arXiv subjects

Peter Stoffer

Publications and source records attributed to Peter Stoffer.

At least 55 records · Page 3Linked to original sources

arXiv2020

Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon

A key ingredient in the evaluation of hadronic light-by-light (HLbL) scattering in the anomalous magnetic moment of the muon $(g-2)_μ$ concerns short-distance constraints (SDCs) that follow from QCD by means of the operator product expansion. Here we concentrate on the most important such constraint, in the longitudinal amplitudes, and show that it can be implemented efficiently in terms of a Regge sum over excited pseudoscalar states, constrained by phenomenological input on masses, two-photon couplings, as well as SDCs on HLbL scattering and the pseudoscalar transition form factors (TFFs). Our estimate of the effect of the longitudinal SDCs on the HLbL contribution is: $Δa_μ^\text{LSDC}=13(6)\times 10^{-11}$. This is significantly smaller than previous estimates, which mostly relied on an ad-hoc modification of the pseudoscalar poles and led to up to a $40\%$ increase with respect to the nominal pseudoscalar-pole contributions, when evaluated with modern input for the relevant TFFs. We also comment on the status of the transversal SDCs and, by matching to perturbative QCD, argue that the corresponding correction will be significantly smaller than its longitudinal counterpart.

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arXiv2019

Computing Tools for the SMEFT

The increasing interest in the phenomenology of the Standard Model Effective Field Theory (SMEFT), has led to the development of a wide spectrum of public codes which implement automatically different aspects of the SMEFT for phenomenological applications. In order to discuss the present and future of such efforts, the "SMEFT-Tools 2019" Workshop was held at the IPPP Durham on the 12th-14th June 2019. Here we collect and summarize the contents of this workshop.

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arXiv2019

Dispersion relations for $γ^γ^\toππ$: helicity amplitudes, subtractions, and anomalous thresholds

We present a comprehensive analysis of the dispersion relations for the doubly-virtual process $γ^*γ^*\toππ$. Starting from the Bardeen-Tung-Tarrach amplitudes, we first derive the kernel functions that define the system of Roy-Steiner equations for the partial-wave helicity amplitudes. We then formulate the solution of these partial-wave dispersion relations in terms of Omnès functions, with special attention paid to the role of subtraction constants as critical for the application to hadronic light-by-light scattering. In particular, we explain for the first time why for some amplitudes the standard Muskhelishvili-Omnès solution applies, while for others a modified approach based on their left-hand cut is required unless subtractions are introduced. In the doubly-virtual case, the analytic structure of the vector-resonance partial waves then gives rise to anomalous thresholds, even for space-like virtualities. We develop a strategy to account for these effects in the numerical solution, illustrated in terms of the $D$-waves in $γ^*γ^*\toππ$, which allows us to predict the doubly-virtual responses of the $f_2(1270)$ resonance. In general, our results form the basis for the incorporation of two-meson intermediate states into hadronic light-by-light scattering beyond the $S$-wave contribution.

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arXiv2019

Two-pion contribution to hadronic vacuum polarization

We present a detailed analysis of $e^+e^-\toπ^+π^-$ data up to $\sqrt{s}=1\,\text{GeV}$ in the framework of dispersion relations. Starting from a family of $ππ$ $P$-wave phase shifts, as derived from a previous Roy-equation analysis of $ππ$ scattering, we write down an extended Omnès representation of the pion vector form factor in terms of a few free parameters and study to which extent the modern high-statistics data sets can be described by the resulting fit function that follows from general principles of QCD. We find that statistically acceptable fits do become possible as soon as potential uncertainties in the energy calibration are taken into account, providing a strong cross check on the internal consistency of the data sets, but preferring a mass of the $ω$ meson significantly lower than the current PDG average. In addition to a complete treatment of statistical and systematic errors propagated from the data, we perform a comprehensive analysis of the systematic errors in the dispersive representation and derive the consequences for the two-pion contribution to hadronic vacuum polarization. In a global fit to both time- and space-like data sets we find $a_μ^{ππ}|_{\leq 1\,\text{GeV}}=495.0(1.5)(2.1)\times 10^{-10}$ and $a_μ^{ππ}|_{\leq 0.63\,\text{GeV}}=132.8(0.4)(1.0)\times 10^{-10}$. While the constraints are thus most stringent for low energies, we obtain uncertainty estimates throughout the whole energy range that should prove valuable in corroborating the corresponding contribution to the anomalous magnetic moment of the muon. As side products, we obtain improved constraints on the $ππ$ $P$-wave, valuable input for future global analyses of low-energy $ππ$ scattering, as well as a determination of the pion charge radius, $\langle r_π^2 \rangle = 0.429(1)(4)\,\text{fm}^2$.

