Search

A recent analysis by the LHCb collaboration suggests the existence of three narrow pentaquark-like states --- the $P_c(4312)$,$P_c(4440)$ and $P_c(4457)$ --- instead of just one in the previous analysis (the $P_c(4450)$). The closeness of the $P_c(4312)$ to the $\bar{D} \Sigma_c$ threshold and the $P_c(4440)$/$P_c(4457)$ to the $\bar{D}^* \Sigma_c$ one suggests a molecular interpretation of these resonances. We show that these three pentaquark-like resonances can be naturally accommodated in a contact-range effective field theory description that incorporates heavy-quark spin symmetry. This description leads to the prediction of all the seven possible S-wave heavy antimeson-baryon molecules (that is, there should be four additional molecular pentaquarks in addition to the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$), providing the first example of a heavy-quark spin symmetry molecular multiplet that is complete. If this is confirmed, it will not only give us an impressive example of the application of heavy-quark symmetries and effective field theories in hadron physics: it will also uncover a clear and powerful ordering principle for the molecular spectrum, reminiscent of the SU(3)-flavor multiplets to which the light hadron spectrum conforms., Comment: Corresponds to the version to be published in Physical Review Letters; 4 pages, 1 table summarizing the results, the names of the scenarios have been exchanged to reflect their theoretical preference (scenario A now corresponds to the more likely scenario in pionless EFT)

