We present technical details of an analysis of pseudo-scalar data from a QCD simulation with staggered fermions. The data were obtained close to the physical point with an inverse lattice spacing of about 3 GeV, and $N_f=2+1+1$. We compare different methods of extracting effective masses and decay constants in lattice units. The results of several correlated and uncorrelated fitting methods are compared, both on the simulated data set, and on a synthetically generated data set.
{"title":"Details of a staggered fermion data analysis","authors":"Maximilian Ammer, S. Durr","doi":"10.22323/1.363.0048","DOIUrl":"https://doi.org/10.22323/1.363.0048","url":null,"abstract":"We present technical details of an analysis of pseudo-scalar data from a QCD simulation with staggered fermions. The data were obtained close to the physical point with an inverse lattice spacing of about 3 GeV, and $N_f=2+1+1$. We compare different methods of extracting effective masses and decay constants in lattice units. The results of several correlated and uncorrelated fitting methods are compared, both on the simulated data set, and on a synthetically generated data set.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90339644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop the $(1+1)$d lattice $U(1)$ gauge theory in order to define $2$-flavor massless Schwinger model, and discuss its connection with Haldane conjecture. We propose to use the central-branch Wilson fermion, which is defined by relating the mass, $m$, and the Wilson parameter, $r$, as $m+2r=0$. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of $m$ is required because the extra $U(1)$ symmetry at the central branch, $U(1)_{bar{V}}$, prohibits the additive mass renormalization. Moreover, we show that Dirac determinant is positive semi-definite and this formulation is free from the sign problem, so the Monte Carlo simulation of the path integral is possible. By identifying the symmetry at low energy, we show that this lattice model has the mixed 't Hooft anomaly between $U(1)_{bar{V}}$, lattice translation, and lattice rotation. We discuss its relation to the anomaly of half-integer anti-ferromagnetic spin chains, so our lattice gauge theory is suitable for numerical simulation of Haldane conjecture. Furthermore, it gives new and strict understanding on parity-broken phase (Aoki phase) of $2$d Wilson fermion.
{"title":"Lattice gauge theory for the Haldane conjecture and central-branch Wilson fermion","authors":"T. Misumi, Y. Tanizaki","doi":"10.1093/PTEP/PTAA003","DOIUrl":"https://doi.org/10.1093/PTEP/PTAA003","url":null,"abstract":"We develop the $(1+1)$d lattice $U(1)$ gauge theory in order to define $2$-flavor massless Schwinger model, and discuss its connection with Haldane conjecture. We propose to use the central-branch Wilson fermion, which is defined by relating the mass, $m$, and the Wilson parameter, $r$, as $m+2r=0$. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of $m$ is required because the extra $U(1)$ symmetry at the central branch, $U(1)_{bar{V}}$, prohibits the additive mass renormalization. Moreover, we show that Dirac determinant is positive semi-definite and this formulation is free from the sign problem, so the Monte Carlo simulation of the path integral is possible. By identifying the symmetry at low energy, we show that this lattice model has the mixed 't Hooft anomaly between $U(1)_{bar{V}}$, lattice translation, and lattice rotation. We discuss its relation to the anomaly of half-integer anti-ferromagnetic spin chains, so our lattice gauge theory is suitable for numerical simulation of Haldane conjecture. Furthermore, it gives new and strict understanding on parity-broken phase (Aoki phase) of $2$d Wilson fermion.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81467400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution to the anomalous magnetic moments of the electron, $a_e^{rm HVP}$, the muon, $a_mu^{rm HVP}$, and the tau, $a_tau^{rm HVP}$, including both the isospin-symmetric QCD term and the leading-order strong and electromagnetic isospin-breaking corrections. Moreover, the contribution to $a_mu^{rm HVP}$ not covered by the MUonE experimen, $a_{MUonE}^{rm HVP}$, is provided. We get $a_e^{rm HVP} = 185.8~(4.2) cdot 10^{-14}$, $a_mu^{rm HVP} = 692.1~(16.3) cdot 10^{-10}$, $a_tau^{rm HVP} = 335.9~(6.9) cdot 10^{-8}$ and $a_{MUonE}^{rm HVP} = 91.6~(2.0) cdot 10^{-10}$. Our results are obtained in the quenched-QED approximation using the QCD gauge configurations generated by the European (now Extended) Twisted Mass Collaboration (ETMC) with $N_f=2+1+1$ dynamical quarks, at three values of the lattice spacing varying from $0.089$ to $0.062$ fm, at several values of the lattice spatial size ($L simeq 1.8 ÷3.5$ fm) and with pion masses in the range between $simeq 220$ and $simeq 490$ MeV.
