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Santiago Peris

Publications and source records attributed to Santiago Peris.

At least 55 records · Page 3Linked to original sources
arXiv2015

Finite-volume effects in the hadronic vacuum polarization

We investigate finite-volume effects in the hadronic vacuum polarization, with an eye toward the corresponding systematic error in the muon anomalous magnetic moment. While it is well known that leading-order chiral perturbation theory does not provide a good description of the hadronic vacuum polarization, it turns out that it gives a much better representation of finite-volume effects. Indications are that finite-volume effects cannot be ignored when the aim is a few percent level accuracy for the hadronic contribution to the muon anomalous magnetic moment, even when $m_πL \sim 4$ and $m_π\sim 200$ MeV.

hep-lat↗
arXiv2015

Low-energy constants from ALEPH hadronic tau decay data

We determined the NLO chiral low-energy constant $L_{10}$, and various combinations of NNLO chiral low-energy constants employing recently revised ALEPH results for the non-strange vector (V) and axial-vector (A) hadronic tau decay distributions and recently updated RBC/UKQCD lattice data for the non-strange V-A two-point function. In this talk, we explain the ingredients of this determination. Our errors are at or below the level expected for contributions of yet higher order in the chiral expansion, suggesting that our results exhaust the possibilities of what can be meaningfully achieved in an NNLO analysis.

hep-ph↗
arXiv2015

$α_s$ from the updated ALEPH data for hadronic $τ$ decays

We extract the strong coupling $α_s(m_τ^2)$ from the recently updated ALEPH non-strange spectral functions obtained from hadronic $τ$ decays. We apply a self-consistent analysis method, first tested in the analysis of OPAL data, to extract $α_s(m_τ^2)$ and non-perturbative contributions. The analysis yields $α_s^{\rm FO}(m_τ^2)=0.296\pm0.010 $, using Fixed Order Perturbation Theory (FOPT), and $α^{\rm CI}_s(m_τ^2)= 0.310\pm0.014$, using Contour Improved Perturbation Theory (CIPT). The weighted average of these results with those previously obtained from OPAL data give $α_s^{\rm FO}(m_τ^2)=0.303\pm 0.009$ and $α_s^{\rm CI}(m_τ^2)=0.319\pm 0.012$, which gives, after evolution to the $Z$ boson mass scale, $α^{\rm FO}_s(m_Z^2)=0.1165\pm0.0012 $ and $α_s^{\rm CI}(m_Z^2)=0.1185\pm0.0015 $, respectively. We observe that non-perturbative effects limit the accuracy with which $α_s$ can be extracted from $τ$ decay data.

hep-ph↗
arXiv2015

Low-energy constants and condensates from ALEPH hadronic $τ$ decay data

We determine the NLO chiral low-energy constant $L_{10}^r$, and combinations $C_{12}^r\pm C_{61}^r+C_{80}^r$, $C_{13}^r-C_{62}^r+C_{81}^r$, $C_{61}^r$, and $C_{87}^r$, of the NNLO chiral low-energy constants incorporating recently revised ALEPH results for the non-strange vector ($V$) and axial-vector ($A$) hadronic $τ$ decay distributions and recently updated RBC/UKQCD lattice data for the non-strange $V-A$ two-point function. In the $\bar{\rm MS}$ scheme, at renormalization scale $μ=770\ {MeV}$, we find $L_{10}^r=-0.00350(17)$, $C_{12}^r+C_{61}^r+C_{80}^r=0.00237(16)\ {GeV}^{-2}$, $C_{12}^r-C_{61}^r+C_{80}^r=-0.00056(15)\ {GeV}^{-2}$, $C_{13}^r-C_{62}^r+C_{81}^r=0.00046(9)\ {GeV}^{-2}$, $C_{61}^r=0.00146(15)\ {GeV}^{-2}$, and $C_{87}^r=0.00510(22)\ {GeV}^{-2}$. With errors here at or below the level expected for contributions of yet higher order in the chiral expansion, the analysis exhausts the possibilities of what can be meaningfully achieved in an NNLO analysis. We also consider the dimension six and dimension eight coefficients in the operator product expansion in the $V-A$ channel.

hep-ph↗
arXiv2015

The strong coupling from the revised ALEPH data for hadronic $τ$ decays

We apply an analysis method previously developed for the extraction of the strong coupling from the OPAL data to the recently revised ALEPH data for non-strange hadronic $τ$ decays. Our analysis yields the values $α_s(m_τ^2)=0.296\pm 0.010$ using fixed-order perturbation theory, and $α_s(m_τ^2)=0.310\pm 0.014$ using contour-improved perturbation theory. Averaging these values with our previously obtained values from the OPAL data, we find $α_s(m_τ^2)=0.303\pm 0.009$, respectively, $α_s(m_τ^2)=0.319\pm 0.012$. We present a critique of the analysis method employed previously, for example in analyses by the ALEPH and OPAL collaborations, and compare it with our own approach. Our conclusion is that non-perturbative effects limit the accuracy with which the strong coupling, an inherently perturbative quantity, can be extracted at energies as low as the $τ$ mass. Our results further indicate that systematic errors on the determination of the strong coupling from analyses of hadronic $τ$-decay data have been underestimated in much of the existing literature.

