Anti-D and B meson in nuclear medium
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Anti-D and B meson in nuclear medium at zero temperature Shigehiro YASUI (KEK) Recent progress in hadron physics -From hadrons to quark and gluon@Yonsei University, 18-22 Feb. 2013 1. Introduction Hadrons in nuclear medium are useful for study of … (i) Interaction between hadron and nucleon Hyperon-nucleon interaction, hyperon-hyperon interaction Kbar-nucleon interaction (ii) Modification of properties of hadron π, ω, ρ, η(’) meson masses and decay widths in nuclear medium (iii) Change of medium caused by embedded hadron Shrink of radii of hypernuclei (“glue” effect by hyperon) Possible high density state in Kbar nuclei Fundamental questions in QCD: Color confinement, Spontaneous chiral symmetry breaking, … 1. Introduction Charm & Bottom → Change of Mass-scale and Symmetry 35 150 ΛQCD≈200 up strange down Chiral Symmetry SU(3)L x SU(3)R 1500 charm Change !! 4700 [MeV] mass bottom Heavy Quark Symmetry SU(2NF) 1. Introduction Charm & Bottom → Change of Mass-scale and Symmetry 150 ΛQCD≈200 1500 up strange down D, D (B, B) mesic nuclei Chiral - D, DSymmetry (B, B)-nucleon interaction? charm 35 Change !! - Modification of D, D (B, B) mesons SU(3) x SU(3) L R in nuclear matter (χSB)? - Change of nuclear matter? - How is QCD concerned? 4700 [MeV] mass bottom Heavy Quark Symmetry SU(2NF) D(cq) or D(cq) 1. Introduction Charm & Bottom → Change of Mass-scale and Symmetry 150 ΛQCD≈200 1500 up strange down D, D (B, B) mesic nuclei Chiral - D, DSymmetry (B, B)-nucleon interaction? charm 35 Change !! - Modification of D, D (B, B) mesons SU(3) x SU(3) L R in nuclear matter (χSB)? - Change of nuclear matter? - How is QCD concerned? 4700 [MeV] mass bottom Heavy Quark Symmetry SU(2NF) D(cq) or D(cq) 5400 MeV “Particle” ≠ “Antiparticle” in nuclear matter 1870 MeV 498 MeV “Particle” Including u, d quark - NO annihilation - NO absorption “Antiparticle” Including u, d antiquark - Annihilation - Absorption Charge Conjugate 1. Introduction What is D/D-nucleon interaction ? D and nucleon D*+N (2947 MeV) D+N (2803 MeV) differen t D and nucleon D*+N (2947 MeV) D+N (2803 MeV) Σc(2800) 1(??) Only DN and D*N channel C<0 π+Σc* (2658 MeV) Λc(2625) 0(3/2-) Λc(2595) 0(1/2-) C>0 π+Σc (2593 MeV) `Exotic channel‘ cqqq q `Baryon channel‘ cqqq q 1. Introduction What is D/D-nucleon interaction ? D and nucleon D*+N (2947 MeV) D+N (2803 MeV) differen t D and nucleon D*+N (2947 MeV) D+N (2803 MeV) Σc(2800) 1(??) Only DN and D*N channel C<0 π+Σc* (2658 MeV) Λc(2625) 0(3/2-) Λc(2595) 0(1/2-) C>0 π+Σc (2593 MeV) `Exotic channel‘ cqqq q `Baryon channel‘ cqqq q 1. Introduction Strangeness, Charm, Bottom, ... vector K* 400 MeV Only NG boson (K) is important in dynamics, and vector meson (K*) is almost irrelevant… In cham/bottom, vector meson is also important! D* pseudoscalar 140 MeV B* 45 MeV K D B 500 MeV 1870 MeV 5280 MeV sq cq bq q=u,d 1. Introduction Strangeness, Charm, Bottom, ... meson-nucleon interaction K D(*) N p, , K N p, , D(*) N One-pion exchange is absent. (short range force) Weinberg-Tomozawa interaction B(*) N p, , N B(*) N One-pion exchange is present. (long range force) One-pion exchange potential (OPEP) SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) 1. Introduction Strangeness, Charm, Bottom, ... meson-nucleon interaction K N D* p, , K N B* p, , N D One-pion exchange is absent. (short range force) Weinberg-Tomozawa interaction N p, , N B N One-pion exchange is present. (long range force) One-pion exchange potential (OPEP) SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) 1. Introduction