反 D 中間子をふくむチャーム原子核 安井 繁宏 (KEK) arXiv: [hep-ph] KEK （東海）研究会「原子核媒質中のハドロン研究 = 魅力と課題 = Aug 共同研究者 須藤 和敬 ( 二松学舎大学 )

1. Introduction to charm (bottom) nuclei 2. Heavy hadron mass and gluon field - Heavy quark effective theory (HQET) with 1/m Q corrections 3. Heavy meson effective theory with 1/M corretions 4. Anti-D (B) meson in nuclear medium 5. Discussion 6. Summary & perspectives Contents チャーム原子核の魅力とは？ 課題とは？

1. Introduction D(cq) Charm hadrons in medium Charmed nuclei D nuclei (C<0) SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) SY and Sudoh, PRC87, (2013) - What are charm hadrons in nuclei? C>0 Λ c (cqq) nuclei C=0 J/Ψ(cc) nuclei C<0 D(cq) nuclei - Questions Light degrees of freedom “q” → Affected by medium effect (Partial restoration of the chiral symmetry breaking?) Bando, Nagata, PTP69, 557 (1983) Brodsky, Schmidt, Teramond PRL64, 1011 (1990) Tsushima et al. PRC59, 2824 (1999) No annihilation/absorption → Clean probe as mesic nuclei! ・ Are they really stable states? ・ How can be produced in experiments? ・ What are the new and interesting things?

1. Introduction D(cq) Charm hadrons in medium Charmed nuclei D nuclei (C<0) SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) SY and Sudoh, PRC87, (2013) - What are charm hadrons in nuclei? C>0 Λ c (cqq) nuclei C=0 J/Ψ(cc) nuclei C<0 D(cq) nuclei - Questions Light degrees of freedom “q” → Affected by medium effect (Partial restoration of the chiral symmetry breaking?) Bando, Nagata, PTP69, 557 (1983) Brodsky, Schmidt, Teramond PRL64, 1011 (1990) Tsushima et al. PRC59, 2824 (1999) No annihilation/absorption → Clean probe as mesic nuclei! ・ Are they really stable states? ・ How can be produced in experiments? ・ What are the new and interesting things?

No annihilation/absorption → Clean probe as mesic nuclei! 1. Introduction D(cq) Charm hadrons in medium Charmed nuclei D nuclei (C<0) - What are charm hadrons in nuclei? C>0 Λ c (cqq) nuclei C=0 J/Ψ(cc) nuclei C<0 D(cq) nuclei Light degrees of freedom “q” → Affected by medium effect (Partial restoration of the chiral symmetry breaking?) Bando, Nagata, PTP69, 557 (1983) Brodsky, Schmidt, Teramond PRL64, 1011 (1990) Tsushima et al. PRC59, 2824 (1999) Quark-meson coupling model QCD sum rulesMean field models Coupled-channel models with contact interactions Perturbation by pion exchanges - Questions SY and Sudoh, PRC87, (2013)

1. Introduction D(cq) Charm hadrons in medium Charmed nuclei D nuclei (C<0) SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) SY and Sudoh, PRC87, (2013) - What are charm hadrons in nuclei? C>0 Λ c (cqq) nuclei C=0 J/Ψ(cc) nuclei C<0 D(cq) nuclei - Questions Light degrees of freedom “q” → Affected by medium effect (Partial restoration of the chiral symmetry breaking?) Bando, Nagata, PTP69, 557 (1983) Brodsky, Schmidt, Teramond PRL64, 1011 (1990) Tsushima et al. PRC59, 2824 (1999) What are the “interesting” and “new” roles of heavy hadrons in medium at finite density? No annihilation/absorption → Clean probe as mesic nuclei! ・ Are they really stable states? ・ How can be produced in experiments? ・ What are the new and interesting things?

1. Introduction D(cq) Charm hadrons in medium Charmed nuclei D nuclei (C<0) SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) SY and Sudoh, PRC87, (2013) - What are charm hadrons in nuclei? C>0 Λ c (cqq) nuclei C=0 J/Ψ(cc) nuclei C<0 D(cq) nuclei - Questions Light degrees of freedom “q” → Affected by medium effect (Partial restoration of the chiral symmetry breaking?) Bando, Nagata, PTP69, 557 (1983) Brodsky, Schmidt, Teramond PRL64, 1011 (1990) Tsushima et al. PRC59, 2824 (1999) No annihilation/absorption → Clean probe as mesic nuclei! ・ Are they really stable states? ・ How can be produced in experiments? ・ What are the new and interesting things? Conclusion in this talk Heavy hadrons probe gluon dynamics in medium.

