Mass Collaboration Research Articles

Lattice QCD determination of the normalization of the leading-twist photon distribution amplitude and susceptibility of the quark condensate

The normalization of the leading-twist photon distribution amplitude (DA), fγ⊥, is an important ingredient in the study of exclusive processes involving the photon emission by means of QCD sum-rules. In this paper we determine the up-, down- and strange-quark contribution to fγ⊥ by exploiting its relation to the zero-momentum two-point correlation function of the electromagnetic current Jemμ and the electric component of the tensor current Tμν. To that end we employ the gauge ensembles obtained by using Nf=2+1+1 Wilson-Clover twisted-mass quark flavors, generated by the Extended Twisted Mass (ETM) Collaboration, and after adding all sources of systematic uncertainties, we obtain a total error of 1.5% and 3.5%, respectively, for the light- (u and d) and strange-quark contribution to fγ⊥(2 GeV) in the MS¯ scheme, thus improving their accuracy by a factor of 2.3 and 2.8, respectively. For the strange-quark contribution fγ,s⊥(2 GeV), we observe a discrepancy with respect to previous lattice calculations. By combining our result with the world average lattice value of the chiral condensate, we obtain for the susceptibility of the quark condensate χdMS¯(2 GeV)≃χuMS¯(2 GeV)=2.17(12) GeV−2. Published by the American Physical Society 2024

Combining Danmaku and Discussion Boards: Toward A Scalable and Sociable Environment for Mass Collaboration in MOOCs

In online learning at scale, wherein instructional videos play a central role, interactive tools are often integrated to counteract passive consumption. For example, the forum or discussion board is widely used, and an emerging functionality, danmaku, which enables messages to be synchronized with video playback, has also been utilized recently. To explore how mass participation is accommodated and what categories of interaction learners implement, this study utilizes analysis of interaction and manual content analysis through learner-generated text data from two specific tools employed in a massive open online course (MOOC) setting: the discussion board (N = 739) and danmaku (N = 2435). Results of the analysis of interaction indicate that mass participation is managed differently by the tools: danmaku fosters a collective space for massive participants, while the discussion board organizes them into threaded small groups. In addition, results of the content analysis show danmaku primarily supports indirect interaction with a focus on the socio-emotional dimension, while the discussion board serves as a platform for direct discussions, particularly in the cognitive dimension. Furthermore, within the context of large-scale engagement, various levels of joint interaction, in addition to collaboration, are discerned and discussed in both socio-emotional and cognitive interactions. The findings offer insights for developing sociable and scalable socio-technical environments in computer-supported collaborative learning (CSCL), addressing emerging educational trends. Practical implications for educational design based on these findings are also discussed.

GeoFOR: A collaborative forensic taphonomy database for estimating the postmortem interval

Accurately assessing the postmortem interval (PMI), or the time since death, remains elusive within forensic science research and application. This paper introduces geoFOR, a web-based collaborative application that utilizes ArcGIS and machine learning to deliver improved PMI predictions. The geoFOR application provides a standardized, collaborative forensic taphonomy database that gives practitioners a readily available tool to enter case information that automates the collection of environmental data and delivers a PMI prediction using statistically robust methods. After case submission, the cross-validating machine learning PMI predictive model results in a R² value of 0.82. Contributors receive a predicted PMI with an 80% confidence interval. The geoFOR database currently contains 2529 entries from across the U.S. and includes cases from medicolegal investigations and longitudinal studies from human decomposition facilities. We present the overall findings of the data collected so far and compare results from medicolegal cases and longitudinal studies to highlight previously poorly understood limitations involved in the difficult task of PMI estimation. This novel approach for building a reference dataset of human decomposition is forensically and geographically representative of the realities in which human remains are discovered which allows for continual improvement of PMI estimations as more data is captured. It is our goal that the geoFOR data repository follow the principles of Open Science and be made available to forensic researchers to test, refine, and improve PMI models. Mass collaboration and data sharing can ultimately address enduring issues associated with accurately estimating the PMI within medicolegal death investigations.

