Parton Distribution in Pseudoscalar Mesons with a Light-Front constituent Quark Model

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1 Parton Distribution in Pseudoscalar Mesons with a Light-Front constituent Quark Model XVI International Conference on Hadron Spectroscopy September 13-18, Newport News, VA - TJLAB J. Pacheco B. C. de Melo a Laboratório de Física Téorica e Computacional-LFTC, UNICSUL (Brazil) Collaborators: Kazuo Tsushima and Isthiaq Ahmed (LFTC), Brazil) 17 de September, 2015 J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with a17 (Brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 1 / Tsush Mode 23

2 Outline 1 Light-Front: Motivations 2 Overview of the Light-Front 3 Electromagnetic Current: General 4 Distribuition Amplitudes 5 Conclusions J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with a17 (Brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 2 / Tsush Mode 23

3 Light-Front: Motivations Light-Front Motivations Ligh-Front is the Ideal Framework to Describe Hadronic Bound States Constituent Picture and Unanbiguous Partons Content of the Hadronic System Light-Front Wavefunctions: Representation of Composite Systems in QFT Invariant Under Boosts Light-Front Vacuum is Trivial After Integrate in k : Bethe-Salpeter Amplitude (Wave Function) LF Lorentz Invariant Hamiltonian: P 2 = P + P P 2 J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with a17 (Brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 3 / Tsush Mode 23

4 Overview of the Light-Front Light-Front Coordinates Four-Vector = x µ = (x 0,x 1,x 2,x 3 ) = (x +,x,x ) x + = t +z x + = x 0 +x 3 = Time x = t z x = x 0 x 3 = Position Metric Tensor and Scalar product x y = x µ y µ = x + y + +x y +x 1 y 1 +x 2 y 2 = x+ y +x y + 2 x y p + = p 0 +p 3, p = p 0 p 3, p = (p 1,p 2 ) J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with a17 (Brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 4 / Tsush Mode 23

5 Electromagnetic Current: General Dirac Matrix and Electromagnetic Current γ + = γ 0 +γ 3 = Electr. Current J + = J 0 +J 3 γ = γ 0 γ 3 = Electr. Current J = J 0 J 3 γ = (γ 1,γ 2 ) = Electr. Current J = (J 1,J 2 ) p µ x µ = p+ x +p x + 2 p x x +,x, x = p +,p, p J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with a17 (Brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 5 / Tsush Mode 23

6 Electromagnetic Current: General p = Light-Front Energy p 2 = p + p ( p ) 2 = p = ( p ) 2 +m 2 p + On-shell Bosons = S F (p) = 1 p 2 m 2 +ıǫ Fermions = S F (p) = /p+m p 2 m 2 +ıǫ + γ+ 2p + Review Papers: Phys. Rept. 301, (1998) , Brodsky, Pauli and Pinsky A. Harindranath, Pramana, Journal of Indian Academy of Sciences Physics Vol.55, Nos 1 & 2, (2000) 241. An Introduction to Light-Front Dynamics for Pedestrians Avaroth Harindranath Light-Front book organizers: James Vary and Frank Wolz,(1997) J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with a17 (Brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 6 / Tsush Mode 23

7 Electromagnetic Current: General k µ P µ γ +, γ k µ P µ P µ γ5 γ5 k µ P µ J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with a17 (Brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 7 / Tsush Mode 23

8 Electromagnetic Current: General Frame q + = q = q 2 sinα q x = q 2 cosα, q y = 0 q 2 = q + q (q ) 2. Breit Frame (α = 0) = q + 0,q = 0 ; q 0 J + π = J 0 +J 3 = No Pair Term Contribuition J π = J0 J 3 = Pair Term Contribuition J.P.B.C. de Melo, T. Frederico and H.L. Naus, Phy.Rev. C59 (1999) 2278 J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with a17 (Brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 8 / Tsush Mode 23

9 Electromagnetic Current: General Effective Lagrangian to Vertex (π,k) q q ˆm L I = ı π qγ 5 τq f (π,k) Electromagnetic Current: J + PS J µ PS = ı2e ˆm2 d 4 k fπ 2 N c (2π) 4Tr[S(k)γ5 S(k P )γ µ S(k P)γ 5 Λ(k,P )Λ(k,P)] S(p) = 1 /p m+ıǫ J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with a17 (Brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 9 / Tsush Mode 23

10 Electromagnetic Current: General Vertex Function Symmetric Vertex Function Λ(k,P) = N (k 2 mr 2 +ıǫ) + N ((P k) 2 mr 2 +ıǫ) J.P.B.C. de Melo, T. Frederico, E. Pace, G. Salme Nucl. Phys. A 707 (2002) J.P.B.C. de Melo, T. Frederico, E. Pace, G. Salme Braz.J.Phys. 33 (2003) G.H.S. Yabusaki, I. Ahmed, M. Paracha, J.P.B.C. de Melo, B.El-Bennich, Phys.Rev. D92 (2015) 3, J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 10 / Tsush Mode 23

11 Electromagnetic Current: General Wave Function, Pion // Kaon Ψ(x,k,p +, p ) + [ 1 (1 x)(m0 2 M 2 (m 2 q,m2 R ] )) 1 1 x(m0 2 M 2 (m 2 R,m2 q )) m0 2 M 2 (mq,m 2 2 q ), + [q q] here: M 2 (m 2 a,m 2 b ) = k2 +m2 a x + (p k)2 +m2 b (1 x) p 2 J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 11 / Tsush Mode 23

