In-medium properties of the nucleon within a pirho-omega model. Ju-Hyun Jung in collaboration with Hyun-Chul Kim and Ulugbek Yakhshiev

Transcription

1 In-medium properties of the nucleon within a pirho-omega model Ju-Hyun Jung in collaboration with Hyun-Chul Kim and Ulugbek Yakhshiev

2 Outline 1. In-medium modified π ρ ω mesonic Lagrangian 2. Structure of nucleon 3. Transverse charge densities

3 Motivation We investigate the modification of hadron properties in nuclear matter within the framework of the inmedium modified π-ρ-ω soliton model A. M. Rakhimov, M. M. Musakhanov, F. C. Khanna, and U. T. Yakhshiev, Phys. Rev. C 58, 1738 (1998)

4 Motivation We consider the modification of meson degrees of freedom in nuclear matter. The mass dropping of the vector mesons in dense matter has been extensively studied theoretically as well as experimentally M. Naruki, et al., KEK-PS E325 Collaboration, Phys. Rev. Lett. 96 (2006)

5 Theoretical framework QCD (Not easily solvable) Quark model π ρ, ω Soliton model The nucleon has a structure, not a pointlike particle The effective Lagrangian

6 Theoretical framework The effective Lagrangian in nuclear medium

7 Medium functionals The parameters stand for the medium functionals Model I : Model II :

8 The effective Lagrangian for pions, rhoand omega-mesons in nuclear medium The modified Lagrangian of the non-linear sigma model in nuclear medium. is pion mass term or chiral symmetry breaking term.

9 The effective Lagrangian for pions, rhoand omega-mesons in nuclear medium Hidden local gauge transformation is introduced to satisfy gauge invariance Local gauge fields are identified with the rho and omega meson as dynamical gauge bosons

10 The effective Lagrangian for pions, rhoand omega-mesons in nuclear medium Coupling constant is fixed by KawarabayashiSuzuki-Riazuddin-Fayyazudin relation Stable soiltion soltution

11 The effective Lagrangian for pions, rhoand omega-mesons in nuclear medium gives the omega coupling to the topologically conserved baryon current Wess-Zumino term

12 Spherically symmetric hedgehog Ansatz Skyrme s Ansatz Wu-Yang- t Hooft-Polyakov Ansatz G. Holzwarth and B. Schwesinger, Rep. Prog. Phys (1986)

13 Topological solitons The funtion U is a mapping These maps are topologically nontrivial and are characterized by a winding number

14 Classical soliton mass The classical soliton mass A minimizaiton of the classical soliton mass is done by solving the equation of motion

15 Equations of motion The equation of motion for each meson field

16 Equations of motion The Boundary conditions are given in the folowing form and they satisfy the baryon number 1 solution

17 The profile functions for mesons inmedium The meson profile functions in free space (solid curves) and and in nuclear matter (dashed curves) with normal nuclear matter density. The results were obtained in framework of the Model I.

18 Rotating Soliton The collective coordinate quantization where 2K denotes the angular velocity of the soliton with the relation

19 Rotating Soliton The time dependent collective Hamiltonian The moment of inertia

20 Rotating Soliton The moment of inertia

21 Rotating Soliton The moment of inertia

22 The profile functions for mesons inmedium The meson profile functions in free space (solid curves) and and in nuclear matter (dashed curves) with normal nuclear matter density. The results were obtained in framework of the Model I.

23 Results Binding energy naturally has a maximum value at around normal nuclear matter. The solid curve represents the Model I The dashed curve represents the Model II

24 Results At normal nuclear matter density decrease is about 30% relatively to its free space value. J. -H. Jung, U. T. Yakhshiev and H. -Ch. Kim, Phys.Lett. B 723 (2013)

25 Motivation The structure of the nucleon The electromagnetic and weak properties

26 Motivation The energy momentum tensor form factors of the nucleon which come from the gravitational interaction have been introduced by Pagel H. R. Pagels, Phys. Rev., (1966)

27 Motivation The proton s EM form factors elastic e p e Q p

28 Motivation The generalized parton distributions (GPDs) of hard exclusive reaction have unveiled a novel aspect of the nucleon structure K. Goeke et al., Prog. Part. Nucl Phys., (2001) exclusive e π, ρ, γ γ e p v Q p

29 Theoretical framework The nucleon matrix element of the EM current is expressed in terms of Dirac and Pauli form factors The EMT tensor are characterized by three form factors

30 Theoretical framework where and describe the nucleon momentum and angular momentum Interpretation of less trivial, but also gives information about nucleon structure

31 Electromagnetic form factors The Dirac and Pauli form factors are related to charge and magnetic form factors They are also related to a generalized parton distributions

32 Electromagnetic form factors The final expressions and normalization conditions zero momentum transfer q^2 = 0

33 Energy-momentum form factors The energy-momentum form factors are defined as following

34 Energy-momentum form factors Analogously to EM form factors, Polarized EMT form factors can also be related GPDs.

35 Energy-momentum form factors The final expressions and normalization conditions

36 Energy-momentum form factors

37 Energy-momentum form factors The final expressions and normalization conditions zero momentum transfer q^2 = 0

38 Results for pressure p(r) The final expressions and normalization conditions

39 Results for pressure p(r)

40 Results for pressure p(r) The stability condition also valid in matter

41 Results for pressure p(r)

42 Results for pressure p(r)

43 Results

44

45

46

47

48 Motivation The Fourier transforms of the nucleon EM form factors in the transverse plane, as viewed from a light front frame moving towards a nucleon, paint a tomographic picture of how the charge densities of quarks are distributed transversely M. Burkardt, Int. J. Mod. Phys., A (2003)

49 Motivation The nucleon form factors and the transverse densities Taken from H.-Ch. Kim s talk

50 Form factors in the transverse plane The two-dimensional Fourier transform of the generalized parton distribution In terms of charge and magnetic FFs

51 Form factors in the transverse plane If the nucleon is polarized in the x-y plane, one can find polarized nucleon density as Nucleon spin operator : B E Induced electric field

52

53

54

55

56 Thank you 감사합니다 Vielen Dank

57 The medium functionals The medium functionals have the following forms which comes from the fitting pi-n scattering data We have tried exponential forms of the dependence on the nuclear density ρ to fit the ground state of nuclear matter Lambda is parameter related to nuclear density λ = 0 : Free space λ = 1 : Normal nuclear matter η : Kinematic factor b0 And c0 : Effective pion- nucleon S and P wave scattering lengths g'0 : Lorentz-Lorenz or correlation factor

58