Periodical Cicadas and the Abundance of Time

The life cycle of periodical cicadas, like the scientists who have studied them, is characterized by periods of long waiting punctuated with spectacular bouts of activity. In remarkable synchrony, every thirteen or seventeen years—depending on the species and the locatio —billions of nymphs crawl from the ground and embark on a relatively short adult life span of three to four weeks. This paper traces three pulses in the scientific study of periodical cicadas, as researchers sought to determine the geographical range of the broods, the number and biological identity of the species found in each brood, and the relationship between the individual and the swarm. Together these threads of research highlight the historical significance of mass collaboration in the scientific study of these charismatic animals and the surprisingly entangled affective relations between human and insect.

The VUCA-nature of modern protest communication

This study introduces several political revolutions from the past and the present for a deeper understanding of the nature of protest communication. Previously, the protests’ success was ensured by the use of printing, telegraph and media innovations, which allowed the protest organizers to evade government control. Today, such technologies provide information and allow participants to communicate proactively in social networks, self-organizing into structures that strengthen and spread protest communication. Social networks enable the realization of the communication potential of each participant based on the organizational model of mass collaboration. This model is not characterized by a system-structural organization, which confounds predictions of the processes of social interaction. Each subsequent event depends on the previous one, complicating the establishment of a trend. This organizational model creates difficulties for the authorities in controlling protests, as it is prone to the stochastic formation of centres of activity, which can be explained from the perspective of field theory, provided in this study. Therefore, from the point of view of the authorities, the situation with the development of the protest acquires the characteristics of VUCA, moving beyond possible control.

Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, ${a}_{\ensuremath{\mu}}^{\mathrm{HVP}}$, in the so-called short and intermediate time-distance windows, ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}$ and ${a}_{\ensuremath{\mu}}^{\mathrm{W}}$, defined by the RBC/UKQCD Collaboration [Phys. Rev. Lett. 121, 022003 (2018)]. We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with ${N}_{f}=2+1+1$ flavors of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavors tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to $\ensuremath{\simeq}0.057$, 0.068 and 0.080 fm with spatial lattice sizes up to $L\ensuremath{\simeq}7.6\text{ }\text{ }\mathrm{fm}$. For the short-distance window we obtain ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}(\mathrm{ETMC})=69.27(34)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which is consistent with the recent dispersive value of ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}({e}^{+}{e}^{\ensuremath{-}})=68.4(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Phys. Lett. B 833, 137313 (2022)]. In the case of the intermediate window we get the value ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{ETMC})=236.3(1.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which is consistent with the result ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{BMW})=236.7(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Nature (London) 593, 51 (2021)] by the BMW Collaboration as well as with the recent determination by the CLS/Mainz group of ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{CLS})=237.30(1.46)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Phys. Rev. D 106, 114502 (2022)]. However, it is larger than the dispersive result of ${a}_{\ensuremath{\mu}}^{\mathrm{W}}({e}^{+}{e}^{\ensuremath{-}})=229.4(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ by approximately 3.6 standard deviations. The tension increases to approximately 4.5 standard deviations if we average our ETMC result with those by BMW and CLS/Mainz. Our accurate lattice results in the short and intermediate windows point to a possible deviation of the ${e}^{+}{e}^{\ensuremath{-}}$ cross section data with respect to Standard Model predictions in the low- and intermediate-energy regions but not in the high-energy region.

