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F. Jegerlehner

Publications and source records attributed to F. Jegerlehner.

At least 19 recordsLinked to original sources
arXiv2020

The anomalous magnetic moment of the muon in the Standard Model

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $α$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $\mathcal{O}(α^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_μ/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $\mathcal{O}(α^2)$ and is due to hadronic vacuum polarization, whereas at $\mathcal{O}(α^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_μ^\text{SM}=116\,591\,810(43)\times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$σ$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.

hep-ph↗
arXiv2020

Theory for the FCC-ee : Report on the 11th FCC-ee Workshop

The Future Circular Collider (FCC) at CERN, a proposed 100-km circular facility with several colliders in succession, culminates with a 100 TeV proton-proton collider. It offers a vast new domain of exploration in particle physics, with orders of magnitude advances in terms of Precision, Sensitivity and Energy. The implementation plan foresees, as a first step, an Electroweak Factory electron-positron collider. This high luminosity facility, operating between 90 and 365 GeV centre-of-mass energy, will study the heavy particles of the Standard Model, Z, W, Higgs, and top with unprecedented accuracy. The Electroweak Factory $e^+e^-$ collider constitutes a real challenge to the theory and to precision calculations, triggering the need for the development of new mathematical methods and software tools. A first workshop in 2018 had focused on the first FCC-ee stage, the Tera-Z, and confronted the theoretical status of precision Standard Model calculations on the Z-boson resonance to the experimental demands. The second workshop in January 2019, which is reported here, extended the scope to the next stages, with the production of W-bosons (FCC-ee-W), the Higgs boson (FCC-ee-H) and top quarks (FCC-ee-tt). In particular, the theoretical precision in the determination of the crucial input parameters, alpha_QED, alpha_QCD, M_W, m_t at the level of FCC-ee requirements is thoroughly discussed. The requirements on Standard Model theory calculations were spelled out, so as to meet the demanding accuracy of the FCC-ee experimental potential. The discussion of innovative methods and tools for multi-loop calculations was deepened. Furthermore, phenomenological analyses beyond the Standard Model were discussed, in particular the effective theory approaches. The reports of 2018 and 2019 serve as white papers of the workshop results and subsequent developments.

hep-ph↗
arXiv2020

BHLS$_2$, a New Breaking of the HLS Model and its Phenomenology

Previous studies have shown that the Hidden Local Symmetry (HLS) Model, supplied with appropriate symmetry breaking, provides an Effective Lagrangian (BHLS) able to encompass a large number of processes within a unified framework. A global fit provides a simultaneous description of the $e^+ e^-$ annihilation into $π^+π^-$, $π^0γ$, $ηγ$, $π^+π^-π^0$, $K^+K^-$, $K_L K_S$, the dipion spectrum in the $τ$ decay and other light meson partial widths. Additional breaking schemes extend its scope to spacelike processes within a new framework (BHLS$_2$). The phenomenology previously explored with BHLS is revisited in the BHLS$_2$ context with emphasis on the $Φ$ mass region. It is shown that BHLS$_2$ addresses the close spacelike region covered by NA7 and Fermilab data; also,the Lattice QCD pion form factor is accurately predicted by BHLS$_2$ using fits to annihilation data only. These channels contribution to $a_μ$ over the range of validity of BHLS$_2$ is shown to strongly reduce the former BHLS systematics. The uncertainty on $a_μ^{\rm th}(\sqrt{s}< 1.05$ GeV) is much improved compared to standard approaches relying on direct integration methods of measured spectra. Using the BHLS$_2$ results, the leading order HVP contribution to the muon anomalous moment is $a_μ^{HVP-LO}= 686.65 \pm 3.01 +(+1.16,-0.75)_{syst.}$ in units of $10^{-10}$. Using a conservative estimate for the light--by--light contribution, our evaluation is $a_μ^{\rm th}=\left [11\,659\,175.96 \pm 4.17 +(+1.16,-0.75)_{syst.}\right]\times 10^{-10}$. The $ρ^0γ$ mixing in dispersive and LQCD approaches is discussed and may amount to a shift $δa_μ[ππ]_{ργ} = +(3.10\pm0.31)\times 10^{-10}$ at LO+NLO, presently treated as additional systematics. Taking this shift into account, $a_μ^{\rm th}-a_μ^{\rm BNL}$ exhibits a significance not smaller than $3.8 σ$.

