Internal structure of the pion inspired by the AdS/QCD correspondence

Transcription

1 Internal structure of the pion inspired by the AdS/QCD correspondence Sabrina Cotogno Vrije Universiteit and Nikhef, Amsterdam Supervisor: Prof. P.J.G. Mulders In collaboration with Prof. Alessandro Bacchetta (UNIPV) Light Cone Conference 2015, Frascati September 2015

2 Overview Light-Front Wave Functions (LFWFs) of the Pion AdS/QCD correspondence Valence and Effective LFWF from AdS/QCD Fitting Procedure Fixing the model free parameters from available data of PDF and FF Implications on the strong coupling behavior Pion transverse structure in 3D momentum space Unpolarized Transverse Momentum Dependent parton distribution (TMD) of the pion from the model Broadening of Conclusions

3 LFWF from AdS/QCD correspondence = + +

4 LFWF from AdS/QCD correspondence = + + Fock state expansion of a hadronic state with momentum P and spin

5 LFWF from AdS/QCD correspondence = + + Fock state expansion of a hadronic state with momentum P and spin LFWFs Overlap representation formulae Parton distribution function

6 LFWF from AdS/QCD correspondence = + + Fock state expansion of a hadronic state with momentum P and spin LFWFs Overlap representation formulae Parton distribution function Electromagnetic Form Factor

7 LFWF from AdS/QCD correspondence = + + Fock state expansion of a hadronic state with momentum P and spin LFWFs Overlap representation formulae Parton distribution function Electromagnetic Form Factor Transverse Momentum Dependent Distribution

8 LFWF from AdS/QCD correspondence String theory in a 5-dimensional Anti-de Sitter space Conformal field theory on the 4-dimensional boundary of the AdS [J.M. Maldacena,Int.J.Theor.Phys. 38 (1999) ] [Brodsky, de Téramond et al., ]

9 LFWF from AdS/QCD correspondence String theory in a 5-dimensional Anti-de Sitter space Conformal field theory on the 4-dimensional boundary of the AdS [J.M. Maldacena,Int.J.Theor.Phys. 38 (1999) ] Applicability to QCD? Massless quarks and non running coupling Confinement Soft wall model (harmonic confining potential ) [Brodsky, de Téramond et al., ]

10 LFWF from AdS/QCD correspondence String theory in a 5-dimensional Anti-de Sitter space Conformal field theory on the 4-dimensional boundary of the AdS [J.M. Maldacena,Int.J.Theor.Phys. 38 (1999) ] Applicability to QCD? Massless quarks and non running coupling Confinement Soft wall model (harmonic confining potential ) Form Factors matching Free current propagating in AdS space Valence LFWF Confining current in a warped AdS space Effective LFWF [Brodsky, de Téramond et al., ]

11 LFWF from AdS/QCD correspondence String theory in a 5-dimensional Anti-de Sitter space Conformal field theory on the 4-dimensional boundary of the AdS [J.M. Maldacena,Int.J.Theor.Phys. 38 (1999) ] Applicability to QCD? Massless quarks and non running coupling Confinement Soft wall model (harmonic confining potential ) Form Factors matching Free current propagating in AdS space Valence LFWF Confining current in a warped AdS space Effective LFWF [Brodsky, de Téramond et al., ]

12 LFWF from AdS/QCD correspondence

13 LFWF from AdS/QCD correspondence Inclusion of the quark masses completion of the invariant mass operator [Brodsky, de Téramond et al., ]

14 LFWF from AdS/QCD correspondence Inclusion of the quark masses completion of the invariant mass operator Model I: Valence [Brodsky, de Téramond et al., ]

15 LFWF from AdS/QCD correspondence Inclusion of the quark masses completion of the invariant mass operator Model I: Valence [Brodsky, de Téramond et al., ] Regardless the origin of this LFWF as being the wave function of the valence Fock state of the pion, we will be treating it as the full pion LFWF.

