arXiv subjects

Maarten Golterman

Publications and source records attributed to Maarten Golterman.

At least 73 records · Page 4Linked to original sources

arXiv2016

Effective pion mass term and the trace anomaly

Recently, we developed an effective theory of pions and a light dilatonic meson for gauge theories with spontaneously broken chiral symmetry that are close to the conformal window. The pion mass term in this effective theory depends on an exponent $y$. We derive the transformation properties under dilatations of the renormalized fermion mass, and use this to rederive $y=3-γ_m^*$, where $γ_m^*$ is fixed-point value of the mass anomalous dimension at the sill of the conformal window. This value for $y$ is consistent with the trace anomaly of the underlying near-conformal gauge theory.

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arXiv2016

The strong coupling from hadronic $τ$ decays: a critical appraisal

Several different analysis methods have been developed to determine the strong coupling via finite-energy sum-rule analyses of hadronic $τ$ decay data. While most methods agree on the existence of the well-known ambiguity in the choice of a resummation scheme due to the slow convergence of QCD perturbation theory at the $τ$ mass, there is an ongoing controversy over how to deal properly with non-perturbative effects. These are small, but not negligible, and include quark-hadron "duality violations" (i.e., resonance effects) which are not described by the operator product expansion (OPE). In one approach, an attempt is made to suppress duality violations enough that they might become negligible. The number of OPE parameters to be fit, however, then exceeds the number of available sum rules, necessitating an uncontrolled OPE truncation, in which a number of higher-dimension OPE contributions in general present in QCD are set to zero by hand. In the second approach, truncation of the OPE is avoided by construction, and duality violations are taken into account explicitly, using a physically motivated model. In this article, we provide a critical appraisal of a recent analysis employing the first approach and demonstrate that it fails to properly account for non-perturbative effects, making the resulting determination of the strong coupling unreliable. The second approach, in contrast, passes all self-consistency tests, and provides a competitive determination of the strong coupling from $τ$ decays.

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arXiv2016

Effective field theory for pions and a dilatonic meson

Numerical simulations of QCD-like theories which are chirally broken but exhibit a very small beta function reveal a flavor-singlet scalar, or "dilatonic meson," which is much lighter than any other states except pions. We develop a systematic low-energy expansion for the pions and the dilatonic meson, in which the presence of the latter is attributed to an approximate scale symmetry. In order to justify the power counting we invoke the Veneziano limit, in which the number of flavors $N_f$ in the fundamental representation grows in proportion with the number of colors $N_c$, while the ratio $N_f/N_c$ is kept close to, but below, the critical value where the conformal window is entered.

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arXiv2016

Low-energy effective action for pions and a dilatonic meson

Numerical simulations of QCD-like theories in which the number of flavors is adjusted so that the beta function is very small, but confinement and chiral symmetry breaking nevertheless take place, appear to reveal the presence of a flavor-singlet scalar meson which can be as light as the pions. Because the breaking of dilatation symmetry, quantified by the beta function, is small relative to QCD, a possible explanation is that the scalar meson is a pseudo Nambu-Goldstone boson associated with the approximate dilatation symmetry. We use this observation to systematically develop a low-energy effective action that accounts for both the pions and the "dilatonic" scalar meson. In order to justify the power counting that controls the couplings of the dilatonic meson we invoke the Veneziano limit, in which the number of fundamental-representation flavors $N_f$ grows in proportion with the number of colors $N_c$, while the ratio $N_f/N_c$ is kept close to, but below, the critical value where the conformal window is entered.

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arXiv2016

One-loop Chiral Perturbation Theory with two fermion representations

We develop Chiral Perturbation Theory for chirally broken theories with fermions in two different representations of the gauge group. Any such theory has a non-anomalous singlet $U(1)_A$ symmetry, yielding an additional Nambu-Goldstone boson when spontaneously broken. We calculate the next-to-leading order corrections for the pseudoscalar masses and decay constants, which include the singlet Nambu-Goldstone boson, as well as for the two condensates. The results can be generalized to more than two representations.