Guest editorial: Mass collaboration and knowledge management: reflections to achieve best practices

Guest editorial: Mass collaboration and knowledge management: reflections to achieve best practices

Effective Organizing on the Fly: Social Capital in Temporary Organizations

ABSTRACT When mass collaborations face situations that are not readily resolvable, just like traditional organizations, they need to form task forces to address these complicated problems. Referred to as temporary organizations, small, task-focused, time-bound, agile groups, these task forces exist in organizations and corporations to address situations outside of existing procedures. Temporary organizations can be created in online platforms, like mass collaborations, to serve a similar purpose, as existing policies and procedures cannot address all situations that arise during collaboration. Given that mass collaborations are people-driven, informal, and voluntary, this study explores the impact of the dimensions of social capital on the success of online temporary organizations, exploring its structural, relational, and cognitive aspects. We suggest that participants’ access to social capital and their willingness to exercise it lead to a greater likelihood of success.

An Organizational and Governance Model to Support Mass Collaborative Learning Initiatives

Mass collaboration can bring about major transformative changes in the way people can work collectively. This emerging paradigm promises significant economic and social benefits and enhanced efficiency across a range of sectors, including learning and education. Accordingly, this article introduces, demonstrates in use, and evaluates an organizational and governance model designed to provide guidance and execution support for the implementation and operation of mass collaborative learning initiatives. The design science research process is adopted to guide the design and development of the proposed model. The model stands on three streams of work, addressing key aspects and elements that have a supporting influence on community learning: (i) identify the positive and negative factors in existing and active examples of mass collaboration; (ii) adopt contributions of collaborative networks in terms of structural and behavioral aspects; and (iii) establish adequate learning assessment indicators and metrics. The model is used for a case study in which vocational education and training meet the needs of collaborative education–enterprise approaches. Initially, the validation of the model is verified by the partners and stakeholders of a particular project in the area of education–enterprises relations to ensure that it is sufficiently appropriate for applications in a digital platform developed by such projects. The three first steps of (the proposed) applicability evaluation (adequacy, feasibility, and effectiveness) are then performed. The positive results gained from model validation and its applicability evaluation in this project indicate that not only is the model fairly adequate, feasible, and effective for applications in the developed digital platform but also that it has a high potential for utilization in supporting and directing the creation, implementation, and operation of mass collaborative learning initiatives. Although the validation was carried out in the context of a single project, in fact, it was based on a large “focus group” of experts involved in this international initiative, which is in accordance with the Design Science Research method. Thus, this article reflects a kind of applied research of a socio-technical nature, aiming to find guidelines and practical solutions to the specific issues, problems, and concerns of mass collaborative learning initiatives.

Lattice calculation of the pion mass difference Mπ+−Mπ0 at order O(αem)

We present a lattice calculation of the charged/neutral pion mass difference $M_{\pi^{+}}-M_{\pi^{0}}$ at order $\mathcal{O}(\alpha_{em})$ using the gauge configurations produced by the Extended Twisted Mass Collaboration with $N_{f}=2+1+1$ dynamical quark flavours at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089~{\rm fm}$) and pion masses in the range $M_{\pi} \simeq 250-500~{\rm MeV}$. We employ the RM123 method and expand the path-integral around the isospin symmetric point at leading order in the electromagnetic coupling $\alpha_{em}$. Making use of the recently proposed RTM scheme, we evaluate the full $\mathcal{O}(\alpha_{em})$ contribution, with the inclusion of the disconnected diagram. At the physical point, after performing the continuum and infinite volume extrapolation, we obtain the value $M_{\pi^{+}}-M_{\pi^{0}}= 4.622~(95)~{\rm MeV}$ which is in good agreement with the experimental result $[ M_{\pi^{+}} - M_{\pi^{0}} ]^{exp.} = 4.5936(5)~{\rm MeV}$.

