the hadronic contributions to the muon anomalous magnetic moment

We summarize recent developments in the Standard-Model evaluation of the anomalous magnetic moment of the muon $a_μ$, both in the hadronic-light-by-light and hadronic-vacuum-polarization contributions. The current situation for the latter is puzzling as we are confronted with multiple discrepancies that are not yet understood. We present updated fits of a dispersive representation of the pion vector form factor to the new CMD-3 data set and quantify the tensions with the other high-statistics $e^+e^-\toπ^+π^-$ experiments in the contribution to $a_μ$ in the energy range up to 1 GeV, as well as in the corresponding contribution to the intermediate Euclidean window.

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arXiv2023

Dispersion relations for hadronic light-by-light scattering in triangle kinematics

We present a new strategy for the dispersive evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon $a_μ$. The new approach directly applies in the kinematic limit relevant for $a_μ$: one of the photons is treated as an external electromagnetic field with vanishing momentum, so that the kinematics corresponds to a triangle. We derive expressions for the relevant single-particle intermediate states, as well as the tensor decompositions of the two-pion sub-processes that appear in addition to those needed in the established dispersive approach. The existing approach is based on a set of dispersion relations for the hadronic light-by-light tensor in four-point kinematics. At present it is not known how to consistently include in this framework resonant intermediate states of spin 2 or larger, due to the appearance of kinematic singularities that can be traced back to the redundancy of the tensor decomposition. We show that our new approach circumvents this problem and enables dispersion relations in the limit of triangle kinematics that are manifestly free from kinematic singularities, paving the way towards a data-driven evaluation of all relevant exclusive hadronic intermediate states.

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arXiv2022

Low-energy effective field theory below the electroweak scale: matching at one loop

We compute the one-loop matching between the Standard Model Effective Field Theory and the low-energy effective field theory below the electroweak scale, where the heavy gauge bosons, the Higgs particle, and the top quark are integrated out. The complete set of matching equations is derived including effects up to dimension six in the power counting of both theories. We present the results for general flavor structures and include both the $CP$-even and $CP$-odd sectors. The matching equations express the masses, gauge couplings, as well as the coefficients of dipole, three-gluon, and four-fermion operators in the low-energy theory in terms of the parameters of the Standard Model Effective Field Theory. Using momentum insertion, we also obtain the matching for the $CP$-violating theta angles. Our results provide an ingredient for a model-independent analysis of constraints on physics beyond the Standard Model. They can be used for fixed-order calculations at one-loop accuracy and represent a first step towards a systematic next-to-leading-log analysis.

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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

One-loop matching for quark dipole operators in a gradient-flow scheme

The quark chromoelectric dipole (qCEDM) operator is a CP-violating operator describing, at hadronic energies, beyond-the-standard-model contributions to the electric dipole moment of particles with nonzero spin. In this paper we define renormalized dipole operators in a regularization-independent scheme using the gradient flow, and we perform the matching at one loop in perturbation theory to renormalized operators of the same and lower dimension in the more familiar MS scheme. We also determine the matching coefficients for the quark chromomagnetic dipole operator (qCMDM), which contributes, for example, to matrix elements relevant to CP-violating and CP-conserving kaon decays. The calculation provides a basis for future lattice QCD computations of hadronic matrix elements of the qCEDM and qCMDM operators.

hep-lat↗
arXiv2021

Effective field theory interpretation of lepton magnetic and electric dipole moments

We perform a model-independent analysis of the magnetic and electric dipole moments of the muon and electron. We give expressions for the dipole moments in terms of operator coefficients of the low-energy effective field theory (LEFT) and the Standard Model effective field theory (SMEFT). We use one-loop renormalization group improved perturbation theory, including the one-loop matching from SMEFT onto LEFT, and one-loop lepton matrix elements of the effective-theory operators. Semileptonic four-fermion operators involving light quarks give sizable non-perturbative contributions to the dipole moments, which are included in our analysis. We find that only a very limited set of the SMEFT operators is able to generate the current deviation of the magnetic moment of the muon from its Standard Model expectation.

hep-ph↗
arXiv2021

Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update

We reassess the impact of short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude on the anomalous magnetic moment of the muon, $a_μ=(g-2)_μ/2$, by comparing different solutions that have recently appeared in the literature. In particular, we analyze the relevance of the exact axial anomaly and its impact on $a_μ$ and conclude that it remains rather limited. We show that all recently proposed solutions agree well within uncertainties on the numerical estimate of the impact of short-distance constraints on $a_μ$, despite differences in the concrete implementation. We also take into account the recently calculated perturbative corrections to the massless quark loop to update our estimate and outline the path towards future improvements.

