arXiv subjects

Martin Hoferichter

Publications and source records attributed to Martin Hoferichter.

At least 91 records · Page 5Linked to original sources

arXiv2021

Towards complete leading-order predictions for neutrinoless double $β$ decay

The amplitude for the neutrinoless double $β$ ($0νββ$) decay of the two-neutron system, $nn\to ppe^-e^-$, constitutes a key building block for nuclear-structure calculations of heavy nuclei employed in large-scale $0νββ$ searches. Assuming that the $0νββ$ process is mediated by a light-Majorana-neutrino exchange, a systematic analysis in chiral effective field theory shows that already at leading order a contact operator is required to ensure renormalizability. In this work, we develop a method to estimate the numerical value of its coefficient in analogy to the Cottingham formula and validate the result by reproducing the charge-independence-breaking contribution to the nucleon-nucleon scattering lengths. Our central result, while derived in the $\overline{\text{MS}}$ scheme, is given in terms of the renormalized amplitude $\mathcal{A}_ν(|\mathbf{p}|,|\mathbf{p}^\prime|)$, matching to which will allow one to determine the contact-term contribution in regularization schemes employed in nuclear-structure calculations. Our results thus greatly reduce a crucial uncertainty in the interpretation of searches for $0νββ$ decay.

nucl-th↗

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.

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

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.

hep-ph↗

arXiv2020

Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses

The cross section for coherent elastic neutrino-nucleus scattering (CE$ν$NS) depends on the response of the target nucleus to the external current, in the Standard Model (SM) mediated by the exchange of a $Z$ boson. This is typically subsumed into an object called the weak form factor of the nucleus. Here, we provide results for this form factor calculated using the large-scale nuclear shell model for a wide range of nuclei of relevance for current CE$ν$NS experiments, including cesium, iodine, argon, fluorine, sodium, germanium, and xenon. In addition, we provide the responses needed to capture the axial-vector part of the cross section, which does not scale coherently with the number of neutrons, but may become relevant for the SM prediction of CE$ν$NS on target nuclei with nonzero spin. We then generalize the formalism allowing for contributions beyond the SM. In particular, we stress that in this case, even for vector and axial-vector operators, the standard weak form factor does not apply anymore, but needs to be replaced by the appropriate combination of the underlying nuclear structure factors. We provide the corresponding expressions for vector, axial-vector, but also (pseudo-)scalar, tensor, and dipole effective operators, including two-body-current effects as predicted from chiral effective field theory. Finally, we update the spin-dependent structure factors for dark matter scattering off nuclei according to our improved treatment of the axial-vector responses.

hep-ph↗

arXiv2020

Beta decays as sensitive probes of lepton flavor universality

Nuclear $β$ decays as well as the decay of the neutron are well-established low-energy probes of physics beyond the Standard Model (SM). In particular, with the axial-vector coupling of the nucleon $g_A$ determined from lattice QCD, the comparison between experiment and SM prediction is commonly used to derive constraints on right-handed currents. Further, in addition to the CKM element $V_{us}$ from kaon decays, $V_{ud}$ from $β$ decays is a critical input for the test of CKM unitarity. Here, we point out that the available information on $β$ decays can be re-interpreted as a stringent test of lepton flavor universality (LFU). In fact, we find that the ratio of $V_{us}$ from kaon decays over $V_{us}$ from $β$ decays (assuming CKM unitarity) is extremely sensitive to LFU violation (LFUV) in $W$-$μ$-$ν$ couplings thanks to a CKM enhancement by $(V_{ud}/V_{us})^2\sim 20$. From this perspective, recent hints for the violation of CKM unitarity can be viewed as further evidence for LFUV, fitting into the existing picture exhibited by semi-leptonic $B$ decays and the anomalous magnetic moments of muon and electron. Finally, we comment on the future sensitivity that can be reached with this LFU violating observable and discuss complementary probes of LFU that may reach a similar level of precision, such as $Γ(π\toμν)/Γ(π\to eν)$ at the PEN and PiENu experiments or even direct measurements of $W\toμν$ at an FCC-ee.