Strangeness, Charm, Bottom, ... meson-nucleon interaction K N D p, , K N p, , N D* One-pion exchange is absent. (short range force) Weinberg-Tomozawa interaction B N p, , N B* N One-pion exchange is present. (long range force) One-pion exchange potential (OPEP) SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) 1. Introduction Strangeness, Charm, Bottom, ... meson-nucleon interaction K N D* p, , K N p, , N D* One-pion exchange is absent. (short range force) Weinberg-Tomozawa interaction B* N p, , N B* N One-pion exchange is present. (long range force) One-pion exchange potential (OPEP) SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) 1. Introduction Strangeness, Charm, Bottom, ... meson-nucleon interaction K D(*) N p, , K N p, , D(*) N One-pion exchange is absent. (short range force) Weinberg-Tomozawa interaction B(*) N p, , N B(*) N One-pion exchange is present. (long range force) One-pion exchange potential (OPEP) SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) 1. Introduction What is D/D-nucleon interaction ? D and nucleon D*+N (2947 MeV) D+N (2803 MeV) Only DN and D*N channel → New mechanism of DN interaction D S-wave N π D* D-wave N π D S-wave N “D-D* mixing” via pion exchange C<0 `Exotic channel‘ cqqq q ・ Mass degeneracy for D and D* MD*-MD = 140 MeV ∝ 1/mc ・ π exchange (tensor force) S-D wave mixing (deuteron-like) → Some bound/resonant states SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) 1. Introduction From hadron-nucleon interaction to a variety of exotic nuclei BN state 6263 MeV DN state 2946 MeV D*N 6217 MeV B*N BN B nuclei ? H dibaryon 2255 MeV Λ(1405) 1433 MeV 2230MeV KN 1330 MeV ΛΛ Hypernuclei K nuclei πΣ ΞN 2807 MeV DN D nuclei ? K(sq), Ξ(ssq), … 1. Introduction From hadron-nucleon interaction to a variety of exotic nuclei BN state 6263 MeV DN state 2946 MeV D*N 6217 MeV B*N BN B nuclei ? H dibaryon 2255 MeV Λ(1405) 1433 MeV 2230MeV KN 1330 MeV ΛΛ Hypernuclei K nuclei πΣ ΞN 2807 MeV DN D nuclei ? D(cq), B(bq) ?? 1. Introduction Quark-meson coupling model (Quark model) ・ K. Tsushima, D. -H. Lu, A. W. Thomas, K. Saito and R. H. Landau, Phys. Rev. C 59, 2824 (1999). ・ A. Sibirtsev, K. Tsushima and A. W. Thomas, Eur. Phys. J. A 6, 351 (1999). ・ K. Tsushima and F. C. Khanna, Phys. Lett. B 552, 138 (2003). From hadron-nucleon interaction sum rule to aQCD variety of exotic nuclei BN state 6263 MeV DN state ・ F. Klingl, S. -s. Kim, S. H. Lee, P. Morath and W. Weise, 2946 Phys. Rev. Lett. 82, 3396 (1999. MeV 6217 MeV ・ Y. -H. Song, S. H. Lee and K. Morita, Phys. Rev. C 79, 014907 (2009). ・ K. Morita and S. H. Lee, Phys. Rev. C 85, 044917 (2012). ・ A. Hayashigaki, Phys. Lett. B 487, 96 (2000). ・ B. Friman, S. H. Lee and T. Song, Phys. Lett. B 548, 153 (2002). ・ T. Hilger, R. Thomas and B. Kampfer, Phys. Rev. C 79, 025202 (2009). ・ T. Hilger, R. Schulze and B. Kampfer, J. Phys. G G 37, 094054 (2010). ・ Z. -G. Wang and T. Huang, Phys. Rev. C 84, 048201 (2011). D*N B*N BN B nuclei ? H dibaryon 2807 MeV 2255 MeV DN ΞN Hadron dynamics I (W-T interaction from SU(4) symmetry with breaking term) ・ A. Mishra, E. L. Bratkovskaya, J. Schaner-Bielich, S. Schramm and H. Stoecker, Phys. Rev. C 69, 015202 (2004). 2230MeV ・ M. F. M. Lutz and C. L. Korpa, Phys. Lett. B 633, 43 (2006). ・ L. Tolos, A. Ramos and T. Mizutani, Phys. Rev. C 77, 015207 (2008). bar (B) 1433 MeV D meson – nucleon interaction ・ A. Mishra and A. Mazumdar, Phys. Rev. C 79, 024908 (2009). must be very interesting !! ・ A. Kumar and A. Mishra, Phys. Rev. C 81, 065204 (2010). ・ C. E. Jimenez-Tejero, A. Ramos, L. Tolos and I. Vidana, Phys. Rev. C 84, 015208 (2011). ・ A. Kumar and A. Mishra, Eur. Phys. J. A 47, 164 (2011). ・ C. Garcia-Recio, J. Nieves, L. L. Salcedo and L. Tolos, Phys. Rev. C 85, 025203 (2012). bar ΛΛ Λ(1405) KN D nuclei ? Hypernuclei K nuclei How is D πΣ II (π exchange interaction) Hadron dynamics (B) meson bound in nuclear matter? 