hep-ph↗
arXiv2017

Measurement of the running of the fine structure constant below 1 GeV with the KLOE Detector

We have measured the running of the effective QED coupling constant $α(s)$ in the time-like region $0.6<\sqrt s< 0.975$ GeV with the KLOE detector at DA$Φ$NE using the Initial State Radiation process $e^+e^-\toμ^+ μ^-γ$. It represents the first measurement of the running of $α(s)$ in this energy region. Our results show a more than 5$σ$ significance of the hadronic contribution to the running of $α(s)$, which is the strongest direct evidence both in time- and space-like regions achieved in a single measurement. By using the $e^+e^-\toπ^+π^-$ cross section measured by KLOE, the real and imaginary part of the shift $Δα(s)$ has been extracted. By a fit of the real part of $Δα(s)$ and assuming the lepton universality the branching ratio $BR(ω\toμ^+μ^-) = (6.6\pm1.4_{stat}\pm1.7_{syst})\cdot 10^{-5} $ has been determined.

hep-ex↗
arXiv2017

Physics Behind Precision

This document provides a writeup of contributions to the FCC-ee mini-workshop on "Physics behind precision" held at CERN, on 2-3 February 2016.

hep-ph↗
arXiv2016

A BHLS model based moment analysis of muon g-2, and its use for lattice QCD evaluations of $a_μ^{\rm had}$

We present an up-to-date analysis of muon $g-2$ evaluations in terms of Mellin-Barnes moments as they might be useful for lattice QCD calculations of $a_μ$. The moments up to 4th order are evaluated directly in terms of $e^+e^-$--annihilation data and improved within the Hidden Local Symmetry (HLS) Model, supplied with appropriate symmetry breaking mechanisms. The model provides a reliable Effective Lagrangian (BHLS) estimate of the two-body channels plus the $πππ$ channel up to 1.05~GeV, just including the $ϕ$ resonance. The HLS piece accounts for 80\% of the contribution to $a_μ$. The missing pieces are evaluated in the standard way directly in terms of the data. We find that the moment expansion converges well in terms of a few moments. The two types of moments which show up in the Mellin-Barnes representation are calculated in terms of hadronic cross--section data in the timelike region and in terms of the hadronic vacuum polarization (HVP) function in the spacelike region which is accessible to lattice QCD (LQCD). In the Euclidean the first type of moments are the usual Taylor coefficients of the HVP and we show that the second type of moments may be obtained as integrals over the appropriately Taylor truncated HVP function. Specific results for the isovector part of $a_μ^{\rm had}$ are determined by means of HLS model predictions in close relation to $τ$--decay spectra.

hep-ph↗
arXiv2015

Muon g-2 estimates : Can one trust Effective Lagrangians and global fits ?

Previous studies have shown that the Hidden Local Symmetry (HLS) Model, supplied with appropriate symmetry breaking mechanisms, provides an Effective Lagrangian (BHLS) which encompasses a large number of processes within a unified framework; a global fit procedure allows for a simultaneous description of the e+ e- annihilation into the 6 final states $π^+ π^-$, $π^0 γ$, $ηγ$, $π^+ π^- π^0$, $K^+ K^-$, $K_l K_s$ and includes the dipion spectrum in the τ decay and some more light meson decay partial widths. The contribution to the muon anomalous magnetic moment $a_{th}$ of these annihilation channels over the range of validity of the HLS model (up to 1.05 GeV) is found much improved compared to its partner derived from integrating the measured spectra directly. However, most spectra for the process $e^+ e^- \to π^+ π^-$ undergo overall scale uncertainties which dominate the other sources, and one may suspect some bias in the dipion contribution to $a_{th}$. However, an iterated fit algorithm, shown to lead to unbiased results by a Monte Carlo study, is defined and applied succesfully to the $e^+ e^- \to π^+ π^-$ data samples from CMD2, SND, KLOE, BaBar and BESSIII. The iterated fit solution is shown to be further improved and leads to a value for $a_μ$ different from $a_{exp}$ above the 4 $σ$ level. The contribution of the $π^+ π^-$ intermediate state up to 1.05 GeV to $a_{th}$ derived from the iterated fit benefits from an uncertainty about 3 times smaller than the corresponding usual estimate. Therefore, global fit techniques are shown to work and lead to improved unbiased results.