hep-ph↗

arXiv2020

Hadronic vacuum polarization: $(g-2)_μ$ versus global electroweak fits

Hadronic vacuum polarization (HVP) is not only a critical part of the Standard Model (SM) prediction for the anomalous magnetic moment of the muon $(g-2)_μ$, but also a crucial ingredient for global fits to electroweak (EW) precision observables due to its contribution to the running of the fine-structure constant encoded in $Δα^{(5)}_\text{had}$. We find that with modern EW precision data, including the measurement of the Higgs mass, the global fit alone provides a competitive, independent determination of $Δα^{(5)}_\text{had}\big|_\text{EW}=270.2(3.0)\times 10^{-4}$. This value actually lies below the range derived from $e^+e^-\to\text{hadrons}$ cross-section data, and thus goes into the opposite direction as would be required if a change in HVP were to bring the SM prediction for $(g-2)_μ$ into agreement with the Brookhaven measurement. Depending on the energy where the bulk of the changes in the cross section occurs, reconciling experiment and SM prediction for $(g-2)_μ$ by adjusting HVP would thus not necessarily weaken the case for physics beyond the SM (BSM), but to some extent shift it from $(g-2)_μ$ to the EW fit. We briefly explore some options of BSM scenarios that could conceivably explain the ensuing tension.

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 $a_μ^{c\text{-quark}}=3(1)\times 10^{-11}$.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

arXiv2019

$\boldsymbol{C\!P}\!$ violation in Higgs-gauge interactions: from tabletop experiments to the LHC

We investigate the interplay between the high- and low-energy phenomenology of $C\!P$-violating interactions of the Higgs boson with gauge bosons. For this purpose we use an effective field theory approach and consider all dimension-6 operators arising in so-called universal theories. We compute their loop-induced contributions to electric dipole moments and the $C\!P$ asymmetry in $B\to X_sγ$, and compare the resulting current and prospective constraints to the projected sensitivity of the LHC. Low-energy measurements are shown to generally have a far stronger constraining power, which results in highly correlated allowed regions in coupling space, a distinctive pattern that could be probed at the high-luminosity LHC.

hep-ph↗

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.

hep-ph↗

arXiv2019

Combined explanations of $(g-2)_μ$, $(g-2)_e$ and implications for a large muon EDM

We consider possible beyond-the-Standard-Model (BSM) effects that can accommodate both the long-standing tension in the anomalous magnetic moment of the muon, $a_μ=(g-2)_μ/2$, as well as the emerging $2.5σ$ deviation in its electron counterpart, $a_e=(g-2)_e/2$. After performing an EFT analysis, we consider BSM physics realized above the electroweak scale and find that a simultaneous explanation becomes possible in models with chiral enhancement. However, this requires a decoupling of the muon and electron BSM sectors to avoid the strong constraints from $μ\to eγ$. In particular, this decoupling implies that there is no reason to expect the muon electric dipole moment (EDM) $d_μ$ to be correlated with the electron EDM $d_e$, avoiding the very stringent limits for the latter. While some of the parameter space for $d_μ$ favored by $a_μ$ could be tested at the $(g-2)_μ$ experiments at Fermilab and J-PARC, a dedicated muon EDM experiment at PSI would be able to probe most of this region.

hep-ph↗

arXiv2019

Nuclear structure factors for general spin-independent WIMP-nucleus scattering

We present nuclear structure factors that describe the generalized spin-independent coupling of weakly interacting massive particles (WIMPs) to nuclei. Our results are based on state-of-the-art nuclear structure calculations using the large-scale nuclear shell model. Starting from quark- and gluon-level operators, we consider all possible coherently enhanced couplings of spin-1/2 and spin-0 WIMPs to one and two nucleons up to third order in chiral effective field theory. This includes a comprehensive discussion of the structure factors corresponding to the leading two-nucleon currents covering, for the first time, the contribution of spin-2 operators. We provide results for the most relevant nuclear targets considered in present and planned dark matter direct detection experiments: fluorine, silicon, argon, and germanium, complementing our previous work on xenon. All results are also publicly available in a Python notebook.

hep-ph↗

arXiv2019

Dark-matter-nucleus scattering in chiral effective field theory

Chiral effective field theory allows one to calculate the response of few-nucleon systems to external currents, both for currents that can be probed in the Standard Model and ones that only exist in Standard-Model extensions. In combination with state-of-the-art many-body methods, the constraints from chiral symmetry can then be implemented in nuclear structure factors that describe the response of atomic nuclei in direct-detection searches for dark matter. We review the present status of this approach, including the role of coherently enhanced two-body currents, the discrimination of dark matter candidates based on the nuclear response functions, and limits on Higgs-portal dark matter.

hep-ph↗

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.

hep-ph↗