1330 MeV ・ S. Yasui, K. Sudoh, Phys. Rev. C87, 015202 (2013). ← Heavy Quark Symmetry + π exchange 1. Introduction 2. Dbar and B mesons bound in nuclear matter 3. “Strong coupling problem“ in heavy mass limit 4. Summary & perspectives Λc 2. Dbar and B mesons in nuclear matter SY and Sudoh, PRC87, 015202 (2013) Heavy meson Lagrangian (heavy quark symmetry & chiral symmetry) ・ Mass degeneracy of Dbar and D*bar in Multiplet field G. Burdman and J.F. Donoghue (1992) M.B. Wise (1992) T.-M. Yan, H.-Y. Cheng, C.-Y. Cheung, heavy limit G.-L. Lin,quark Y.C. Lin and H.-L. Yu (1997) vector + pseudoscalar ・ Vertex strength: gπDD*=gP*=D* (spin bar πD*D*bar P=Dsymmetry) from experimental value of deacy width of D*→Dπ Coupling const. Self-energy of D in nuclear matter D π π N D* D* D D π at order of two pion exchange D N N D π N π D* N suppressedin byvacuum 1/mD, 1/mD*, 1/mN DN scattering Cf. Nuclear matter Kaiser, Fritsch, Weise, NPB697, 255 (2002); ibid. A750, 259 (2005) Fiorilla, Kaiser, Weise, Prog. Part. Nucl. Phys. 67, 317 (2012) Hypernuclear matter Kaiser, Weise, PRC71, 015203 (2005) Kaiser, PRC71, 068201 (2005) N N π D nucleon propagator in-medium (Pauli exclusion principle) D self-energy in matter 2. Dbar and B mesons in nuclear matter SY and Sudoh, PRC87, 015202 (2013) Self-energy of D in nuclear matter In-medium fermion propagator (kF: Fermi momentum) D D* D D π π D* N “particle” D “hole” Free Pauli exclusion in Fermi surface “particle” “hole” 2. Dbar and B mesons in nuclear matter SY and Sudoh, PRC87, 015202 (2013) Self-energy of D* in nuclear matter D* D* D* π π D* D* D* D D* D N “particle” D* “particle” D* “hole” D* “hole” 2. Dbar and B mesons in nuclear matter momentum cutoff : 1.27 × 0.7 GeV for Dbar 1.22 × 0.7 GeV for B Numerical results radius ratio × hyperon cutoff self-energy of D, B mesons in nuclear matter D -35 MeV Negative self-energies Bound in nuclear matter B -107 MeV Normal nuclear matter density 2. Dbar and B mesons in nuclear matter Numerical results momentum cutoff : 1.27 × 0.7 GeV for Dbar 1.22 × 0.7 GeV for B radius ratio × hyperon cutoff self-energy of D*, B* mesons in nuclear matter D*-150 – i160 MeV Negative self-energies (real), but large imaginary parts B* Bound but unstable in nuclear matter -200 – i120 MeV Normal nuclear matter density 2. Dbar and B mesons in nuclear matter SY and Sudoh, PRC87, 015202 (2013) Applications ・ Atomic nuclei with D meson ・ Isospin polarization V0=-35 MeV δ : density difference between p and n embedded in symmetric nuclear matter Fine splittings (≈ten MeV) “Stable” distribution of isospin density Cf. “Isovector deformation” in Kbar nuclei Dote, Akaishi, Horiuchi, Yamazaki, PLB590, 51 (2004) → “Unstable” distribution of isospin density 2. Dbar and B mesons in nuclear matter Discussion on spin in heavy quark limit in QCD in vacuum Dbar (0-) : Qbar + q + qbarqq + gq + … ↑ “brown muck” - everything that is degenerate ↓ not the heavy quark (Isgur) D*bar (1-) : Qbar + q + qbarqq + gq + … ↑ ↑ Dbar and D*bar should be degenerate in vacuum. (Bottom is much better.) 2. Dbar and B mesons in nuclear matter Discussion on spin in heavy quark limit in QCD in medium Dbar (0-) : Qbar + q + qbarqq + gq + … + matter ↑ “in-medium brown muck” degenerate ↓ D*bar (1-) : Qbar + q + qbarqq + gq + … + matter ↑ ↑ Dbar and D*bar should be degenerate in vacuum. (Bottom is much better.) 