arXiv subjects

Peter Stoffer

Publications and source records attributed to Peter Stoffer.

At least 19 recordsLinked to original sources

arXiv2026

One-loop matching of the LEFT to the QCD gradient flow

We present the complete one-loop matching of the baryon- and lepton-number-conserving low-energy effective field theory (LEFT) to the QCD gradient flow. Using Euclidean conventions and the background-field formulation of the gradient flow, we derive the short-flow-time expansion for the full LEFT operator basis up to mass dimension six. The matching is performed in dimensional regularization in the algebraically consistent 't Hooft-Veltman scheme, including a systematic treatment of evanescent operators and the finite counterterms required to restore chiral symmetry in the spurion sense. Keeping fully generic flavor structures, we verify the cancellation of spurious chiral-symmetry-violating terms with the known finite symmetry-restoring counterterms. This demonstrates that the gradient flow as a gauge-invariant ultraviolet regulator enables an efficient extraction of both divergent and finite counterterms in addition to the matching contributions. We provide the matching coefficients both before and after field redefinitions that remove redundant operators, as well as power-divergent mixings into lower-dimensional operators. Our results establish a consistent perturbative link between continuum LEFT calculations and gradient-flow-based lattice-QCD matrix elements, enabling precision low-energy phenomenology beyond leading-logarithmic accuracy.

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arXiv2025

Two-loop anomalous dimensions for baryon-number-violating operators in SMEFT

We compute the two-loop renormalization-group equations for the baryon-number-violating dimension-six operators in the SMEFT. This includes all three gauge interactions, the Yukawa, and Higgs self-interaction contributions. In addition, we present the one-loop matching of the $S_1$ scalar leptoquark on the SMEFT, which can generate the Wilson coefficients of all four gauge-invariant baryon-number-violating SMEFT operators. Using this example, we demonstrate the cancellation of scheme and matching-scale dependences. Together with the known two-loop renormalization-group evolution below the electroweak scale in the LEFT, as well as the one-loop matching of SMEFT onto LEFT, our results enable consistent next-to-leading-log analyses of nucleon decays, provided that the relevant matrix elements are known at next-to-leading-order accuracy.

hep-ph↗

arXiv2025

Renormalization-group equations of the LEFT at two loops: dimension-six operators

We present the third part of a systematic calculation of the two-loop anomalous dimensions for the low-energy effective field theory below the electroweak scale (LEFT): insertions of dimension-six operators that conserve baryon number. In line with our previous publications, we obtain the results in the algebraically consistent 't Hooft-Veltman scheme for $\gamma_5$, corrected for evanescent as well as chiral-symmetry-breaking effects through finite renormalizations. We compute the renormalization of the dimension-six four-fermion and three-gluon operators, as well as the power corrections to lower-dimension operators in the presence of masses, i.e., the down-mixing into dimension-five dipole operators, masses, gauge couplings, and theta terms. Our results are of interest for a broad range of low-energy precision searches for physics beyond the Standard Model.

hep-ph↗

arXiv2025

Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators

We present the second part of a systematic calculation of the two-loop anomalous dimensions for the low-energy effective field theory below the electroweak scale (LEFT): the baryon-number-violating sector at dimension six in the power counting. We obtain the results in two different schemes: in the algebraically consistent 't Hooft-Veltman scheme for $\gamma_5$, corrected for evanescent as well as chiral-symmetry-breaking effects through finite renormalizations; and in naive dimensional regularization, which in the considered sector of the theory does not lead to any ill-defined $\gamma_5$-odd traces. Our results are of interest for a reanalysis of the constraints on physics beyond the Standard Model from proton-decay searches within an EFT framework at next-to-leading-logarithmic accuracy.

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arXiv2025

Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$

In Refs. [1,2] we provided a complete dispersive evaluation of the hadronic light-by-light (HLbL) contribution to the anomalous magnetic moment of the muon. While the evaluation strategy was developed for the kinematic situation determined by the muon mass, a similar approach also applies to the HLbL corrections to the anomalous magnetic moments of the electron and $\tau$ lepton, shifting the sensitivity in the loop integrals to smaller and larger momenta, respectively. In this Letter, we propagate the corresponding uncertainties of the various contributions, obtaining $a_e^\text{HLbL}= 3.51(23)\times 10^{-14}$ and $a_\tau^\text{HLbL}= 3.77(29)\times 10^{-8}$.

