φ and J / Ψ mesons in cold nuclear matter Javier Cobos C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ exico City, M´ exico. 8th International Conference Quarks and Nuclear Physics Tsukuba, Ibaraki, Japan. November 13-17, 2018 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
Introduction 1 Effective Lagrangians approach 2 The quark meson coupling model 3 Results 4 Nuclear matter Finite Conclusions 5 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
A bit of advertising Parts of this presentation are based on “Phi-meson mass and width in nuclear matter and nuclei” arXiv:1703.05367 [nucl-th] (Physics Letters B 771 (2017). 113-118) “Phi-meson nuclear bound states” arXiv:1705.06653 [nucl-th] Physical Review C 96 (2017) no.3, 035201. “ η c - and J / Ψ-nuclear bound states”–In Preparation. In collaboration with Kazuo Tsushima–Laborat´ orio de F´ ısica Te´ oorica e Computacional, Universidade Cruzeiro do Sul, S˜ ao Paulo, Brazil. Gast˜ ao Krein–Instituto de F´ ısica Te´ orica, Universidade Estadual Paulista, S˜ ao Paulo, Brazil. Anthony Thomas–Special Research Centre for the Subatomic Structure of Matter University of Adelaide, Adelaide, Australia. 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
Vector mesons There has been much theoretical and experimental interest over the last few decades. There is still, however, experimental controversy in the measurements of the mass shift–specially for the φ . There are planned experiments at JLab, KEK, and GSI. Partial restoration of chiral symmetry at high densities. The mass shift of the φ -meson is related to the strangeness content of the nucleon. As the φ -meson is nearly pure ss state and gluonic interactions are flavor blind studying it (in nuclear matter) serves to test theories of multi-gluon interactions. Role of QCD van der Waals forces, which are believed to play a role in the binding of J / Ψ and other exotic heavy-quarkonia to matter. 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
φ -meson in nuclear matter We are interested in the vector-meson mass shift in nuclear matter φ − m vac ∆ m ∗ φ = m ∗ φ m ∗ φ is the φ meson mass in nuclear matter. m vac = 1020 MeV its vacuum value φ We are also interested in the φ decay width in nuclear matter Γ ∗ φ . Both will be computed from the φ self energy in a hybrid approach: Effective Lagrangians. Quark meson coupling (QMC) model (See talks of K. Tsushima, P. Hutauruk, and T. Miyatsu) 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
Effective Lagrangians approach Π φ ( p ) renormalises the φ meson mass: g µν − p µ p ν + p µ p ν 1 � � D µν ( p ) = p 2 − m 2 p 2 m 4 φ − Π φ ( p ) Both m ∗ φ and Γ ∗ φ will be computed from Π φ ( p ). We use an effective Lagrangian to compute the φ meson self-energy Π φ ( p ): L φ KK = i g φ φ µ � � K ( ∂ µ K ) − ( ∂ µ K ) K , � K + � � 0 � K − K where K = , K = . K 0 At order g 2 φ : K φ φ K 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
Effective Lagrangians approach to Π φ ( p ) At order g 2 φ K 3 Π µν Π φ ( p ) = − 1 φ φ φ ( p ) . K Π φ ( p ) acquires an imaginary part when m φ > 2 m K ( m φ = 1020 MeV, m K = 497 MeV). The φ meson mass and decay width in vacuum ( m φ , Γ φ ) and in nuclear matter ( m ∗ φ , Γ ∗ φ ) are determined self-consistently by ( m φ ) 2 + ℜ Π φ ( m 2 m 2 = φ ) φ − 1 ℑ Π( m 2 Γ φ ( m φ ) = φ ) m φ 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