2. Dbar and B mesons in nuclear matter Discussion on spin in heavy quark limit in QCD QCD-based result in medium Dbar (0-) : Qbar + q + qbarqq + gq + … + matter ↑ “in-medium brown muck” degenerate ↓ A. Yes. Dbar and D*bar in matter are degenerate bar in heavy mass limit (Δ∝mD*-mD→0). D*bar (1-) : Qbar + q + q qq + gq + … + matter ↑ ↑ Dbar and D*bar should be degenerate also in matter. (Bottom is much better.) 1. Introduction 2. Dbar and B mesons bound in nuclear matter 3. “Strong coupling problem“ in heavy mass limit 4. Summary & perspectives 3. “Strong coupling problem” in heavy mass limit Heavy quark limit exists in matter as well as in vacuum. BUT always so? “Dbar, B meson” We critically discuss heavy mass limit in matter at zero temperature. “Nuclear matter” Heavy “flavorerd” particle Φ (mass: MB→∞) Fermi gas by fermion ψ 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle = + + +… hole 1st order 2nd order (tree) (one-loop) 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle = + + +… hole 1st order 2nd order (tree) (one-loop) ≈ GBMB λf・λB ≈ GB2MB Log(MB) λf・λB Logarithmic enhancement in loop diagram in heavy mass limit (MB→∞) 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle = + + +… hole 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle = + + +… hole Fermi surface MB: heavy boson mass, m: fermion mass 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle = + + +… hole MB = ∞ case denominator = 0 for Singularity on Fermi surface Fermi surface MB: heavy boson mass, m: fermion mass 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle = + + +… hole MB = finite case denominator = 0 for No singularity on Fermi surface Fermi surface MB: heavy boson mass, m: fermion mass 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle = + + +… hole Fermi surface MB = finite Log MB MB= ∞ No singularity Logarithmic Singularity MB: heavy boson mass, m: fermion mass 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle = + + +… hole 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB ↑ = +↑ particle ↑↑ ↑+↑ ↑ ↑+ … hole 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB ↑ = +↑ particle ↑ ↑ ↑↑ + ↑↑ ↑ ↑+ … ↑ ↑ hole 1. Spin non-flip in intermediate state → Logarithmic singularity at Fermi surface is canceled. 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB ↑ = +↑ particle ↓ ↓ ↑↑ + ↑↑ ↑ ↑+ … ↓ ↓ hole 2. Spin flip in intermediate state 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB ↑ = +↑ particle ↓ ↓ ↑↑ + ↑↑ ↑ ↑+ … ↓ ↓ hole 2. Spin flip in intermediate state → Logarithmic singularity at Fermi surface is NOT canceled. Cf. “Kondo problem” by J. Kondo (1964); log|q-kF| for q→kF, MB=∞. 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle = + + +… hole 1st order 2nd order (tree) (one-loop) ≈ GBMB λf・λB ≈ GB2MB Log(MB) λf・λB Logarithmic enhancement in loop diagram in heavy mass limit (MB→∞) 3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv.1301.6830 Heavy boson Φ in matter Fermion ψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle = + + +… hole 1st order 2nd order (tree) (one-loop) ≈ GBMB λf・λB ≈ GB2MB Log(MB) λf・λB “Strong coupling problem” in λf・λB-dependent interaction in MB→∞ (isospin) 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion ψ and heavy fermion Ψ Heavy fermion Ψ in matter Fermion ψ (matter) Heavy fermion Ψ with mass MF 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion ψ and heavy fermion Ψ Heavy fermion Ψ in matter Fermion ψ (matter) Heavy fermion Ψ with mass MF particle = + + +… hole 1st order 2nd order (tree) (one-loop) ≈ GF λf・λF ≈ GF2 Log(MF) λf・λF “Strong coupling problem” in λf・λF-dependent interaction in MF→∞ 