hep-ph↗

arXiv2025

Improved evaluation of the electroweak contribution to muon $g-2$

A precise evaluation of the electroweak contribution to the anomalous magnetic moment of the muon requires control over all aspects of the Standard Model, ranging from Higgs physics, over multi-loop computations for bosonic and (heavy-)fermion diagrams, to non-perturbative effects in the presence of light quarks. Currently, the dominant uncertainties arise from such hadronic effects in the vector-vector-axial-vector three-point function, an improved understanding of which has recently emerged in the context of hadronic light-by-light scattering. Profiting from these developments as well as new perturbative and non-perturbative input for the charm contribution, we obtain $a_\mu^\text{EW}=154.4(4)\times 10^{-11}$.

hep-ph↗

arXiv2025

Dispersive analysis of the pion vector form factor without zeros

We perform an updated analysis of $e^+e^-\to\pi^+\pi^-$ cross-section data using a dispersive representation of the pion vector form factor. We show that the available data are compatible with the assumption that the form factor is free of complex zeros and that under this assumption the largest systematic uncertainty in a previous analysis can be eliminated. We investigate both a constrained Omn\`es representation as well as a hybrid phase-modulus representation and we quantify the discrepancies in the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon based on different $e^+e^-$ data sets. We find that the dispersive constraints exacerbate these discrepancies. Together with the assumption of the absence of zeros, the pion charge radius becomes a useful observable to discriminate between the different data sets. This provides an opportunity for future improved lattice-QCD determinations to probe the discrepancies independently of full computations of hadronic vacuum polarization. We also reevaluate the two-pion contribution to Euclidean windows and we observe that systematic discrepancies between the data sets persist even at very long distances.

hep-ph↗

arXiv2024

Renormalization-group equations of the LEFT at two loops: dimension-five effects

We present the first part of a systematic calculation of the two-loop anomalous dimensions in the low-energy effective field theory (LEFT): the effects at dimension five in the power counting. Our calculation is performed in a basis with generic mass matrices, we employ the algebraically consistent 't Hooft-Veltman scheme for $\gamma_5$, and we correct for evanescent as well as chiral-symmetry-breaking effects by including the appropriate finite counterterms. We also provide results for the $CP$-even sector in a scheme that coincides with naive dimensional regularization. We discuss two methods to avoid the explicit construction of gauge-variant operators, which in principle are needed for the cancellation of sub-divergences, even in the background-field method. The two methods are consistent with each other and with existing partial results. Our work is a further step towards a complete EFT framework for physics beyond the Standard Model at next-to-leading-logarithmic accuracy.

hep-ph↗

arXiv2024

Dispersion relation for hadronic light-by-light scattering: subleading contributions

In this work, we present an evaluation of subleading effects in the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. Using a recently derived optimized basis, we first study the matching of axial-vector contributions to short-distance constraints at the level of the scalar basis functions, finding that also the tails of the pseudoscalar poles and tensor mesons play a role. We then develop a matching strategy that allows for a combined evaluation of axial-vector and short-distance constraints, supplemented by an estimate of tensor-meson contributions based on simplified assumptions for their transition form factors. Uncertainties are primarily propagated from the axial-vector transition form factors and the variation of the matching scale, but we also consider estimates of the low-energy effect of hadronic states not explicitly included. In total, we obtain $a_\mu^\text{HLbL}\big|_\text{subleading}=33.2(7.2)\times 10^{-11}$, which in combination with previously evaluated contributions in the dispersive approach leads to $a_\mu^\text{HLbL}\big|_\text{total}=101.9(7.9)\times 10^{-11}$.

hep-ph↗

arXiv2024

Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$

Hadronic light-by-light (HLbL) scattering defines one of the critical contributions in the Standard-Model prediction of the anomalous magnetic moment of the muon. In this Letter, we present a complete evaluation using a dispersive formalism, in which the HLbL tensor is reconstructed from its discontinuities, expressed in terms of simpler hadronic matrix elements that can be extracted from experiment. Profiting from recent developments in the determination of axial-vector transition form factors, short-distance constraints for the HLbL tensor, and the vector-vector-axial-vector correlator, we obtain $a_\mu^\text{HLbL}=101.9(7.9)\times 10^{-11}$, which meets the precision requirements set by the final result of the Fermilab experiment.

hep-ph↗

arXiv2024

Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^+ e^-$ collisions

We present the results of Phase I of an ongoing review of Monte Carlo tools relevant for low-energy hadronic cross sections. This includes a detailed comparison of Monte Carlo codes for electron-positron scattering into a muon pair, pion pair, and electron pair, for scan and radiative-return experiments. After discussing the various approaches that are used and effects that are included, we show differential cross sections obtained with AfkQed, BabaYaga@NLO, KKMC, MCGPJ, McMule, Phokhara, and Sherpa, for scenarios that are inspired by experiments providing input for the dispersive evaluation of the hadronic vacuum polarisation.