cd. autorów: L. Cao48,‡, G. Caria145,‡, G. Casarosa57,‡, C. Cecchi56,‡,D. Cˇ ervenkov10,‡,M.-C. Chang22,‡, P. Chang92,‡, R. Cheaib146,‡, V. Chekelian83,‡, Y. Chen154,‡, B. G. Cheon28,‡, K. Chilikin77,‡, K. Cho70,‡, J. Choi14,‡, S.-K. Choi27,‡, S. Choudhury35,‡, D. Cinabro170,‡, L. M. Cremaldi146,‡, D. Cuesta47,‡, S. Cunliffe16,‡, N. Dash33,‡, E. de la Cruz Burelo9,‡, E. de Lucia52,‡, G. De Nardo54,‡, †Editor. ‡Belle II Collaborator. §Theory or external contributing author. M. De Nuccio16,‡, G. De Pietro59,‡, A. De Yta Hernandez9,‡, B. Deschamps129,‡, M. Destefanis60,‡, S. Dey116,‡, F.Di Capua54,‡, S.Di Carlo75,‡, J. Dingfelder129,‡, Z. Doležal10,‡, I. Domínguez Jiménez125,‡, T.V. Dong30,26,‡, D. Dossett145,‡, S. Duell129,‡, S. Eidelman6,96,77,‡, D. Epifanov6,96,‡, J. E. Fast100,‡, T. Ferber16,‡, S. Fiore18,‡, A. Fodor85,‡, F. Forti57,‡, A. Frey24,‡, O. Frost16,‡, B. G. Fulsom100,‡, M. Gabriel83,‡, N. Gabyshev6,96,‡, E. Ganiev61,‡, X. Gao3,‡, B. Gao23,‡, R. Garg101,‡, A. Garmash6,96,‡, V. Gaur169,‡, A. Gaz90,‡, T. Geßler65,‡, U. Gebauer24,‡, M. Gelb48,‡, A. Gellrich16,‡, D. Getzkow65,‡, R. Giordano54,‡, A. Giri35,‡, A. Glazov16,‡, B. Gobbo61,‡, R. Godang157,‡, O. Gogota110,‡, P. Goldenzweig48,‡, B. Golob141,109,‡,W. Gradl63,‡, E. Graziani59,‡, M. Greco60,‡, D. Greenwald114,‡, S. Gribanov6,96,‡, Y. Guan17,‡, E. Guido60,‡, A. Guo41,‡, S. Halder111,‡, K. Hara30,26,‡, O. Hartbrich138,‡, T. Hauth48,‡, K. Hayasaka94,‡, H. Hayashii91,‡, C. Hearty130,‡, I. Heredia De La Cruz9,‡, M. Hernandez Villanueva9,‡, A. Hershenhorn130,‡, T. Higuchi66,‡,M. Hoek63,‡, S. Hollitt124,‡, N. T. HongVan44,‡, C.-L. Hsu160,‡, Y. Hu41,‡, K. Huang92,‡, T. Iijima89,90,‡, K. Inami90,‡, G. Inguglia40,‡,A. Ishikawa119,‡, R. Itoh30,26,‡, Y. Iwasaki30,‡, M. Iwasaki97,‡, P. Jackson124,‡, W. W. Jacobs37,‡, I. Jaegle137,‡, H. B. Jeon73,‡, X. Ji41,‡, S. Jia3,‡,Y. Jin162,‡, C. Joo66,‡,M. Künzel16,‡, I. Kadenko110,‡, J. Kahn78,‡, H. Kakuno121,‡, A. B. Kaliyar36,‡, J. Kandra10,‡, K. H. Kang73,‡, Y. Kato90,‡, T. Kawasaki68,‡, C. Ketter138,‡, M. Khasmidatul143,‡, H. Kichimi30,‡, J. B. Kim71,‡, K. T. Kim71,‡, H. J. Kim73,‡, D.Y. Kim108,‡, K. Kim172,‡, Y. Kim172,‡, T. D. Kimmel169,‡, H. Kindo30,26,‡, K. Kinoshita135,‡, T. Konno68,‡, A. Korobov6,96,‡, S. Korpar144,109,‡, D. Kotchetkov138,‡, R. Kowalewski165,‡, P. Križan141,109,‡, R. Kroeger146,‡, J.-F. Krohn145,‡, P. Krokovny6,96,‡, W. Kuehn65,‡, T. Kuhr78,‡, R. Kulasiri67,‡, M. Kumar81,‡, R. Kumar101,‡, T. Kumita121,‡, A. Kuzmin6,96,‡, Y.-J. Kwon172,‡, S. Lacaprara55,‡, Y.-T. Lai30,‡, K. Lalwani81,‡, J. S. Lange65,‡, S. C. Lee73,‡, J.Y. Lee106,‡, P. Leitl83,‡, D. Levit114,‡, S. Levonian16,‡, S. Li3,‡, L. K. Li41,‡, Y. Li41,‡,Y. B. Li103,‡, Q. Li103,‡, L. Li Gioi83,‡, J. Libby36,‡, Z. Liptak138,‡, D. Liventsev169,‡, S. Longo165,‡, A. Loos158,‡, G. Lopez Castro9,‡, M. Lubej109,‡, T. Lueck57,‡, F. Luetticke129,‡, T. Luo23,‡, F. Müller16,‡, Th. Müller48,‡, C. MacQueen145,‡, Y. Maeda90,‡, M. Maggiora60,‡, S. Maity33,‡, E. Manoni56,‡, S. Marcello60,‡, C. Marinas129,‡, M. Martinez Hernandez4,‡, A. Martini59,‡, D. Matvienko6,96,77,‡, J. A. McKenna130,‡, F. Meier160,‡, M. Merola54,‡, F. Metzner48,‡, C. Miller165,‡, K. Miyabayashi91,‡, H. Miyake30,26,‡, H. Miyata94,‡, R. Mizuk77,88,87,‡, G. B. Mohanty111,163,‡, H. K. Moon71,‡, T. Moon106,‡,A. Morda55,‡, T. Morii66,‡, M. Mrvar109,‡, G. Muroyama90,‡, R. Mussa60,‡, I. Nakamura30,26,‡, T. Nakano99,‡, M. Nakao30,26,‡, H. Nakayama30,26,‡, H. Nakazawa92,‡, T. Nanut109,‡, M. Naruki72,‡, K. J. Nath34,‡, M. Nayak116,‡, N. Nellikunnummel151,‡, D. Neverov90,‡, C. Niebuhr16,‡, J. Ninkovic84,‡, S. Nishida30,26,‡, K. Nishimura138,‡, M. Nouxman143,‡, G. Nowak93,‡, K. Ogawa94,‡, Y. Onishchuk110,‡, H. Ono94,‡, Y. Onuki162,‡, P. Pakhlov77,88,‡, G. Pakhlova87,‡, B. Pal5,‡, E. Paoloni57,‡, H. Park73,‡, C.-S. Park172,‡, B. Paschen129,‡, A. Passeri59,‡, S. Paul114,‡, T. K. Pedlar80,‡, M. Perelló46,‡, I. M. Peruzzi52,‡, R. Pestotnik109,‡, L. E. Piilonen169,‡, L. Podesta Lerma125,‡, V. Popov87,‡, K. Prasanth111,‡, E. Prencipe21,‡, M. Prim48,‡, M. V. Purohit158,‡, A. Rabusov114,‡, R. Rasheed47,‡, S. Reiter65,‡, M. Remnev6,96,‡, P. K. Resmi36,‡, I. Ripp-Baudot47,‡, M. Ritter78,‡, M. Ritzert139,‡, G. Rizzo57,‡, L. Rizzuto141,109,‡, S. H. Robertson85,‡, D. Rodriguez Perez125,‡, J. M. Roney165,‡, C. Rosenfeld158,‡, A. Rostomyan16,‡, N. Rout36,‡, S. Rummel78,‡, G. Russo54,‡, D. Sahoo111,‡, Y. Sakai30,26,‡, M. Salehi143,78,‡, D. A. Sanders146,‡, S. Sandilya135,‡, A. Sangal135,‡, L. Santelj47,‡, J. Sasaki162,‡, Y. Sato30,‡, V. Savinov151,‡, B. Scavino63,‡, M. Schram100,‡, H. Schreeck24,‡, J. Schueler138,‡,C. Schwanda40,‡,A. J. Schwartz135,‡,R.M. Seddon85,‡,Y. Seino94,‡, K. Senyo171,‡, O. Seon90,‡, I. S. Seong138,‡, M. E. Sevior145,‡, C. Sfienti63,‡, M. Shapkin38,‡, C. P. Shen3,‡,M. Shimomura91,‡, J.-G. Shiu92,‡, B. Shwartz6,96,‡,A. Sibidanov165,‡, F. Simon83,113,‡, J. B. Singh101,‡, R. Sinha42,‡, S. Skambraks83,‡, K. Smith145,‡, R. J. Sobie165,‡, A. Soffer116,‡, A. Sokolov38,‡, E. Solovieva77,87,‡, B. Spruck63,‡, S. Staniˇc149,‡, M. Stariˇc109,‡, N. Starinsky147,‡, U. Stolzenberg24,‡, Z. Stottler169,‡, R. Stroili55,‡, J. F. Strube100,‡, J. Stypula93,‡, M. Sumihama25,‡, K. Sumisawa30,26,‡, T. Sumiyoshi121,‡, D. Summers146,‡, W. Sutcliffe48,‡, S. Y. Suzuki30,26,‡, M. Tabata13,‡, M. Takahashi16,‡, M. Takizawa107,‡, U. Tamponi60,‡, J. Tan145,‡, S. Tanaka30,26,‡, K. Tanida2,‡, N. Taniguchi30,‡, Y. Tao137,‡, P. Taras147,‡, G. Tejeda Munoz4,‡, F. Tenchini16,‡, U. Tippawan12,‡, E. Torassa55,‡, K. Trabelsi30,26,‡, T. Tsuboyama30,26,‡, M. Uchida120,‡, S. Uehara30,26,‡, T. Uglov77,87,‡, Y. Unno28,‡, S. Uno30,26,‡, Y. Ushiroda30,26,162,‡, Y. Usov6,96,‡, S. E. Vahsen138,‡, R. van Tonder48,‡, G. Varner138,‡, K. E. Varvell160,‡, A. Vinokurova6,96,‡, L.Vitale61,‡,M.Vos46,‡,A.Vossen17,‡,E.Waheed145,‡,H.Wakeling85,‡,K.Wan162,‡, M.-Z.Wang92,‡, X. L. Wang23,‡, B. Wang135,‡, A. Warburton85,‡, J. Webb145,‡, S. Wehle16,‡, C. Wessel129,‡, J. Wiechczynski93,‡, P. Wieduwilt24,‡, E. Won71,‡, Q. Xu41,‡, X. Xu41,‡, B. D. Yabsley160,‡, S. Yamada30,‡, H. Yamamoto119,‡, W. Yan3,‡, W. Yan154,‡, S. B. Yang71,‡, H. Ye16,‡, I. Yeo70,‡, J. H. Yin41,‡, M. Yonenaga121,‡, T. Yoshinobu94,‡, W. Yuan55,‡, C. Z. Yuan41,‡, Y. Yusa94,‡, S. Zakharov77,87,‡, L. Zani57,‡, M. Zeyrek86,‡, J. Zhang41,‡,Y. Zhang23,‡,Y. Zhang154,‡, X. Zhou3,‡, V. Zhukova77,‡, V. Zhulanov6,96,‡, and A. Zupanc141,109,‡ †Editor. ‡Belle II Collaborator. §Theory or external contributing author., "The Belle II Theory Interface Platform (B2TiP) was created as a physics prospects working group of the Belle II collaboration in June 2014. It offered a platform where theorists and experimentalists could work together to elucidate the potential impacts of the Belle II program, which includes a wide scope of physics topics: B physics, charm, τ , quarkonium physics, electroweak precision measurements, and dark sector searches. It is composed of nine working groups (WGs), which 6/654 Downloaded from https://academic.oup.com/ptep/article-abstract/2019/12/123C01/5685006 by Uniwersytet Slaski Biblioteka Glowna user on 20 February 2020 PTEP 2019, 123C01 E. Kou et al. are coordinated by teams of theory and experiment conveners: WG1, Semileptonic and leptonic B Decays; WG2, Radiative and Electroweak Penguins; WG3, φ1 and φ2 (Time-Dependent CP Violation) Measurements; WG4, φ3 Measurement; WG5, Charmless Hadronic B Decay; WG6, Charm; WG7, Quarkonium(-like); WG8, τ and Low-Multiplicity Processes; WG9, New Physics. We organized workshops twice a year from 2014 until 2016, which moved from KEK in Japan to Europe and the Americas, gathering experts in the respective fields for discussions with Belle II members. One of the goals for B2TiP was to propose so-called “golden and silver channels”: we asked each working group to choose, among numerous possible measurements, those that would have the highest potential impact and to focus on them for the writeup. Theorists scrutinized the role of those measurements in terms of understanding the theory behind them, and estimated the theoretical uncertainties now achievable as well as prospects for the future. For flavor physics, having tight control of hadronic uncertainties is one of the most crucial aspects in the field, and this is considered an important criterion in determining the golden or silver channels. Experimentalists, on the other hand, investigated the expected improvements with data from Belle II. For the channels where the errors are dominated by statistical uncertainties, or where systematic errors are reducible, the errors can decrease rapidly as more data becomes available. The impact of the upgraded performance from Belle II is a crucial element in reducing the uncertainties: we therefore include the latest available studies of the detector efficiency using Monte Carlo simulated events.We list the golden and silver channel table in the introductory chapter, as a guide for the chapters that follow. This book is not a collection of reports based on talks given at the workshops. The working group conveners endeavored to construct a coherent document that can be used by Belle II collaborators, and others in the field of flavor physics, as a reference. Two books of a similar type have been produced in the past: The BaBar Book [1] and The Physics of the B Factories [2]. In order to avoid too much repetition with respect to those references, we refer to them wherever possible for introductory material. We would like to thank the section editors and contributing authors for the many stimulating discussions and their tremendous efforts in bringing the book together." (Preface)

