Review on Hadron Spectroscopy and Spectroscopy and Resonances - PowerPoint PPT Presentation

Review on Hadron Review on Hadron Spectroscopy and Spectroscopy and Resonances Resonances Chuan Liu Introduction Chuan Liu The conventional spectrum Institute of Theoretical Physics and Center for High Energy Physics Single School of Physics, Peking University, Beijing 100871, China channel scattering Summary and outlooks . . . . . .

Disclaimer Review on Hadron Spectroscopy and Resonances Chuan Liu I would like to thank... Introduction LOC for the kind invitation The my collaborators at CLQCD: conventional spectrum Y. Chen, M. Gong, N. Li, Z. Liu, J.P. Ma, Y.B. Liu, Single J.B. Zhang channel scattering people who sent me information/plots: S. Aoki, G. Bali, S. D¨ urr, D. Leinweber, K.-F. Liu, Summary and outlooks G. Schierholz, C. Urbach, etc. . . . . . .

Things to be covered Review on Hadron Spectroscopy and Resonances A good way to start preparing a plenary talk Chuan Liu looking at previous plenary talks Introduction However, there was no plenary talks on spectrum last year The that means that I should cover two years... conventional spectrum � There is no way to cover so much in 45 min. Single the conventional spectrum computations √ channel scattering single-channel meson-meson scattering √ Summary and outlooks multi-channel scattering......see Wilson’s talk! baryon-baryon scattering......see Savage’s talk ...... . . . . . .

Outline Review on Methodologies Hadron Spectroscopy The conventional one (the GEVP) and Resonances The not so conventional ones Chuan Liu L¨ uscher formalism Not of L¨ uscher: HEFT, HALQCD, etc. Introduction The The Conventional spectrum conventional spectrum QCD+QED computations Single Simulations near the physical point channel scattering Excited neucleon states Summary and Single-channel scattering outlooks pion-pion scattering charmed meson scattering others... Summary and outlooks Where we stand and what to expect next . . . . . .

1 . METHODS Review on Hadron Spectroscopy and Resonances Chuan Liu Introduction The conventional spectrum Single channel scattering Summary and outlooks . . . . . .

The first step: GEVP in a typical lattice spectrum calculation Review on A set of interpolating operators with the “right” quantum Hadron Spectroscopy numbers: {O α : α = 1 , 2 , · · · , N op } and Resonances Compute the correlation matrix: Chuan Liu C αβ ( t , 0) = ⟨O α ( t ) O † β (0) ⟩ , (1) Introduction The Solve the so-called Generalized Eigen-Value Problem conventional spectrum (GEVP) for the eigenvalues λ α ’s, Single channel C ( t , 0) · v α = λ α ( t , t 0 ) C ( t 0 , 0) · v α , (2) scattering Summary and for some appropriately chosen t 0 outlooks From the eigenvalues λ α ( t , t 0 ), extract the corresponding eigenvalues of the Hamiltonian: E α via λ α ( t , t 0 ) ∼ e − E α ( t − t 0 ) . (3) Pass the E α ’s to the second step . . . . . .

Complications Review on Hadron Spectroscopy and Resonances Chuan Liu 1 E α ’s are NOT hadron mass values! Introduction E α is the eigenvalue of the QCD Hamiltonian The (in a latticized finite box!) conventional spectrum Most hadrons are resonances Single channel 2 Many types of operators enter (operator mixing)! scattering single hadron operators Summary and outlooks multi-hadron operators (esp. beyond the threshold)... . . . . . .

The second step Relate the E α ’s to the spectral quantity Review on Hadron Spectroscopy and 0 E α ’s are ”approximate” hadron masses Resonances Chuan Liu only if the hadron is stable or the resonance is ”narrow” enough Introduction 1 Using a version of the L¨ uscher formalism The conventional single channel version has matured over the years spectrum multi-channel applications, see Dr. Wilson’s talk Single channel more channels,rather complicated scattering Summary and 2 Using other approaches outlooks the effective Hamiltonian approach the HALQCD approach the optical potential approach . . . . . .

L¨ uscher’s approach in theory (e.g. M. L¨ uscher, NPB354, 531, 1991 ) Review on Hadron original: single-channel spinless two-particle elastic Spectroscopy and scattering in COM frame, Resonances Chuan Liu E α ( L ) ⇔ δ ( E α ) . (4) Introduction The conventional π 3 / 2 q  spectrum tan δ (¯ k ) = Z 00 (1 , q 2 ) ,   Single (5) channel scattering √ ¯  k 2 + m 2 = E ( L ) , q = kL / (2 π ) . 2  Summary and outlooks extensions over the years to particles with spin to multi-channels different BC’s, different frames, ... . . . . . .