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arXiv2019

Non-Perturbative Effects in $μ\to e γ$

We compute the non-perturbative contribution of semileptonic tensor operators $(\bar q σ^{μν} q)(\bar \ell σ_{μν} \ell)$ to the purely leptonic process $μ\to e γ$ and to the electric and magnetic dipole moments of charged leptons by matching onto chiral perturbation theory at low energies. This matching procedure has been used extensively to study semileptonic and leptonic weak decays of hadrons. In this paper, we apply it to observables that contain no strongly interacting external particles. The non-perturbative contribution to $μ\to e $ processes is used to extract the best current bound on lepton-flavor-violating semileptonic tensor operators, $Λ_\text{BSM} \gtrsim 450$ TeV. We briefly discuss how the same method applies to dark-matter interactions.

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arXiv2017

Hadronic light-by-light contribution to $(g-2)_μ$: a dispersive approach

After a brief introduction on ongoing experimental and theoretical activities on $(g-2)_μ$, we report on recent progress in approaching the calculation of the hadronic light-by-light contribution with dispersive methods. General properties of the four-point function of the electromagnetic current in QCD, its Lorentz decomposition and dispersive representation are discussed. On this basis a numerical estimate for the pion box contribution and its rescattering corrections is obtained. We conclude with an outlook for this approach to the calculation of hadronic light-by-light.

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arXiv2017

Dispersion relations for $η'\toηππ$

We present a dispersive analysis of the decay amplitude for $η'\toηππ$ that is based on the fundamental principles of analyticity and unitarity. In this framework, final-state interactions are fully taken into account. Our dispersive representation relies only on input for the $ππ$ and $πη$ scattering phase shifts. Isospin symmetry allows us to describe both the charged and neutral decay channel in terms of the same function. The dispersion relation contains subtraction constants that cannot be fixed by unitarity. We determine these parameters by a fit to Dalitz-plot data from the VES and BES-III experiments. We study the prediction of a low-energy theorem and compare the dispersive fit to variants of chiral perturbation theory.

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arXiv2017

Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon

We present a first model-independent calculation of $ππ$ intermediate states in the hadronic-light-by-light (HLbL) contribution to the anomalous magnetic moment of the muon $(g-2)_μ$ that goes beyond the scalar QED pion loop. To this end we combine a recently developed dispersive description of the HLbL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, $a_μ^{π\text{-box}}=-15.9(2)\times 10^{-11}$. We then construct suitable input for the $γ^*γ^*\toππ$ helicity partial waves based on a pion-pole left-hand cut and show that for the dominant charged-pion contribution this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate $S$-wave rescattering effects to the full pion box and leads to our final estimate for the sum of these two contributions: $a_μ^{π\text{-box}} + a_{μ,J=0}^{ππ,π\text{-pole LHC}}=-24(1)\times 10^{-11}$.

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arXiv2017

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon $(g-2)_μ$, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of $γ^*γ^*\toππ$. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, $a_μ^{π\text{-box}}=-15.9(2)\times 10^{-11}$. As an application of the partial-wave formalism, we present a first calculation of $ππ$-rescattering effects in HLbL scattering, with $γ^*γ^*\toππ$ helicity partial waves constructed dispersively using $ππ$ phase shifts derived from the inverse-amplitude method. In this way, the isospin-$0$ part of our calculation can be interpreted as the contribution of the $f_0(500)$ to HLbL scattering in $(g-2)_μ$. We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its $S$-wave rescattering corrections reads $a_μ^{π\text{-box}} + a_{μ,J=0}^{ππ,π\text{-pole LHC}}=-24(1)\times 10^{-11}$.

