arXiv subjects

Maarten Golterman

Publications and source records attributed to Maarten Golterman.

At least 55 records · Page 3Linked to original sources

arXiv2019

The $ε$-regime of dilaton chiral perturbation theory

The $ε$-regime of dilaton chiral perturbation theory is introduced. We compute the dilaton mass, the chiral condensate and the topological susceptibility in the $ε$-regime, as a function of the fermion mass. The microscopic spectral density of the Dirac operator is obtained from dilaton chiral perturbation theory. Our main result is that the chiral condensate and the spectral density are related to their counterparts from ordinary chiral perturbation theory via a simple scaling relation. This relation originates from the mass dependence of the dilaton potential, and is valid in both the $ε$-regime and the $p$-regime. In the $ε$-regime, moreover, all results agree with the universal predictions to leading order in $ε$.

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arXiv2019

Evidence against naive truncations of the OPE from $e^+e^- \to$ hadrons below charm

The operator product expansion (OPE), truncated in dimension, is employed in many contexts. An example is the extraction of the strong coupling, $α_s$, from hadronic $τ$-decay data, using a variety of analysis methods based on finite-energy sum rules. Here, we reconsider a long-used method, which parametrizes non-perturbative contributions to the $I=1$ vector and axial vacuum polarizations with the OPE, setting several higher-dimension coefficients to zero in order to implement the method in practice. The assumption that doing this has a negligible effect on the value of $α_s$ is tantamount to the assumption that the low-dimension part of the OPE converges rapidly with increasing dimension near the $τ$ mass. Were this assumption valid, it would certainly have to be valid at energies above the $τ$ mass as well. It follows that the method can be tested using data obtained from $e^+e^-\to\mbox{hadrons}$, as they are not limited by the kinematic constraints of $τ$ decays. We carry out such an investigation using a recent high-precision compilation for the $R$-ratio, arguing that it provides insights into the validity of the strategy, even if it probes a different, though related channel. We find that $e^+e^-$-based tests call into question the implied assumption of rapid convergence of the low-dimension part of the OPE around the $τ$ mass, and thus underscore the need to restrict finite-energy sum-rule analyses to observables which receive only contributions from lower-order terms in the OPE.

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arXiv2019

Phase ambiguity of the measure for continuum Majorana fermions

Integrating over a continuum Majorana fermion formally yields a functional pfaffian. We show that the phase of this pfaffian is ambiguous, as it depends on the choice of basis. This ambiguity is naturally resolved within a non-perturbative lattice definition, allowing us to discuss the relation between the phase of the lattice pfaffian and the effective $θ$ angle of the theory. We also resolve an apparent paradox regarding the induced $θ$ angle when a theory of $N$ Dirac fermions in a real representation of the gauge group is re-expressed in terms of $2N$ Majorana fermions. We discuss how all this is reflected in chiral perturbation theory.

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arXiv2019

Radiative contribution to the composite-Higgs potential in a two-representation lattice model

Working in a two-representation lattice gauge theory that is close to a composite Higgs model, we calculate the low-energy constant CLR which controls the contribution of the electroweak gauge bosons to the Higgs potential. In QCD, the corresponding low-energy constant governs the mass splitting of the pion multiplet. Taking the continuum and chiral limits, we find that CLR, in units of the pseudoscalar decay constant, is roughly of the same size as its QCD counterpart.

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arXiv2018

HISQ 2+1+1 light quark hadronic vacuum polarization at the physical point

We report on the computation of the light quark vacuum polarization with 2+1+1 flavors of H ISQ fermions at the physical point and its contribution to the muon anomalous magnetic moment. Three ensembles, generated by the MILC collaboration, are used to take the continuum limit. We compare our result with recent ones in the literature.

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arXiv2018

The strong coupling from $e^+e^-\to$ hadrons

We use a new compilation of the hadronic $R$-ratio from available data for the process $e^+e^-\to$ hadrons below the charm mass to determine the strong coupling $α_s$, using finite-energy sum rules. Quoting our results at the $τ$ mass to facilitate comparison to the results obtained from similar analyses of hadronic $τ$-decay data, we find $α_s(m_τ^2)=0.298\pm 0.016\pm 0.006$ in fixed-order perturbation theory, and $α_s(m_τ^2)=0.304\pm 0.018\pm 0.006$ in contour-improved perturbation theory, where the first error is statistical, and the second error combines various systematic effects. These values are in good agreement with a recent determination from the OPAL and ALEPH data for hadronic $τ$ decays. We briefly compare the $R(s)$-based analysis with the $τ$-based analysis.

