Pub Date : 2019-05-30DOI: 10.1103/physrevd.102.054510
M. Asaduzzaman, S. Catterall, J. Unmuth-Yockey
We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first order formalism in which the local frame and spin connection are treated as independent fields. Recasting this lattice theory as a tensor network allows us to study the theory at strong coupling without encountering a sign problem. In two dimensions this tensor network is exactly soluble and we show that the system has a series of critical points that occur for pure imaginary coupling and are associated with first order phase transitions. We show evidence that the lattice theory is purely topological in nature by formulating it on lattices with differing topologies and show that the partition function depends only on the Euler character of the triangulation.
{"title":"Tensor network formulation of two-dimensional gravity","authors":"M. Asaduzzaman, S. Catterall, J. Unmuth-Yockey","doi":"10.1103/physrevd.102.054510","DOIUrl":"https://doi.org/10.1103/physrevd.102.054510","url":null,"abstract":"We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first order formalism in which the local frame and spin connection are treated as independent fields. Recasting this lattice theory as a tensor network allows us to study the theory at strong coupling without encountering a sign problem. In two dimensions this tensor network is exactly soluble and we show that the system has a series of critical points that occur for pure imaginary coupling and are associated with first order phase transitions. We show evidence that the lattice theory is purely topological in nature by formulating it on lattices with differing topologies and show that the partition function depends only on the Euler character of the triangulation.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77295849","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}
B. Brandt, M. Cè, A. Francis, T. Harris, H. Meyer, O. Philipsen, H. Wittig
We study the thermal transition of QCD with two degenerate light flavours by lattice simulations using $mathcal{O}(a)$-improved Wilson quarks. Particular emphasis lies on the pattern of chiral symmetry restoration, which we probe via the static screening correlators. On $32^3$ volumes we observe that the screening masses in transverse iso-vector vector and axial-vector channels become degenerate at the transition temperature. The splitting between the screening masses in iso-vector scalar and pseudoscalar channels is strongly reduced compared to the splitting at zero temperature and is actually consistent with zero within uncertainties. In this proceedings article we extend our studies to matrix elements and iso-singlet correlation functions. Furthermore, we present results on larger volumes, including first results at the physical pion mass.
{"title":"Testing the strength of the UA(1) anomaly at the chiral phase transition in two-flavour QCD","authors":"B. Brandt, M. Cè, A. Francis, T. Harris, H. Meyer, O. Philipsen, H. Wittig","doi":"10.22323/1.317.0055","DOIUrl":"https://doi.org/10.22323/1.317.0055","url":null,"abstract":"We study the thermal transition of QCD with two degenerate light flavours by lattice simulations using $mathcal{O}(a)$-improved Wilson quarks. Particular emphasis lies on the pattern of chiral symmetry restoration, which we probe via the static screening correlators. On $32^3$ volumes we observe that the screening masses in transverse iso-vector vector and axial-vector channels become degenerate at the transition temperature. The splitting between the screening masses in iso-vector scalar and pseudoscalar channels is strongly reduced compared to the splitting at zero temperature and is actually consistent with zero within uncertainties. In this proceedings article we extend our studies to matrix elements and iso-singlet correlation functions. Furthermore, we present results on larger volumes, including first results at the physical pion mass.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88556826","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}
C. Helmes, C. Jost, B. Knippschild, B. Kostrzewa, Liuming Liu, F. Pittler, C. Urbach, M. Werner
We summarize our lattice QCD determinations of the pion-pion, pion-kaon and kaon-kaon s-wave scattering lengths at maximal isospin with a particular focus on the extrapolation to the physical point and the usage of next-to-leading order chiral perturbation theory to do so. We employ data at three values of the lattice spacing and pion masses ranging from around 230 MeV to around 450 MeV, applying Luescher's finite volume method to compute the scattering lengths. We find that leading order chiral perturbation theory is surprisingly close to our data even in the kaon-kaon case for our entire range of pion masses.
{"title":"Meson-meson scattering lengths at maximum isospin from lattice QCD","authors":"C. Helmes, C. Jost, B. Knippschild, B. Kostrzewa, Liuming Liu, F. Pittler, C. Urbach, M. Werner","doi":"10.22323/1.317.0071","DOIUrl":"https://doi.org/10.22323/1.317.0071","url":null,"abstract":"We summarize our lattice QCD determinations of the pion-pion, pion-kaon and kaon-kaon s-wave scattering lengths at maximal isospin with a particular focus on the extrapolation to the physical point and the usage of next-to-leading order chiral perturbation theory to do so. We employ data at three values of the lattice spacing and pion masses ranging from around 230 MeV to around 450 MeV, applying Luescher's finite volume method to compute the scattering lengths. We find that leading order chiral perturbation theory is surprisingly close to our data even in the kaon-kaon case for our entire range of pion masses.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85565706","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 : 2018-12-18DOI: 10.1103/physrevresearch.2.033039
Indrakshi Raychowdhury, Jesse R. Stryker
We show that using the loop-string-hadron (LSH) formulation of SU(2) lattice gauge theory (arXiv:1912.06133) as a basis for digital quantum computation easily solves an important problem of fundamental interest: implementing gauge invariance (or Gauss's law) exactly. We first discuss the structure of the LSH Hilbert space in $d$ spatial dimensions, its truncation, and its digitization with qubits. Error detection and mitigation in gauge theory simulations would benefit from physicality "oracles,'"so we decompose circuits that flag gauge invariant wavefunctions. We then analyze the logical qubit costs and entangling gate counts involved with the protocols. The LSH basis could save or cost more qubits than a Kogut-Susskind-type representation basis, depending on how that is digitized as well as the spatial dimension. The numerous other clear benefits encourage future studies into applying this framework.