hep-ph↗
arXiv2013

Constraining the Hadronic Contributions to the Muon Anomalous Magnetic Moment

The mini-proceedings of the Workshop on "Constraining the hadronic contributions to the muon anomalous magnetic moment" which included the "13th meeting of the Radio MonteCarLow WG" and the "Satellite meeting R-Measurements at BES-III" held in Trento from April 10th to 12th, 2013, are presented. This collaboration meeting aims to bring together the experimental e+e- collider communities from BaBar, Belle, BESIII, CMD2, KLOE, and SND, with theorists working in the fields of meson transitions form factors, hadronic contributions to (g-2)_μand effective fine structure constant, and development of Monte Carlo generator and Radiative Corrections for precision e+e- and tau physics.

hep-ph↗
arXiv2013

An Update of the HLS Estimate of the Muon g-2

A global fit of parameters allows us to pin down the Hidden Local Symmetry (HLS) effective Lagrangian, which we apply for the prediction of the leading hadronic vacuum polarization contribution to the muon g-2. The latter is dominated by the annihilation channel e+e- -> pi+pi-, for which data are available by scan (CMD-2 and SND) and ISR (KLOE-2008, KLOE-2010 and BaBar) experiments. It is well known that the different data sets are not in satisfactory agreement. In fact it is possible to fix the model parameters without using the pi+pi- data, by using instead the dipion spectra measured in the tau decays together with experimental spectra for the pi0 gamma, eta gamma, pi+pi-pi0, K+K-, K0bar K0 final states supplemented by specific meson decay properties. Among these, the accepted decay width for rho0 -> e+e- and the partial widths and phase information for the omega/phi -> pi+pi- transitions, are considered. It is then shown that, relying on this global data set, the HLS model, appropriately broken, allows to predict accurately the pion form factor up to 1.05 GeV. It is shown that the data samples provided by CMD-2, SND and KLOE-2010 behave consistently with each other and with the other considered data. Consistency problems with the KLOE-2008 and BaBar data samples are substantiated. "All data" global fits are investigated by applying reweighting the conflicting data sets. Constraining to our best fit, the broken HLS model yields a_mu(th) = (11659169.55 [+1.26 -0.59]_phi +[+0.00 -2.00]_tau +/- 5.21_(th))~10**-10 associated with a very good global fit probability. Correspondingly, we find that Delta a_mu=a_mu (exp)- a_mu (th) exhibits a significance ranging between 4.7 and 4.9 sigma.

hep-ph↗
arXiv2011

Upgraded Breaking Of The HLS Model: A Full Solution to the tau-e+e- and phi Decay Issues And Its Consequences On g-2 VMD Estimates