In a previous publication, two of us derived a relation between the scattering amplitude of three identical bosons, $\mathcal M_3$, and a real function referred to as the {divergence-free} K matrix and denoted $\mathcal K_{\text{df},3}$. The result arose in the context of a relation between finite-volume energies and $\mathcal K_{\text{df},3}$, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between $\mathcal K_{\text{df},3}$ and $\mathcal M_3$. We show that, for any real choice of $\mathcal K_{\text{df},3}$, $\mathcal M_3$ satisfies the three-particle unitarity constraint to all orders. Given that $\mathcal K_{\text{df},3}$ is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role)., Comment: 19 pages, 4 figures, JLAB-THY-19-2945, CERN-TH-2019-078

37th International Symposium on Lattice Field Theory, Lattice 2019, Wuhan, China, 16 Jun 2019 - 22 Jun 2019; Proceedings of Science / International School for Advanced Studies (LATTICE2019), 110 (2019). doi:10.22323/1.363.0110, We present a lattice calculation of the leading hadronic contribution to the anomalous magnetic moment of the muon. This work is based on a subset of the CLS ensembles with $N_f = 2+1$ dynamical quarks and a quenched charm quark. Noise reduction techniques are used to improve significantly the statistical precision of the dominant light quark contribution. The main source of systematic error comes from finite size effects which are estimated using the formalism described in Ref. [7] and based on our knowledge of the timelike pion form factor. The strange and charm quark contributions are under control and an estimate of the quark-disconnected contribution is included. Isospin breaking effects will be studied in a future publication but are included in the systematic error using an estimate based on published lattice results. Our final result, $a_\mu^{\rm hvp}$ = (720.0\pm 12.4 $\pm$ 6.8)\times $10^{-10}$, has a precision of about 2%., Published by SISSA, Trieste

We report preliminary results for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment. Several ensembles using 2+1 flavors of M\"obius domain-wall fermions, generated by the RBC/UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find $a_\mu^{\rm HLbL} = (7.41\pm6.33)\times 10^{-10}$, Comment: 8 pages, 19 figures, to appear in the proceedings of Rencontres de Moriond (EW)

We determine non-perturbatively the normalisation constant Z_m*Z_P/Z_A as well as the Symanzik coefficients b_m and b_A-b_P, required in O(a) improved quark mass renormalisation with Wilson fermions. The strategy underlying their computation involves simulations in N_f=3 QCD with O(a) improved massless sea and non-degenerate valence quarks in the finite-volume Schroedinger functional scheme. Our results, which cover the typical gauge coupling range of large-volume N_f=2+1 QCD simulations with Wilson fermions at lattice spacings below 0.1 fm, are of particular use for the non-perturbative calculation of O(a) improved renormalised quark masses., Comment: 36 pages including figures and tables, latex2e; version published in Eur. Phys. J. C; small additions to the text and reference added; results unchanged

On March 26th, 2019, at the Rencontres de Moriond QCD conference, the LHCb Collaboration reported the observation of three new pentaquarks, namely $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, which are consistent with the loosely bound molecular hidden-charm pentaquark states composed of an S-wave charmed baryon $\Sigma_c$ and an S-wave anti-charmed meson ($\bar{D}, \bar{D}^*$). In this work, we present a direct calculation by the one-boson-exchange (OBE) model and demonstrate explicitly that the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ do correspond to the loosely bound $\Sigma_c\bar{D}$ with $(I=1/2,J^P=1/2^-)$, $\Sigma_c\bar{D}^*$ with $(I=1/2,J^P=1/2^-)$ and $\Sigma_c\bar{D}^*$ with $(I=1/2,J^P=3/2^-)$, respectively., Comment: 5 pages, 1 table and 2 figures. Accepted by Phys. Rev. D as Rapid Communication