{"title":"Solving Gauss's law on digital quantum computers with loop-string-hadron digitization","authors":"Indrakshi Raychowdhury, Jesse R. Stryker","doi":"10.1103/physrevresearch.2.033039","DOIUrl":"https://doi.org/10.1103/physrevresearch.2.033039","url":null,"abstract":"We show that using the loop-string-hadron (LSH) formulation of SU(2) lattice gauge theory (arXiv:1912.06133) as a basis for digital quantum computation easily solves an important problem of fundamental interest: implementing gauge invariance (or Gauss's law) exactly. We first discuss the structure of the LSH Hilbert space in $d$ spatial dimensions, its truncation, and its digitization with qubits. Error detection and mitigation in gauge theory simulations would benefit from physicality \"oracles,'\"so we decompose circuits that flag gauge invariant wavefunctions. We then analyze the logical qubit costs and entangling gate counts involved with the protocols. The LSH basis could save or cost more qubits than a Kogut-Susskind-type representation basis, depending on how that is digitized as well as the spatial dimension. The numerous other clear benefits encourage future studies into applying this framework.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78500009","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 : 2018-12-14DOI: 10.1016/S0034-4877(20)30015-X
O. Borisenko, S. Voloshyn, V. Chelnokov
{"title":"Su(N) Polynomial Integrals and Some Applications","authors":"O. Borisenko, S. Voloshyn, V. Chelnokov","doi":"10.1016/S0034-4877(20)30015-X","DOIUrl":"https://doi.org/10.1016/S0034-4877(20)30015-X","url":null,"abstract":"","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80992501","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 : 2018-07-31DOI: 10.1393/NCC/I2019-19149-Y
D. Giusti
Isospin is an almost exact symmetry of strong interactions and the corrections to the isosymmetric limit are, in general, at the percent level. For several hadronic quantities relevant for flavour physics phenomenology, such as pseudoscalar meson masses or the kaon leptonic and semileptonic decay rates, these effects are of the same order of magnitude of the uncertainties quoted in current large-scale QCD simulations on the lattice and cannot be neglected anymore. In this contribution I discuss some recent results for the leptonic decay rates of light pseudoscalar mesons obtained by the Soton--RM123 Collaboration including the leading-order electromagnetic and strong isospin-breaking corrections in first principles lattice simulations. The adopted strategy is within the reach of present lattice technologies and it allows to determine electromagnetic corrections to physical observables for which delicate cancellations of infrared divergences occur in the intermediate steps of the calculation. The application of the developed method to the study of heavy-light meson and semileptonic decay rates is currently underway.
{"title":"QCD+QED lattice calculation of hadronic decay rates","authors":"D. Giusti","doi":"10.1393/NCC/I2019-19149-Y","DOIUrl":"https://doi.org/10.1393/NCC/I2019-19149-Y","url":null,"abstract":"Isospin is an almost exact symmetry of strong interactions and the corrections to the isosymmetric limit are, in general, at the percent level. For several hadronic quantities relevant for flavour physics phenomenology, such as pseudoscalar meson masses or the kaon leptonic and semileptonic decay rates, these effects are of the same order of magnitude of the uncertainties quoted in current large-scale QCD simulations on the lattice and cannot be neglected anymore. In this contribution I discuss some recent results for the leptonic decay rates of light pseudoscalar mesons obtained by the Soton--RM123 Collaboration including the leading-order electromagnetic and strong isospin-breaking corrections in first principles lattice simulations. The adopted strategy is within the reach of present lattice technologies and it allows to determine electromagnetic corrections to physical observables for which delicate cancellations of infrared divergences occur in the intermediate steps of the calculation. The application of the developed method to the study of heavy-light meson and semileptonic decay rates is currently underway.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84752259","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 : 2018-07-01DOI: 10.1007/978-3-030-43465-6_11
T. Hartung, K. Jansen, H. Leovey, J. Volmer
{"title":"Avoiding the Sign Problem in Lattice Field Theory","authors":"T. Hartung, K. Jansen, H. Leovey, J. Volmer","doi":"10.1007/978-3-030-43465-6_11","DOIUrl":"https://doi.org/10.1007/978-3-030-43465-6_11","url":null,"abstract":"","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83070933","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 : 2018-06-07DOI: 10.1051/epjconf/201817505020
G. Bali, S. Collins, D. Mohler, M. Padmanath, S. Piemonte, S. Prelovsek, S. Weishaeupl
The nature of resonances and excited states near decay thresholds is encoded in scattering amplitudes, which can be extracted from single-particle and multiparticle correlators in finite volumes. Lattice calculations have only recently reached the precision required for a reliable study of such correlators. The distillation method represents a significant improvement insofar as it simplifies quark contractions and allows one to easily extend the operator basis used to construct interpolators. We present preliminary results on charmonium bound states and resonances on the Nf = 2+1 CLS ensembles. The long term goal of our investigation is to understand the properties of the X resonances that do not fit into conventional models of quark-antiquark mesons. We tune various parameters of the distillation method and the charm quark mass. As a first result, we present the masses of the ground and excited states in the 0++ and 1−− channels