2. Heavy hadron mass and gluon field Heavy quark effective theory (HQET)

2. Heavy hadron mass and gluon field Heavy quark effective theory (HQET) Effective heavy quark field (four-velocity v) Covariant derivative Tensor field of gluon (chromoelectric G 0i, chromomagnetic G ij ) QvQv Light quarks & gluons HQET 1/m Q expansion

2. Heavy hadron mass and gluon field Heavy quark effective theory (HQET) Mass of heavy meson H containing a heavy quark Q (in vacuum) LO NLO O(1/m Q ) HQS conserved HQS broken HQS = Heavy quark symmetry, HQFS=Heavy quark flavor symmetry, HQSS=Heavy quark spin symmetry rest frame HQFS conserved HQSS conserved HQFS broken HQSS conserved HQFS broken HQSS broken QvQv Light quarks & gluons HQET 1/m Q expansion Matrix elements D-D* (B-B*) mass approximate degeneracy

2. Heavy hadron mass and gluon field Heavy quark effective theory (HQET) Mass of heavy meson H containing a heavy quark Q (in vacuum) LO NLO O(1/m Q ) HQS conserved HQS broken HQS = Heavy quark symmetry rest frame Bigi, Shifman, Uraltsev, Vainshtein, PRD52, 196 (1995) Neubert, PLB322, 419 (1994) “the virial theorem” QvQv Light quarks & gluons HQET 1/m Q expansion Matrix elements

2. Heavy hadron mass and gluon field Heavy quark effective theory (HQET) Mass of heavy meson H containing a heavy quark Q (in medium at T and ρ) LO NLO O(1/m Q ) HQS conserved HQS broken HQS = Heavy quark symmetry rest frame QvQv Light quarks & gluons HQET 1/m Q expansion Matrix elements

2. Heavy hadron mass and gluon field Heavy quark effective theory (HQET) ratios = matrix elements in medium at T and ρ matrix elements in vacuum LO HQS conserved NLO O(1/m Q ) HQS broken scale anomaly in QCD chromomagnetic gluon chromoelectric gluon in-medium modifications of... Probing gluon dynamics by hadrons with a heavy quark

Heavy meson effective theory (HMET) 3. Heavy meson effective theory with 1/M corr.

How are anti-D (B) mesons are modified in nuclear medium? → We use the heavy meson effective theory (HMET) with 1/M expansion. M: heavy hadron mass Point 2. 1/m Q expansion (m Q =m c, m b ). Point 1. How can we calculate in-medium masses? (LQCD is not applicable.)

3. Heavy meson effective theory with 1/M corr. How are anti-D (B) mesons are modified in nuclear medium? Point 2. 1/m Q expansion (m Q =m c, m b ). Point 1. How can we calculate in-medium masses? (LQCD is not applicable.) → We use the heavy meson effective theory (HMET) with 1/M expansion. M: heavy hadron mass Point 2. → O(1/m Q 0 ) = O(1/M 0 ) O(1/m Q 1 ) = O(1/M 1 ) From M=m Q +Λ+..., we obtain 1/M=1/m Q +... Point 1. → Effective degrees of freedom in confinement phase are hadrons NN -1

3. Heavy meson effective theory with 1/M corr. How are anti-D (B) mesons are modified in nuclear medium? We need the heavy meson effective Lagrangian with 1/M corrections. Point 2. 1/m Q expansion (m Q =m c, m b ). → We use the heavy meson effective theory (HMET) with 1/M expansion. M: heavy hadron mass Point 2. → O(1/m Q 0 ) = O(1/M 0 ) O(1/m Q 1 ) = O(1/M 1 ) From M=m Q +Λ+..., we obtain 1/M=1/m Q +... Point 1. → Effective degrees of freedom in confinement phase are hadrons NN -1 Point 1. How can we calculate in-medium masses? (LQCD is not applicable.)

3. Heavy meson effective theory with 1/M corr. Heavy meson effective theory with 1/M corrections Heavy-meson effective field and separation of momentum four-velocity + residual momentum v w H v (x) H w (x) Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994) vector meson pseudoscalar mesonSpin degeneracy at LO 1/M correction (NLO) : uncertainty of four-velocity or residual momentum (change of frame with v to frame with w)

3. Heavy meson effective theory with 1/M corr. Heavy meson effective theory with 1/M corrections Heavy-meson effective field and separation of momentum 1/M correction (NLO) : uncertainty of four-velocity or residual momentum (change of frame with v to frame with w) four-velocity + residual momentum v w H v (x) H w (x) p/M Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994) vector meson pseudoscalar mesonSpin degeneracy at LO