L¨ uscher’s approach in practice Review on Hadron Spectroscopy and Resonances Chuan Liu Introduction The conventional spectrum Single scalar λϕ 4 theory F. Zimmermann et al, hep-lat/9211029; NPB425, 413, 1994 channel scattering pion-pion scattering Summary and outlooks quenched 1992; Gupta et al, PRD48, 388, 1993 unquenched since 2005 or so has matured in recent years � complicated for multi-channels . . . . . .

Other approaches: the HEFT approach see e.g. J.M.M. Hall et al, PRD87;094510,2013; arXiv:1303.4157 Review on Hadron Spectroscopy and Resonances Chuan Liu Introduction The conventional spectrum Single channel scattering Summary and Needs to construct the appropriate hamiltonian outlooks model parameters are determined by fitting low-energy data, e.g. for N ∗ (1535) study, Z.-W. Liu et al, PRL116, 082004, 2016; 1512.00140 effective Hamiltonian in a finite volume . . . . . .

comparison of the levels Review on Hadron Spectroscopy and Resonances Chuan Liu Introduction The conventional spectrum Single channel scattering Summary and outlooks The finite volume levels from Z.-W. Liu et al, PRL116, 082004, 2016; 1512.00140 . . . . . .

Other approaches: the HALQCD method see e.t. N. Ishii et al, PRL99, 022001,2007; PLB712,437,2012. Review on Hadron Spectroscopy and starts from the so-called NBS wavefunction (a four-point Resonances function) Chuan Liu F N Ω ( x − y , t − t 0 ) = ⟨ 0 | N α ( x , t )Ω β, l ( y , t )¯ Introduction J N Ω ( t 0 ) | 0 ⟩ (6) The conventional the potential is obtained via the time-dependent HALQCD spectrum Single approach, channel scattering V C ( r ) ≃ 1 2 µ ∇ 2 R ( r , t ) / R ( r , t ) − ∂ Summary and ∂ t ln R ( r , t ) , (7) outlooks with R ( r , t ) = F N Ω ( t , t ) / e − ( m N + m Ω ) t . � no need for GEVP . . . . . .

Other approaches: the optical potential see e.g. D. Agadjanov et al, arXiv: 1603.07205 Review on Hadron Spectroscopy and Resonances Chuan Liu measure the optical potential directly Introduction analytically continue W ( E ) to W ( E + i ε ) The taking L → ∞ , then ε → 0 conventional done by smoothing spectrum Single can handle multi-channels, or more than 2 particles channel scattering relatively new, needs further study Summary and outlooks In particular, what is the relation with HALQCD approach? . . . . . .

My list again Review on Hadron Spectroscopy and Resonances Chuan Liu QCD+QED computations: BMW, QCDSF+UKQCD Introduction The simulation at the physical point by ETMC conventional spectrum excited nucleon spectrum: CSSM and χ QCD Single channel pion-pion scattering: ETMC & other groups scattering charmed meson scattering: XYZ particles Summary and outlooks . . . . . .

2 . 1 THE NORMAL Review on Hadron Spectroscopy and Resonances Chuan Liu Introduction The conventional spectrum Single channel scattering Summary and outlooks . . . . . .

proton & neutron Review on Hadron Spectroscopy and Resonances Chuan Liu Introduction The conventional spectrum & Single channel scattering Summary and outlooks . . . . . .

QCD+QED by BMW Review on Hadron Spectroscopy and Resonances Chuan Liu Introduction QCD+QED The conventional spectrum by Single channel scattering BMW Summary and outlooks . . . . . .

QCD+QED by BMW: The formalism N f = 1 + 1 + 1 + 1 simulations, non-compact QED BMW, Science 347:1452,2015; 1406.4088 Review on Hadron Use non-compact QED description Spectroscopy and Resonances Fix to Coulomb gauge (Feynman − > Coulomb) Chuan Liu treating the zero-mode of A µ ( x ) field in QED L prescription Introduction The Dirac operator, The conventional (4 + m ) δ x , y − 1 spectrum ( F ( U ) µν, x + eqF ( A ) ∑ ( D ) x , y = µν, x ) σ µν δ x , y Single 2 channel ν>µ scattering 1 [ ∑ (1 + γ µ ) e ieqA µ, x U µ, x δ x +ˆ Summary and − µ, y outlooks 2 µ ] (1 − γ µ ) e − ieqA µ, x − µ U † + µ, x − µ δ x − ˆ (8) µ, y � Main focus: octec baryons . . . . . .

QCD+QED by BMW N f = 1 + 1 + 1 + 1 simulations, non-compact QED BMW, Science 347:1452,2015; 1406.4088 Review on Hadron Spectroscopy lowest pion mass and Resonances 195MeV, largest Chuan Liu volume extent 8fm Introduction finite volume The corrections due to conventional spectrum QED in Coulomb Single gauge channel scattering treating zero-mode Summary and in QED L prescription outlooks Using ∆ M Σ to separate QED and QCD corrections Akaike’s information criterion (AIC) used . . . . . . to extract masses