{"title":"Charmonium resonances on the lattice","authors":"G. Bali, S. Collins, D. Mohler, M. Padmanath, S. Piemonte, S. Prelovsek, S. Weishaeupl","doi":"10.1051/epjconf/201817505020","DOIUrl":"https://doi.org/10.1051/epjconf/201817505020","url":null,"abstract":"The nature of resonances and excited states near decay thresholds is encoded in scattering amplitudes, which can be extracted from single-particle and multiparticle correlators in finite volumes. Lattice calculations have only recently reached the precision required for a reliable study of such correlators. The distillation method represents a significant improvement insofar as it simplifies quark contractions and allows one to easily extend the operator basis used to construct interpolators. We present preliminary results on charmonium bound states and resonances on the Nf = 2+1 CLS ensembles. The long term goal of our investigation is to understand the properties of the X resonances that do not fit into conventional models of quark-antiquark mesons. We tune various parameters of the distillation method and the charm quark mass. As a first result, we present the masses of the ground and excited states in the 0++ and 1−− channels","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86437439","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 : 2018-03-29DOI: 10.5506/aphyspolbsupp.11.551
L. Mueller, M. Wagner
We study the structure of the hybrid static potential flux tube in the $Pi_u$ sector in SU(2) lattice Yang-Mills theory. To this end, we compute the squares of the chromoelectric and chromomagnetic field strengths in the presence of a static quark-antiquark pair. We show clear evidence that the gluon distribution is significantly different compared to that of the ordinary static potential with quantum numbers $Sigma_g^+$.
{"title":"Structure of hybrid static potential flux tubes in SU(2) lattice Yang-Mills theory","authors":"L. Mueller, M. Wagner","doi":"10.5506/aphyspolbsupp.11.551","DOIUrl":"https://doi.org/10.5506/aphyspolbsupp.11.551","url":null,"abstract":"We study the structure of the hybrid static potential flux tube in the $Pi_u$ sector in SU(2) lattice Yang-Mills theory. To this end, we compute the squares of the chromoelectric and chromomagnetic field strengths in the presence of a static quark-antiquark pair. We show clear evidence that the gluon distribution is significantly different compared to that of the ordinary static potential with quantum numbers $Sigma_g^+$.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78343393","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 : 2018-03-26DOI: 10.1051/EPJCONF/201817513011
P. Boyle, R. Hudspith, T. Izubuchi, A. Jüttner, C. Lehner, R. Lewis, K. Maltman, H. Ohki, A. Portelli, M. Spraggs
We propose and apply a novel approach to determining |V us | which uses inclusive strange hadronic tau decay data and hadronic vacuum polarization functions (HVPs) computed on the lattice. The experimental and lattice data are related through dispersion relations which employ a class of weight functions having poles at space-like momentum. Implementing this approach using lattice data generated by the RBC/UKQCD collaboration, we show examples of weight functions which strongly suppress spectral integral contributions from the region where experimental data either have large uncertainties or do not exist while at the same time allowing accurate determinations of relevant lattice HVPs. Our result for |V us | is in good agreement with determinations from K physics and 3-family CKM unitarity. The advantages of the new approach over the conventional sum rule analysis will be discussed.
{"title":"|Vus| determination from inclusive strange tau decay and lattice HVP","authors":"P. Boyle, R. Hudspith, T. Izubuchi, A. Jüttner, C. Lehner, R. Lewis, K. Maltman, H. Ohki, A. Portelli, M. Spraggs","doi":"10.1051/EPJCONF/201817513011","DOIUrl":"https://doi.org/10.1051/EPJCONF/201817513011","url":null,"abstract":"We propose and apply a novel approach to determining |V us | which uses inclusive strange hadronic tau decay data and hadronic vacuum polarization functions (HVPs) computed on the lattice. The experimental and lattice data are related through dispersion relations which employ a class of weight functions having poles at space-like momentum. Implementing this approach using lattice data generated by the RBC/UKQCD collaboration, we show examples of weight functions which strongly suppress spectral integral contributions from the region where experimental data either have large uncertainties or do not exist while at the same time allowing accurate determinations of relevant lattice HVPs. Our result for |V us | is in good agreement with determinations from K physics and 3-family CKM unitarity. The advantages of the new approach over the conventional sum rule analysis will be discussed.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83963913","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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