hep-ph↗
arXiv2014

A Hybrid Strategy for the Lattice Evaluation of the Leading Order Hadronic Contribution to $(g-2)_μ$

The leading-order hadronic contribution to the muon anomalous magentic moment, $a_μ^{\rm LO,HVP}$, can be expressed as an integral over Euclidean $Q^2$ of the vacuum polarization function. We point out that a simple trapezoid-rule numerical integration of the current lattice data is good enough to produce a result with a less-than-$1\%$ error for the contribution from the interval above $Q^2\gtrsim 0.1-0.2\ \mathrm{GeV}^2$. This leaves the interval below this value of $Q^2$ as the one to focus on in the future. In order to achieve an accurate result also in this lower window $Q^2\lesssim 0.1-0.2\ \mathrm{GeV}^2$, we indicate the usefulness of three possible tools. These are: Padé Approximants, polynomials in a conformal variable and a NNLO Chiral Perturbation Theory representation supplemented by a $Q^4$ term. The combination of the numerical integration in the upper $Q^2$ interval together with the use of these tools in the lower $Q^2$ interval provides a hybrid strategy which looks promising as a means of reaching the desired goal on the lattice of a sub-percent precision in the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

hep-lat↗
arXiv2014

$α_{s}$ from the (revised) ALEPH data for $τ$ decay

We present a new analysis of $α_s$ from hadronic $τ$ decays based on the recently revised ALEPH data. The analysis is based on a strategy which we previously applied to the OPAL data. We critically compare our strategy to the one traditionally used and comment on the main differences. Our analysis yields the values $α_s(m_τ^2)=0.296\pm 0.010$ using fixed-order perturbation theory, and $α_s(m_τ^2)=0.310\pm 0.014$ using contour-improved perturbation theory. Averaging these values with our previously obtained values from the OPAL data, we find $α_s(m_τ^2)=0.303\pm 0.009$, respectively, $α_s(m_τ^2)=0.319\pm 0.012$, as the most reliable results for $α_s$ from $τ$ decays currently available.

hep-ph↗
arXiv2014

A new strategy for evaluating the LO HVP contribution to $(g-2)_μ$ on the lattice

A highly physical model of the subtracted $I=1$ vector polarization, obtained using a dispersive representation with precise hadronic $τ$ decay data as input, is used to investigate systematic issues in the lattice evaluation of the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. The model is also employed to study possible resolutions of these problems. A hybrid approach to analyzing lattice data, involving low-order Padé, low-degree conformal-variable polynomial, or supplemented NNLO ChPT fits for $Q^2$ below $\sim 0.1-0.2$ GeV$^2$ and direct numerical integration of lattice data above this point, is shown to bring the systematic issues identified under control at the sub-$1\%$ level.

hep-lat↗
arXiv2014

Functional-analysis based tool for testing quark-hadron duality

Quark-hadron duality is a key concept in QCD, allowing for the description of physical hadronic observables in terms of quark-gluon degrees of freedom. The modern theoretical framework for its implementation is Wilson's operator product expansion (OPE), supplemented by analytic extrapolation from large Euclidean momenta, where the OPE is defined, to the Minkowski axis, where observable quantities are defined. Recently, the importance of additional terms in the expansion of QCD correlators near the Minkowski axis, responsible for quark-hadron duality violations (DVs), was emphasized. In this paper we introduce a mathematical tool that might be useful for the study of DVs in QCD. It is based on finding the minimal distance, measured in the $L^\infty$ norm along a contour in the complex momentum plane, between a class of admissible functions containing the physical amplitude and the asymptotic expansion predicted by the OPE. This minimal distance is given by the norm of a Hankel matrix that can be calculated exactly, using as input the experimental spectral function on a finite interval of the timelike axis. We also comment on the relation between the new functional tool and the more commonly used $χ^2$-based analysis. The approach is illustrated on a toy model for the QCD polarization function recently proposed in the literature.

hep-ph↗
arXiv2014

A New Strategy for the Lattice Evaluation of the Leading Order Hadronic Contribution to $(g-2)_μ$

A reliable evaluation of the integral giving the hadronic vacuum polarization contribution to the muon anomalous magnetic moment should be possible using a simple trapezoid-rule integration of lattice data for the subtracted electromagnetic current polarization function in the Euclidean momentum interval $Q^2>Q^2_{min}$, coupled with an $N$-parameter Padé or other representation of the polarization in the interval $0<Q^2<Q^2_{min}$, for sufficiently high $Q^2_{min}$ and sufficiently large $N$. Using a physically motivated model for the $I=1$ polarization, and the covariance matrix from a recent lattice simulation to generate associated fake "lattice data," we show that systematic errors associated with the choices of $Q^2_{min}$ and $N$ can be reduced to well below the 1% level for $Q^2_{min}$ as low as 0.1 GeV$^2$ and rather small $N$. For such low $Q^2_{min}$, both an NNLO chiral representation with one additional NNNLO term and a low-order polynomial expansion employing a conformally transformed variable also provide representations sufficiently accurate to reach this precision for the low-$Q^2$ contribution. Combined with standard techniques for reducing other sources of error on the lattice determination, this hybrid strategy thus looks to provide a promising approach to reaching the goal of a sub-percent precision determination of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment on the lattice.

