arXiv subjects

Martin Hoferichter

Publications and source records attributed to Martin Hoferichter.

At least 109 records · Page 6Linked to original sources

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, $\langle r_π^2 \rangle = 0.429(1)(4)\,\text{fm}^2$.

hep-ph↗

arXiv2018

Combined explanations of $(g-2)_{μ,e}$ and implications for a large muon EDM

With the long-standing tension between experiment and Standard-Model (SM) prediction in the anomalous magnetic moment of the muon, $a_μ=(g-2)_μ/2$, at the level of 3-4$σ$, it is natural to ask if there could be a sizable effect in the electric dipole moment (EDM) $d_μ$ as well. In this context it has often been argued that in UV complete models the electron EDM, which is very precisely measured, excludes a large effect in $d_μ$. However, the recently observed 2.5$σ$ tension in $a_e=(g-2)_e/2$, if confirmed, requires that the muon and electron sectors effectively decouple to avoid constraints from $μ\to eγ$. We briefly discuss UV complete models that possess such a decoupling, which can be enforced by an Abelian flavor symmetry $L_μ-L_τ$. We show that, in such scenarios, there is no reason to expect a correlation between the electron and muon EDM, so that the latter can be sizable. New limits on $d_μ$ improved by up to two orders of magnitude are expected from the upcoming $(g-2)_μ$ experiments at Fermilab and J-PARC. Beyond, a proposed dedicated muon EDM experiment at PSI could further advance the limit. In this way, future improved measurements of $a_e$, $a_μ$, as well as the fine-structure constant $α$ are not only set to provide exciting precision tests of the SM, but, in combination with EDMs, to reveal crucial insights into the flavor structure of physics beyond the SM.

hep-ph↗

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.

hep-ph↗

arXiv2018

Pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon

The $π^0$ pole constitutes the lowest-lying singularity of the hadronic light-by-light (HLbL) tensor, and thus provides the leading contribution in a dispersive approach to HLbL scattering in the anomalous magnetic moment of the muon $(g-2)_μ$. It is unambiguously defined in terms of the doubly-virtual pion transition form factor, which in principle can be accessed in its entirety by experiment. We demonstrate that, in the absence of a direct measurement, the full space-like doubly-virtual form factor can be reconstructed very accurately based on existing data for $e^+e^-\to 3π$, $e^+e^-\to e^+e^-π^0$, and the $π^0\toγγ$ decay width. We derive a representation that incorporates all the low-lying singularities of the form factor, matches correctly onto the asymptotic behavior expected from perturbative QCD, and is suitable for the evaluation of the $(g-2)_μ$ loop integral. The resulting value, $a_μ^{π^0\text{-pole}}=62.6^{+3.0}_{-2.5}\times 10^{-11}$, for the first time, represents a complete data-driven determination of the pion-pole contribution with fully controlled uncertainty estimates. In particular, we show that already improved singly-virtual measurements alone would allow one to further reduce the uncertainty in $a_μ^{π^0\text{-pole}}$.

hep-ph↗

arXiv2018

A no-go theorem for non-standard explanations of the $τ\to K_Sπν_τ$ CP asymmetry

The CP asymmetry in $τ\to K_Sπν_τ$, as measured by the BaBar collaboration, differs from the Standard Model prediction by $2.8σ$. Most non-standard interactions do not allow for the required strong phase needed to produce a non-vanishing CP asymmetry, leaving only new tensor interactions as a possible mechanism. We demonstrate that, contrary to previous assumptions in the literature, the crucial interference between vector and tensor phases is suppressed by at least two orders of magnitude due to Watson's final-state-interaction theorem. Furthermore, we find that the strength of the relevant CP-violating tensor interaction is strongly constrained by bounds from the neutron electric dipole moment and $D$-$\bar{D}$ mixing. These observations together imply that it is extremely difficult to explain the current $τ\to K_Sπν_τ$ measurement in terms of physics beyond the Standard Model originating in the ultraviolet.

hep-ph↗

arXiv2017

Radiative resonance couplings in $γπ\toππ$

Studies of the reaction $γπ\toππ$, in the context of the ongoing Primakoff program of the COMPASS experiment at CERN, give access to the radiative couplings of the $ρ(770)$ and $ρ_3(1690)$ resonances. We provide a vector-meson-dominance estimate of the respective radiative width of the $ρ_3$, $Γ_{ρ_3\toπγ}=48(18)$ keV, as well as its impact on the $F$-wave in $γπ\toππ$. For the $ρ(770)$, we establish the formalism necessary to extract its radiative coupling directly from the residue of the resonance pole by analytic continuation of the $γπ\toππ$ amplitude to the second Riemann sheet, without any reference to the vector-meson-dominance hypothesis.

hep-ph↗

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.

hep-ph↗

arXiv2017

Extracting the sigma-term from low-energy pion-nucleon scattering

We present an extraction of the pion-nucleon ($πN$) scattering lengths from low-energy $πN$ scattering, by fitting a representation based on Roy-Steiner equations to the low-energy data base. We show that the resulting values confirm the scattering-length determination from pionic atoms, and discuss the stability of the fit results regarding electromagnetic corrections and experimental normalization uncertainties in detail. Our results provide further evidence for a large $πN$ $σ$-term, $σ_{πN}=58(5)$ MeV, in agreement with, albeit less precise than, the determination from pionic atoms.

