Wolfgang Bietenholz, Luigi Scorzato Institut für Physik, Humboldt Universität zu Berlin Newtonstr... more Wolfgang Bietenholz, Luigi Scorzato Institut für Physik, Humboldt Universität zu Berlin Newtonstr. 15, D-12489 Berlin, Germany Email: [email protected], [email protected] ... Silvia Necco Centre de Physique Théorique, ...
We present lattice results for the a_0(980) state using a variational approach with a variety of ... more We present lattice results for the a_0(980) state using a variational approach with a variety of creation operators: quark-antiquark, mesonic molecule, diquark-antidiquark as well as two-meson type. Focus is put on recent technical advances, in particular the computation of singly disconnected diagrams.
We propose a new algorithm based on the Metropolis sampling method to perform Monte Carlo integra... more We propose a new algorithm based on the Metropolis sampling method to perform Monte Carlo integration for path integrals in the recently proposed formulation of quantum field theories on the Lefschetz thimble. The algorithm is based on a mapping between the curved manifold defined by the Lefschetz thimble of the full action and the flat manifold associated with the corresponding quadratic action. We discuss an explicit method to calculate the residual phase due to the curvature of the Lefschetz thimble. Finally, we apply this new algorithm to a simple one-plaquette model where our results are in perfect agreement with the analytic integration. We also show that for this system the residual phase does not represent a sign problem.
We review the status of an ongoing long-term lattice investigation of the spectrum and structure ... more We review the status of an ongoing long-term lattice investigation of the spectrum and structure of tetraquark candidates. We focus on the light scalar meson a0(980). First steps regarding the study of a possibly existing cccc tetraquark are also outlined.
Recently, we have introduced a novel approach to deal with the sign problem that prevents the Mon... more Recently, we have introduced a novel approach to deal with the sign problem that prevents the Monte Carlo simulations of a class of quantum field theories (QFTs). The idea is to formulate the QFT on a Lefschetz thimble. Here we review the formulation of our approach and describe the Aurora Monte Carlo algorithm that we are currently testing on a scalar field theory with a sign problem.
ABSTRACT We present a high order perturbative computation of the renormalization constants Z_V, Z... more ABSTRACT We present a high order perturbative computation of the renormalization constants Z_V, Z_A and of the ratio Z_P/Z_S for Wilson fermions. The computational setup is the one provided by the RI'-MOM scheme. Three- and four-loop expansions are made possible by Numerical Stochastic Perturbation Theory. Results are given for various numbers of flavours and/or (within a finite accuracy) for generic n_f up to three loops. For the case n_f=2 we also present four-loop results. Finite size effects are well under control and the continuum limit is taken by means of hypercubic symmetric Taylor expansions. The main indetermination comes from truncation errors, which should be assessed in connection with convergence properties of the series. The latter is best discussed in the framework of Boosted Perturbation Theory, whose impact we try to assess carefully. Final results and their uncertainties show that high-loop perturbative computations of Lattice QCD RC's are feasible and should not be viewed as a second choice. As a by-product, we discuss the perturbative expansion for the critical mass, also for which results are for generic n_f up to three loops, while a four-loop result is obtained for n_f=2.
It is mostly agreed that Popper's criterion of falsifiability fails to provide a useful distincti... more It is mostly agreed that Popper's criterion of falsifiability fails to provide a useful distinction between science and pseudo-science, because ad-hoc assumptions are always able to save any theory that conflicts with the empirical data (this is the Duhem-Quine problem), and a characterization of ad-hoc assumptions is lacking. Moreover, adding some testable predictions is not very difficult. It should be emphasized that the Duhem-Quine argument does not simply make the distinction approximate (if it were so, all our problems would be solved!), but it makes it totally useless. Indeed, no philosophical criterion of demarcation is presently able to rule out even some of the most blatant cases of pseudo-science, not even approximatively (in any well defined sense of approximation). This is in sharp contrast with our firm belief that some theories are clearly not scientific. Where does this belief come from? In this paper I argue that it is necessary and possible to recognize the notion of syntactic simplicity that is able to tell the difference between empirically equivalent scientific and non-scientific theories, with a precision that is adequate to many important practical purposes, and it fully agrees with the judgments generally held in the scientific community.