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion ψ and heavy fermion Ψ Heavy fermion Ψ in matter Fermion ψ (matter) Heavy fermion Ψ with mass MF particle = + Nuclear matter with isospin SU(2) ψ: nucleon Ψ: Λc baryon ??? Not applicable, because Λc is NOT doublet in SU(2) !! + +… hole 1st order 2nd order (tree) (one-loop) ≈ GF λf・λF ≈ GF2 Log(MF) λf・λF “Strong coupling problem” in λf・λF-dependent interaction in MF→∞ 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion ψ and heavy fermion Ψ Heavy fermion Ψ in matter Fermion ψ (matter) Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark → 3c representation of color SU(3) Heavy fermion Ψ with mass MF particle = + + +… hole 1st order 2nd order (tree) (one-loop) ≈ GF λf・λF ≈ GF2 Log(MF) λf・λF “Strong coupling problem” in λf・λF-dependent interaction in MF→∞ (color) 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion ψ and heavy fermion Ψ Heavy fermion Ψ in matter Fermion ψ (matter) Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark → 3c representation of color SU(3) Heavy fermion Ψ with mass MF R = +R particle R R R R R +R R R 1st order 2nd order (tree) (one-loop) ≈ GF λf・λF R R+ … hole “color non-flip” ≈ GF2 Log(MF) λf・λF “Strong coupling problem” in λf・λF-dependent interaction in MF→∞ (color) 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion ψ and heavy fermion Ψ Heavy fermion Ψ in matter Fermion ψ (matter) Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark → 3c representation of color SU(3) Heavy fermion Ψ with mass MF R = +R particle B B R R R +R B B 1st order 2nd order (tree) (one-loop) ≈ GF λf・λF R R+ … hole “color flip” ≈ GF2 Log(MF) λf・λF “Strong coupling problem” in λf・λF-dependent interaction in MF→∞ (color) 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion ψ and heavy fermion Ψ Heavy fermion Ψ in matter Fermion ψ (matter) Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark → 3c representation of color SU(3) Heavy fermion Ψ with mass MF R = +R particle B B R R R +R B B 1st order 2nd order (tree) (one-loop) ≈ GF λf・λF R R+ … hole ≈ GF2 Log(MF) λf・λF Quark matter with charm (bottom) quark at zero temperature may not be perturbative system, but be strongly coupled one!! 4. Summary & perspectives ・ Heavy quark symmetry & chiral symmetry is important to understand open charm and bottom mesons in nuclear medium. ・ Pseudoscalar (Dbar, B) mesons are bound in nuclear matter. Vector (Dbar*, B*) mesons are bound, but with large widths. ・ For embedded particle, λf・λB/F-dependent interaction will become strong by logarithmic enhancement in heavy mass limit. ・ How to deal with “strong coupling problem”? Application to nuclear matter and quark matter? ・ Charmed nuclei are interesting for experiments at J-PARC. → Dbar, D, J/Ψ, Λc, Σc(*) embedded in atomic nuclei To study “new” physics in charmed (bottom) nuclear systems will be important for J-PARC (and others). 2. Dbar and B mesons in nuclear matter Comparison with other works Binding energy [MeV] Quark-meson coupling model QCD rum rule Mean field Hadron dynamics Channel-coupling (w/o π exchange) π exchange [6] K. Tsushima, D. -H. Lu, A. W. Thomas, K. Saito and R. H. Landau, Phys. Rev. C 59, 2824 (1999). [7] A. Sibirtsev, K. Tsushima and A. W. Thomas, Eur. Phys. J. A 6, 351 (1999). [15] T. Hilger, R. Thomas and B. Kampfer, Phys. Rev. C 79, 025202 (2009). [16] T. Hilger, R. Schulze and B. Kampfer, J. Phys. G G 37, 094054 (2010). [17] Z. -G. Wang and T. Huang, Phys. Rev. C 84, 048201 (2011). [18] A. Mishra, E. L. Bratkovskaya, J. Schaner-Bielich, S. Schramm and H. Stoecker, Phys. Rev. C 69, 015202 (2004). [19] M. F. M. Lutz and C. L. Korpa, Phys. Lett. B 633, 43 (2006). [20] L. Tolos, A. Ramos and T. Mizutani, Phys. Rev. C 77, 015207 (2008). [21] A. Mishra and A. Mazumdar, Phys. Rev. C 79, 024908 (2009). [22] A. Kumar and A. Mishra, Phys. Rev. C 81, 065204 (2010). [23] C. E. Jimenez-Tejero, A. Ramos, L. Tolos and I. Vidana, Phys. Rev. C 84, 015208 (2011). [24] A. Kumar and A. Mishra, Eur. Phys. J. A 47, 164 (2011). [25] C. Garcia-Recio, J. Nieves, L. L. Salcedo and L. Tolos, Phys. Rev. C 85, 025203 (2012). 