The measurement of the anomalous magnetic moment of the muon and its prediction allow for a high-precision test of the Standard Model (SM). In this proceedings article we present ongoing work combining lattice QCD and continuum QED in order to determine an important SM contribution to the magnetic moment, the hadronic light-by-light contribution. We compute the quark-connected contribution in the Mainz position-space approach and investigate the long-distance part of our data using calculations of the $\pi^0$-pole and charged pion loop contributions., Comment: 7 pages, 10 figures

Motivated by the boost-invariant Glasma state in the initial stages in heavy-ion collisions, we perform classical-statistical simulations of SU(2) gauge theory in 2+1 dimensional space-time both with and without a scalar field in the adjoint representation. We show that irrespective of the details of the initial condition, the far-from-equilibrium evolution of these highly occupied systems approaches a unique universal attractor at high momenta that is the same for the gauge and scalar sectors. We extract the scaling exponents and the form of the distribution function close to this non-thermal fixed point. We find that the dynamics are governed by an energy cascade to higher momenta with scaling exponents $\alpha = 3\beta$ and $\beta = -1/5$. We argue that these values can be obtained from parametric estimates within kinetic theory indicating the dominance of small momentum transfer in the scattering processes. We also extract the Debye mass non-perturbatively from a longitudinally polarized correlator and observe an IR enhancement of the scalar correlation function for low momenta below the Debye mass., Comment: 12 pages, 7 figures; v2: accepted by PRD, references added, minor changes

We investigate the possibility of qq'$ \bar {Q}\bar {Q}' $ tetraquark bound states using nf = 2 + 1 lattice QCD with pion masses ≃ 164, 299 and 415 MeV. Two types of lattice interpolating operator are chosen, reflecting first diquarkantidiquark and second meson-meson structure. Performing variational analysis using these operators and their mixings, we determine the ground and first excited states from the lattice correlators. Using non-relativistic QCD to simulate the bottom quarks and the Tsukuba formulation of relativistic heavy quarks for charm quarks, we study the ud$ \bar {b}\bar {b} $, ℓs$ \bar {b}\bar {b} $ as well as ud$ \bar {c}\bar {b} $, channels with ℓ= u, d. In the case of the ud$ \bar {b}\bar {b} $ and ℓs$ \bar {b}\bar {b} $ channels unambiguous signals for JP=1+ tetraquarks are found with binding energies 189(10) and 98(7) MeV below the corresponding free two-meson thresholds at the physical point. These tetraquarks are therefore strong-interaction stable, implying they are stable under strong as well as electromagnetic interactions while they can decay weakly. So far these are the first exotic hadrons predicted to have this feature. Further evidence for binding is found in the ud$ \bar {c}\bar {b} $ channel, whereby the binding energy broadly straddles the electromagnetic stability threshold. Studying further the quark mass dependence we vary the heavy quark mass in ud$ \bar {Q}\bar {Q} $, ℓs$ \bar {Q}\bar {Q} $ as well as ud$ \bar {Q}\bar {b} $, ℓs$ \bar {Q}\bar {b} $ between roughly 0.7 and 6.3 times the bottom quark mass. The observed mass dependence of these four flavor channels closely follows a behaviour argued from phenomenological considerations of the heavy baryon spectrum.

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD in quark and lepton flavor physics. New data generated at Belle II, LHCb, BES III, NA62, KOTO, and Fermilab E989, combined with precise calculations of the relevant hadronic physics, may reveal what lies beyond the Standard Model. We outline a path toward improvements of the precision of existing lattice-QCD calculations and discuss groundbreaking new methods that allow lattice QCD to access new observables., Comment: USQCD whitepaper

37th International Symposium on Lattice Field Theory, Wuhan, China, 16 Jun 2019 - 22 Jun 2019; PoS(LATTICE 2019)010 (2019)., The electromagnetic coupling $\alpha$ and the electroweak mixing angle $\theta_{\mathrm{W}}$ are parameters of the Standard Model (SM) that enter precision SM tests and play a fundamental r\^ole in beyond SM physics searches. Their values are energy dependent, and non-perturbative hadronic contributions are the main source of uncertainty to the theoretical knowledge of the running with energy. We present a lattice study of the leading hadronic contribution to the running of $\alpha$ and $\sin^2\theta_{\mathrm{W}}$. The former is related to the hadronic vacuum polarization (HVP) function of electromagnetic currents, and the latter to the HVP mixing of the electromagnetic current with the vector part of the weak neutral currents. We use the time-momentum representation (TMR) method to compute the HVP on the lattice, estimating both connected and disconnected contributions on $N_{\mathrm{f}}=2+1$ non-perturbatively $O(a)$-improved Wilson fermions ensembles from the Coordinated Lattice Simulations (CLS) initiative. The use of different lattice spacings and quark masses allows us to reliably extrapolate the results to the physical point.

We present a nearly final analysis of the $u/d$ and $s$ quark masses, extracted using the PCAC quark masses reported in [PRD 95 (2017) 074504]. The data is based on the CLS $N_f = 2 + 1$ simulations with Wilson/Clover quarks and L\"uscher-Weisz gauge action, at four $\beta$ values (i.e. lattice spacings) and a range of quark masses. We use the ALPHA results of [EPJC 78 (2018) 387] for non-perturbative quark mass renormalisation and RG-running from hadronic to electroweak scales in the Schr\"odinger Functional scheme. Quark masses are quoted both in the $\overline{\rm MS}$ scheme and as RGI quantities., Comment: Talk presented at the 36th Annual International Symposium on Lattice Field Theory (Lattice 2018), 22-28 July 2018, Michigan, USA

In this work we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to $\textbf 2 + \mathcal J \to \textbf 2$ transition amplitudes. We also give various details relevant for the implementation of this formalism in a realistic numerical lattice QCD calculation. Particular focus is given to the role of single-particle form factors in disentangling finite-volume effects from the triangle diagram that arise when $\mathcal J$ couples to one of the two hadrons. This also leads to a new finite-volume function, denoted $G$, the numerical evaluation of which is described in detail. As an example we discuss the determination of the $\pi \pi + \mathcal J \to \pi \pi$ amplitude in the $\rho$ channel, for which the single-pion form factor, $F_\pi(Q^2)$, as well as the scattering phase, $\delta_{\pi\pi}$, are required to remove all power-law finite-volume effects. The formalism presented here holds for local currents with arbitrary Lorentz structure, and we give specific examples of insertions with up to two Lorentz indices., Comment: 42 pages, 11 figures, JLAB-THY-18-2878, CERN-TH-2018-263

