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Mesons and Baryons in Basis Light Front Quantization Mesons and Baryons in Basis Light Front Quan4za4on James P. Vary Department of Physics and Astronomy Iowa State University Ames, USA LC2018 JLAB, Newport News, Virginia May 14-18, 2018 Dirac’s forms of relativistic dynamics [Dirac, Rev. Mod. Phys. 21, 392 1949] Dirac’s Instant Forms form is the of well-known Relativistic form of dynamics Dynamics starting with x0 [Dirac,= t = 0 Rev.Mod.Phys. ’49] FrontK i = M form0i , J definesi = 1 ε i QCDjk M jk , onε ijk = the (+1,- light1,0) frontfor (cyc (LF)lic, antx+i-cycltic+, rezpe=0ated). indeces 2 , Front form defines relativistic dynamics on the light front (LF): x+ = x0+x3 = t+z = 0 0 3 ~ 1 2 0 3 1 2 i +i P ± , P P , P ? , (P ,P ), x± , x x , ~x ? , (x ,x ), E = M , + +± i i i 0i i ±1 ijk jk E = M −, F = M − , K = M , J = 2 ✏ M . instant form front form point form time variable t = x0 x+ x0 + x3 ⌧ pt2 ~x 2 a2 , , − − quantization surface 0 0 3 µ Hamiltonian H = P P − P P P , − ~ ~ ~ + ~ + − ~ ~ kinematical P,J P ?,P , E?,E ,J Jz J,K 0 0 dynamical K,P~ F~ ?,P− P,P~ dispersion 0 2 2 + µ µ 2 p = p~ 2 + m2 p− =(p~ + m )/p p = mv (v =1) relation ? Yang Li, Iowa Statep U, May 20, 2016 2/1 Baryons 2016, Tallahassee,Adapted FL from talk by Yang Li Light Front (LF) Hamiltonian Defined by its Elementary Vertices in LF Gauge QED & QCD QCD Light-Front Wavefunctions (LFWFs) ~ + h(P, j, λ) = [dµn] n/h( ki ,xi,λi n) p~ i ,pi ,λi n | i { ? } |{ ? } i n Z LFWFs are frame-independentX (boost invariant) and depend only on the + + relative variables: xi p /P ,~ki p~ i xiP~ ⌘ i ? ⌘ ? − ? LFWFs provides intrinsic information of the structure of hadrons, and are indispensable for exclusive processes in DIS [Lepage ’80] I Overlap of LFWFs: structure functions (e.g. PDFs), form factors, ... I Integrating out LFWFs: light-cone distributions (e.g. DAs) “Hadron Physics without LFWFs is like Biology without DNA!” —StanleyJ.Brodsky GTMDs d2b d2k ~k ~r , ∆~ ~b , Z dx Z ? Z ? ? $ ? ? $ ? ~b = ~r R~ TMFFs ? ? − ? TMDs GPDs [Lorc´e& Pasquini ’11] TMSDs FFs PDFs charges hadron tomography 9/55 Discretized Light Cone Quantization [H.C. Pauli & S.J. Brodsky, PRD32 (1985)] Basis Light Front Quantization [J.P. Vary, et al., PRC81 (2010)] ! ! ! k , x ⎡ f k , x a f * k , x a† ⎤ φ( ⊥ )= ∑ ⎢ α ( ⊥ ) α + α ( ⊥ ) α ⎥ α ⎣ ⎦ where {aα } satisfy usual (anti-) commutation rules. ! Furthermore, fα (x) are arbitrary except for conditions: ! ! 