We present a lattice QCD calculation of the up, down, strange and charm quark masses performed us... more We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with N f = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210 ÷ 450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI -MOM method. The results for the quark masses converted to the MS scheme are: m ud (2 GeV) = 3.70(17) MeV, m s (2 GeV) = 99.6(4.3) MeV and m c (m c ) = 1.348(46) GeV. We obtain also the quark mass ratios m s /m ud = 26.66(32) and m c /m s = 11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate m u /m d = 0.470(56), leading to m u = 2.36(24) MeV and m d = 5.03(26) MeV.
We propose an efficient method to compute the so-called residual phase that appears when performi... more We propose an efficient method to compute the so-called residual phase that appears when performing Monte Carlo calculations on a Lefschetz thimble. The method is stochastic and its cost scales linearly with the physical volume, linearly with the number of stochastic estimators and quadratically with the length of the extra dimension along the gradient flow. This is a drastic improvement over previous estimates of the cost of computing the residual phase. We also report on basic tests of correctness and scaling of the code.
One of the main goals of scientific research is to provide a description of the empirical data wh... more One of the main goals of scientific research is to provide a description of the empirical data which is as accurate and comprehensive as possible, while relying on as few and simple assumptions as possible. In this paper, I propose a definition of the notion of few and simple assumptions that is not affected by known problems. This leads to the introduction of a simple model of scientific progress that is based only on empirical accuracy and conciseness. An essential point in this task is the understanding of the role played by measurability in the formulation of a scientific theory. This is the key to prevent artificially concise formulations. The model is confronted here with many possible objections and with challenging cases of real progress. Although I cannot exclude that the model might have some limitations, it includes all the cases of genuine progress examined here, and no spurious one. In this model, I stress the role of the state of the art, which is the collection of all the theories that are the only legitimate source of scientific predictions. Progress is a global upgrade of the state of the art.
We compute the so called residual mass in Lattice Heavy Quark Effective Theory to αs3 order in th... more We compute the so called residual mass in Lattice Heavy Quark Effective Theory to αs3 order in the nf=2nf=2 (unquenched) case. The control of this additive mass renormalization is crucial for the determination of the heavy quark mass from lattice simulations. We discuss the impact on an unquenched determination of the b-quark mass.
We compute renormalization constants for Lattice QCD by means of Numerical Stochastic Perturbatio... more We compute renormalization constants for Lattice QCD by means of Numerical Stochastic Perturbation Theory. As an example we discuss Wilson quark bilinears and in particular the “gold plated” case of Zp/ZsZp/Zs for which we can evaluate the perturbative series up to four loops. By making use of the knowledge of anomalous dimension up to 3 loops in the RI'-MOM scheme, the generic bilinears ca be computed to the same (3rd) order. Finite volume effects are carefully assessed and the continuum limit of the computation is taken in a clean way. The convergence properties of the series can be assessed and a comparison with non-perturbative evaluations of the same quantities can be done. In the end, Lattice Perturbation Theory to high loops is a valuable tool to evaluate renormalization constants for lattice QCD with a very high precision.
The dependence of pseudo-scalar masses and decay constants on the sea and valence quark masses is... more The dependence of pseudo-scalar masses and decay constants on the sea and valence quark masses is investigated in the pseudo- Goldstone boson sector of QCD with two light quark flavours. The sea quark masses are at present in the range whereas the valence quark masses satisfy . The values of the Gasser-Leutwyler low energy constants L4, L5, L6 and L8 are estimated. The computation is done with the Wilson-quark lattice action at gauge coupling β = 5.1 on 164 lattices. (a) effects are taken into account by applying chiral perturbation theory for the Wilson lattice action as proposed by Rupak and Shoresh.