The topological susceptibility is computed in the SU(3) gauge theory at temperatures $T$ above the critical temperature $T_{\rm c}$ using master-field simulations of very large lattices, where the infamous topology-freezing issue is effectively bypassed. Up to $T=2.0\,T_{\rm c}$ no unusually large lattice effects are observed and the results obtained in the continuum limit confirm the expected rapid decay of the susceptibility with increasing temperature. As a byproduct, the reference gradient-flow time $t_0$ is determined in the range of lattice spacings from $0.023$ to $0.1\,{\rm fm}$ with a precision of 2 per mille., Comment: 19 pages, 6 figures, plain TeX source

Using the complex φ4-model as a prototype for a system which is simulated by a worm algorithm, we show that not only the charged correlator 〈φ*(x)φ(y)〉, but also more general correlators such as 〈|φ(x)||φ(y)|〉 or 〈arg (φ(x))arg (φ(y))〉, as well as condensates like 〈|φ|〉, can be measured at every step of the Monte Carlo evolution of the worm instead of on closed-worm configurations only. The method generalizes straightforwardly to other systems simulated by worms, such as spin or sigma models., Nuclear Physics B, 909, ISSN:0550-3213, ISSN:1873-1562

The use of Heavy Quark Effective Theory (HQET) on the lattice as an approach to B-physics phenomenology is based on a non-perturbative matching of HQET to QCD in finite volume. As a first step to apply the underlying strategy in the three-flavor ($N_f = 2+1$) theory, we determine the renormalization constant and improvement coefficients relating the renormalized current and subtracted quark mass of (quenched) valence quarks in $\mathcal{O}(a)$ improved $N_f=3$ lattice QCD. We present our strategy and first results for the relevant parameter region towards weak couplings along a line of constant physics, which corresponds to lattice resolutions $a\leq 0.02\,$fm and fixes the physical extent of the matching volume to $L\approx 0.5\,$fm., 7 pages including 7 figures, latex2e; Proceedings of the 36th International Symposium on Lattice Field Theory (Lattice 2018), 22-28 July 2018, Michigan State University, East Lansing, Michigan, USA

PDFs can be studied directly using lattice QCD by evaluating matrix elements of non-local operators. A number of groups are pursuing numerical calculations and investigating possible systematic uncertainties. One systematic that has received less attention is the effect of calculating in a finite spacetime volume. Here we present first attempts to assess the role of the finite volume for spatially non-local operators. We find that these matrix elements may suffer from large finite-volume artifacts and more careful investigation is needed., 6 pages, 3 figures, Conference: The 36th Annual International Symposium on Lattice Field Theory - LATTICE2018, 22-28 July, 2018, Michigan State University, East Lansing, Michigan, USA

In this talk, we present a framework for studying structural information of resonances and bound states coupling to two-hadron scattering states. This makes use of a recently proposed finite-volume formalism to determine a class of observables that are experimentally inaccessible but can be accessed via lattice QCD. In particular, we shown that finite-volume two-body matrix elements with one current insertion can be directly related to scattering amplitudes coupling to the external current. For two-hadron systems with resonances or bound states, one can extract the corresponding form factors of these from the energy-dependence of the amplitudes., Comment: 7 pages, 2 figures, Proceedings of Lattice 2018

We present a preliminary lattice calculation of the leading-order electromagnetic and strong isospin-breaking corrections to the Hadronic Vacuum Polarization (HVP) contribution of the light quarks to the anomalous magnetic moment of the muon. The results are obtained in the quenched-$QED$ approximation using the $QCD$ gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ dynamical quarks, at three values of the lattice spacing varying from $0.089$ to $0.062 ~ \mbox{fm}$, at several lattice volumes and with pion masses in the range $M_\pi \simeq 220 \div 490 ~ \mbox{MeV}$., Comment: 7 pages, 1 figure. Talk given at the XXXVI Annual International Symposium on Lattice Field Theory (LATTICE18), East Lansing, Michigan (USA), 22-28 July 2018

We determine two improvement coefficients which are relevant to cancel mass-dependent cutoff effects in correlation functions with operator insertions of the non-singlet local QCD vector current. This determination is based on degenerate three-flavor QCD simulations of non-perturbatively O(a) improved Wilson fermions with tree-level improved gauge action. Employing a very robust strategy that has been pioneered in the quenched approximation leads to an accurate estimate of a counterterm cancelling dynamical quark cutoff effects linear in the trace of the quark mass matrix. To our knowledge this is the first time that such an effect has been determined systematically with large significance., 15 pages, 4 figures, 3 tables, published version (typo corrected)

Physical review / D 99(7), 074505 (2019). doi:10.1103/PhysRevD.99.074505, We present a lattice QCD spectroscopy study in the isospin singlet, strangeness $-2$ sectors relevant for the conjectured $H$ dibaryon. We employ both hexaquark and two-baryon interpolating operators to isolate the ground state in the rest frame and in moving frames. Calculations are performed using two flavors of O($a$)-improved Wilson fermions and a quenched strange quark. Our initial point-source method for constructing correlators does not allow for two-baryon operators at the source; nevertheless, results from using these operators at the sink indicate that they provide an improved overlap onto the ground state in comparison with the hexaquark operators. We also present results, in the rest frame, using a second method based on distillation to compute a hermitian matrix of correlators with two-baryon operators at both the source and the sink. This method yields a much more precise and reliable determination of the ground-state energy. In the flavor-SU(3) symmetric case, we apply Lüscher's finite-volume quantization condition to the rest-frame and moving-frame energy levels to determine the $S$-wave scattering phase shift, near and below the two-particle threshold. For a pion mass of 960 MeV, we find that there exists a bound $H$ dibaryon with binding energy ${\Delta}E=(19\pm10)$ MeV. In the 27-plet (dineutron) sector, the finite-volume analysis suggests that the existence of a bound state is unlikely., Published by Soc., [S.l.]