{"title":"Lepton anomalous magnetic moments in Lattice QCD+QED","authors":"Davide Giusti, S. Simula","doi":"10.22323/1.363.0104","DOIUrl":"https://doi.org/10.22323/1.363.0104","url":null,"abstract":"We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution to the anomalous magnetic moments of the electron, $a_e^{rm HVP}$, the muon, $a_mu^{rm HVP}$, and the tau, $a_tau^{rm HVP}$, including both the isospin-symmetric QCD term and the leading-order strong and electromagnetic isospin-breaking corrections. Moreover, the contribution to $a_mu^{rm HVP}$ not covered by the MUonE experimen, $a_{MUonE}^{rm HVP}$, is provided. We get $a_e^{rm HVP} = 185.8~(4.2) cdot 10^{-14}$, $a_mu^{rm HVP} = 692.1~(16.3) cdot 10^{-10}$, $a_tau^{rm HVP} = 335.9~(6.9) cdot 10^{-8}$ and $a_{MUonE}^{rm HVP} = 91.6~(2.0) cdot 10^{-10}$. Our results are obtained in the quenched-QED approximation using the QCD gauge configurations generated by the European (now Extended) Twisted Mass Collaboration (ETMC) with $N_f=2+1+1$ dynamical quarks, at three values of the lattice spacing varying from $0.089$ to $0.062$ fm, at several values of the lattice spatial size ($L simeq 1.8 ÷3.5$ fm) and with pion masses in the range between $simeq 220$ and $simeq 490$ MeV.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85723991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I. Campos, M. D. Brida, G. D. Divitiis, A. Lytle, M. Papinutto, A. Vladikas
We employ the chirally rotated Schrodinger functional ($chi$SF) to study two-point fermion bilinear correlation functions used in the determination of $Z_{A,V,S,P,T}$ on a series of well-tuned ensembles. The gauge configurations, which span renormalisation scales from 4 to 70~GeV, are generated with $N_{rm f}=3$ massless flavors and Schrodinger Functional (SF) boundary conditions. Valence quarks are computed with $chi$SF boundary conditions. We show preliminary results on the tuning of the $chi$SF Symanzik coefficient $z_f$ and the scaling of the axial current normalization $Z_{rm A}$. Moreover we carry out a detailed comparison with the expectations from one-loop perturbation theory. Finally we outline how automatically $mathrm{O}(a)$-improved $B_{rm K}$ matrix elements, including BSM contributions, can be computed in a $chi$SF renormalization scheme.
{"title":"$chi$SF near the electroweak scale","authors":"I. Campos, M. D. Brida, G. D. Divitiis, A. Lytle, M. Papinutto, A. Vladikas","doi":"10.22323/1.363.0202","DOIUrl":"https://doi.org/10.22323/1.363.0202","url":null,"abstract":"We employ the chirally rotated Schrodinger functional ($chi$SF) to study two-point fermion bilinear correlation functions used in the determination of $Z_{A,V,S,P,T}$ on a series of well-tuned ensembles. The gauge configurations, which span renormalisation scales from 4 to 70~GeV, are generated with $N_{rm f}=3$ massless flavors and Schrodinger Functional (SF) boundary conditions. Valence quarks are computed with $chi$SF boundary conditions. We show preliminary results on the tuning of the $chi$SF Symanzik coefficient $z_f$ and the scaling of the axial current normalization $Z_{rm A}$. Moreover we carry out a detailed comparison with the expectations from one-loop perturbation theory. Finally we outline how automatically $mathrm{O}(a)$-improved $B_{rm K}$ matrix elements, including BSM contributions, can be computed in a $chi$SF renormalization scheme.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85629747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Darvish, R. Brett, J. Bulava, Jacob Fallica, Andrew D. Hanlon, Ben Horz, C. Morningstar
Lattice QCD allows us to probe the low-lying hadron spectrum in finite-volume using a basis of single- and multi-hadron interpolating operators. Here we examine the effect of including tetraquark operators on the spectrum in the scalar meson sectors containing the $K_0^*(700)$ ($kappa$) and the $a_0(980)$ in $N_f = 2 + 1$ QCD, with $m_pi approx 230$ MeV. Preliminary results of additional finite-volume states found using tetraquark operators are shown, and possible implications of these states are discussed.