Dynamics of the social construction of knowledge: an empirical study of Zhihu in China

This study examined how the knowledge market promotes knowledge construction on question-and-answer (Q&A) websites. Data were collected from Zhihu, one of the largest Q&A sites in China. Hierarchical linear modeling was employed to estimate the dynamics of information accumulation, that is, the provision of informative content as factual construction. By employing information accumulation as the objective measure of knowledge construction, we determined that online knowledge construction was facilitated by a competitive marketplace of ideas. In addition, participation, temporal, and discourse features affected the dynamics of information accumulation. In specific, active users contributed significantly less to information accumulation than did ordinary users. Information accumulation shows a naturally decaying process represented as a function of answer order. The time interval between answers at the two preceding time points reduced the informativeness of answers at the subsequent time point. Answers with a higher readability score reduced the informativeness of subsequent answers. The results indicate that knowledge construction on Q&A sites unfolds as a process of mass collaboration among users.

Extracting the low-energy constant at three flavors from pion-kaon scattering

Based on our analysis of the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude, we provide the first determination of the only free low-energy constant at , known as , in SU (4∣1) Partially-Quenched Chiral Perturbation theory using the data from the Extended Twisted Mass collaboration, . The theory uncertainties originate from the unphysical scattering length, the physical low-energy constants, the higher-order chiral corrections, the (lattice) meson masses and the pion decay constant, respectively.

A Design Framework for Social Product Development

Social product development (SPD) is defined as a group of “coalescing tools and socio-technologies” represented by several tenants including crowdsourcing, internet-based mass collaboration, open innovation, and cloud-based design and manufacture. Existing examples of SPD have resulted in enhanced collaboration in design teams, shorter lead times, and significant reductions in R&D costs. Despite these potential benefits, guidance on how to conduct SPD is lacking in existing literature and the use of SPD tenants in the industry is limited. The aim of this article is to present a framework to guide the application of SPD. As part of this framework, the authors present a tool for the selection of SPD tenants that allows users to select an SPD tenant based on their requirements and capabilities. The framework allows practitioners to consider how SPD tenants can be used to solve design problems and allows the user to design SPD tenants with consideration of their own needs. This article concludes with a validation activity and discussion on future research directions in this field.

Modeling Support for Mass Collaboration in Open Innovation Initiatives—The Facilitation Process Model 2.0

Many governments and organizations recognize the potential of open innovation (OI) models to create value with large numbers of people beyond the organization. It can be challenging, however, to design an effective collaborative process for a massive group. Collaboration engineering (CE) is an approach for the design and deployment of repeatable collaborative work practices that can be executed by practitioners themselves without the ongoing support of external collaboration engineers. To manage the complexity of the design process, they use a modeling technique called facilitation process models (FPM) to capture high-level design decisions that serve different purposes, such as documenting and communicating a design, etc. FPM, however, was developed to support designs for groups of fewer than 100 people. It does not yet represent design elements that become important when designing for groups of hundreds or thousands of participants, which can be found in many OI settings. We use a design science approach to identify the limitations of the original FPM and derive requirements for extending FPM. This article contributes to the CE and to the OI literature by offering an FPM 2.0 that assists CE designers to design new OI processes, with a special focus on outside-in OI.

Meta-Governance Framework to Guide the Establishment of Mass Collaborative Learning Communities

The application of mass collaboration in different areas of study and work has been increasing over the last few decades. For example, in the education context, this emerging paradigm has opened new opportunities for participatory learning, namely, “mass collaborative learning (MCL)”. The development of such an innovative and complementary method of learning, which can lead to the creation of knowledge-based communities, has helped to reap the benefits of diversity and inclusion in the creation and development of knowledge. In other words, MCL allows for enhanced connectivity among the people involved, providing them with the opportunity to practice learning collectively. Despite recent advances, this area still faces many challenges, such as a lack of common agreement about the main concepts, components, applicable structures, relationships among the participants, as well as applicable assessment systems. From this perspective, this study proposes a meta-governance framework that benefits from various other related ideas, models, and methods that together can better support the implementation, execution, and development of mass collaborative learning communities. The proposed framework was applied to two case-study projects in which vocational education and training respond to the needs of collaborative education–enterprise approaches. It was also further used in an illustration of the MCL community called the “community of cooks”. Results from these application cases are discussed.