We present numerical results showing how our recently proposed relativistic three-particle quantization condition can be used in practice. Using the isotropic (generalized $s$-wave) approximation, and keeping only the leading terms in the effective range expansion, we show how the quantization condition can be solved numerically in a straightforward manner. In addition, we show how the integral equations that relate the intermediate three-particle infinite-volume scattering quantity, $\mathcal K_{\text{df},3}$, to the physical scattering amplitude can be solved at and below threshold. We test our methods by reproducing known analytic results for the $1/L$ expansion of the threshold state, the volume dependence of three-particle bound-state energies, and the Bethe-Salpeter wavefunctions for these bound states. We also find that certain values of $\mathcal K_{\text{df},3}$ lead to unphysical finite-volume energies, and give a preliminary analysis of these artifacts., 32 pages, 21 figures, JLAB-THY-18-2657, CERN-TH-2018-046; version 2: corrected typos, updated references, minor stylistic changes---consistent with published version

Anisotropic lattice spacings are mandatory to reach the high temperatures where chiral symmetry is restored in the strong-coupling limit of lattice QCD. Here, we propose a simple criterion for the nonperturbative renormalization of the anisotropy coupling in strongly coupled SU(Nc) or U(Nc) lattice QCD with massless staggered fermions. We then compute the renormalized anisotropy, and the strong-coupling analogue of Karsch’s coefficients (the running anisotropy), for Nc = 3. We achieve high precision by combining diagrammatic Monte Carlo and multihistogram reweighting techniques. We observe that the mean field prediction in the continuous time limit captures the nonperturbative scaling, but receives a large, previously neglected correction on the unit prefactor. Using our nonperturbative prescription in place of the mean field result, we observe large corrections of the same magnitude to the continuous time limit of the static baryon mass and of the location of the phase boundary associated with chiral symmetry restoration. In particular, the phase boundary, evaluated on different finite lattices, has a dramatically smaller dependence on the lattice time extent. We also estimate, as a byproduct, the pion decay constant and the chiral condensate of massless SU(3) QCD in the strong-coupling limit at zero temperature., Physical Review D, 97 (3), ISSN:1550-7998, ISSN:0556-2821, ISSN:1550-2368

We determine from first principles the quark mass anomalous dimension in Nf=3 QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and non-perturbative regimes of the Standard Model in the hadronic sector. The computation is carried out to high accuracy, employing massless O(a)-improved Wilson quarks and finite-size scaling techniques. We also provide the matching factors required in the renormalisation of light quark masses from lattice computations with O(a)-improved Wilson fermions and a tree-level Symanzik improved gauge action. The total uncertainty due to renormalisation and running in the determination of light quark masses in the SM is thus reduced to about 1%., 41 pages, 10 tables, 7 figures, published version (minimal text improvements)

We perform a non-perturbative study of the scale-dependent renormalisation factors of a complete set of dimension-six four-fermion operators. The renormalisation-group (RG) running is determined in the continuum limit for a specific Schr\"dinger Functional (SF) renormalisation scheme in the framework of lattice QCD with two dynamical flavours ( $N_f = 2$ ). The theory is regularised on a lattice with a plaquette Wilson action and $\mathcal{O}(a)$-improved Wilson fermions. For one of these operators, the computation had been performed in ref. [1]; the present work completes the study for the rest of the operator basis, on the same simulations (configuration ensembles). The related weak matrix elements arise in several operator product expansions; in $\Delta F = 2$ transitions they contain the QCD long-distance effects, including contributions from beyond-Standard Model (BSM) processes. Some of these operators mix under renormalisation and their RG-running is governed by anomalous dimension matrices. In ref. [2] the RG formalism for the operator basis has been worked out in full generality and the anomalous dimension matrix has been calculated in NLO perturbation theory. Here the discussion is extended to the matrix step-scaling functions (matrix-SSFs), which are used in finite-size recursive techniques. We rely on these matrix-SSFs to obtain non-perturbative estimates of the operator anomalous dimensions for scales ranging from $\mathcal{O}(\Lambda_{\rm QCD})$ to $\mathcal{O}(M_W)$., Comment: 45 pages, 17 figures

Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. To quote credible estimates of the systematic uncertainties in these calculations, one must understand, among other things, the size of the finite-volume effects when such matrix elements are extracted from numerical lattice calculations. In this work, we estimate finite-volume effects for matrix elements of non-local operators, composed of two currents displaced in a spatial direction by a distance $\xi$. We find that the finite-volume corrections depend on the details of the matrix element. If the external state is the lightest degree of freedom in the theory, e.g.~the pion in QCD, then the volume corrections scale as $ e^{-m_\pi (L- \xi)} $, where $m_\pi$ is the mass of the light state. For heavier external states the usual $e^{- m_\pi L}$ form is recovered, but with a polynomial prefactor of the form $L^m/|L - \xi|^n$ that can lead to enhanced volume effects. These observations are potentially relevant to a wide variety of observables being studied using lattice QCD, including parton distribution functions, double-beta-decay and Compton-scattering matrix elements, and long-range weak matrix elements., Comment: 15 pages, 4 figures

We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility Xt is measured directly, and by the slab method, which is based on the topological content of sub-volumes (“slabs”) and estimates Xt even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, ξ2). This ongoing study is based on direct measurements of Xt in L × L lattices, at L/ξ ≃6., EPJ Web of Conferences, 175, ISSN:2100-014X, ISSN:2101-6275

In previous work, we have developed a relativistic, model-independent three-particle quantization condition, but only under the assumption that no poles are present in the two-particle K matrices that appear as scattering subprocesses. Here we lift this restriction, by deriving the quantization condition for identical scalar particles with a G-parity symmetry, in the case that the two-particle K matrix has a pole in the kinematic regime of interest. As in earlier work, our result involves intermediate infinite-volume quantities with no direct physical interpretation, and we show how these are related to the physical three-to-three scattering amplitude by integral equations. This work opens the door to study processes such as $a_2 \to \rho \pi \to \pi \pi \pi$, in which the $\rho$ is rigorously treated as a resonance state., Comment: 46 pages, 9 figures, JLAB-THY-18-2819, CERN-TH-2018-216

