arXiv subjects

Kim Maltman

Publications and source records attributed to Kim Maltman.

At least 37 records · Page 2Linked to original sources

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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arXiv2018

Novel $|V_{us}|$ Determination Using Inclusive Strange $τ$ Decay and Lattice HVPs

We propose and apply a new approach to determining $|V_{us}|$ using dispersion relations with weight functions having poles at Euclidean (space-like) momentum which relate strange hadronic $τ$ decay distributions to hadronic vacuum polarization functions (HVPs) obtained from lattice QCD. We show examples where spectral integral contributions from the region where experimental data have large errors or do not exist are strongly suppressed but accurate determinations of the relevant lattice HVP combinations remain possible. The resulting $|V_{us}|$ agrees well with determinations from $K$ physics and 3-family CKM unitarity. Advantages of this new approach over the conventional hadronic $τ$ decay determination employing flavor-breaking sum rules are also discussed.

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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

Evidence for charm-bottom tetraquarks and the mass dependence of heavy-light tetraquark states from lattice QCD

We continue our study of heavy-light four-quark states and find evidence from lattice QCD for the existence of a strong-interaction-stable $I(J^P)=0(1^+)$ $ud\bar{c}\bar{b}$ tetraquark with mass in the range of 15 to 61 MeV below $\bar{D}B^*$ threshold. Since this range includes the electromagnetic $\bar{D}Bγ$ decay threshold, current uncertainties do not allow us to determine whether such a state would decay electromagnetically, or only weakly. We also perform a study at fixed pion mass, with NRQCD for the heavy quarks, simulating $qq^\prime \bar{b}^\prime \bar{b}$ and $q q^\prime \bar{b}^\prime\bar{b}^\prime$ tetraquarks with $q,\, q^\prime =ud$ or $\ell s$ and variable, unphysical $m_{b^\prime}$ in order to investigate the heavy mass-dependence of such tetraquark states. We find that the dependence of the binding energy follows a phenomenologically-expected form and that, though NRQCD breaks down before $m_{b^\prime}=m_c$ is reached, the results at higher $m_{b^\prime}$ clearly identify the $ud\bar{b}^\prime \bar{b}$ channel as the most likely to support a strong-interaction-stable tetraquark state at $m_{b^\prime}=m_c$. This observation serves to motivate the direct $ud\bar{c}\bar{b}$ simulation. Throughout we use dynamical $n_f=2+1$ ensembles with pion masses $m_π=$415, 299, and 164 MeV reaching down almost to the physical point, a relativistic heavy quark prescription for the charm quark, and NRQCD for the bottom quark(s).

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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.

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arXiv2018

$α_s$ from the Lattice Hadronic Vacuum Polarisation

We present a determination of the QCD coupling constant, $α_s$, obtained by fitting lattice results for the flavour $ud$ hadronic vacuum polarisation function to continuum perturbation theory. We use $n_f=2+1$ flavours of Domain Wall fermions generated by the RBC/UKQCD collaboration and three lattice spacings $a^{-1}=1.79,\, 2.38$ and $3.15\ \text{GeV}$. Several sources of potential systematic error are identified and dealt with. After fitting and removing expected leading cut-off effects, we find for the five-flavour $\overline{\text{MS}}$ coupling the value $α_s(M_Z)=0.1181(27)^{+8}_{-22}$, where the first error is statistical and the second systematic.

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arXiv2018

A resolution of the inclusive flavor-breaking $τ$ $|V_{us}|$ puzzle

We revisit the puzzle of $|V_{us}|$ values obtained from the conventional implementation of hadronic-$τ$-decay-based flavor-breaking finite-energy sum rules lying $>3 σ$ below the expectations of three-family unitarity. Significant unphysical dependences of $|V_{us}|$ on the choice of weight, w, and upper limit, $s_0$, of the experimental spectral integrals entering the analysis are confirmed, and a breakdown of assumptions made in estimating higher dimension, $D>4$, OPE contributions is identified as the main source of these problems. A combination of continuum and lattice results is shown to suggest a new implementation of the flavor-breaking sum rule approach in which not only $|V_{us}|$, but also $D>4$ effective condensates, are fit to data. Lattice results are also used to clarify how to reliably treat the slowly converging D=2 OPE series. The new sum rule implementation is shown to cure the problems of the unphysical w- and $s_0$-dependence of $|V_{us}|$ and to produce results $\sim 0.0020$ higher than those of the conventional implementation. With B-factory input, and using, in addition, dispersively constrained results for the $Kπ$ branching fractions, we find $\vert V_{us}\vert =0.2231(27)_{exp}(4)_{th}$, in excellent agreement with the result from $K_{\ell 3}$, and compatible within errors with the expectations of three-family unitarity, thus resolving the long-standing inclusive $τ$ $|V_{us}|$ puzzle.

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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

More on heavy tetraquarks in lattice QCD at almost physical pion mass

We report on our progress in studying exotic, heavy tetraquark states, $qq\prime \bar Q\bar Q\prime$. Using publicly available dynamical $n_f =2+1$ Wilson-Clover gauge configurations, generated by the PACS-CS collaboration, with pion masses $\simeq$164, 299 and 415 MeV, we extend our previous analysis to heavy quark components containing heavier than physical bottom quarks $\bar Q\bar Q\prime=\bar b\prime\bar b\prime$ or $\bar Q\bar Q\prime=\bar b\bar b\prime$, charm and bottom quarks $\bar c\bar b$ and also only charm quarks $\bar c\bar c$. Throughout we employ NRQCD and relativistic heavy quarks for the heavier than bottom, bottom and charm quarks. Using our previously established diquark-antidiquark and meson-meson operator basis we comment in particular on the dependence of the binding energy on the mass of the heavy quark component $\bar Q\bar Q$, with heavy quarks ranging from $m_Q=0.85\ldots 6.3\cdot m_b$. In the heavy flavor non-degenerate case, $\bar Q\bar Q\prime$, and especially for the tetraquark channel $ud\bar c\bar b$, we extend our work to utilize a $3\times 3$ GEVP to study the ground and threshold states thereby enabling a clear identification of possible binding. Finally, we present initial work on the $\bar Q\bar Q\prime=\bar c\bar c$ system where a much larger operator basis is available in comparison to flavor combinations with NRQCD quarks.

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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.

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arXiv2017

Lattice Prediction for Deeply Bound Doubly Heavy Tetraquarks

We investigate the possibility of $qq^\prime \bar b \bar b$ tetraquark bound states using $n_f=2+1$ lattice QCD ensembles with pion masses $\simeq 164$, $299$, and $415$ MeV. Motivated by observations from heavy baryon phenomenology, we consider two lattice interpolating operators both of which are expected to couple efficiently to tetraquark states: one with diquark-antidiquark and one with a meson-meson structure. Using nonrelativistic QCD to simulate the bottom quarks, we study the $ud\bar b \bar b$, $\ell s\bar b \bar b$ channels with $\ell=u,d$, and find unambiguous signals for strong-interaction-stable $J^P=1^+$ tetraquarks. These states are found to lie $189(10)$ and $98(7)$ MeV below the corresponding free two-meson thresholds.

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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.

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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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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

$α_s$ 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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