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arXiv2018

The large-mass regime of confining but nearly conformal gauge theories

We apply a recently developed dilaton-pion effective field theory for asymptotically free gauge theories near the conformal window to the $SU(3)$ gauge theory with $N_f=8$ fermions in the fundamental representation. Numerical data for this theory suggest the existence of a large-mass regime, where the fermion mass is not small but nevertheless the effective theory is applicable because of the parametric proximity of the conformal window. In this regime, we find that the mass dependence of hadronic quantities is similar to that of a a mass-deformed conformal theory, so that distinguishing infrared conformality from confinement requires the study of subleading effects.

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arXiv2018

The large-mass regime of the dilaton-pion low-energy effective theory

Numerical data of the SU(3) gauge theory with $N_f=8$ fermions in the fundamental representation suggest the existence of a large-mass regime, where the fermion mass is not small relative to the confinement scale, but nevertheless the dilaton-pion low-energy theory is applicable thanks to the parametric proximity of the conformal window. In this regime, the leading hyperscaling relations are similar to those of a mass-deformed conformal theory, so that distinguishing infrared conformality from confinement requires the study of subleading effects. Assuming that the $N_f=8$ theory confines, we estimate how light the fermion mass should be to enter the small-mass regime, where the pions become much lighter than the dilatonic scalar meson.

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arXiv2018

The strong coupling from $e^+e^-\to$ hadrons below charm

We use a new compilation of the hadronic $R$-ratio from available data for the process $e^+e^-\to\mbox{hadrons}$ to determine the strong coupling, $α_s$. We make use of all data for the $R$-ratio from threshold to a center-of-mass energy of 2 GeV by employing finite-energy sum rules. Data above 2 GeV, for which at present far fewer high-precision experimental data are available, do not provide much additional constraint but are fully consistent with the values for $α_s$ we obtain. Quoting our results at the $τ$ mass to facilitate comparison to the results obtained from analogous analyses of hadronic $τ$-decay data, we find $α_s(m_τ^2)=0.298\pm 0.016\pm 0.006$ in fixed-order perturbation theory, and $α_s(m_τ^2)=0.304\pm 0.018\pm 0.006$ in contour-improved perturbation theory, where the first error is statistical, and the second error reflects our estimate of various systematic effects. These values are in good agreement with a recent determination from the OPAL and ALEPH data for hadronic $τ$ decays.

hep-ph↗

arXiv2018

Spectroscopy of SU(4) composite Higgs theory with two distinct fermion representations

We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. Such theories arise naturally in the context of composite Higgs models that include a partially composite top quark. We describe the low-lying meson spectrum of the theory and fit the pseudoscalar masses and decay constants to chiral perturbation theory. We infer as well the mass and decay constant of the Goldstone boson corresponding to the non-anomalous U(1) symmetry of the model. Our results are broadly consistent with large-Nc scaling and vector-meson dominance.

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arXiv2018

Effective potential in ultraviolet completions for composite Higgs models

We consider a class of composite Higgs models based on asymptotically free $SO(d)$ gauge theories with $d$ odd, with fermions in two irreducible representations, and in which the Higgs field arises as a pseudo Nambu-Goldstone boson and the top quark is partially composite. The Nambu-Goldstone coset containing the Higgs field, or Higgs coset, is either $SU(4)/Sp(4)$ or $SU(5)/SO(5)$, whereas the top partners live in two-index representations of the relevant flavor group ($SU(4)$ or $SU(5)$). In both cases, there is a large number of terms in the most general four-fermion lagrangian describing the interaction of third-generation quarks with the top partners. We derive the top-induced effective potential for the Higgs coset together with the singlet pseudo Nambu-Goldstone boson associated with the non-anomalous axial symmetry, to leading order in the couplings between the third-generation quarks and the composite sector. We obtain expressions for the low-energy constants in terms of top-partner two-point functions. We revisit the effective potential of another composite Higgs model that we have studied previously, which is based on an $SU(4)$ gauge theory and provides a different realization of the $SU(5)/SO(5)$ coset. The top partners of this model live in the fundamental representation of $SU(5)$, and, as a result, the effective potential of this model is qualitatively different from the $SO(d)$ gauge theories. We also discuss the role of the isospin-triplet fields contained in the $SU(5)/SO(5)$ coset, and show that, without further constraints on the four-fermion couplings, an expectation value for the the Higgs field will trigger the subsequent condensation of an isospin-triplet field.