We continue our study of heavy-light four-quark states and find evidence from lattice QCD for the existence of a strong-interaction-stable $I(J^P)=0(1^+)$ $ud\bar{c}\bar{b}$ tetraquark with mass in the range of 15 to 61 MeV below $\bar{D}B^*$ threshold. Since this range includes the electromagnetic $\bar{D}B\gamma$ decay threshold, current uncertainties do not allow us to determine whether such a state would decay electromagnetically, or only weakly. We also perform a study at fixed pion mass, with NRQCD for the heavy quarks, simulating $qq^\prime \bar{b}^\prime \bar{b}$ and $q q^\prime \bar{b}^\prime\bar{b}^\prime$ tetraquarks with $q,\, q^\prime =ud$ or $\ell s$ and variable, unphysical $m_{b^\prime}$ in order to investigate the heavy mass-dependence of such tetraquark states. We find that the dependence of the binding energy follows a phenomenologically-expected form and that, though NRQCD breaks down before $m_{b^\prime}=m_c$ is reached, the results at higher $m_{b^\prime}$ clearly identify the $ud\bar{b}^\prime \bar{b}$ channel as the most likely to support a strong-interaction-stable tetraquark state at $m_{b^\prime}=m_c$. This observation serves to motivate the direct $ud\bar{c}\bar{b}$ simulation. Throughout we use dynamical $n_f=2+1$ ensembles with pion masses $m_\pi=$415, 299, and 164 MeV reaching down almost to the physical point, a relativistic heavy quark prescription for the charm quark, and NRQCD for the bottom quark(s)., Comment: 24 pages, 4 figures

We present exploratory results from dynamical simulations of QCD in isolation, as well as QCD coupled to QED, with C* boundary conditions. In finite volume, the use of C* boundary conditions allows for a gauge invariant and local formulation of QED without zero modes. In particular we show that the simulations reproduce known results and that masses of charged mesons can be extracted in a completely gauge invariant way. For the simulations we use a modified version of the HiRep code. The primary features of the simulation code are presented and we discuss some details regarding the implementation of C* boundary conditions and the simulated lattice action., 8 pages, 2 figures. Talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain

We show recent results from the Mainz group using $N_f = 2 + 1$ CLS ensembles generated at the $SU(3)$ symmetric point. Temporal correlation functions using two-baryon interpolating operators are calculated with the distillation method. In addition to the spin-0 operators relevant for studying the $H$ dibaryon, we added spin-1 operators to our basis, thereby extending our results to other flavor sectors. These preliminary results show a finite-volume energy below the $\Lambda \Lambda$ threshold. Further calculations are necessary to establish whether the $H$ dibaryon is bound at the physical point., Comment: 7 pages, 3 figures, 1 table, Proceedings for the 36th Annual International Symposium on Lattice Field Theory, 22-28 July 2018, Michigan State University, East Lansing, Michigan, USA

Journal of high energy physics 1806(06), 025 (2018). doi:10.1007/JHEP06(2018)025, We discuss the problem of lattice artefacts in QCD simulations enhanced by the introduction of dynamical charmed quarks. In particular, we advocate the use of a massive renormalization scheme with a close to realistic charm mass. To maintain O(a) improvement for Wilson type fermions in this case we define a finite size scheme and carry out a nonperturbative estimation of the clover coefficient $c_\mathrm{sw}$. It is summarized in a fit formula $c_\mathrm{sw}(g_0^2)$ that defines an improved action suitable for future dynamical charm simulations., Published by Springer Nature, Cham

Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schr\"odinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale $1/L_0\approx 4$ GeV through $\bar{g}^2(L_0) =2.012$, we quote $L_0 \Lambda^{N_{\rm f}=3}_{\overline{\rm MS}} =0.0791(21)$. This error is dominated by statistics; in particular, the remnant perturbative uncertainty is negligible and very well controlled, by connecting to infinite renormalization scale from different scales $2^n/L_0$ for $n=0,1,\ldots,5$. An intermediate step in this connection may involve any member of a one-parameter family of SF couplings. This provides an excellent opportunity for tests of perturbation theory some of which have been published in a letter [1]. The results indicate that for our target precision of 3 per cent in $L_0 \Lambda^{N_{\rm f}=3}_{\overline{\rm MS}}$, a reliable estimate of the truncation error requires non-perturbative data for a sufficiently large range of values of $\alpha_s=\bar{g}^2/(4\pi)$. In the present work we reach this precision by studying scales that vary by a factor $2^5= 32$, reaching down to $\alpha_s\approx 0.1$. We here provide the details of our analysis and an extended discussion., Comment: 40 pages, 11 figures

We describe recent work on the relativistic three-particle quantization condition, generalizing and applying the original formalism of Hansen and Sharpe, and of Brice\~no, Hansen and Sharpe. In particular, we sketch three recent developments: the generalization of the formalism to include K-matrix poles; the numerical implementation of the quantization condition in the isotropic approximation; and ongoing work extending the description of the three-particle divergence-free K matrix beyond the isotropic approximation., Comment: 7 pages, 1 figure, Proceedings of Lattice 2018

Journal of high energy physics 1812(12), 061 (2018). doi:10.1007/JHEP12(2018)061, We perform a systematic study of the correlation functions of two quark currents in a pion using lattice QCD. We obtain good signals for all but one of the relevant Wick contractions of quark fields. We investigate the quark mass dependence of our results and test the importance of correlations between the quark and the antiquark in the pion. Our lattice data are compared with predictions from chiral perturbation theory., Published by Springer Nature, Cham

In lattice QCD and other field theories with a mass gap, the field variables in distant regions of a physically large lattice are only weakly correlated. Accurate stochastic estimates of the expectation values of local observables may therefore be obtained from a single representative field. Such master-field simulations potentially allow very large lattices to be simulated, but require various conceptual and technical issues to be addressed. In this talk, an introduction to the subject is provided and some encouraging results of master-field simulations of the SU(3) gauge theory are reported., Comment: Talk given at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain; LaTeX source with 6 figures

Several important observables, like the quark condensate and the Taylor coefficients of the expansion of the QCD pressure with respect to the chemical potential, are based on the trace of the inverse Dirac operator and of its powers. Such traces are traditionally estimated with “noise vectors” sandwiching the operator. We explore alternative approaches based on polynomial approximations of the inverse Dirac operator., EPJ Web of Conferences, 175, ISSN:2100-014X, ISSN:2101-6275