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arXiv2015

Dispersion relation for hadronic light-by-light scattering: theoretical foundations

In this paper we make a further step towards a dispersive description of the hadronic light-by-light (HLbL) tensor, which should ultimately lead to a data-driven evaluation of its contribution to $(g-2)_μ$. We first provide a Lorentz decomposition of the HLbL tensor performed according to the general recipe by Bardeen, Tung, and Tarrach, generalizing and extending our previous approach, which was constructed in terms of a basis of helicity amplitudes. Such a tensor decomposition has several advantages: the role of gauge invariance and crossing symmetry becomes fully transparent; the scalar coefficient functions are free of kinematic singularities and zeros, and thus fulfill a Mandelstam double-dispersive representation; and the explicit relation for the HLbL contribution to $(g-2)_μ$ in terms of the coefficient functions simplifies substantially. We demonstrate explicitly that the dispersive approach defines both the pion-pole and the pion-loop contribution unambiguously and in a model-independent way. The pion loop, dispersively defined as pion-box topology, is proven to coincide exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors.

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arXiv2015

A perturbed lepton-specific two-Higgs-doublet model facing experimental hints for physics beyond the Standard Model

The BaBar, Belle, and LHCb collaborations have reported evidence for new physics in $B\to Dτν$ and $B\to D^*τν$ of approximately $3.8σ$. There is also the long lasting discrepancy of about $3σ$ in the anomalous magnetic moment of the muon, and the branching ratio for $τ\toμνν$ is $1.8σ$ ($2.4σ$) above the Standard Model expectation using the HFAG (PDG) values. Furthermore, CMS found hints for a non-zero decay rate of $h\toμτ$. Interestingly, all these observations can be explained by introducing new scalars. In this article we consider these processes within a lepton-specific two-Higgs doublet model (i.e. of type X) with additional non-standard Yukawa couplings. It is found that one can accommodate $τ\toμνν$ with modified Higgs--$τ$ couplings. The anomalous magnetic moment of the muon can be explained if the additional neutral CP-even Higgs $H$ is light (below 100 GeV). Also $R(D)$ and $R(D^*)$ can be easily explained by additional $t$--$c$--Higgs couplings. Combining these $t$--$c$ couplings with a light $H$ the decay rate for $t\to H c$ can be in a testable range for the LHC. Effects in $h\toμτ$ are also possible, but in this case a simultaneous explanation of the anomalous magnetic moment of the muon is difficult due to the unavoidable $τ\toμγ$ decay.

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arXiv2015

A Dispersive Treatment of $K_{\ell4}$ Decays

$K_{\ell4}$ decays offer several reasons of interest: they allow an accurate measurement of $ππ$-scattering lengths; they provide the best source for the determination of some low-energy constants of ChPT; one form factor is directly related to the chiral anomaly, which can be measured here. We present a dispersive treatment of $K_{\ell4}$ decays that provides a resummation of $ππ$- and $Kπ$-rescattering effects. The free parameters of the dispersion relation are fitted to the data of the high-statistics experiments E865 and NA48/2. The matching to ChPT at NLO and NNLO enables us to determine the LECs $L_1^r$, $L_2^r$ and $L_3^r$. With recently published data from NA48/2, the LEC $L_9^r$ can be determined as well. In contrast to a pure chiral treatment, the dispersion relation describes the observed curvature of one of the form factors, which we understand as a rescattering effect beyond NNLO.