Open ventilator evaluation framework: A synthesized database of regulatory requirements and technical standards for emergency use ventilators from Australia, Canada, UK, and US

Development of emergency use ventilators has attracted significant attention and resources during the COVID-19 pandemic. To facilitate mass collaboration and accelerate progress, many groups have adopted open-source development models, inspired by the long history of open-source development in software. According to the Open-source Hardware Association (OSHWA), Open-source Hardware (OSH) is a term for tangible artifacts — machines, devices, or other physical things — whose design has been released to the public in such a way that anyone can make, modify, and use them. One major obstacle to translating the growing body of work on open-source ventilators into clinical practice is compliance with regulations and conformance with mandated technical standards for effective performance and device safety. This is exacerbated by the inherent complexity of the regulatory process, which is tailored to traditional centralized development models, as well as the rapid changes and alternative pathways that have emerged during the pandemic. As a step in addressing this challenge, this paper provides developers, evaluators, and potential users of emergency ventilators with the first iteration of a pragmatic, open-source assessment framework that incorporates existing regulatory guidelines from Australia, Canada, UK and USA. We also provide an example evaluation for one open-source emergency ventilator design. The evaluation process has been divided into three levels: 1. Adequacy of open-source project documentation; 2. Clinical performance requirements, and 3. Conformance with technical standards.

Quark and Gluon Momentum Fractions in the Pion from N_{f}=2+1+1 Lattice QCD.

We perform the first full decomposition of the pion momentum into its gluon and quark contributions. We employ an ensemble generated by the Extended Twisted Mass Collaboration with N_{f}=2+1+1 Wilson twisted mass clover fermions at maximal twist tuned to reproduce the physical pion mass. We present our results in the MS[over ¯] scheme at 2GeV. We find ⟨x⟩_{u+d}=0.601(28), ⟨x⟩_{s}=0.059(13), ⟨x⟩_{c}=0.019(05), and ⟨x⟩_{g}=0.52(11) for the separate contributions, respectively, whose sum saturates the momentum sum rule.

Constraints for the semileptonic B→D(*) form factors from lattice QCD simulations of two-point correlation functions

In this work we present the first nonperturbative determination of the hadronic susceptibilities that constrain the form factors entering the semileptonic $B\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ transitions due to unitarity and analyticity. The susceptibilities are obtained by evaluating moments of suitable two-point correlation functions obtained on the lattice. Making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with ${N}_{f}=2+1+1$ dynamical quarks at three values of the lattice spacing ($a\ensuremath{\simeq}0.062$, 0.082, 0.089 fm) and with pion masses in the range $\ensuremath{\simeq}210--450\text{ }\text{ }\mathrm{MeV}$, we evaluate the longitudinal and transverse susceptibilities of the vector and axial-vector polarization functions at the physical pion point and in the continuum and infinite volume limits. The ETMC ratio method is adopted to reach the physical $b$-quark mass ${m}_{b}^{\mathrm{phys}}$. At zero momentum transfer for the $b\ensuremath{\rightarrow}c$ transition we get ${\ensuremath{\chi}}_{{0}^{+}}({m}_{b}^{\mathrm{phys}})=7.58(59)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, ${\ensuremath{\chi}}_{{1}^{\ensuremath{-}}}({m}_{b}^{\mathrm{phys}})=6.72(41)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}2}$, ${\ensuremath{\chi}}_{{0}^{\ensuremath{-}}}({m}_{b}^{\mathrm{phys}})=2.58(17)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and ${\ensuremath{\chi}}_{{1}^{+}}({m}_{b}^{\mathrm{phys}})=4.69(30)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}2}$ for the scalar, vector, pseudoscalar and axial susceptibilities, respectively. In the case of the vector and pseudoscalar channels the one-particle contributions due to ${B}_{c}^{*}$ and ${B}_{c}$ mesons are evaluated and subtracted to improve the bounds, obtaining ${\ensuremath{\chi}}_{{1}^{\ensuremath{-}}}^{\mathrm{sub}}({m}_{b}^{\mathrm{phys}})=5.84(44)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}2}$ and ${\ensuremath{\chi}}_{{0}^{\ensuremath{-}}}^{\mathrm{sub}}({m}_{b}^{\mathrm{phys}})=2.19(19)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, respectively.

