Light Meson Structure from Basis Lightfront Quantization Outline
Light Meson Structure from Basis Light-front Quantization
Outline • Basis Light-front Quantization approach • Application to Light Mesons – Leading Fock sector (based on NJL interacton) – With one dynamical gluon • Summary and Future Plan 2
![Light-front Quantization [Dirac, 1949] Equal time quantization Light-front quantization Prof. Zhao’s talk QCD and](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-3.jpg "Light-front Quantization [Dirac, 1949] Equal time quantization Light-front quantization Prof. Zhao’s talk QCD and")
Light-front Quantization [Dirac, 1949] Equal time quantization Light-front quantization Prof. Zhao’s talk QCD and hadron structure-A 8 12: 35 -12: 55
![Basis Light-front Quantization [Vary et al, 2008] Prof. Zhao’s talk QCD and hadron structure-A](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-4.jpg "Basis Light-front Quantization [Vary et al, 2008] Prof. Zhao’s talk QCD and hadron structure-A")
Basis Light-front Quantization [Vary et al, 2008] Prof. Zhao’s talk QCD and hadron structure-A 8 12: 35 -12: 55 4
PDF from BLFQ and QCD Evolution for Light Mesons PDF for the valence quark result from the light-front wave functions obtain by diagonalizing the effective Hamiltonian. Pion PDF [Lan, Mondal, Jia, Zhao, Vary, PRL 122, 172001(2019)] Valence u PDF Kaon/Pion Agree with experimental results 5
The Moments of Pion Valence Quark PDF Valence Gluon Sea BLFQ-NJL 0. 489 0. 398 0. 113 [Ding et. al. , BSE model 2019’] 0. 48(3) 0. 41(2) 0. 11(2) [Lan, Mondal, Jia, Zhao, Vary, PRD 101, 034024(2020)] Agree with other results
![Drell-Yan Cross Section [S. D. Drell and T. -M. Yan, PRL (1970)] [T. Becher](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-7.jpg "Drell-Yan Cross Section [S. D. Drell and T. -M. Yan, PRL (1970)] [T. Becher")
Drell-Yan Cross Section [S. D. Drell and T. -M. Yan, PRL (1970)] [T. Becher et al, JKEP 07(2008)030]; [P. C. Barry et al, PRL 121(2018)152001] [C. Anastasiou et al, PRL 91(2003)182002] [n. CTEQ 2015] W W C W Pt Agree with experimental data (FNAL E 615, 326, 444, & CERN NA 3, WA-039). [Lan, Mondal, Jia, Zhao, Vary, PRD 101, 034024(2020)]
Interaction Part of Hamiltonian 0 9
Light-front QCD Hamiltonian 12
![Mass Spectrum DC[Me. V] Fix the parameters by fitting six blue states [Lan, Fu,](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-11.jpg "Mass Spectrum DC[Me. V] Fix the parameters by fitting six blue states [Lan, Fu,")
Mass Spectrum DC[Me. V] Fix the parameters by fitting six blue states [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954] 0. 492 138 0. 486 129 0. 370 0 0. 324 11 0. 284 53 0. 320 0 0. 002 0 0. 312 46
![Mass Spectrum DC[Me. V] Fischer 14’ [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106.](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-12.jpg "Mass Spectrum DC[Me. V] Fischer 14’ [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106.")
Mass Spectrum DC[Me. V] Fischer 14’ [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954] 0. 492 138 0. 486 129 0. 370 0 0. 306 0 0. 324 11 0. 284 53 0. 320 0 0. 002 0 0. 312 46
Pion Mass, DC, Radii BLFQ 139. 57 PDG 139. 57 775. 26 138. 2 [Tanabashi, et al, PRD(2018)] BLFQ-NJL 139. 57 [Jia, Vary, PRC(2018)] BLFQ [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954] 129. 0 0. 516~1. 456 0. 492
![Pion Electromagnetic Form Factor [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954]](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-14.jpg "Pion Electromagnetic Form Factor [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954]")
Pion Electromagnetic Form Factor [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954]
Pion PDA Ads/QCD p. QCD • Endpoint behavior agrees with p. QCD [Jia and Vary, PRC 99, 035206 (2019] 17
![Pion initial PDF [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954]](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-16.jpg "Pion initial PDF [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954]")
Pion initial PDF [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954]
![Pion PDF [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954] Valence Gluon Sea](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-17.jpg "Pion PDF [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954] Valence Gluon Sea")
Pion PDF [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954] Valence Gluon Sea BLFQ 0. 483 0. 421 0. 096 BLFQ-NJL 0. 489 0. 398 0. 113 [BSE 2019’] 0. 48(3) 0. 41(2) 0. 11(2)
![[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-18.jpg "[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303")
[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303 (1988) 607]; [M. L. Mangano, et al, NPB 405 (1993) 507] [n. CTEQ 2015] (from Chang, et al PRD 20’ ) CEM Agree with experimental data (FNAL E 672, E 706). [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954]
![[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-19.jpg "[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303")
[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303 (1988) 607]; [M. L. Mangano, et al, NPB 405 (1993) 507] [n. CTEQ 2015] (from Chang, et al PRD 20’ ) CEM Agree with experimental data (FNAL E 705). [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954] 7%Li 6+93%Li 7
![[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-20.jpg "[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303")
[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303 (1988) 607]; [M. L. Mangano, et al, NPB 405 (1993) 507] [n. CTEQ 2015] (from Chang, et al PRD 20’ ) CEM Agree with experimental data (CERN NA 3). [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954]
![[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-21.jpg "[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303")
[Wen-Chen Chang, et al, PRD 102 (2020) 054024]; [P. Nason, et al, NPB 303 (1988) 607]; [M. L. Mangano, et al, NPB 405 (1993) 507] [n. CTEQ 2015] (from Chang, et al PRD 20’ ) CEM Agree with experimental data (CERN W 11). [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954]
![CEM [n. CTEQ 2015] [Chang, et al, PRD 102 (2020) 054024]; [Nason, et al,](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-22.jpg "CEM [n. CTEQ 2015] [Chang, et al, PRD 102 (2020) 054024]; [Nason, et al,")
CEM [n. CTEQ 2015] [Chang, et al, PRD 102 (2020) 054024]; [Nason, et al, NPB 303 (1988) 607]; [Mangano, et al, NPB 405 (1993) 507] Agree with experimental data (FNAL E 672, E 706, E 705, CERN NA 3, WA 11). [Lan, Fu, Mondal, Zhao, Vary, ar. Xiv 2106. 04954]
![Pion Structure Function [Lan, Mondal, Jia, Zhao, Vary, PRD 101, 034024(2020)] better than BLFQ-NJL](http://slidetodoc.com/presentation_image_h2/5253b1e5211823091b1c7e4b0b74c02b/image-23.jpg "Pion Structure Function [Lan, Mondal, Jia, Zhao, Vary, PRD 101, 034024(2020)] better than BLFQ-NJL")
Pion Structure Function [Lan, Mondal, Jia, Zhao, Vary, PRD 101, 034024(2020)] better than BLFQ-NJL results Ø Higher initial scale Ø less gluon/sea quark at small x in future 25
Conclusions • Systematically expandable by including higher Fock sectors Thank you ! Questions/suggestions: jiangshanlan@impcas. ac. cn 24
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