16 LFWF from AdS/QCD correspondence Inclusion of the quark masses completion of the invariant mass operator Model I: Valence [Brodsky, de Téramond et al., ] Regardless the origin of this LFWF as being the wave function of the valence Fock state of the pion, we will be treating it as the full pion LFWF. Model II: Effective

17 LFWF from AdS/QCD correspondence Inclusion of the quark masses completion of the invariant mass operator Model I: Valence [Brodsky, de Téramond et al., ] Regardless the origin of this LFWF as being the wave function of the valence Fock state of the pion, we will be treating it as the full pion LFWF. Model II: Effective Goal: Fixing the free parameters of the model ( )

18 LFWF from AdS/QCD correspondence - Model I

19 LFWF from AdS/QCD correspondence - Model I S. R. Amendolia et al.,nucl. Phys.B (1986) P. Braueln et al., Z. Phys. C 3,101 (1979) J. Volmer et al. Phys. Rev. Lett. 86 (2001), 1713 C. J. Bebek et al.,phys. Rev. D17,1693 (1978) K. Wijesooriya, P. E. Reimer, and R. J. Holt Phys. Rev. C 72,

20 LFWF from AdS/QCD correspondence - Model I S. R. Amendolia et al.,nucl. Phys.B (1986) P. Braueln et al., Z. Phys. C 3,101 (1979) J. Volmer et al. Phys. Rev. Lett. 86 (2001), 1713 C. J. Bebek et al.,phys. Rev. D17,1693 (1978) K. Wijesooriya, P. E. Reimer, and R. J. Holt Phys. Rev. C 72,

21 LFWF from AdS/QCD correspondence - Model I S. R. Amendolia et al.,nucl. Phys.B (1986) P. Braueln et al., Z. Phys. C 3,101 (1979) J. Volmer et al. Phys. Rev. Lett. 86 (2001), 1713 C. J. Bebek et al.,phys. Rev. D17,1693 (1978) K. Wijesooriya, P. E. Reimer, and R. J. Holt Phys. Rev. C 72,

22 LFWF from AdS/QCD correspondence - Model I S. R. Amendolia et al.,nucl. Phys.B (1986) P. Braueln et al., Z. Phys. C 3,101 (1979) J. Volmer et al. Phys. Rev. Lett. 86 (2001), 1713 C. J. Bebek et al.,phys. Rev. D17,1693 (1978) K. Wijesooriya, P. E. Reimer, and R. J. Holt Phys. Rev. C 72,

23 LFWF from AdS/QCD correspondence - Model II

24 LFWF from AdS/QCD correspondence - Model II S. R. Amendolia et al.,nucl. Phys.B (1986) P. Braueln et al., Z. Phys. C 3,101 (1979) J. Volmer et al. Phys. Rev. Lett. 86 (2001), 1713 C. J. Bebek et al.,phys. Rev. D17,1693 (1978) K. Wijesooriya, P. E. Reimer, and R. J. Holt Phys. Rev. C 72,

25 LFWF from AdS/QCD correspondence - Model II S. R. Amendolia et al.,nucl. Phys.B (1986) P. Braueln et al., Z. Phys. C 3,101 (1979) J. Volmer et al. Phys. Rev. Lett. 86 (2001), 1713 C. J. Bebek et al.,phys. Rev. D17,1693 (1978) K. Wijesooriya, P. E. Reimer, and R. J. Holt Phys. Rev. C 72,

26 LFWF from AdS/QCD correspondence - Model II S. R. Amendolia et al.,nucl. Phys.B (1986) P. Braueln et al., Z. Phys. C 3,101 (1979) J. Volmer et al. Phys. Rev. Lett. 86 (2001), 1713 C. J. Bebek et al.,phys. Rev. D17,1693 (1978) K. Wijesooriya, P. E. Reimer, and R. J. Holt Phys. Rev. C 72,

27 LFWF from AdS/QCD correspondence - Model II S. R. Amendolia et al.,nucl. Phys.B (1986) P. Braueln et al., Z. Phys. C 3,101 (1979) J. Volmer et al. Phys. Rev. Lett. 86 (2001), 1713 C. J. Bebek et al.,phys. Rev. D17,1693 (1978) K. Wijesooriya, P. E. Reimer, and R. J. Holt Phys. Rev. C 72,

28 LFWF from AdS/QCD correspondence - Model II S. R. Amendolia et al.,nucl. Phys.B (1986) P. Braueln et al., Z. Phys. C 3,101 (1979) J. Volmer et al. Phys. Rev. Lett. 86 (2001), 1713 C. J. Bebek et al.,phys. Rev. D17,1693 (1978) K. Wijesooriya, P. E. Reimer, and R. J. Holt Phys. Rev. C 72,

29 Strong couplings in AdS/QCD [Brodsky, de Téramond, Deur, Phys. Rev. D 81, (2010)] [Erlich,Katz, Son, Stephanov, Phys.Lett. B 582, 211 (2005)] [Brodsky, Lu, Phys.Rev. D51,3652 (1995)] [Brodsky et al. Phys.Rev. D 58, (1998)]