We extend the phase diagram of SU(N) gauge-fermion theories as function of number of flavours and colours to the region in which asymptotic freedom is lost. We argue, using large $N_f$ results, for the existence of an ultraviolet interacting fixed point at sufficiently large number of flavours opening up to a second ultraviolet conformal window in the number of flavours vs colours phase diagram. We first review the state-of-the-art for the large $N_f$ beta function and then estimate the lower boundary of the ultraviolet window. The theories belonging to this new region are examples of safe non-abelian quantum electro dynamics, termed here {\it safe QCD}. Therefore, according to Wilson, they are fundamental. An important critical quantity is the fermion mass anomalous dimension at the ultraviolet fixed point that we determine at leading order in $1/N_f$. We discover that its value is comfortably below the bootstrap bound. We also investigate the abelian case and find that at the potential ultraviolet fixed point the related fermion mass anomalous dimension has a singular behaviour suggesting that a more careful investigation of its ultimate fate is needed., 5 pages, 2 figures, minor changes

We study the conformal to non-conformal transition in strongly-coupled theories using holography, trying to understand the presence of light scalars as recent lattice simulations seem to suggest. This can have important implications for solutions to the hierarchy problem via TeV strong-dynamics and their searches at the LHC.

The framework of shifted boundary conditions has proven to be a very powerful tool for the non-perturbative investigation of thermal quantum field theories. For instance, it has been successfully considered for the determination of the equation of state of SU(3) Yang-Mills theory with high accuracy. The set-up can be generalized to QCD and it is expected to lead to a similar breakthrough. We present first results for QCD with three flavours of non-perturbatively O($a$)-improved Wilson fermions and shifted boundary conditions., Comment: 8 pages, 1 figure; Proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest. This renaissance has been possible both due to significant analytical progress in understanding how to set up the bootstrap equations and the development of numerical techniques for finding or constraining their solutions. These developments have led to a number of groundbreaking results, including world record determinations of critical exponents and correlation function coefficients in the Ising and $O(N)$ models in three dimensions. This article will review these exciting developments for newcomers to the bootstrap, giving an introduction to conformal field theories and the theory of conformal blocks, describing numerical techniques for the bootstrap based on convex optimization, and summarizing in detail their applications to fixed points in three and four dimensions with no or minimal supersymmetry.

The LLR method is a novel algorithm that enables us to evaluate the density of states in lattice gauge theory. We present our study of the ergodicity properties of the LLR algorithm for the model of Yang Mills SU(3). We show that the use of the replica exchange method alleviates significantly the topological freeze-out that severely affects other algorithms., 8 pages, 10 figures, proceedings of Lattice2017, Granada, Spain

We present a consistent embedding of the matter and gauge content of the Standard Model into an underlying asymptotically-safe theory, that has a well-determined in- teracting UV fixed point in the large colour/flavour limit. The scales of symmetry breaking are determined by two mass-squared parameters with the breaking of elec- troweak symmetry being driven radiatively. There are no other free parameters in the theory apart from gauge couplings., Comment: 17 pages, 4 figures

Tensor currents are the only quark bilinear operators lacking a non-perturbative determination of their renormalisation group (RG) running between hadronic and electroweak scales. We develop the setup to carry out the computation in lattice QCD via standard recursive finite-size scaling techniques, and provide results for the RG running of tensor currents in $N_f = 0$ and $N_f = 2$ QCD in the continuum for various Schr\"odinger Functional schemes. The matching factors between bare and renormalisation group invariant currents are also determined for a range of values of the lattice spacing relevant for large-volume simulations, thus enabling a fully non-perturbative renormalization of physical amplitudes mediated by tensor currents., Comment: 50 pages, 14 Figures

We present a lattice determination of the $\Lambda$ parameter in three-flavor QCD and the strong coupling at the Z pole mass. Computing the nonperturbative running of the coupling in the range from $0.2\,$GeV to $70\,$GeV, and using experimental input values for the masses and decay constants of the pion and the kaon, we obtain $\Lambda_{\overline{\rm MS}}^{(3)}=341(12)\,$MeV. The nonperturbative running up to very high energies guarantees that systematic effects associated with perturbation theory are well under control. Using the four-loop prediction for $\Lambda_{\overline{\rm MS}}^{(5)}/\Lambda_{\overline{\rm MS}}^{(3)}$ yields $\alpha^{(5)}_{\overline{\rm MS}}(m_{\rm Z}) = 0.11852(84)$., Comment: Correction in the comparison to the LHC value for alpha(1.5TeV) which was given by CMS in the 5-flavor theory. The agreement is improved. Also 1 Reference added and a few typos corrected

The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schr\"odinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit., Comment: 35 pages, 4 figures; v2: corrected typos, coincides with published version

Anomalous magnetic moment of the muon, $a_{\mu}=(g_{\mu}-2)/2$, is one of the most precisely measured quantities in particle physics and it provides a stringent test of the Standard Model. The planned improvements of the experimental precision at Fermilab and at J-PARC propel further reduction of the theoretical uncertainty of $a_{\mu}$. The hope is that the efforts on both sides will help resolve the current discrepancy between the experimental measurement of $a_{\mu}$ and its theoretical prediction, and potentially gain insight into new physics. The dominant sources of the uncertainty in the theoretical prediction of $a_{\mu}$ are the errors of the hadronic contributions. I will discuss recent progress on determination of hadronic contributions to $a_{\mu}$ from lattice calculations., Comment: 8 pages, 1 table, 2 figures, invited talk presented at Light Cone 2016, September 5-8, 2016. Accepted for publication in Few-Body Systems (Light-Cone 2016, Topical Collection)

Numerical stochastic perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice field theory. The standard algorithms based on the Langevin equation, however, suffer from several limitations which in practice restrict the potential of this technique. In this work we investigate some alternative methods which could in principle improve on the standard approach. In particular, we present a study of the recently proposed Instantaneous Stochastic Perturbation Theory, as well as a formulation of numerical stochastic perturbation theory based on Generalized Hybrid Molecular Dynamics algorithms. The viability of these methods is investigated in $\varphi^4$ theory., Comment: 45 pages, 12 figures. Added new section on cost comparison with Langevin NSPT. Matches published version

In recent years, exotic hadrons called X, Y, Z which cannot be explained by the quark model have been found one after another. The tetra-quark state, which is one of the typical scenarios to interpret the exotic state, is based on the existence of a diquark state. The discovery of a pentaquark state at CERN in 2015 also makes a diquark state even more important. Therefore, it is considered that a diquark state plays an important role in many kinds of QCD physics. We discuss existence of such diquarks from the viewpoint of a first principle calculation.