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion and heavy flavor boson 1st order (tree level) ≈ GBMB Fermion ψ (matter) Heavy flavor boson Φ with mass MB GBMB a(’), b(’)=1, …, n 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion and heavy flavor boson 2nd order (one-loop level) Fermion ψ (matter) Heavy flavor boson Φ with mass MB GBMB GBMB GBMB GBMB 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion and heavy flavor boson Logarithmic enhancement 2nd order (one-loop level) ≈ GB2MB Log(MB) in heavy mass limit (M →∞) !! B Fermion ψ (matter) Heavy flavor boson Φ with mass MB GBMB GBMB GBMB (Log MB)/MB Log MB from loop contribution with particles and holes MB: heavy boson mass, m: fermion mass GBMB (Log MB)/MB 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion and heavy flavor boson Logarithmic enhancement 2nd order (one-loop level) ≈ GB2MB Log(MB) in heavy mass limit (M →∞) !! B Fermion ψ (matter) Heavy flavor boson Φ with mass MB GBMB GBMB GBMB (Log MB)/MB GBMB (Log MB)/MB λf・λB-independent term → Log MB λf・λB-dependent term → Log MB MB: heavy boson mass, m: fermion mass 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermion and heavy flavor boson Logarithmic enhancement 2nd order (one-loop level) ≈ GB2MB Log(MB) in heavy mass limit (M →∞) !! B Fermion ψ (matter) Heavy flavor λ ・λ f B boson Φ with mass MB λf・λB <0 λf・λB λf・λB >0 Opposite signs in λf・λB are important for presence of Log(MB). 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Brief summary Nuclear matter with isospin SU(n=2) ψ: nucleon Φ: Dbar (B) meson Heavy boson in matter Fermion ψ (matter) Heavy flavor boson Φ with mass MB + λf・λB λf・λB + ≈ GBMB λf・λB λf・λB ≈ GB2MB Log(MB) Logarithmic enhancement in loop diagram in heavy mass limit (MB→∞) “Strong coupling problem” in λf・λB-dependent interaction (isospin) λf・λB 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Brief summary Nuclear matter with isospin SU(n=2) ψ: nucleon Ψ: Λc and Σc(*) baryon ??? Not applicable, because Λc and Σc(*) are NOT doublet in SU(2) !! Heavy fermion in matter Fermion ψ (matter) Heavy flavor fermion Ψ with mass MF λf・λF ≈ GF + λf・λF + λf・λF λf・λF ≈ GF2 Log(MF) Logarithmic enhancement in loop diagram in heavy mass limit (MF→∞) “Strong coupling problem” in λf・λF-dependent interaction (isospin) λf・λF 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Brief summary Quark matter with color SU(n=3) ψ: light quark Ψ: charm (bottom) quark → 3c representation of color SU(3) Heavy fermion in matter Fermion ψ (matter) Heavy flavor fermion Ψ with mass MF λf・λF ≈ GF + λf・λF + λf・λF λf・λF ≈ GF2 Log(MF) Logarithmic enhancement in loop diagram in heavy mass limit (MF→∞) “Strong coupling problem” in λf・λF-dependent interaction (color) Quark matter with charm (bottom) quark at zero temperature may not be perturbative system, but be strongly coupled one!! λf・λF 1. Introduction What is D/D-nucleon interaction ? D*+N D and nucleon D*+N (2947 MeV) resonant states D+N (2803 MeV) Only DN and D*N channel C<0 `Exotic channel‘ cqqq q D+N bound state SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) Heavy quark symmetry + π exchange (tensor force)
