arXiv subjects

Eduardo de Rafael

Publications and source records attributed to Eduardo de Rafael.

At least 19 recordsLinked to original sources

arXiv2024

Hadronic Vacuum Polarization Contribution to $\boldsymbol{g_μ-2}$ as a function of the external lepton mass

The hadronic vacuum polarization contribution to the anomalous magnetic moment of a lepton is considered as a function of the lepton mass. We show how the analyticity properties of this function allow for its full reconstruction when it is only known in a restricted mass region. Assuming that LQCD could evaluate it in an optimal mass region we show, within the framework of a phenomenological model, how to reconstruct the function elsewhere, in particular at the muon mass value.

hep-ph↗

arXiv2023

On the Time Momentum Representation of Hadronic Vacuum Polarization and $\boldsymbol{g_μ-2}$

We propose a new set of model independent approximants adapted to the time momentum representation (TMR) of hadronic vacuum polarization (HVP) and its contribution to $g_μ-2$. They provide a way to extrapolate lattice QCD (LQCD) results obtained in an optimal time-region, to the full range required for an evaluation of the HVP contribution to $g_μ-2$. They offer as well a new way to confront LQCD results in restricted TMR regions, with the full contribution obtained from data driven determinations.

hep-ph↗

arXiv2022

Hadronic Vacuum Polarization and the MUonE proposal

The MUonE proposal at the CERN SPS consists in extracting the value of the hadronic vacuum polarization self-energy function (HVP) from its contribution to the differential cross-section of elastic muon-electron scattering. The HVP contribution to the muon anomalous magnetic moment can then be obtained from a weighted integral of the measured HVP self-energy function. This, however, requires a knowledge of the HVP function in its full integration domain. This paper discusses a procedure to reconstruct the HVP function in the regions not directly accessible to measurement. The method is based on the so-called transfer theorems, due to Flajolet and Odlyzko, which we explain and adapt to HVP.

hep-ph↗

arXiv2020

On Constraints Between $Δα_{\rm had}(M_Z^2)$ and $(g_μ-2)_{\rm HVP}$

I discuss the possibility of estimating the shift $δΔα(M_Z^2)$ on the running of the EM-coupling to the $M_Z$ scale, induced by the discrepancy $Δa_μ$ between two precise determinations of the hadronic vacuum polarization contribution to $g_μ-2$. It is shown that the size of $Δa_μ$ implies rigorous bounds on the $δΔα(M_Z^2)$-shift. Any extra contribution to this minimal shift necessarily depends on the specific shape of the underlying spectral function $\frac{1}π\ImmΔ(t)$ responsible for the $Δa_μ$-discrepancy. I show that, in the case of a quark model, the total $Δα(M_Z^2)$-shift remains small. I also discuss the scenario where $\frac{1}π\ImmΔ(t)$ is a constant in a finite $t$-region and show that in this case, up to a $t_{\rm max}\precsim 5~\GeV^2$, the size of the total $δΔα_{\rm had}^{(5)}(M_Z^2)$-shift, remains below or of the order of the present error value on $Δα_{\rm had}^{(5)}(M_Z^2)$.

hep-ph↗

arXiv2018

The Mellin-Barnes Approach to Hadronic Vacuum Polarization and $g_μ-2$

It is shown that with a precise determination of a few derivatives of the hadronic vacuum polarization (HVP) self-energy function $Π(Q^2)$ at $Q^2=0$, from lattice QCD (LQCD) or from a dedicated low-energy experiment, one can obtain an evaluation of the lowest order HVP contribution to the anomalous magnetic moment of the muon $a_μ^{\rm HVP}$ with an accuracy comparable to the one reached using the $e^+ e^-$ annihilation cross-section into hadrons. The technique of Mellin-Barnes approximants (MBa) that we propose is illustrated in detail with the example of the two loop vacuum polarization function in QED. We then apply it to the first few moments of the hadronic spectral function obtained from experiment and show that the resulting MBa evaluations of $a_μ^{\rm HVP}$ converge very quickly to the full experimental determination.

hep-ph↗

arXiv2017

Hadronic Vacuum Polarization in QCD and its Evaluation in the Euclidean

We discuss a new technique to evaluate integrals of QCD Green's functions in the Euclidean based on their Mellin-Barnes representation. We present as a first application the evaluation of the lowest order Hadronic Vacuum Polarization (HVP) contribution to the anomalous magnetic moment of the muon $\frac{1}{2}(g_μ-2)_{\rm\tiny HVP}\equiv a_μ^{\rm HVP}$. It is shown that with a precise determination of the slope and curvature of the HVP function at the origin from lattice QCD (LQCD), one can already obtain a result for $a_μ^{\rm HVP}$ which may serve as a test of the determinations based on experimental measurements of the $e^+ e^-$ annihilation cross-section into hadrons.

hep-ph↗

arXiv2014

Moment Analysis of Hadronic Vacuum Polarization - Proposal for a lattice QCD evaluation of $g_μ-2$

I suggest a new approach to the determination of the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon $a_μ^{\rm HVP}$ in lattice QCD. It is based on properties of the Mellin transform of the hadronic spectral function and their relation to the HVP self energy in the Euclidean. I show how $a_μ^{\rm HVP}$ is very well approximated by a few moments associated to this Mellin transform and how these moments can be evaluated in lattice QCD, providing thus a series of tests when compared with the corresponding determinations using experimental data.