30 Strong couplings in AdS/QCD [Brodsky, de Téramond, Deur, Phys. Rev. D 81, (2010)] [Erlich,Katz, Son, Stephanov, Phys.Lett. B 582, 211 (2005)] [Brodsky, Lu, Phys.Rev. D51,3652 (1995)] [Brodsky et al. Phys.Rev. D 58, (1998)]

31 Strong couplings in AdS/QCD [Brodsky, de Téramond, Deur, Phys. Rev. D 81, (2010)] [Erlich,Katz, Son, Stephanov, Phys.Lett. B 582, 211 (2005)] [Brodsky, Lu, Phys.Rev. D51,3652 (1995)] [Brodsky et al. Phys.Rev. D 58, (1998)]

32 Strong couplings in AdS/QCD

33 Strong couplings in AdS/QCD Effective

34 Strong couplings in AdS/QCD Effective

35 Strong couplings in AdS/QCD Effective Valence

36 Strong couplings in AdS/QCD Effective Valence

37 Transverse structure of the pion

38 Transverse structure of the pion Valence

39 Transverse structure of the pion Valence Effective

40 Transverse structure of the pion Valence Effective

41 Transverse structure of the pion

42 Transverse structure of the pion Valence model comparison constituent quark masses scenario

43 Transverse structure of the pion Valence model comparison constituent quark masses scenario Effective model comparison zero quark masses scenario

44 Transverse structure after QCD evolution

45 Transverse structure after QCD evolution Valence model evolved to Q=1 GeV, constituent quark masses scenario

46 Transverse structure after QCD evolution Valence model evolved to Q=1 GeV, constituent quark masses scenario

47 Transverse structure after QCD evolution Valence model evolved to Q=1 GeV, constituent quark masses scenario

48 Transverse structure after QCD evolution Valence model evolved to Q=1 GeV, constituent quark masses scenario Effective model evolved to Q=1 GeV, zero quark masses scenario

49 Transverse structure after QCD evolution Valence model evolved to Q=1 GeV, constituent quark masses scenario Effective model evolved to Q=1 GeV, zero quark masses scenario

50 Transverse structure - Broadening of

51 Transverse structure - Broadening of Valence model, constituent quark masses scenario

52 Transverse structure - Broadening of Valence model, constituent quark masses scenario

53 Transverse structure - Broadening of Valence model, constituent quark masses scenario

54 Transverse structure - Broadening of Valence model, constituent quark masses scenario Effective model, zero quark masses scenario

55 Transverse structure - Broadening of Valence model, constituent quark masses scenario Effective model, zero quark masses scenario

56 Transverse structure - Broadening of Valence model, constituent quark masses scenario Effective model, zero quark masses scenario

57 Summary, Conclusions and Outlook

58 Summary, Conclusions and Outlook Study of two functional forms of pion LFWFs from LF Holographic models with minimal modifications; Analysis of hadronic observables built from these LFWFs; Qualitative predictions on the pion TMD; Possibility to obtain a qualitatively reasonably matching between the non perturbative and the perturbative regimes of strong interactions;

59 Summary, Conclusions and Outlook Study of two functional forms of pion LFWFs from LF Holographic models with minimal modifications; Analysis of hadronic observables built from these LFWFs; Qualitative predictions on the pion TMD; Possibility to obtain a qualitatively reasonably matching between the non perturbative and the perturbative regimes of strong interactions; Possibility to study other hadronic observables; Modifications in the LFWF expressions in order to study the Boer-Mulders TMD of the pion;

60 Summary, Conclusions and Outlook Study of two functional forms of pion LFWFs from LF Holographic models with minimal modifications; Analysis of hadronic observables built from these LFWFs; Qualitative predictions on the pion TMD; Possibility to obtain a qualitatively reasonably matching between the non perturbative and the perturbative regimes of strong interactions; Possibility to study other hadronic observables; Modifications in the LFWF expressions in order to study the Boer-Mulders TMD of the pion; Thank you for your attention!

61 Backup slides

62 Expressions for PDF, Form Factor and TMD Model I: Valence Model II: Effective

63 Strong couplings in AdS/QCD - Cont d

64 Strong couplings in AdS/QCD - Cont d [Deur, Burkert, Chen, Korsch, Phys. Lett. B 650 (4) (2007)] [Brodsky, de Téramond, Deur, Phys. Rev. D 81, (2010)] [Deur, Brodsky, de Téramond, arxiv: [hep-ph], 2014] [Deur, Brodsky, de Téramond v1 [hep-ph], Sep 2015]