{"title":"Including tetraquark operators in the low-lying scalar meson sectors in lattice QCD","authors":"D. Darvish, R. Brett, J. Bulava, Jacob Fallica, Andrew D. Hanlon, Ben Horz, C. Morningstar","doi":"10.1063/5.0008966","DOIUrl":"https://doi.org/10.1063/5.0008966","url":null,"abstract":"Lattice QCD allows us to probe the low-lying hadron spectrum in finite-volume using a basis of single- and multi-hadron interpolating operators. Here we examine the effect of including tetraquark operators on the spectrum in the scalar meson sectors containing the $K_0^*(700)$ ($kappa$) and the $a_0(980)$ in $N_f = 2 + 1$ QCD, with $m_pi approx 230$ MeV. Preliminary results of additional finite-volume states found using tetraquark operators are shown, and possible implications of these states are discussed.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73134745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Brett, J. Bulava, D. Darvish, Jacob Fallica, Andrew D. Hanlon, Ben Horz, C. Morningstar
Lattice calculations allow us to probe the low-lying, non-perturbative spectrum of QCD using first principles numerical methods. Here we present the low-lying spectrum in the scalar sector with vacuum quantum numbers including, in fully dynamical QCD for the first time, the mixing between glueball, q-qbar, and meson-meson operators.
{"title":"Spectroscopy from the lattice: The scalar glueball","authors":"R. Brett, J. Bulava, D. Darvish, Jacob Fallica, Andrew D. Hanlon, Ben Horz, C. Morningstar","doi":"10.1063/5.0008566","DOIUrl":"https://doi.org/10.1063/5.0008566","url":null,"abstract":"Lattice calculations allow us to probe the low-lying, non-perturbative spectrum of QCD using first principles numerical methods. Here we present the low-lying spectrum in the scalar sector with vacuum quantum numbers including, in fully dynamical QCD for the first time, the mixing between glueball, q-qbar, and meson-meson operators.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89233070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kei Suzuki, S. Aoki, Y. Aoki, G. Cossu, H. Fukaya, S. Hashimoto
Using lattice QCD simulations with $N_f = 2$ dynamical fermions, we study the axial $U(1)$ symmetry, topological charge, and Dirac eigenvalue spectra in the high-temperature phase in which the chiral symmetry is restored. Our gauge ensembles are generated with Mobius domain-wall fermions, but the measurements such as susceptibilities are reweighted to those for the overlap fermions by using overlap/domain-wall reweighting technique. We find that the $U(1)_A$ and topological susceptibilities are strongly suppressed in the small quark mass region, which is related to the reduction of chiral-zero and low-nonzero modes on the Dirac spectra. We also examine their volume dependence.
{"title":"Axial U(1) symmetry, topology, and Dirac spectra at high temperature in Nf=2 lattice QCD","authors":"Kei Suzuki, S. Aoki, Y. Aoki, G. Cossu, H. Fukaya, S. Hashimoto","doi":"10.22323/1.317.0085","DOIUrl":"https://doi.org/10.22323/1.317.0085","url":null,"abstract":"Using lattice QCD simulations with $N_f = 2$ dynamical fermions, we study the axial $U(1)$ symmetry, topological charge, and Dirac eigenvalue spectra in the high-temperature phase in which the chiral symmetry is restored. Our gauge ensembles are generated with Mobius domain-wall fermions, but the measurements such as susceptibilities are reweighted to those for the overlap fermions by using overlap/domain-wall reweighting technique. We find that the $U(1)_A$ and topological susceptibilities are strongly suppressed in the small quark mass region, which is related to the reduction of chiral-zero and low-nonzero modes on the Dirac spectra. We also examine their volume dependence.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82553324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As the only lattice vector current that does not require renormalisation is the point-split conserved current it is convenient to have a robust, precise and computationally cheap methodology for the calculation of vector current renormalisation factors, $Z_V$. Momentum subtraction schemes, such as RI-SMOM, implemented nonperturbatively on the lattice provide such a method if it can be shown that the systematic errors, e.g. from condensates, are well controlled. We present $Z_V$ calculations for the conserved current in both the RI-SMOM and RI$'$-MOM momentum subtraction schemes as well as local current renormalisation in the RI-SMOM scheme. By performing these calculations at various values of the momentum scale $mu$ and different lattice spacings we can investigate the presence of power suppressed nonperturbative contributions and compare the results to expectations arising from the Ward-Takahashi identity. Our results show that the RI-SMOM scheme provides a well controlled determination of $Z_V$ but the standard RI$'$-MOM scheme does not. We then present some preliminary uses of these $Z_V$ calculations in charm physics.
