Bottom and Charm Mass Determinations with a Convergence Test

We present new determinations of the MS-bar charm quark mass using relativistic QCD sum rules at O(alpha_s^3) from the moments of the vector and the pseudoscalar current correlators. We use available experimental measurements from e+e- collisions and lattice simulation results, respectively. Our analysis of the theoretical uncertainties is based on different implementations of the perturbative series and on independent variations of the renormalization scales for the mass and the strong coupling. Taking into account the resulting set of series to estimate perturbative uncertainties is crucial, since some ways to treat the perturbative expansion can exhibit extraordinarily small scale dependence when the two scales are set equal. As an additional refinement, we address the issue that double scale variation could overestimate the perturbative uncertainties. We supplement the analysis with a test that quantifies the convergence rate of each perturbative series by a single number. We find that this convergence test allows to determine an overall and average convergence rate that is characteristic for the series expansions of each moment, and to discard those series for which the convergence rate is significantly worse. We obtain mc(mc) = 1.288 +- 0.020 GeV from the vector correlator. The method is also applied to the extraction of the MS-bar bottom quark mass from the vector correlator. We compute the experimental moments including a modeling uncertainty associated to the continuum region where no data is available. We obtain mb(mb) = 4.176 +- 0.023 GeV.Comment: 53 pages, 16 figures, 19 tables; v2 typos fixed, references added, modification of section 6.3, results for bottom moments and bottom mass updated, matches published versio

Charm and Bottom Masses from Sum Rules with a Convergence Test

In this talk we discuss results of a new extraction of the MS-bar charm quark mass using relativistic QCD sum rules at O(as**3) based on moments of the vector and the pseudoscalar current correlators and using the available experimental measurements from e+e- collisions and lattice results, respectively. The analysis of the perturbative uncertainties is based on different implementations of the perturbative series and on independent variations of the renormalization scales for the mass and the strong coupling following a work we carried out earlier. Accounting for the perturbative series that result from this double scale variation is crucial since some of the series can exhibit extraordinarily small scale dependence, if the two scales are set equal. The new aspect of the work reported here adresses the problem that double scale variation might also lead to an overestimate of the perturbative uncertainties. We supplement the analysis by a convergence test that allows to quantify the overall convergence of QCD perturbation theory for each moment and to discard series that are artificially spoiled by specific choices of the renormalization scales. We also apply the new method to an extraction of the MS-bar bottom quark mass using experimental moments that account for a modeling uncertainty associated to the continuum region where no experimental data is available. We obtain m_c(m_c) = 1.287 +- 0.020 GeV and m_b(m_b) = 4.167 +- 0.023 GeV.Comment: 6 pages, 2 figures. Presented at the International Workshop on the CKM Unitarity Triangle Vienna, Austria, September 8-12, 201

Top Quark Mass Calibration for Monte Carlo Event Generators -- An Update

We generalize and update our former top quark mass calibration framework for Monte Carlo (MC) event generators based on the $e^+e^-$ hadron-level 2-jettiness $\tau_2$ distribution in the resonance region for boosted $t\bar t$ production, that was used to relate the PYTHIA 8.205 top mass parameter $m_t^{\rm MC}$ to the MSR mass $m_t^{\rm MSR}(R)$ and the pole mass $m_t^{\rm pole}$. The current most precise direct top mass measurements specifically determine $m_t^{\rm MC}$. The updated framework includes the addition of the shape variables sum of jet masses $\tau_s$ and modified jet mass $\tau_m$, and the treatment of two more gap subtraction schemes to remove the ${\cal O}(\Lambda_{\rm QCD})$ renormalon related to large-angle soft radiation. These generalizations entail implementing a more versatile shape-function fit procedure and accounting for a certain type of $(m_t/Q)^2$ power corrections to achieve gap-scheme and observable independent results. The theoretical description employs boosted heavy-quark effective theory (bHQET) at next-to-next-to-logarithmic order (N$^2$LL), matched to soft-collinear effective theory (SCET) at N$^2$LL and full QCD at next-to-leading order (NLO), and includes the dominant top width effects. Furthermore, the software framework has been modernized to use standard file and event record formats. We update the top mass calibration results by applying the new framework to PYTHIA 8.205, HERWIG 7.2 and SHERPA 2.2.11. Even though the hadron-level resonance positions produced by the three generators differ significantly for the same top mass parameter $m_t^{\rm MC}$ value, the calibration shows that these differences arise from the hadronization modeling. Indeed, we find that $m_t^{\rm MC}$ agrees with m_t^{\rm MSR}(1\,\mbox{GeV}) within $200$ MeV for the three generators and differs from the pole mass by $350$ to $600$ MeV.Comment: 70 pages, 15 figure