We explore gauge actions for lattice QCD, which are constructed such that the occurrence of small... more We explore gauge actions for lattice QCD, which are constructed such that the occurrence of small plaquette values is strongly suppressed. Such actions originate from the admissibility condition in order to conserve the topological charge. The suppression of small plaquette values is expected to be advantageous for numerical studies in the ε-regime and also for simulations with dynamical quarks. Performing simulations at a lattice spacing of about 0.1 fm, we present numerical results for the static potential, the physical scale r 0 , the stability of the topological charge history, the condition number of the kernel of the overlap operator and the acceptance rate against the step size in local HMC algorithm.
We discuss the inclusion of fermionic loops contributions in Numerical Stochastic Perturbation Th... more We discuss the inclusion of fermionic loops contributions in Numerical Stochastic Perturbation Theory for Lattice Gauge Theories. We show how the algorithm implementation is in principle straightforward and report on the status of the project.
We study light scalar mesons with particular focus on the a 0 (980) using lattice QCD with 2+1+1 ... more We study light scalar mesons with particular focus on the a 0 (980) using lattice QCD with 2+1+1 dynamical quark flavors. To investigate the structure of these scalar mesons and to identify, whether a sizeable tetraquark component is present, we use a large set of operators, including diquarkantidiquark, mesonic molecule and two-meson operators. We find that the low-lying states overlap essentially exclusively with two-meson states. This indicates that in the channels investigated no tightly bound four-quark states of either molecular or diquark-antidiquark type exist.
Wolfgang Bietenholz, Luigi Scorzato Institut für Physik, Humboldt Universität zu Berlin Newtonstr... more Wolfgang Bietenholz, Luigi Scorzato Institut für Physik, Humboldt Universität zu Berlin Newtonstr. 15, D-12489 Berlin, Germany Email: [email protected], [email protected] ... Silvia Necco Centre de Physique Théorique, ...
We present lattice results for the a_0(980) state using a variational approach with a variety of ... more We present lattice results for the a_0(980) state using a variational approach with a variety of creation operators: quark-antiquark, mesonic molecule, diquark-antidiquark as well as two-meson type. Focus is put on recent technical advances, in particular the computation of singly disconnected diagrams.
We propose a new algorithm based on the Metropolis sampling method to perform Monte Carlo integra... more We propose a new algorithm based on the Metropolis sampling method to perform Monte Carlo integration for path integrals in the recently proposed formulation of quantum field theories on the Lefschetz thimble. The algorithm is based on a mapping between the curved manifold defined by the Lefschetz thimble of the full action and the flat manifold associated with the corresponding quadratic action. We discuss an explicit method to calculate the residual phase due to the curvature of the Lefschetz thimble. Finally, we apply this new algorithm to a simple one-plaquette model where our results are in perfect agreement with the analytic integration. We also show that for this system the residual phase does not represent a sign problem.
We review the status of an ongoing long-term lattice investigation of the spectrum and structure ... more We review the status of an ongoing long-term lattice investigation of the spectrum and structure of tetraquark candidates. We focus on the light scalar meson a0(980). First steps regarding the study of a possibly existing cccc tetraquark are also outlined.
Recently, we have introduced a novel approach to deal with the sign problem that prevents the Mon... more Recently, we have introduced a novel approach to deal with the sign problem that prevents the Monte Carlo simulations of a class of quantum field theories (QFTs). The idea is to formulate the QFT on a Lefschetz thimble. Here we review the formulation of our approach and describe the Aurora Monte Carlo algorithm that we are currently testing on a scalar field theory with a sign problem.
ABSTRACT We present a high order perturbative computation of the renormalization constants Z_V, Z... more ABSTRACT We present a high order perturbative computation of the renormalization constants Z_V, Z_A and of the ratio Z_P/Z_S for Wilson fermions. The computational setup is the one provided by the RI'-MOM scheme. Three- and four-loop expansions are made possible by Numerical Stochastic Perturbation Theory. Results are given for various numbers of flavours and/or (within a finite accuracy) for generic n_f up to three loops. For the case n_f=2 we also present four-loop results. Finite size effects are well under control and the continuum limit is taken by means of hypercubic symmetric Taylor expansions. The main indetermination comes from truncation errors, which should be assessed in connection with convergence properties of the series. The latter is best discussed in the framework of Boosted Perturbation Theory, whose impact we try to assess carefully. Final results and their uncertainties show that high-loop perturbative computations of Lattice QCD RC's are feasible and should not be viewed as a second choice. As a by-product, we discuss the perturbative expansion for the critical mass, also for which results are for generic n_f up to three loops, while a four-loop result is obtained for n_f=2.