hep-lat↗
arXiv2013

The muon anomalous magnetic moment, a view from the lattice

We review some of the issues that arise in attempts to compute the hadronic corrections to the muon anomalous magnetic moment using Lattice QCD. We concentrate on the dominant contribution, which requires an accurate evaluation of the hadronic vacuum polarization.

hep-lat↗
arXiv2013

The hadronic vacuum polarization with twisted boundary conditions

The leading-order hadronic contribution to the muon anomalous magnetic moment is given by a weighted integral over the subtracted hadronic vacuum polarization. This integral is dominated by euclidean momenta of order the muon mass, i.e., momenta not accessible on current lattice volumes with periodic boundary conditions. Twisted boundary conditions can in principle help in accessing momenta of any size even in a finite volume, but their use leads to a modification of the Ward-Takahashi identity that normally guarantees transversality of the vacuum polarization. As a result, the vacuum polarization contains a non-transversal, quadratically divergent term, which arises as an artifact of using twisted boundary conditions in a finite volume. In this article, we show how to determine and remove this term from the vacuum polarization.

hep-lat↗
arXiv2013

Tests of hadronic vacuum polarization fits for the muon anomalous magnetic moment

Using experimental spectral data for hadronic tau decays from the OPAL experiment, supplemented by a phenomenologically successful parameterization for the high-s region not covered by the data, we construct a physically constrained model of the isospin-one vector-channel polarization function. Having such a model as a function of Euclidean momentum Q^2 allows us to explore the systematic error associated with fits to the Q^2 dependence of lattice data for the hadronic electromagnetic current polarization function which have been used in attempts to compute the leading order hadronic contribution, a_μ^HLO, to the muon anomalous magnetic moment. In contrast to recent claims made in the literature, we find that a final error in this quantity of the order of a few percent does not appear possible with current lattice data, given the present lack of precision in the determination of the vacuum polarization at low Q^2. We also find that fits to the vacuum polarization using fit functions based on Vector Meson Dominance are unreliable, in that the fit error on a_μ^HLO is typically much smaller than the difference between the value obtained from the fit and the exact model value. The use of a sequence of Pade approximants known to converge to the true vacuum polarization appears to represent a more promising approach.

hep-lat↗
arXiv2013

Narrow Tetraquarks at Large N

Following a recent suggestion by Weinberg, we use the large-N expansion in QCD to discuss the decay amplitudes of tetraquarks into ordinary mesons as well as their mixing properties. We find that the flavor structure of the tetraquark is a crucial ingredient to determine both this mixing as well as the decays. Although in some cases tetraquarks should be expected to be as narrow as ordinary mesons, they may get to be even narrower, depending on this flavor structure.

hep-ph↗
arXiv2013

Low-energy constants and condensates from the tau hadronic spectral functions

We use results of fits to the OPAL spectral data, obtained from non-strange hadronic τdecays, to evaluate the difference between the vector and axial current correlators, Π_{V-A}(Q^2). The behavior of Π_{V-A}(Q^2) near euclidean momentum Q^2=0 is used to determine the effective low-energy constants L_10^eff and C_87^eff related to the renormalized low-energy constants L_10^r and C_87^r in the chiral lagrangian. We also investigate how well two-loop chiral perturbation theory describes Π_{V-A}(Q^2) as a function of Q^2. This is the first determination of L_10^eff and C_87^eff to employ a fully self-consistent model for the violations of quark-hadron duality in both the vector and axial channels. We also discuss the values of the coefficients C_{6,V-A} and C_{8,V-A} governing the dimension six and eight contributions to the operator product expansion representation of Π_{V-A}(Q^2).

hep-ph↗
arXiv2012

The strong coupling from tau decays without prejudice

We review our recent determination of the strong coupling α_s from the OPAL data for non-strange hadronic tau decays. We find that α_s(m^2_τ) =0.325+-0.018 using fixed-order perturbation theory, and α_s(m^2_τ)=0.347+-0.025 using contour-improved perturbation theory. At present, these values supersede any earlier determinations of the strong coupling from hadronic tau decays, including those from ALEPH data.

hep-ph↗
arXiv2012

Pade approximants and g-2 for the muon

The leading hadronic contribution to the muon anomalous magnetic moment is given by a weighted euclidean momentum integral of the hadronic vacuum polarization. This integral is dominated by momenta of order the muon mass. Since in lattice QCD it is difficult to compute the vacuum polarization at a large number of low momenta, a parametrization of the vacuum polarization is required to extrapolate the data. Most fits to date are based on vector meson dominance, which introduces model dependence into the lattice computation of the magnetic moment. Here we introduce a model-independent extrapolation method, and present a few first tests of this new method.

hep-lat↗