12 Electromagnetic Current: General Motivation: The present model work well (Symmetric Vertex)! Observables: Decay constant and charge radius f 0 (MeV) r 0 m u (π + ) m d (π + ) m d (k + ) m s (k + ) Pion Kaon m R = 600 MeV, (all masses in MeV and radius in fm ) Ex.(Pion): f π = 92.4±0.021 MeV, r π = 0.672±0.08 fm (PDG) Ex.(Kaon): f k + = ± MeV, r k + = 0.560±0.031 (PDG) Ref.: J. P. B. C. de Melo, T. Frederico, E. Pace and G. Salmè, Nucl. Phys. A707, 399 (2002); Braz. J. Phys. 33, 301 (2003). George H. S. Yabusaki, Ishtiaq Ahmed, M. Ali Paracha, J. P. B. C. de Melo and Bruno El-Bennich Phys.Rev. D92 (2015) 3, J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 12 / Tsush Mode 23

13 Electromagnetic Current: General 1 F π (q 2 ) m R = 0.1 GeV m R = 0.3 GeV m R = 0.6 GeV m R = 0.8 GeV m R = 1 GeV Q 2 =-q 2 [GeV/c] 2 m q = GeV J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 13 / Tsush Mode 23

14 Electromagnetic Current: General F K +(q 2 ) Amendolia (Exp.) Dally (Exp.) m R = 0.4 GeV m R = 0.5 GeV m R = 0.6 GeV m R = 0.8 GeV m R = 1 GeV Q 2 = -q 2 [(GeV/c) 2 ] m q = GeV, m s = GeV J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 14 / Tsush Mode 23

15 Distribuition Amplitudes Hard Exclusive Pion Production CLEO (1998) Belle (2012) Babar (2009) Pion Form Factor λ=10 Perturbative Γ= 0.3 znpi0=15 QCDGauss=80 m q =0.384 GeV npion=10 Gaussian m q =0.220 GeV Gaussian: m q =0.330 GeV Hydrogen m q =0.220 GeV Hydrogen: m q =0.330 GeV AdS/QCD Free Current (Brodsky et al.) Q 2 F πγγ (q 2 ) Q 2 [GeV/c] 2 = Sensitive to Pion Quark Valence Distribution: Pion DA El-Bennich, de Melo, Frederico, Few Body Syst. 54 (2013) ibid. de Melo, El-Bennich, Frederico, Few Body Syst. 55 (2014) J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 15 / Tsush Mode 23

16 Distribuition Amplitudes Preliminary Results Def.: DA s Normalization: φ ps (x) = 2 6 f ps d 2 k (16π 3 ) Ψ ps(x, k ). 1 0 dx Pion Asymptotic Wave Function d 2 k 16π 3Ψ(x, k ) = f ps 2 6 φ as π (x,µ2 ) 6x(1 x) J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 16 / Tsush Mode 23

17 Distribuition Amplitudes Pion Asymptotic Kaon ( quark u on-shell) Kaon (quark s on-shell) φ Κ,π (x) x J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 17 / Tsush Mode 23

18 Distribuition Amplitudes Pion Kaon ( quark u on-shell) Kaon (quark s on-shell) 0.8 xφ π,κ (x) x J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 18 / Tsush Mode 23

19 Distribuition Amplitudes 1.4 quark u on-shell quark s on-shell 1.2 φ Κ (x)/φ π (x) x J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 19 / Tsush Mode 23

20 Distribuition Amplitudes Pion ( this work) Kaon (quark s on-shell) (this work) Kaon ( quark u on-shell) (this work) Pion (No-local quark model) Kaon (quark s on-shell) (No-local quark model) Kaon (quark u on-shell) ( No-local quark model) xφ π,κ (x) x Ref.: S. Nam, C. W. Kao, Phy. Rev. D85 (2012) ibid. Phy. Rev. D86 (2012) J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 20 / Tsush Mode 23

21 Distribuition Amplitudes Next φ(x) φ(x,q 2 ) Gegenbauer expansion Here: C F = N2 c 1 2N c φ(x,q 2 ) = x(1 x) γ n = C F β n=0,even 2 a n C 3/2 n (2x 1)ln ( Q 2 Λ 2 ( ) n k 2 (n+1)(n +2) and β = 11Nc 2N f 3 ( ) ln Q 2 γn 2n+3 a n Λ 2 = 4 (n+1)(n +2) 1 If Q 2 = Asymptotic behavior of the DA 0 ) γn dxc 3/2 n (2x 1)φ(x,Q) J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 21 / Tsush Mode 23

22 Conclusions Conclusions Electromagnetic Current: { Present Work : J + Future Works : J and J = Correlation q q - PS = Pion and Kaon with J and J = Rho Meson = Nucleon Parton Distribuition = DAs and PDFs in the medium J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 22 / Tsush Mode 23

23 Conclusions. Thanks to the Organizers XVI International Conference on Hadron Spectroscopy - TJLAB Support LFTC and Brazilian Agencies FAPESP, CNPq and CAPES Thanks (Obrigado)!! J. Pacheco B. C. de Melo ( a Laboratório departon Física Téorica Distribution e Computacional-LFTC, in Pseudoscalar Mesons UNICSUL with17 a(brazil) Light-Front de September, Collaborators: constituent 2015 Kazuo Quark 23 / Tsush Mode 23

arxiv: v1 [hep-ph] 13 May 2016

arxiv: v1 [hep-ph] 13 May 2016 The pion electromagnetic structure with self-energy arxiv:605.04342v [hep-ph] 3 May 206 Clayton Santos Mello a, J. P. B. C. de Melo b and T. Frederico a a Instituto Tecnológico de Aeronáutica, DCTA, 2.228-900