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arXiv2016

$α_s$ analyses from hadronic tau decays with OPAL and ALEPH data

Recently, we extracted the strong coupling, $α_s(m_τ^2)$, from the revised ALEPH data for non-strange hadronic tau decays. Our analysis is based on a method previously used for the determination of the strong coupling from OPAL data. In our strategy, we employ different moments of the spectral functions both with and without pinching, including Duality Violations, in order to obtain fully self-consistent analyses that do not rely on untested assumptions (such as the smallness of higher dimension contributions in the OPE). Here we discuss the $α_s$ values obtained from the ALEPH and the OPAL data, the robustness of the analysis, as well as non-perturbative contributions from DVs and the OPE. We show that, although the $α_s$ determination is sound, non-perturbative effects limit the accuracy with which one can extract the strong coupling from tau decay data. Finally, we discuss the compatibility of the data sets and the possibility of a combined analysis.

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arXiv2016

The case for duality violations in the analysis of hadronic $τ$ decays

We discuss why, in the determination of $α_s(m_τ^2)$ from hadronic $τ$ decays, two important assumptions made in most of previous analyses, namely the neglect of higher-dimension condensates and of Duality Violations (DVs), have introduced uncontrolled systematic errors into this determination. Although the use of pinched weights is usually offered as a justification of these assumptions, we explain why it is not possible to simultaneously suppress these two contributions; particularly since the Operator Product Expansion is expected to be an asymptotic, rather than a convergent expansion. There is not only experimental and theoretical evidence for DVs, but they also affect the extraction of $α_s(m_τ^2)$.

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arXiv2016

Finite-volume effects in the muon anomalous magnetic moment on the lattice

We investigate finite-volume effects in the hadronic vacuum polarization, with an eye toward the corresponding systematic error in the muon anomalous magnetic moment. We consider both recent lattice data as well as lowest-order, finite-volume chiral perturbation theory, in order to get a quantitative understanding. Even though leading-order chiral perturbation theory does not provide a good description of the hadronic vacuum polarization, it turns out that it gives a good representation of finite-volume effects. We find that finite-volume effects cannot be ignored when the aim is a few percent level accuracy for the leading-order hadronic contribution to the muon anomalous magnetic moment, even when using ensembles with $m_πL> 4$ and $m_π\sim 200$ MeV.

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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.

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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.

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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.

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arXiv2015

Vacuum alignment and lattice artifacts: Wilson fermions

Confinement in asymptotically free gauge theories is accompanied by the spontaneous breaking of the global flavor symmetry. If a subgroup of the flavor symmetry group is coupled weakly to additional gauge fields, the vacuum state tends to align such that the gauged subgroup is unbroken. Independently, a lattice discretization of the continuum theory typically reduces the manifest flavor symmetry, and, in addition, can give rise to new lattice-artifact phases with spontaneously broken symmetries. Here, we study the interplay of these two phenomena for Wilson fermions, using chiral lagrangian techniques. We consider two examples: electromagnetic corrections to QCD, and a prototype composite-Higgs model.

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arXiv2015

Vacuum alignment and lattice artifacts: staggered fermions

In confining lattice gauge theories in which part of the flavor group is coupled weakly to additional gauge fields, both the dynamics of the weak gauge fields as well as lattice artifacts may have non-trivial effects on the orientation of the vacuum in flavor space. Here we discuss this issue for lattice gauge theories employing staggered fermions. Staggered fermions break flavor symmetries to a much smaller group on the lattice, and orientations in flavor space that are equivalent in the continuum may be distinct on the lattice. Assuming universality, we show that in the continuum limit the weakly gauged flavor symmetries are always vector-like, disproving a recent claim in the literature.

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arXiv2015

Top quark induced effective potential in a composite Higgs model

We consider non-perturbative aspects of a composite Higgs model that serves as a prototype for physics beyond the Standard Model, in which a new strongly interacting sector undergoes chiral symmetry breaking, and generates the Higgs particle as a pseudo Nambu-Goldstone boson. In addition, the top quark couples linearly to baryons of the new strong sector, thereby becoming partially composite. We study the dynamics leading to the top quark Yukawa coupling as well as the top quark contribution to the effective potential for the Higgs, obtaining expressions for these couplings in terms of baryonic correlation functions in the underlying strongly interacting theory. We then show that a large-N limit exists in which the top quark contribution to the Higgs effective potential overcomes that of the weak gauge bosons, inducing electroweak symmetry breaking. The same large-N limit also suggests that the baryons that couple to the top quark may be relatively light. This composite Higgs model, and similar ones, can be studied on the lattice with the methods developed for lattice QCD.

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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.

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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.

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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.

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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.

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