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arXiv2014

Dispersive Treatments of $K_{\ell4}$ Decays and Hadronic Light-by-Light Scattering

In this thesis, I present dispersive treatments of two hadronic processes: the semileptonic kaon decay $K_{\ell4}$ and hadronic light-by-light scattering. The $K_{\ell4}$ decay is one of the best sources of information on some of the parameters of chiral perturbation theory. The dispersion relation for $K_{\ell4}$ provides a resummation of $ππ$- and $Kπ$-rescattering effects. In contrast to a pure chiral treatment, it reproduces the observed curvature of one of the form factors. The matching of the dispersion relation to the chiral representation of the form factors allows the extraction of the values of three low-energy constants. Hadronic light-by-light scattering appears as a virtual process in the calculation of the anomalous magnetic moment of the muon $(g-2)_μ$. For more than a decade, a discrepancy of about $3σ$ has persisted between the experimental determination and the standard-model prediction of the $(g-2)_μ$. It is expected that within a few years hadronic light-by-light scattering will dominate the uncertainty of the theory prediction of the $(g-2)_μ$. So far, only model calculations of the hadronic light-by-light contribution are available. However, in view of forthcoming $(g-2)_μ$ experiments at Fermilab and J-PARC it is crucial that the hadronic light-by-light calculation can be improved systematically. The dispersive description presented here provides a formalism for a data-driven determination of hadronic light-by-light scattering and hence opens up an avenue towards a model-independent evaluation of the $(g-2)_μ$.

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arXiv2014

Towards a data-driven analysis of hadronic light-by-light scattering

The hadronic light-by-light contribution to the anomalous magnetic moment of the muon was recently analyzed in the framework of dispersion theory, providing a systematic formalism where all input quantities are expressed in terms of on-shell form factors and scattering amplitudes that are in principle accessible in experiment. We briefly review the main ideas behind this framework and discuss the various experimental ingredients needed for the evaluation of one- and two-pion intermediate states. In particular, we identify processes that in the absence of data for doubly-virtual pion-photon interactions can help constrain parameters in the dispersive reconstruction of the relevant input quantities, the pion transition form factor and the helicity partial waves for $γ^*γ^*\toππ$.

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arXiv2014

Dispersive approach to hadronic light-by-light scattering

Based on dispersion theory, we present a formalism for a model-independent evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. In particular, we comment on the definition of the pion pole in this framework and provide a master formula that relates the effect from pi pi intermediate states to the partial waves for the process gamma^* gamma^* --> pi pi. All contributions are expressed in terms of on-shell form factors and scattering amplitudes, and as such amenable to an experimental determination.

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arXiv2014

Remarks on higher-order hadronic corrections to the muon g-2

Recently, it was shown that insertions of hadronic vacuum polarization at O(alpha^4) generate non-negligible effects in the calculation of the anomalous magnetic moment of the muon. This result raises the question if other hadronic diagrams at this order might become relevant for the next round of g-2 measurements as well. In this note we show that a potentially enhanced such contribution, hadronic light-by-light scattering in combination with electron vacuum polarization, is already sufficiently suppressed.

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arXiv2013

Isospin Breaking Effects in $K_{\ell4}$ Decays

In the framework of chiral perturbation theory with photons and leptons, the one-loop isospin breaking effects in $K_{\ell4}$ decays due to both the photonic contribution and the quark and meson mass differences are computed. A comparison with the isospin breaking corrections applied by recent high statistics $K_{e4}$ experiments is performed. The calculation can be used to correct the existing form factor measurements by isospin breaking effects that have not yet been taken into account in the experimental analysis. Based on the present work, possible forthcoming experiments on $K_{e4}$ decays could correct the isospin breaking effects in a more consistent way.

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arXiv2013

Virtual photon-photon scattering

Based on analyticity, unitarity, and Lorentz invariance the contribution from hadronic vacuum polarization to the anomalous magnetic moment of the muon is directly related to the cross section of e^+e^- --> hadrons. We review the main difficulties that impede such an approach for light-by-light scattering and identify the required ingredients from experiment. Amongst those, the most critical one is the scattering of two virtual photons into meson pairs. We analyze the analytic structure of the process gamma^* gamma^* --> pi pi and show that the usual Muskhelishvili-Omnes representation can be amended in such a way as to remain valid even in the presence of anomalous thresholds.

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