hep-lat↗

arXiv2014

Asymptotic Behaviour of Pion--Pion Total Cross-Sections

We derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the $ππ$ total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading $\log^2 s$ behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for $π^+ π^-$, $π^{\pm} π^0$ and $π^0 π^0$ scattering within the framework of the constituent chiral quark model (C$χ$QM) in the limit of a large number of colours $\Nc$ and discuss their asymptotic behaviours. The same $ππ$ cross sections are also discussed within the general framework of Large-\Nc~QCD and we show that it is possible to make an Ansatz for the isospin $I=1$ and $I=0$ spectrum which satisfy the Froissart-Martin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-\Nc~counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the $σ_{π^{\pm}π^0}^{\rm total}(s)$ cross section predicted by the C$χ$QM with the high energy behaviour predicted by the Large-$\Nc$ Ansatz. The magnitude of these cross sections at very high energies is of the order of those observed for the $pp$ and $p{\bar p}$ scattering total cross sections.

hep-ph↗

arXiv2013

The Muon (g-2) Theory Value: Present and Future

This White Paper briefly reviews the present status of the muon (g-2) Standard-Model prediction. This value results in a 3 - 4 standard-deviation difference with the experimental result from Brookhaven E821. The present experimental uncertainty is $\pm 63 \times 10^{-11}$ (0.54~ppm), and the Standard-Model uncertainty is $\simeq \pm 49 \times 10^{-11}$. Fermilab experiment E989 has the goal to reduce the experimental error to $\pm 16 \times 10^{-11}$. Improvements in the Standard-Model value, which should be achieved between now and when the first results from Fermilab E989 could be available, should lead to a Standard-Model uncertainty of $\sim \,\pm 35 \times 10^{-11}$. These improvements would halve the uncertainty on the difference between experiment and theory, and should clarify whether the current difference points toward New Physics, or to a statistical fluctuation. At present, the (g-2) result is arguably the most compelling indicator of physics beyond the Standard Model and, at the very least, it represents a major constraint for speculative new theories such as supersymmetry, dark gauge bosons or extra dimensions.

hep-ph↗

arXiv2013

The Froissart--Martin Bound for $ππ$ Scattering in QCD

The Froissart--Martin bound for total $ππ$ scattering cross sections is reconsidered in the light of QCD properties such as spontaneous chiral symmetry breaking and the counting rules for a large number of colours $\Nc$.

hep-ph↗

arXiv2012

Update of the Electron and Muon g-Factors

I give an overview of the different contributions to the electron and muon anomalous magnetic moments in the Standard Model. Special emphasis is given to recent QED results as well as to the hadronic light-by-light scattering contribution to the muon anomaly.

hep-ph↗

arXiv2012

Hadronic Contributions to the Muon Anomaly in the Constituent Chiral Quark Model

The hadronic contributions to the anomalous magnetic moment of the muon which are relevant for the confrontation between theory and experiment at the present level of accuracy, are evaluated within the same framework: the constituent chiral quark model. This includes the contributions from the dominant hadronic vacuum polarization as well as from the next--to--leading order hadronic vacuum polarization, the contributions from the hadronic light-by-light scattering, and the contributions from the electroweak hadronic $Zγγ$ vertex. They are all evaluated as a function of only one free parameter: the constituent quark mass. We also comment on the comparison between our results and other phenomenological evaluations.

hep-ph↗

arXiv2011

Large Nc QCD and Harmonic Sums

In the Large-Nc limit of QCD, two--point functions of local operators become Harmonic Sums. I review some properties which follow from this fact and which are relevant for phenomenological applications. This has led us to consider a class of Analytic Number Theory Functions as toy models of Large-Nc QCD which I also discuss.

hep-ph↗

arXiv2011

On Anomaly Matching and Holography

We discuss the possible validity in QCD of a relation between Green's functions which has been recently suggested by Son and Yamamoto, based on a class of AdS/CFT-inspired models of QCD. Our conclusion is that the relation in question is unlikely to be implemented in QCD.

hep-ph↗

arXiv2011

The Constituent Chiral Quark Model Revisited

We reconsider the Constituent Chiral Quark Model of Manohar and Georgi in the presence of $SU(3)_{L}\times SU(3)_{R}$ external sources. As recently emphasized by Weinberg, the corresponding effective Lagrangian is renormalizable in the Large--${\rm N_c}$ limit. We show, however, that the number of the required counterterms depends crucially on the value of $g_A$ and it is minimized for $g_A =1$. We then find that with a rather small value for the constituent quark mass, which we fix phenomenologically to $M_Q =(190\pm 40)\MeV$, the model reproduces rather well the values of several well known low energy constants. We also comment on the limitations of the model as well as on a few {\it exceptional} applications, to more complicated low--energy observables, where one can expect the model to make reasonably good predictions.

hep-ph↗

arXiv2010

Large-Nc QCD, Harmonic Sums and the Riemann Zeros

It is shown that in Large-Nc QCD, two--point functions of local operators become Harmonic Sums. We comment on the properties which follow from this fact. This has led us to an aside observation concerning the zeros of the Riemann zeta--function seen from the point of view of Dispersion Relations in Quantum Theory.

hep-th↗

arXiv2009

Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment

We review the current status of theoretical calculations of the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment. Different approaches and related issues such as OPE constraints and large breaking of chiral symmetry are discussed. Combining results of different models with educated guesses on the errors we come to the estimate $$a^{\rm HLbL}=(10.5\pm 2.6)\times 10^{-10}.$$ The text is prepared as a contribution to the {\it Glasgow White Paper on the present status of the Muon Anomalous Magnetic Moment}.

hep-ph↗

arXiv2007

Bounds on the Light Quark Masses: the scalar channel revisited

We evaluate lower bounds on the sum of the up and down quark masses. The bounds follow from the constraints provided by the dispersion relation obeyed by the two--point function of the scalar current density when combined with properties of the scalar spectral function at long--distances and perturbative QCD at short--distances. Our results point to values of $m_u+m_d$ somewhat higher than those reported recently in the literature using lattice QCD simulations.

hep-ph↗