The muon anomalous magnetic moment $a_μ$ and the hadronic vacuum polarization are examined using data analyzed within the framework of a suitably broken HLS model. The analysis relies on all available scan data samples and leaves provisionally aside the existing ISR data. Our HLS model based global fit approach allows for a better check of consistency between data sets and we investigate how results depend on different strategies which may be followed. Relying on global fit qualities, we find several acceptable solutions leading to ambiguities in the reconstructed value for $(a_μ)_{th}$. Among these, the most conservative solution is $a_μ^{\rm had,LO}[{\rm HLS \ improved}]=687.72(4.63) \times 10^{-10}$ and $(a_μ)_{th}=11\,659\,175.37(5.31)\times 10^{-10}$ corresponding to a $4.1 σ$ significance for the difference $Δa_μ=(a_μ)_{exp}-(a_μ)_{th}$. It is also shown that the various contributions accessible through the model yield uniformly a factor 2 improvement of their uncertainty. The breaking procedure implemented in the HLS model is an extension of the former procedure based on the BKY mechanism. This yields a quite satisfactory simultaneous description of most $e^+e^-$ annihilation channels up to and including the $ϕ$ meson ($π^+π^-$, $π^0γ$, $ηγ$, $π^+π^-π^0$, $K^+K^-$, $K^0 \bar{K}^0$) and of a set of 10 (mostly radiative) decay widths of light mesons. It also allows to achieve the proof of consistency between the $e^+e^- \to π^+π^-$ annihilation and the $τ^\pm \ra π^\pmπ^0 ν$ decay and gives a solution to the reported problem concerning the measured partial width ratio $Γ(ϕ\to K^+K^-)/Γ(ϕ\to K^0 \bar{K}^0)$. Prospects for improving the VMD based estimates of $a_μ$ are emphasized.

hep-ph↗
arXiv2010

Physics with the KLOE-2 experiment at the upgraded DA$ϕ$NE

Investigation at a $ϕ$--factory can shed light on several debated issues in particle physics. We discuss: i) recent theoretical development and experimental progress in kaon physics relevant for the Standard Model tests in the flavor sector, ii) the sensitivity we can reach in probing CPT and Quantum Mechanics from time evolution of entangled kaon states, iii) the interest for improving on the present measurements of non-leptonic and radiative decays of kaons and eta/eta$^\prime$ mesons, iv) the contribution to understand the nature of light scalar mesons, and v) the opportunity to search for narrow di-lepton resonances suggested by recent models proposing a hidden dark-matter sector. We also report on the $e^+ e^-$ physics in the continuum with the measurements of (multi)hadronic cross sections and the study of gamma gamma processes.

hep-ex↗
arXiv2009

Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data

We present the achievements of the last years of the experimental and theoretical groups working on hadronic cross section measurements at the low energy e+e- colliders in Beijing, Frascati, Ithaca, Novosibirsk, Stanford and Tsukuba and on tau decays. We sketch the prospects in these fields for the years to come. We emphasise the status and the precision of the Monte Carlo generators used to analyse the hadronic cross section measurements obtained as well with energy scans as with radiative return, to determine luminosities and tau decays. The radiative corrections fully or approximately implemented in the various codes and the contribution of the vacuum polarisation are discussed.

hep-ph↗
arXiv2008

The running fine structure constant alpha(E) via the Adler function

We present an up-to-date analysis for a precise determination of the effective fine structure constant and discuss the prospects for future improvements. We advocate to use a determination monitored by the Adler function which allows us to exploit perturbative QCD in an optimal well controlled way. Together with a long term program of hadronic cross section measurements at energies up to a few GeV, a determination of alpha(M_Z) at a precision comparable to the one of the Z mass M_Z should be feasible. Presently alpha(E) at E>1 GeV is the least precisely known of the fundamental parameters of the SM. Since, in spite of substantial progress due to new BaBar exclusive data, the region 1.4 to 2.4 GeV remains the most problematic one a major step in the reduction of the uncertainties are expected from VEPP-2000 and from a possible ``high-energy'' option DAFNE-2 at Frascati. The up-to-date evaluation reads Delta alpha^{(5)}_{had}(M_Z^2) = 0.027515 +/- 0.000149 or alpha^{-1}(M_Z)=128.957 +/- 0.020.