Ratio of kaon and pion leptonic decay constants with Nf=2+1+1 Wilson-clover twisted-mass fermions

We present a determination of the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (isoQCD), $f_K / f_\pi$, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks, including configurations close to the physical point for all dynamical flavors. The simulations are carried out at three values of the lattice spacing ranging from $\sim 0.068$ to $\sim 0.092$ fm with linear lattice size up to $L \sim 5.5$~fm. The scale is set by the PDG value of the pion decay constant, $f_\pi^{isoQCD} = 130.4~(2)$ MeV, at the isoQCD pion point, $M_\pi^{isoQCD} = 135.0~(2)$ MeV, obtaining for the gradient-flow (GF) scales the values $w_0 = 0.17383~(63)$ fm, $\sqrt{t_0} = 0.14436~(61)$ fm and $t_0 / w_0 = 0.11969~(62)$ fm. The data are analyzed within the framework of SU(2) Chiral Perturbation Theory (ChPT) without resorting to the use of renormalized quark masses. At the isoQCD kaon point $M_K^{isoQCD} = 494.2~(4)$ MeV we get $(f_K / f_\pi)^{isoQCD} = 1.1995~(44)$, where the error includes both statistical and systematic uncertainties. Implications for the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{us}|$ and for the first-row CKM unitarity are discussed.

First direct lattice calculation of the chiral perturbation theory low-energy constant ℓ7

We evaluate by means of lattice QCD calculations the low-energy constant ${\ensuremath{\ell}}_{7}$ which parametrizes strong isospin effects at next-to-leading order (NLO) in SU(2) chiral perturbation theory. Among all low-energy constants at NLO, ${\ensuremath{\ell}}_{7}$ is the one known less precisely, and its uncertainty is currently larger than 50%. Our strategy is based on the RM123 approach in which the lattice path-integral is expanded in powers of the isospin breaking parameter $\mathrm{\ensuremath{\Delta}}m=({m}_{d}\ensuremath{-}{m}_{u})/2$. In order to evaluate the relevant lattice correlators we make use of the recently proposed rotated twisted-mass (RTM) scheme. Within the RM123 approach, it is possible to cleanly extract the value of ${\ensuremath{\ell}}_{7}$ from either the pion mass splitting ${M}_{{\ensuremath{\pi}}^{+}}\ensuremath{-}{M}_{{\ensuremath{\pi}}^{0}}$ induced by strong isospin breaking at order $\mathcal{O}((\mathrm{\ensuremath{\Delta}}m{)}^{2})$ (mass method), or from the coupling of the neutral pion ${\ensuremath{\pi}}^{0}$ to the isoscalar operator $(\overline{u}{\ensuremath{\gamma}}_{5}u+\overline{d}{\ensuremath{\gamma}}_{5}d)/\sqrt{2}$ at order $\mathcal{O}(\mathrm{\ensuremath{\Delta}}m)$ (matrix element method). In this pilot study we limit the analysis to a single ensemble generated by the Extended Twisted Mass Collaboration (ETMC) with ${N}_{f}=2+1+1$ dynamical quark flavors, which corresponds to a lattice spacing $a\ensuremath{\simeq}0.095\text{ }\text{ }\mathrm{fm}$ and to a pion mass ${M}_{\ensuremath{\pi}}\ensuremath{\simeq}260\text{ }\text{ }\mathrm{MeV}$. We find that the matrix element method outperforms the mass method in terms of resulting statistical accuracy. Our determination, ${\ensuremath{\ell}}_{7}=2.5(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, is in agreement and improves previous calculations.