{"title":"Vector current renormalisation in momentum subtraction schemes using the HISQ action","authors":"D. Hatton, C. Davies, G. Lepage, A. Lytle","doi":"10.22323/1.363.0016","DOIUrl":"https://doi.org/10.22323/1.363.0016","url":null,"abstract":"As the only lattice vector current that does not require renormalisation is the point-split conserved current it is convenient to have a robust, precise and computationally cheap methodology for the calculation of vector current renormalisation factors, $Z_V$. Momentum subtraction schemes, such as RI-SMOM, implemented nonperturbatively on the lattice provide such a method if it can be shown that the systematic errors, e.g. from condensates, are well controlled. \u0000We present $Z_V$ calculations for the conserved current in both the RI-SMOM and RI$'$-MOM momentum subtraction schemes as well as local current renormalisation in the RI-SMOM scheme. By performing these calculations at various values of the momentum scale $mu$ and different lattice spacings we can investigate the presence of power suppressed nonperturbative contributions and compare the results to expectations arising from the Ward-Takahashi identity. Our results show that the RI-SMOM scheme provides a well controlled determination of $Z_V$ but the standard RI$'$-MOM scheme does not. \u0000We then present some preliminary uses of these $Z_V$ calculations in charm physics.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78451829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-29DOI: 10.1103/physrevd.102.014507
F. Stokes, W. Kamleh, D. Leinweber
The recent development of the parity-expanded variational analysis (PEVA) technique makes lattice QCD studies of the form factors of baryon excitations possible. In this paper, we present Sachs electromagnetic form factors for excitations of the proton and neutron. We study the two lowest lying odd-parity excitations and demonstrate that at heavier pion masses, these states are dominated by behaviour consistent with constituent quark models for the N(1535) and N(1650), respectively. At pion masses approaching the physical point, meson-baryon contributions are observed to play an increasing role. We also study the lowest-lying localised even-parity excitation, and find that its form factors are consistent with a radial excitation of the ground state nucleon. A comparison of the results from the PEVA analysis with those from a conventional variational analysis exposes the necessity of the PEVA approach in baryon excited-state studies.
{"title":"Elastic form factors of nucleon excitations in lattice QCD","authors":"F. Stokes, W. Kamleh, D. Leinweber","doi":"10.1103/physrevd.102.014507","DOIUrl":"https://doi.org/10.1103/physrevd.102.014507","url":null,"abstract":"The recent development of the parity-expanded variational analysis (PEVA) technique makes lattice QCD studies of the form factors of baryon excitations possible. In this paper, we present Sachs electromagnetic form factors for excitations of the proton and neutron. We study the two lowest lying odd-parity excitations and demonstrate that at heavier pion masses, these states are dominated by behaviour consistent with constituent quark models for the N(1535) and N(1650), respectively. At pion masses approaching the physical point, meson-baryon contributions are observed to play an increasing role. We also study the lowest-lying localised even-parity excitation, and find that its form factors are consistent with a radial excitation of the ground state nucleon. A comparison of the results from the PEVA analysis with those from a conventional variational analysis exposes the necessity of the PEVA approach in baryon excited-state studies.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89626414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-22DOI: 10.1103/physrevd.101.034513
F. Bruckmann, M. Puhr
Perturbative expansions in many physical systems yield 'only' asymptotic series which are not even Borel resummable. Interestingly, the corresponding ambiguities point to nonperturbative physics. We numerically verify this renormalon mechanism for the first time in two-dimensional sigma models, that, like four-dimensional gauge theories, are asymptotically free and generate a strong scale through dimensional transmutation. We perturbatively expand the energy through a numerical version of stochastic quantization. In contrast to the first energy coefficients, the high order coefficients are independent on the rank of the model. Technically, they require a sophisticated analysis of finite volume effects and the continuum limit of the discretized model. Although the individual coefficients do not grow factorially (yet), but rather decrease strongly, the ratio of consecutive coefficients clearly obey the renormalon asymptotics.
{"title":"Universal renormalons in principal chiral models","authors":"F. Bruckmann, M. Puhr","doi":"10.1103/physrevd.101.034513","DOIUrl":"https://doi.org/10.1103/physrevd.101.034513","url":null,"abstract":"Perturbative expansions in many physical systems yield 'only' asymptotic series which are not even Borel resummable. Interestingly, the corresponding ambiguities point to nonperturbative physics. We numerically verify this renormalon mechanism for the first time in two-dimensional sigma models, that, like four-dimensional gauge theories, are asymptotically free and generate a strong scale through dimensional transmutation. We perturbatively expand the energy through a numerical version of stochastic quantization. In contrast to the first energy coefficients, the high order coefficients are independent on the rank of the model. Technically, they require a sophisticated analysis of finite volume effects and the continuum limit of the discretized model. Although the individual coefficients do not grow factorially (yet), but rather decrease strongly, the ratio of consecutive coefficients clearly obey the renormalon asymptotics.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87240273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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