hep-ph↗

arXiv2024

Dispersion relations for the hadronic VVA correlator

We derive two types of dispersion relations for the hadronic vector-vector-axial-vector (VVA) correlator: one in generic three-point kinematics with fixed photon virtualities, the second in the kinematic limit of one soft photon. The VVA correlator enters in the electroweak contribution to the muon anomalous magnetic moment and it also emerges as the leading term in the operator-product expansion for hadronic light-by-light scattering in the limit of two large photon momenta. Previously, this correlator was only described in terms of hadronic models. Our new dispersive treatments are in analogy to the established and the newly proposed dispersive approaches to hadronic light-by-light. The VVA correlator allows us to investigate the relation between the two types of dispersion relations in a simpler example and to elucidate the reshuffling of different hadronic contributions in this comparison. As a byproduct, we reduce the theoretical uncertainties on the first-family VVA contribution to the muon anomalous magnetic moment by combining the dispersive representation with both asymptotic and low-energy constraints.

hep-ph↗

arXiv2024

An optimized basis for hadronic light-by-light scattering

We present a new basis for the hadronic light-by-light (HLbL) tensor that is optimized for the evaluation of narrow-resonance contributions to HLbL scattering in the anomalous magnetic moment of the muon. As main advantage, kinematic singularities are manifestly absent for pseudoscalar, scalar, and axial-vector states, while the remaining singularities for tensor resonances are minimized, even avoided for special cases, and simple crossing relations among the scalar functions maintained. We scrutinize the properties of this new basis for the scalar-QED pion box, demonstrating that the partial-wave convergence even slightly improves compared to our previous work, and discuss the physical sum rules that ensure basis independence of the HLbL contribution. Finally, we provide explicit expressions for narrow (pseudo-)scalar, axial-vector, and tensor intermediate states in terms of their respective transition form factors.

hep-ph↗

arXiv2023

Low-energy effective field theory below the electroweak scale: one-loop renormalization in the 't Hooft-Veltman scheme

The low-energy effective field theory below the electroweak scale (LEFT) describes the effects at low energies of both the weak interaction and physics beyond the Standard Model. We study the one-loop renormalization of the LEFT in the 't Hooft-Veltman scheme, which offers an algebraically consistent definition of the Levi-Civita symbol and $\gamma_5$ in dimensional regularization. However, in connection with minimal subtraction this scheme leads to a spurious breaking of chiral symmetry in intermediate steps of the calculation. Based on the 't Hooft-Veltman prescription, we define a renormalization scheme that restores chiral symmetry by including appropriate finite counterterms. To this end, we extend the physical LEFT operator basis by a complete set of off-shell and one-loop-evanescent operators and we perform the renormalization at one loop. We determine the finite counterterms to the physical parameters that compensate both the insertions of evanescent operators, as well as the chiral-symmetry-breaking terms from the renormalizable part of the Lagrangian in $D$ dimensions. Our results can be applied in next-to-leading-log calculations in the 't Hooft-Veltman scheme: using our renormalization scheme instead of pure minimal subtraction separates the physical sector from the unphysical evanescent sector and leads to results that are manifestly free of spurious chiral-symmetry-breaking terms.

hep-ph↗

arXiv2023

One-loop matching of the $CP$-odd three-gluon operator to the gradient flow

The calculation of the neutron electric dipole moment within effective field theories for physics beyond the Standard Model requires non-perturbative hadronic matrix elements of effective operators composed of quark and gluon fields. In order to use input from lattice computations, these matrix elements must be translated from a scheme suitable for lattice QCD to the minimal-subtraction scheme used in the effective-field-theory framework. The accuracy goal in the context of the neutron electric dipole moment necessitates at least a one-loop matching calculation. Here, we provide the one-loop matching coefficients for the $CP$-odd three-gluon operator between two different minimally subtracted 't Hooft-Veltman schemes and the gradient flow. This completes our program to obtain the one-loop gradient-flow matching coefficients for all $CP$-violating and flavor-conserving operators in the low-energy effective field theory up to dimension six.

hep-lat↗

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 $a_\mu$, 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 $e^+e^-\to\pi^+\pi^-$ experiments in the contribution to $a_\mu$ in the energy range up to 1 GeV, as well as in the corresponding contribution to the intermediate Euclidean window.

hep-ph↗

arXiv2023

Computing Tools for Effective Field Theories

In recent years, theoretical and phenomenological studies with effective field theories have become a trending and prolific line of research in the field of high-energy physics. In order to discuss present and future prospects concerning automated tools in this field, the SMEFT-Tools 2022 workshop was held at the University of Zurich from 14th-16th September 2022. The current document collects and summarizes the content of this workshop.

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 $e^+e^-\to3\pi$ 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.

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