It is mostly agreed that Popper's criterion of falsifiability fails to provide a useful distincti... more It is mostly agreed that Popper's criterion of falsifiability fails to provide a useful distinction between science and pseudo-science, because ad-hoc assumptions are always able to save any theory that conflicts with the empirical data (this is the Duhem-Quine problem), and a characterization of ad-hoc assumptions is lacking. Moreover, adding some testable predictions is not very difficult. It should be emphasized that the Duhem-Quine argument does not simply make the distinction approximate (if it were so, all our problems would be solved!), but it makes it totally useless. Indeed, no philosophical criterion of demarcation is presently able to rule out even some of the most blatant cases of pseudo-science, not even approximatively (in any well defined sense of approximation). This is in sharp contrast with our firm belief that some theories are clearly not scientific. Where does this belief come from? In this paper I argue that it is necessary and possible to recognize the notion of syntactic simplicity that is able to tell the difference between empirically equivalent scientific and non-scientific theories, with a precision that is adequate to many important practical purposes, and it fully agrees with the judgments generally held in the scientific community.
We present a lattice QCD calculation of the up, down, strange and charm quark masses performed us... more We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with N f = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210 ÷ 450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI -MOM method. The results for the quark masses converted to the MS scheme are: m ud (2 GeV) = 3.70(17) MeV, m s (2 GeV) = 99.6(4.3) MeV and m c (m c ) = 1.348(46) GeV. We obtain also the quark mass ratios m s /m ud = 26.66(32) and m c /m s = 11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate m u /m d = 0.470(56), leading to m u = 2.36(24) MeV and m d = 5.03(26) MeV.
We propose an efficient method to compute the so-called residual phase that appears when performi... more We propose an efficient method to compute the so-called residual phase that appears when performing Monte Carlo calculations on a Lefschetz thimble. The method is stochastic and its cost scales linearly with the physical volume, linearly with the number of stochastic estimators and quadratically with the length of the extra dimension along the gradient flow. This is a drastic improvement over previous estimates of the cost of computing the residual phase. We also report on basic tests of correctness and scaling of the code.
One of the main goals of scientific research is to provide a description of the empirical data wh... more One of the main goals of scientific research is to provide a description of the empirical data which is as accurate and comprehensive as possible, while relying on as few and simple assumptions as possible. In this paper, I propose a definition of the notion of few and simple assumptions that is not affected by known problems. This leads to the introduction of a simple model of scientific progress that is based only on empirical accuracy and conciseness. An essential point in this task is the understanding of the role played by measurability in the formulation of a scientific theory. This is the key to prevent artificially concise formulations. The model is confronted here with many possible objections and with challenging cases of real progress. Although I cannot exclude that the model might have some limitations, it includes all the cases of genuine progress examined here, and no spurious one. In this model, I stress the role of the state of the art, which is the collection of all the theories that are the only legitimate source of scientific predictions. Progress is a global upgrade of the state of the art.
We compute the so called residual mass in Lattice Heavy Quark Effective Theory to αs3 order in th... more We compute the so called residual mass in Lattice Heavy Quark Effective Theory to αs3 order in the nf=2nf=2 (unquenched) case. The control of this additive mass renormalization is crucial for the determination of the heavy quark mass from lattice simulations. We discuss the impact on an unquenched determination of the b-quark mass.
We compute renormalization constants for Lattice QCD by means of Numerical Stochastic Perturbatio... more We compute renormalization constants for Lattice QCD by means of Numerical Stochastic Perturbation Theory. As an example we discuss Wilson quark bilinears and in particular the “gold plated” case of Zp/ZsZp/Zs for which we can evaluate the perturbative series up to four loops. By making use of the knowledge of anomalous dimension up to 3 loops in the RI'-MOM scheme, the generic bilinears ca be computed to the same (3rd) order. Finite volume effects are carefully assessed and the continuum limit of the computation is taken in a clean way. The convergence properties of the series can be assessed and a comparison with non-perturbative evaluations of the same quantities can be done. In the end, Lattice Perturbation Theory to high loops is a valuable tool to evaluate renormalization constants for lattice QCD with a very high precision.