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arXiv2017

Hyperasymptotics and quark-hadron duality violations in QCD

We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex $q^2$ plane. Starting from the dispersive representation for the associated polarization, the analytic continuation of the operator product expansion from the Euclidean to the Minkowski region is performed by means of a generalized Borel-Laplace transform, borrowing techniques from hyperasymptotics. We establish a connection between singularities in the Borel plane and quark-hadron duality violating contributions. Starting with the assumption that for QCD at $N_c=\infty$ the spectrum approaches a Regge trajectory at large energy, we obtain an expression for quark-hadron duality violations at large, but finite $N_c$.

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arXiv2017

Pion mass dependence of the HVP contribution to muon $g-2$

One of the systematic errors in some of the current lattice computations of the HVP contribution to the muon anomalous magnetic moment $g-2$ is that associated with the extrapolation to the physical pion mass. We investigate this extrapolation assuming lattice pion masses in the range of 220 to 440 MeV with the help of two-loop chiral perturbation theory, and find that such an extrapolation is unlikely to lead to control of this systematic error at the 1% level. This remains true even if various proposed tricks to improve the chiral extrapolation are taken into account.

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arXiv2017

Hadronic tau decays and the strong coupling

We provide an overview of recent determinations of the strong coupling, $α_s$, from hadronic $τ$ decays. We contrast two analysis methods, the "truncated-OPE approach" and the "DV-model approach," highlighting the assumptions going into each of these. We argue that a detailed study based on ALEPH data shows the truncated-OPE approach to be quantitatively unreliable, while the DV-model approach passes all tests. New data for hadronic $τ$ decays from Belle and Belle-II could provide more stringent tests of the DV-model approach, and thus potentially lead to a more precise value of $α_s$ from hadronic $τ$ decays.

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arXiv2017

Determination of the NNLO low-energy constant $C_{93}$

Experimental data from hadronic $τ$ decays allow for a precision determination of the slope of the $I=1$ vacuum polarization at zero momentum. We use this information to provide a value for the next-to-next-to-leading order (NNLO) low-energy constant $C_{93}$ in chiral perturbation theory. The largest systematic error in this determination results from the neglect of terms beyond NNLO in the effective chiral Lagrangian, whose presence in the data will, in general, make the effective $C_{93}$ determined in an NNLO analysis mass dependent. We estimate the size of this effect by using strange hadronic $τ$-decay data to perform an alternate $C_{93}$ determination based on the slope of the strange vector polarization at zero momentum, which differs from that of the $I=1$ vector channel only through $SU(3)$ flavor-breaking effects. We also comment on the impact of such higher order effects on ChPT-based estimates for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

hep-ph↗

arXiv2017

Chiral extrapolation of the leading hadronic contribution to the muon anomalous magnetic moment

A lattice computation of the leading-order hadronic contribution to the muon anomalous magnetic moment can potentially help reduce the error on the Standard Model prediction for this quantity, if sufficient control of all systematic errors affecting such a computation can be achieved. One of these systematic errors is that associated with the extrapolation to the physical pion mass from values on the lattice larger than the physical pion mass. We investigate this extrapolation assuming lattice pion masses in the range of 200 to 400MeV with the help of two-loop chiral perturbation theory, and find that such an extrapolation is unlikely to lead to control of this systematic error at the 1% level. This remains true even if various tricks to improve the reliability of the chiral extrapolation employed in the literature are taken into account. In addition, while chiral perturbation theory also predicts the dependence on the pion mass of the leading-order hadronic contribution to the muon anomalous magnetic moment as the chiral limit is approached, this prediction turns out to be of no practical use, because the physical pion mass is larger than the muon mass that sets the scale for the onset of this behavior.

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arXiv2016

The status of the strong coupling from tau decays in 2016

While the idea of using the operator product expansion (OPE) to extract the strong coupling from hadronic $τ$ decay data is not new, there is an ongoing controversy over how to include quark-hadron "duality violations" (i.e., resonance effects) which are not described by the OPE. One approach attempts to suppress duality violations enough that they might become negligible, but pays the price of an uncontrolled OPE truncation. We critically examine a recent analysis using this approach and show that it fails to properly account for non-perturbative effects, making the resulting determination of the strong coupling unreliable. In a different approach duality violations are taken into account with a model, avoiding the OPE truncation. This second approach provides a self-consistent determination of the strong coupling from $τ$ decays.

hep-ph↗

arXiv2016

$α_s$ in 2016 from the (revised) ALEPH data for $τ$ decay

We summarize a comparison of the two strategies which are currently available in the literature for determining the value of $α_s(m_τ)$. We will refer to these as the truncated Operator Product Expansion model and the Duality Violation model. After describing the main features of both approaches, we explain why the former fails to pass crucial tests. The latter, on the other hand, passes all the tests known up to date and, therefore, should be currently considered the only reliable method.

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