Monte Carlo Top Quark Mass Calibration

The most precise top quark mass measurements use kinematic reconstruction methods, determining the top mass parameter of a Monte Carlo event generator, $m_t^{\rm MC}$. Due to the complicated interplay of hadronization and parton shower dynamics in Monte Carlo event generators relevant for kinematic reconstruction, relating $m_t^{\rm MC}$ to field theory masses is a non-trivial task. In this talk we report on a calibration procedure to determine this relation using hadron level QCD predictions for 2-Jettiness in $e^+e^-$ annihilation, an observable which has kinematic top mass sensitivity and a close relation to the invariant mass of the particles coming from the top decay. The theoretical ingredients of the QCD prediction are reviewed. Fitting $e^+e^-$ 2-Jettiness calculations at NLL/NNLL order to PYTHIA 8.205, we find that $m_t^{\rm MC}$ agrees with the MSR mass $m_{t,1\,{\rm GeV}}^{\rm MSR}$ within uncertainties. At NNLL we find $m_t^{\rm MC} = m_{t,1\,{\rm GeV}}^{\rm MSR} + (0.18 \pm 0.22)\,{\rm GeV}$. $m_t^{\rm MC}$ can differ from the pole mass $m_t^{\rm pole}$ by up to $600\,{\rm MeV}$, and using the pole mass generally leads to larger uncertainties. At NNLL we find $m_t^{\rm MC} = m_t^{\rm pole} + (0.57 \pm 0.28)\,{\rm GeV}$ as the fit result. In contrast, converting $m_{t,1\,{\rm GeV}}^{\rm MSR}$ obtained at NNLL to the pole mass gives a result for $m_t^{\rm pole}$ that is substantially larger and incompatible with the fit result. We also explain some theoretical aspects relevant for employing the C-parameter as an alternative calibration observable.Comment: Talk presented at the 13th International Symposium on Radiative Corrections (RADCOR 2017), St. Gilgen, Austria, 24-29 September 2017. 7 pages, 1 figur

Top Quark Mass Calibration for Monte Carlo Event Generators

United States. Department of Energy (DE-SC0011090

The photon energy spectrum in B→XsγB\to X_s\gamma at N3LL′\mathrm{N}^3\mathrm{LL'}

The smallest element of the CKM matrix, $|V_{ub}|$, can be extracted from measurements of semileptonic B meson decay $B\to X_ul\bar{\nu}$. However, the experimental signal of this process is obscured by large backgrounds, which are absent only at the edge of the phasespace. Resummation of perturbative series is essential in this kinematic region. Furthermore, this region is sensitive to Fermi motion of the b-quark inside the B-meson. Factorization theorems derived in Soft-Collinear Effective Theory are used to separate dynamics at different energy scales. The factorization also isolates nonperturbative effects in a so-called shape function. The shape function cannot be calculated perturbatively, but it can be measured in $B\to X_s\gamma$ decay.I will present our preliminary predictions of $B\to X_s\gamma$ spectrum at ${\rm N^3LL'{+}N^3LO}$. We parameterize the few unknown 3-loop perturbative ingredients, - a hard function coefficient and nonsingular contributions - using nuisance parameters. The variation of these nuisance parameters provides a robust estimate of the uncertainty that arises from our ignorance of these 3-loop terms.In order to arrive at stable predictions it is essential to use a short-distance scheme for the b-quark mass. It is well-known that the pole mass scheme suffers from a renormalon problem, which leads to very poor convergence. We demonstrate that predictions in 1S mass scheme, which has been used for this process in the past, start to break down at ${\rm N^3LO}$ due to a mismatch between the 1S scale and the soft scale of this process. I will show that the MSR mass scheme yields much more stable results

The photon energy spectrum in B→XsγB\to X_s\gamma at N3LL′\mathrm{N}^3\mathrm{LL'}

The smallest element of the CKM matrix, $|V_{ub}|$, can be extracted from measurements of semileptonic B meson decay $B\to X_ul\bar{\nu}$. However, the experimental signal of this process is obscured by large backgrounds, which are absent only at the edge of the phasespace. Resummation of perturbative series is essential in this kinematic region. Furthermore, this region is sensitive to Fermi motion of the b-quark inside the B-meson. Factorization theorems derived in Soft-Collinear Effective Theory are used to separate dynamics at different energy scales. The factorization also isolates nonperturbative effects in a so-called shape function. The shape function cannot be calculated perturbatively, but it can be measured in $B\to X_s\gamma$ decay.I will present our preliminary predictions of $B\to X_s\gamma$ spectrum at ${\rm N^3LL'{+}N^3LO}$. We parameterize the few unknown 3-loop perturbative ingredients, - a hard function coefficient and nonsingular contributions - using nuisance parameters. The variation of these nuisance parameters provides a robust estimate of the uncertainty that arises from our ignorance of these 3-loop terms.In order to arrive at stable predictions it is essential to use a short-distance scheme for the b-quark mass. It is well-known that the pole mass scheme suffers from a renormalon problem, which leads to very poor convergence. We demonstrate that predictions in 1S mass scheme, which has been used for this process in the past, start to break down at ${\rm N^3LO}$ due to a mismatch between the 1S scale and the soft scale of this process. I will show that the MSR mass scheme yields much more stable results

The photon energy spectrum in B→XsγB\to X_s\gamma at N3LL′\mathrm{N}^3\mathrm{LL'}

SCET lies at the foundation of our understanding of inclusive B meson decays. It allows us to factorize the spectrum into hard, jet, and hadronic soft functions. The hadronic soft function can be further factorized into perturbative partonic soft function and nonperturbative shape function. The shape function is a necessary ingredient for extraction of $|V_{ub}|$ CKM matrix element from $B\to X_ul\nu$ spectrum, and it can be extracted from inclusive measurements of $B\to X_s\gamma$ spectrum.I will present our preliminary predictions of $B\to X_s\gamma$ spectrum at ${\rm N^3LL'{+}N^3LO}$, which we implemented in the SCETlib library. Although only the soft and jet functions are fully known at ${\rm N^3LO}$, we parameterize the unknown 3-loop hard function coefficient and nonsingular contributions in terms of nuisance parameters. The variation of these nuisance parameters provides a robust estimate of the uncertainty that arises from our ignorance of these 3-loop terms.In order to arrive at stable predictions it is essential to use a short-distance scheme for the b-quark mass. It is well-known that the pole mass scheme suffers from a renormalon problem, which leads to very poor convergence. We demonstrate that predictions in 1S mass scheme, which has been used for this process in the past, start to break down at ${\rm N^3LL'}$ due to a mismatch between the 1S scale and the soft scale of this process. I will show that the MSR mass scheme yields much more stable results