hep-ph↗

arXiv2017

Improved limits for Higgs-portal dark matter from LHC searches

Searches for invisible Higgs decays at the Large Hadron Collider constrain dark matter Higgs-portal models, where dark matter interacts with the Standard Model fields via the Higgs boson. While these searches complement dark matter direct-detection experiments, a comparison of the two limits depends on the coupling of the Higgs boson to the nucleons forming the direct-detection nuclear target, typically parameterized in a single quantity $f_N$. We evaluate $f_N$ using recent phenomenological and lattice-QCD calculations, and include for the first time the coupling of the Higgs boson to two nucleons via pion-exchange currents. We observe a partial cancellation for Higgs-portal models that makes the two-nucleon contribution anomalously small. Our results, summarized as $f_N=0.308(18)$, show that the uncertainty of the Higgs-nucleon coupling has been vastly overestimated in the past. The improved limits highlight that state-of-the-art nuclear physics input is key to fully exploiting experimental searches.

hep-ph↗

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: $a_μ^{π\text{-box}} + a_{μ,J=0}^{ππ,π\text{-pole LHC}}=-24(1)\times 10^{-11}$.

hep-ph↗

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 $a_μ^{π\text{-box}} + a_{μ,J=0}^{ππ,π\text{-pole LHC}}=-24(1)\times 10^{-11}$.

hep-ph↗

arXiv2016

Probing lepton flavour (universality) violation at NA62 and future kaon experiments

Recent results from the LHC's first run have revealed intriguing departures from lepton flavour universality in the semi-leptonic decays of $B$-mesons. We discuss the complementary role that rare kaon decays can provide in testing new physics explanations of these flavour anomalies. In the framework of minimal flavour violation, we relate the chiral low-energy constants involved in $K\toπ\ell\ell'$ and $K\to\ell\ell'$ ($\ell = μ\mbox{ or } e$) with the new physics Wilson coefficients of the $b\to s$ effective Hamiltonian. We comment on the determination of these low-energy constants at NA62 and future kaon experiments, as well as the required improvements in sensitivity necessary to test the $B$-physics anomalies in the kaon sector.

hep-ph↗

arXiv2016

Analysis strategies for general spin-independent WIMP-nucleus scattering

We propose a formalism for the analysis of direct-detection dark-matter searches that covers all coherent responses for scalar and vector interactions and incorporates QCD constraints imposed by chiral symmetry, including all one- and two-body WIMP-nucleon interactions up to third order in chiral effective field theory. One of the free parameters in the WIMP-nucleus cross section corresponds to standard spin-independent searches, but in general different combinations of new-physics couplings are probed. We identify the interference with the isovector counterpart of the standard spin-independent response and two-body currents as the dominant corrections to the leading spin-independent structure factor, and discuss the general consequences for the interpretation of direct-detection experiments, including minimal extensions of the standard spin-independent analysis. Fits for all structure factors required for the scattering off xenon targets are provided based on state-of-the-art nuclear shell-model calculations.

hep-ph↗

arXiv2016

Remarks on the pion-nucleon sigma-term

The pion-nucleon $σ$-term can be stringently constrained by the combination of analyticity, unitarity, and crossing symmetry with phenomenological information on the pion-nucleon scattering lengths. Recently, lattice calculations at the physical point have been reported that find lower values by about $3σ$ with respect to the phenomenological determination. We point out that a lattice measurement of the pion-nucleon scattering lengths could help resolve the situation by testing the values extracted from spectroscopy measurements in pionic atoms.

hep-lat↗

arXiv2016

Lepton flavor (universality) violation in rare kaon decays

Recent anomalies in the decays of $B$ mesons and the Higgs boson provide hints towards lepton flavor (universality) violating physics beyond the Standard Model. We observe that four-fermion operators which can explain the $B$-physics anomalies have corresponding analogs in the kaon sector, and we analyze their impact on $K\toπ\ell \ell'$ and $K\to\ell \ell'$ decays $(\ell=μ,e)$. For these processes, we note the corresponding physics opportunities at the NA62 experiment. In particular, assuming minimal flavor violation, we comment on the required improvements in sensitivity necessary to test the $B$-physics anomalies in the kaon sector.

hep-ph↗

arXiv2016

Roy-Steiner-equation analysis of pion-nucleon scattering

We review the structure of Roy-Steiner equations for pion-nucleon scattering, the solution for the partial waves of the t-channel process $ππ\to \bar N N$, as well as the high-accuracy extraction of the pion-nucleon S-wave scattering lengths from data on pionic hydrogen and deuterium. We then proceed to construct solutions for the lowest partial waves of the s-channel process $πN\to πN$ and demonstrate that accurate solutions can be found if the scattering lengths are imposed as constraints. Detailed error estimates of all input quantities in the solution procedure are performed and explicit parameterizations for the resulting low-energy phase shifts as well as results for subthreshold parameters and higher threshold parameters are presented. Furthermore, we discuss the extraction of the pion-nucleon $σ$-term via the Cheng-Dashen low-energy theorem, including the role of isospin-breaking corrections, to obtain a precision determination consistent with all constraints from analyticity, unitarity, crossing symmetry, and pionic-atom data. We perform the matching to chiral perturbation theory in the subthreshold region and detail the consequences for the chiral convergence of the threshold parameters and the nucleon mass.

hep-ph↗

arXiv2015

Matching pion-nucleon Roy-Steiner equations to chiral perturbation theory

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ(1232) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

nucl-th↗

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.

hep-ph↗