2 * d k⊥dx Orthonormal: fα (k⊥, x) fα ' (k⊥, x) 3 = δαα ' ∫ (2π ) 2x(1− x) ! ! ! ! f k , x f * k′ , x′ 16 3 x(1 x) 2 k k′ x x′ Complete: ∑ α ( ⊥ ) α ( ⊥ )= π − δ ( ⊥ − ⊥)δ ( − ) α For mesons we adopt (later extended to baryons): [Y. Li, et al., PLB758 (2016)] ! ! fα={nml} (k⊥, x)= φnm (k⊥ x(1− x))χl (x) φnm 2D-HO functions a b χl Jacobi polynomials times x (1− x) Set of Transverse 2D HO Modes for n=4 m=0 m=1 m=2 m=3 m=4 J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath, G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, PRC 81, 035205 (2010) Normalized longitudinal basis functions Jacobi polynomials Applications of the BLFQ to Mesons and Baryons at LC2018 Guangyao Chen, Yang Li, Pieter Maris, Kirill Tuchin and James P. Vary, “Diffractive charmonium spectrum in high energy collisions in the basis light-front quantization approach,” Phys. Letts. B 769, 477 (2017); arXiv: 1610.04945. [Talk on Thursday morning] Sofia Leitao, Yang Li, Pieter Maris, M.T. Pena, Alfred Stadler, James P. Vary and Elmar P. Biernat, “Comparison of two Minkowski-space approaches to heavy quarkonia”, Eur. Phys. J. C 77, 696 (2017); arXiv: 1705:06178 [Talk on Friday] Meijian Li, Yang Li, Pieter Maris and James P. Vary, “Radiative transitions between 0-+ and 1-- heavy quarkonia on the light front,” arXiv:1803.11519 [Talk on Thursday in session 3B] Shaoyang Jia, et al., “Basis Light-Front Quantization for the Light Mesons,” in preparation [Talk on Thursday in session 3B] Chandan Mondal, et al., “Baryons in a BLFQ approach,” in preparation [Talk on Thursday in session 3B] BLFQ Symmetries & Constraints All J ≥ Jz states Baryon number b B ∑ i = i in one calculation Charge q Q ∑ i = i Angular momentum projection (M-scheme) (m s ) J ∑ i + i = z i k Finite basis Longitudinal momentum (Bjorken sum rule) x i 1 ∑ i = ∑ = i i K regulators Transverse mode regulator (2D HO) (2n m 1) N ∑ i+ i + ≤ max i Longitudinal mode regulator (Jacobi) l L ∑ i ≤ i Global Color Singlets (QCD) Light Front Gauge Optional Fock-Space Truncation Preserve transverse H → H +λHCM boost invariance Light-Front Regularization and Renormalization Schemes 1. Regulators in BLFQ (Nmax, L) 2. Additional Fock space truncations (if any) 3. Counterterms identified/tested* 4. Sector-dependent renormalization** 5. RGPEP (Glazek, Gomez-Rocha, and others, e.g. arXiv:1805.03436) 6. SRG & OLS in NCSM*** - adapted to BLFQ (future) *D. Chakrabarti, A. Harindranath and J.P. Vary, Phys. Rev. D 69, 034502 (2004) *P. Wiecki, Y. Li, X. Zhao, P. Maris and J.P. Vary, Phys. Rev. D 91, 105009 (2015) **V. A. Karmanov, J.-F. Mathiot, and A. V. Smirnov, Phys. Rev. D 77, 085028 (2008); Phys. Rev. D 86, 085006 (2012) **Y. Li, V.A. Karmanov, P. Maris and J.P. Vary, Phys. Letts. B. 748, 278 (2015); arXiv: 1504.05233 **X. Zhao, invited talk at noon on Thursday at LC2018 ***B.R. Barrett, P. Navratil and J.P. Vary, Prog. Part. Nucl. Phys. 69, 131 (2013) _ Effective Hamiltonian in the qq sector Adopt a running coupling with regulated IR behavior: improves UV properties of BLFQ applications 1. s(0), IR LO pQCD Nf =4 0.4, 1.03GeV 0.8 0.6, 0.55GeV For meson 0.8, 0.40GeV results here 2 s (M ) (Q2)= Z s 2 2 0.6 2 Q +IR 1 + s (MZ) 0 ln 2 2 MZ+IR ) Q ( s 0.4 0.2 0. 