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arXiv2021

A dispersive estimate of scalar contributions to hadronic light-by-light scattering

We consider the contribution of scalar resonances to hadronic light-by-light scattering in the anomalous magnetic moment of the muon. While the $f_0(500)$ has already been addressed in previous work using dispersion relations, heavier scalar resonances have only been estimated in hadronic models so far. Here, we compare an implementation of the $f_0(980)$ resonance in terms of the coupled-channel $S$-waves for $γ^*γ^*\to ππ/\bar K K$ to a narrow-width approximation, which indicates $a_μ^{\text{HLbL}}[f_0(980)]=-0.2(2)\times 10^{-11}$. With a similar estimate for the $a_0(980)$, the combined effect is thus well below $1\times 10^{-11}$ in absolute value. We also estimate the contribution of heavier scalar resonances. In view of the very uncertain situation concerning their two-photon couplings we suggest to treat them together with other resonances of similar mass when imposing the matching to short-distance constraints. Our final result is a refined estimate of the $S$-wave rescattering effects in the $ππ$ and $\bar K K$ channel up to about $1.3$ GeV and including a narrow-width evaluation of the $a_0(980)$: $a_μ^\text{HLbL}[\text{scalars}]=-9(1)\times 10^{-11}$.

hep-ph↗
arXiv2021

Constraints on the two-pion contribution to hadronic vacuum polarization

At low energies hadronic vacuum polarization (HVP) is strongly dominated by two-pion intermediate states, which are responsible for about $70\%$ of the HVP contribution to the anomalous magnetic moment of the muon, $a_μ^\text{HVP}$. Lattice-QCD evaluations of the latter indicate that it might be larger than calculated dispersively on the basis of $e^+e^-\to\text{hadrons}$ data, at a level which would contest the long-standing discrepancy with the $a_μ$ measurement. In this Letter we study to which extent this $2π$ contribution can be modified without, at the same time, producing a conflict elsewhere in low-energy hadron phenomenology. To this end we consider a dispersive representation of the $e^+e^- \to 2π$ process and study the correlations which thereby emerge between $a_μ^\text{HVP}$, the hadronic running of the fine-structure constant, the $P$-wave $ππ$ phase shift, and the charge radius of the pion. Inelastic effects play an important role, despite being constrained by the Eidelman-Lukaszuk bound. We identify scenarios in which $a_μ^\text{HVP}$ can be altered substantially, driven by changes in the phase shift and/or the inelastic contribution, and illustrate the ensuing changes in the $e^+e^-\to 2π$ cross section. In the combined scenario, which minimizes the effect in the cross section, a uniform shift around $4\%$ is required. At the same time both the analytic continuation into the space-like region and the pion charge radius are affected at a level that could be probed in future lattice-QCD calculations.

hep-ph↗
arXiv2020

Non-perturbative renormalization scheme for the CP-odd three-gluon operator

We define a regularization-independent momentum-subtraction scheme for the $CP$-odd three-gluon operator at dimension six. This operator appears in effective field theories for heavy physics beyond the Standard Model, describing the indirect effect of new sources of $CP$-violation at low energies. In a hadronic context, it induces permanent electric dipole moments. The hadronic matrix elements of the three-gluon operator are non-perturbative objects that should ideally be evaluated with lattice QCD. We define a non-perturbative renormalization scheme that can be implemented on the lattice and we compute the scheme transformation to $\overline{\text{MS}}$ at one loop. Our calculation can be used as an interface to future lattice-QCD calculations of the matrix elements of the three-gluon operator, in order to obtain theoretically robust constraints on physics beyond the Standard Model from measurements of the neutron electric dipole moment.

hep-ph↗
arXiv2020

Asymptotic behavior of meson transition form factors

One of the open issues in evaluations of the contribution from hadronic light-by-light scattering to the anomalous magnetic moment of the muon $(g-2)_μ$ concerns the role of heavier scalar, axial-vector, and tensor-meson intermediate states. The coupling of axial vectors to virtual photons is suppressed for small virtualities by the Landau-Yang theorem, but otherwise there are few rigorous constraints on the corresponding form factors. In this paper, we first derive the Lorentz decomposition of the two-photon matrix elements into scalar functions following the general recipe by Bardeen, Tung, and Tarrach. Based on this decomposition, we then calculate the asymptotic behavior of the meson transition form factors from a light-cone expansion in analogy to the asymptotic limits for the pseudoscalar transition form factor derived by Brodsky and Lepage. Finally, we compare our results to existing data as well as previous models employed in the literature.

hep-ph↗
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.

hep-ph↗
arXiv2020

Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2)_μ$ with large-$N_c$ Regge models

While the low-energy part of the hadronic light-by-light (HLbL) tensor can be constrained from data using dispersion relations, for a full evaluation of its contribution to the anomalous magnetic moment of the muon $(g-2)_μ$ also mixed- and high-energy regions need to be estimated. Both can be addressed within the operator product expansion (OPE), either for configurations where all photon virtualities become large or one of them remains finite. Imposing such short-distance constraints (SDCs) on the HLbL tensor is thus a major aspect of a model-independent approach towards HLbL scattering. Here, we focus on longitudinal SDCs, which concern the amplitudes containing the pseudoscalar-pole contributions from $π^0$, $η$, $η'$. Since these conditions cannot be fulfilled by a finite number of pseudoscalar poles, we consider a tower of excited pseudoscalars, constraining their masses and transition form factors from Regge theory, the OPE, and phenomenology. Implementing a matching of the resulting expressions for the HLbL tensor onto the perturbative QCD quark loop, we are able to further constrain our calculation and significantly reduce its model dependence. We find that especially for the $π^0$ the corresponding increase of the HLbL contribution is much smaller than previous prescriptions in the literature would imply. Overall, we estimate that longitudinal SDCs increase the HLbL contribution by $Δa_μ^\text{LSDC}=13(6)\times 10^{-11}$. This number does not include the contribution from the charm quark, for which we find $a_μ^{c\text{-quark}}=3(1)\times 10^{-11}$.

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