hep-ph↗
arXiv2007

Essentials of the Muon g-2

The muon anomalous magnetic moment is one of the most precisely measured quantities in particle physics. Recent high precision measurements (0.54ppm) at Brookhaven reveal a ``discrepancy'' by 3 standard deviations from the electroweak Standard Model which could be a hint for an unknown contribution from physics beyond the Standard Model. This triggered numerous speculations about the possible origin of the ``missing piece''. The remarkable 14-fold improvement of the previous CERN experiment, actually animated a multitude of new theoretical efforts which lead to a substantial improvement of the prediction of a_mu. The dominating uncertainty of the prediction, caused by strong interaction effects, could be reduced substantially, due to new hadronic cross section measurements in electron-positron annihilation at low energies. After an introduction and a brief description of the principle of the experiment, I present a major update and review the status of the theoretical prediction and discuss the role of the hadronic vacuum polarization effects and the hadronic light--by--light scattering contribution. Prospects for the future will be briefly discussed. As, in electroweak precision physics, the muon g-2 shows the largest established deviation between theory and experiment at present, it will remain one of the hot topics for further investigations.

hep-ph↗
arXiv2006

Precision measurements of sigma_hadronic for alpha_eff(E) at ILC energies and (g-2)_mu

A more precise determination of the effective fine structure constant alpha_eff(E) is mandatory for confronting data from future precision experiments with precise SM predictions. At a future e+e- collider like the ILC, as at LEP before, alpha_eff(E) plays the role the static zero momentum alpha=alpha_eff(0) plays in low energy physics. However, by going to the effective version of alpha one loses about a factor 2 times 10^2 at E=m_mu to 10^5 at E=M_Z in precision, such that for physics at the gauge boson mass scale and beyond alpha_eff(E) is the least known basic parameter, about a factor 20 less precise than the neutral gauge boson mass M_Z and by about a factor 60 less precise than the Fermi constant G_F. We discuss a strategy which should be able to reach a factor 10 improvement by appropriate efforts in performing dedicated measurements of sigma_hadronic in a wide energy range as well as efforts in theory and in particular improving the precision of the QCD parameters alpha_s, m_c and m_b. Projects at VEPP-2000 (Novosibirsk) and DANAE/KLOE-2 (Frascati) are particularly important for improving on alpha_eff(M_Z) as well as alpha_eff(m_mu). We present an up-to-date analysis including the recent data from KLOE, SND, CMD-2 and BABAR. The analysis based on e+e- data yields Delta alpha_had^(5)(M_Z) = 0.027593 +/- 0.000169 [alpha^-1(M_Z) = 128.938 +/- 0.023] and a_mu^had=(692.1 +/- 5.6) x 10^{-10}. We emphasize the very high improvement potential of the VEPP-2000 and DANAE/KLOE-2 projects.

hep-ph↗
arXiv2006

Non-renormalization of the full correlator at two-loop order

By explicit calculation of the two-loop QCD corrections we show that for singlet axial and vector currents the full off-shell correlation function in the limit of massless fermions is proportional to the one-loop result, when calculated in the MS-bar scheme. By the same finite renormalization which is needed to make the one-loop anomaly exact to all orders, we arrive at the conclusion that two-loop corrections are absent altogether, for the complete correlator not only its anomalous part. In accordance with the one-loop nature of the correlator, one possible amplitude, which seems to be missing by accident at the one-loop level, also does not show up at the two-loop level.

hep-th↗
arXiv2005

Explicit Results for the Anomalous Three Point Function and Non-Renormalization Theorems

Two-loop corrections for the correlator of the singlet axial and vector currents in QCD are calculated in the chiral limit for arbitrary momenta. Explicit calculations confirm the non-renormalization theorems derived recently by Vainshtein and Knecht et.al. We find that as in the one-loop case also at the two loops the correlator has only 3 independent form-factors instead of 4. From the explicit results we observe that the two-loop correction to the correlator is equal to the one-loop result times the constant factor C_2(R) alpha_s/pi in the MSbar scheme. This holds for the full correlator, for the anomalous longitudinal as well as for the non- anomalous thansversal amplitudes. The finite overall alpha_s dependent constant has to be normalized away by renormalizing the axial current according to Witten's algebraic/geometrical constraint on the anomalous Ward identity. Our observations, together with known facts, suggest that in perturbation theory the correlator is proportional to the one-loop term to all orders and that the non- renormalization theorem of the Adler-Bell-Jackiw anomaly carries over to the full correlator.

hep-ph↗