0.01 0.1 1. 10. 100. 1000. Q [GeV] _ Q = average 4-momentum transfer between q and q Y. Li, P. Maris and J.P. Vary, PRD96, 016022 (2017) Spectroscopy [YL,[Li, Maris & Vary, PRD ’17; TanG, Li, Maris & Vary, in preparaon] Maris & Vary, PRD ’17; Tang, YL, Maris, & Vary in preparation] Heavy mesons: rms deviaons 31 – 38 MeV 7.6 7.6 7.47.4 fitting parameters: 7.27.2 mc,mb,qQ = c MqQ ) BD threshold [cf. Dosch ’17] (HQET, ) 7.0 7.0 p ( ) ( ) 6.8( 6.8 rms deviation: 31–38 MeV 6.6 6.6 6.4 BLFQ 6.4 () () BLFQ 6.2 PDG 6.2 PDG Lattice 6.0 6.0 0- 1- 0+ 1+ 2+ 2- 3- 3+ 4+ 0- 1- 0+ 1+ 2+ 2- 3- 3+ 4+ 18 D. Radiative transitions 1. Vector Pseudo-scalar (or Scalar Axial-vector) Radiave transiHons between 0According to Equation-+ (C93), and 1 we-- define heavy thequarkonia transition form factor of from a vector to a pseudo- scalar, γ, V(Q2), as V ! P Meijian Li, et al.; arXiv: 1803.11519 LC2018 talk on Thursday 3:00 pm2 µ 2V(Q ) µ ↵ β σ (P0) J (0) (P, m ) = ✏ P0 P e (P, m ) , (69) hP | |V j i m + m ↵ j P V 2 µ 2V(Q ) µ↵ (P0) J (0) (P, m ) = ✏ P0 P e (P, m ) , (70) hP | |V j i m + m ↵ β σ j P V µ µ µ 2 2 where the momentum transfer q = P0 P , Q q . momentum transfer: − ⌘ The transition form factor V(Q2) is Lorentz invariant, or in other words, frame independent. So Impulse approximaon : we first carry out the calculation without choosing any specific frame, while later we would switch to a frame that is convenient for the calculation of helicity matrix. For any transverse vector (kx, ky), we will write its complex form as kR = kx + iky and kL = kx iky. − 0, m j = 0 R R 2 8 i P0 P + 2V(Q ) > + + 0 , = > P P0 , m j = 1 (P ) J (0) (P m j) > P + − P+ (71) hP | |V i mP + mV > p2 0 > L L > i + + P0 P < P P0 , m = 1 > + + j >− p2 P0 − P − > > Light-front wavefuncons: Yang Li, Pieter Maris, James P. Vary. Phys. Rev. D 96, 016022 (2017:> ) R L L R im (P P0 P P0 ), m = 0 V − j 2 R R R L 2 R R R L 2 8 i m P + P P0 P0 m P0 + P P P0 2V(Q ) > P V , m = 1 (P0) J−(0) (P, m j) = > + + j hP | |V i mP + mV > p2 P0 − P > 2 L L R L 2 L L L R > i m P + P P0 P0 m P0 + P P P0 <> P + V , = > + + m j 1 > p2 − P0 P − > > (72) :> R R + P0 P imV P0 + + , m j = 0 − P0 − P R R 2 8 i P0 P R 2V(Q ) > R + P0 J P, m = > P P0 , m j = 1 ( ) (0) ( j) > + + hP | |V i mP + mV > p2 P0 − P > 2 2 L L > i + + mV mP R P P0 < P P0 ( ) + P0 ( ) , m = 1 > + 2 + 2 + + j > p2 (P ) − (P0 ) P − P0 − > > (73) :> Radiave transiHons between 0-+ and 1-- heavy quarkonia Meijian Li, et al.; arXiv: 1803.11519 LC2018 talk on Thursday 3:00 pm Decay width: BLFQ Predicons [PDG] C.Patrignani, et aL., CPC40,2016.
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