Effective Lagrangians approach to Π φ ( p ) At order g 2 φ K 3 Π µν Π φ ( p ) = − 1 φ φ φ ( p ) . K Π φ ( p ) acquires an imaginary part when m φ > 2 m K ( m φ = 1020 MeV, m K = 497 MeV). The φ meson mass and decay width in vacuum ( m φ , Γ φ ) and in nuclear matter ( m ∗ φ , Γ ∗ φ ) are determined self-consistently by ( m φ ) 2 + ℜ Π φ ( m 2 m 2 = φ ) φ − 1 ℑ Π( m 2 Γ φ ( m φ ) = φ ) m φ Essentially, in nuclear matter m φ → m ∗ φ , Γ φ → Γ ∗ φ , m K → m ∗ K . 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
Effective Lagrangians approach to Π φ ( p ) At order g 2 φ K 3 Π µν Π φ ( p ) = − 1 φ φ φ ( p ) . K Π φ ( p ) acquires an imaginary part when m φ > 2 m K ( m φ = 1020 MeV, m K = 497 MeV). The φ meson mass and decay width in vacuum ( m φ , Γ φ ) and in nuclear matter ( m ∗ φ , Γ ∗ φ ) are determined self-consistently by ( m φ ) 2 + ℜ Π φ ( m 2 m 2 = φ ) φ − 1 ℑ Π( m 2 Γ φ ( m φ ) = φ ) m φ Essentially, in nuclear matter m φ → m ∗ φ , Γ φ → Γ ∗ φ , m K → m ∗ K . m ∗ K is computed in the quark meson coupling model (QMC). 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
Effective Lagrangians approach to Π φ ( p ) For a φ meson at rest, the scalar self-energy Π φ ( p ) is given by d 4 q i Π φ ( p ) = − 8 � 3 g 2 q 2 D K ( q ) D K ( q − p ) , (2 π ) 2 � φ � − 1 is the kaon propagator. q 2 − m 2 � D K ( q ) = K + i ǫ m K the kaon mass. The integral in Π φ ( p ) divergent and needs regularization. We use a phenomenological form factor, with a cutoff parameter Λ K : � 2 � Λ K + m 2 q 2 + m 2 � 1 / 2 φ q 2 ) = q 2 ) = u ( � , ω K ( � � � q 2 + 4 ω 2 K q 2 ) � K ( � We study the dependence on Λ K . 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
The quark meson coupling model [PPNP 58, 1 (2007)] Crucial for our results in nuclear matter is the in-medium kaon mass. K is calculated in the QMC model. m ∗ The QMC model is a quark-based, relativistic mean field model of nuclear matter and nuclei. Here the relativistically moving confined light quarks in the nucleon bags (MIT bag) self-consistently interact directly with the scalar-isoscalar σ , vector-isoscalar ω , and vector-isovector ρ mean fields (Hartree approximation) generated by the light quarks in the other nucleons. The meson mean fields are responsible for nuclear binding. The self-consistent response of the bound light quarks to the mean field σ field leads to novel saturation mechanism for nuclear matter. The model has opened tremendous opportunities for studies of the structure of finite nuclei and hadron properties in a nuclear medium (nuclei) with a model based on the underlying quarks dof. 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
The quark meson coupling model [PPNP 58, 1 (2007)] QMC results for the in-medium kaon mass m ∗ K : 500 m* 480 K 460 * (MeV) 440 m K 420 400 380 0 0.5 1 1.5 2 2.5 3 -3 ) ρ B / ρ 0 (ρ 0 = 0.15 fm K at normal nuclear matter density ρ 0 = 0 . 15 fm − 3 decreases The m ∗ by 13%. 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
Results: φ mass shift and decay width in nuclear matter φ = ( m φ ) 2 + ℜ Π φ ( m 2 Recall m 2 φ ) 0 -10 -20 φ - m φ (MeV) -30 -40 m* Λ K = 2000 MeV -50 Λ K = 3000 MeV Λ K = 4000 MeV -60 0 0.5 1 1.5 2 2.5 3 -3 ) ρ B / ρ 0 (ρ 0 = 0.15 fm Mass shift average of − 24 MeV (2% decrease) at ρ 0 , with a 5 MeV spread. The mass shift depends on the value of Λ K . 8th International Conference Quarks and Nuclea Javier Cobos (C´ atedra CONACyT, High Energy Physics Group, CINVESTAV M´ φ and J / Ψ mesons in cold nuclear matter exico City, M´ exico.) / 26
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