The dependence of pseudo-scalar masses and decay constants on the sea and valence quark masses is... more The dependence of pseudo-scalar masses and decay constants on the sea and valence quark masses is investigated in the pseudo- Goldstone boson sector of QCD with two light quark flavours. The sea quark masses are at present in the range whereas the valence quark masses satisfy . The values of the Gasser-Leutwyler low energy constants L4, L5, L6 and L8 are estimated. The computation is done with the Wilson-quark lattice action at gauge coupling β = 5.1 on 164 lattices. (a) effects are taken into account by applying chiral perturbation theory for the Wilson lattice action as proposed by Rupak and Shoresh.
We explore gauge actions for lattice QCD, which are constructed such that the occurrence of small... more We explore gauge actions for lattice QCD, which are constructed such that the occurrence of small plaquette values is strongly suppressed. Such actions originate from the admissibility condition in order to conserve the topological charge. The suppression of small plaquette values is expected to be advantageous for numerical studies in the ε-regime and also for simulations with dynamical quarks. Performing simulations at a lattice spacing of about 0.1 fm, we present numerical results for the static potential, the physical scale r 0 , the stability of the topological charge history, the condition number of the kernel of the overlap operator and the acceptance rate against the step size in local HMC algorithm.
We discuss the inclusion of fermionic loops contributions in Numerical Stochastic Perturbation Th... more We discuss the inclusion of fermionic loops contributions in Numerical Stochastic Perturbation Theory for Lattice Gauge Theories. We show how the algorithm implementation is in principle straightforward and report on the status of the project.
We study light scalar mesons with particular focus on the a 0 (980) using lattice QCD with 2+1+1 ... more We study light scalar mesons with particular focus on the a 0 (980) using lattice QCD with 2+1+1 dynamical quark flavors. To investigate the structure of these scalar mesons and to identify, whether a sizeable tetraquark component is present, we use a large set of operators, including diquarkantidiquark, mesonic molecule and two-meson operators. We find that the low-lying states overlap essentially exclusively with two-meson states. This indicates that in the channels investigated no tightly bound four-quark states of either molecular or diquark-antidiquark type exist.
Popper’s criterion of falsifiability fails to provide a useful demarcation between science and no... more Popper’s criterion of falsifiability fails to provide a useful demarcation between science and non-science, because ad-hoc assumptions (which lack a definition) are always able to save any theory that conflicts with the data; and, adding some testable predictions is easy. This argument does not simply make the demarcation approximate: it makes it totally useless. Currently, no philosophical criterion is able to rule out even some of the most blatant cases of pseudo-science, not even approximatively (in any well defined sense of approximation). This conflicts with our firm belief that some theories are clearly not scientific. In this paper I argue that it is necessary and possible to recognise the notion of syntactic simplicity that is able to tell the difference between empirically equivalent scientific and non-scientific theories, with a precision that is adequate to many important practical purposes, and it fully agrees with the judgments generally held in the scientific community.
Lecture 3: Numerical Linear Algebra LU and QR algorithms Typical problems of Numerical Linear Alg... more Lecture 3: Numerical Linear Algebra LU and QR algorithms Typical problems of Numerical Linear Algebra:
Lecture 5: Nonlinear algebraic equations • Naive (linear conv. with possibly bad coefficient) • B... more Lecture 5: Nonlinear algebraic equations • Naive (linear conv. with possibly bad coefficient) • Bisection (linear conv.) • Newton-Raphson (quadratic conv.) • Method of the Secante (conv. ~1.6, works also for non differentiables) • Real Life algorithms • Exercise: basin of attraction of the 3 roots of x 3 -1=0, as obtained by Newton-Raphson.
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Papers by Luigi Scorzato