3. Heavy meson effective theory with 1/M corr. Heavy meson effective theory with 1/M corrections Axial-currents composed by H v :

3. Heavy meson effective theory with 1/M corr. Heavy meson effective theory with 1/M corrections Axial-currents composed by H v : HQSS conserved (Γ=1, iγ 5, γ μ ) HQSS=Heavy quark spin symmetry O(1/M 0 ) or O(1/M 1 )

3. Heavy meson effective theory with 1/M corr. Heavy meson effective theory with 1/M corrections Axial-currents composed by H v : HQSS broken (Γ=γ μ γ 5, σ μν ) smaller than or equal to O(1/M 1 ) HQSS=Heavy quark spin symmetry

3. Heavy meson effective theory with 1/M corr. Heavy meson effective theory with 1/M corrections Axial-currents composed by H v : O(1/M 0 ) or O(1/M 1 ) HQSS conserved O(1/M 1 ) HQSS broken HQSS=Heavy quark spin symmetry

3. Heavy meson effective theory with 1/M corr. Heavy meson effective theory with 1/M corrections Effective Lagrangian for HMET Kitazawa, Kurimoto, PLB323, 65 (1994) P-P* mass splitting Axial-vector current by pions

3. Heavy meson effective theory with 1/M corr. Heavy meson effective theory with 1/M corrections Effective Lagrangian for HMET --- How to fix couplings g, g 1 and g 2 ? --- LONLO Lattice QCD simulations by Detmold, Lin, Meinel, PRD.85, (2012) g g=

3. Heavy meson effective theory with 1/M corr. Heavy meson effective theory with 1/M corrections Effective Lagrangian for HMET --- How to fix couplings g, g 1 and g 2 ? --- LONLO Decay width of D* → Dπ (PDG2012) ( g, g 1 /M D, g 2 /M D ) = (0.5, 0, -0.07) for g=0.5 (Set 1) (0.4, 0, -0.17) for g=0.4 (Set 2) Constraint on g 1 and g 2 We assume g 1 =0 (conclusion is insensitive to g 1 )

4. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter NNNN -1 anti-D mesonanti-D* meson 1/M corrections from HMET Cf. Λ-Σ mixing

4. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter NNNN -1 1/M corrections from HMET anti-D mesonanti-D* meson Cf. Λ-Σ mixing

4. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter scale anomaly in QCD chromomagnetic gluon chromoelectric gluon at normal density

4. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter scale anomaly in QCD chromomagnetic gluon chromoelectric gluon in-medium modifications of... at normal density

4. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter scale anomaly in QCD chromomagnetic gluon chromoelectric gluon in-medium modifications of... at normal density suppressed enhanced suppressed

4. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter scale anomaly in QCD chromomagnetic gluon chromoelectric gluon in-medium modifications of... → suppressed → enhanced → suppressed normal density ( g, g 1 /M D, g 2 /M D ) = (0.5, 0, -0.07) (0.4, 0, -0.17) normal density

4. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter scale anomaly in QCD chromomagnetic gluon chromoelectric gluon in-medium modifications of... → suppressed → enhanced → suppressed Energy contribution from gluons becomes small. (Suppression of quantum effects.) Kinetic energy becomes large, due to the binding energy. D-D* (B-B*) splitting become small. (Extended brown muck dressed by nucleon-hole pairs in medium?) normal density ( g, g 1 /M D, g 2 /M D ) = (0.5, 0, -0.07) (0.4, 0, -0.17) normal density

5. Discussion Heavy baryon with a heavy quark Non-exotic baryons (Qqq) Exotic baryons (Qqqqq) SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011); ibid. 85, (2012)

5. Discussion Heavy baryon with a heavy quark Non-exotic baryons (Qqq) Exotic baryons (Qqqqq) Chromoelectric gluon → enhanced SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011); ibid. 85, (2012)

5. Discussion Heavy baryon with a heavy quark Non-exotic baryons (Qqq) Exotic baryons (Qqqqq) Chromomagnetic gluon → suppressed SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011); ibid. 85, (2012)

5. Discussion Heavy baryon with a heavy quark Non-exotic baryons (Qqq) Exotic baryons (Qqqqq) Chromomagnetic gluon → suppressed SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011); ibid. 85, (2012)

6. Summary & perspectives Heavy meson masses give information about gluon dynamics. We discuss in-medium masses of anti-D ( * ) and B ( * ) meson in nuclear matter. → Heavy meson effective theory with 1/M expansion We find in nuclear matter that... (1) Scale anomaly from QCD is suppressed. (2) Chromoelectric gluons are enhanced. (3) Chromomagnetic gluons are suppressed. We also discuss gluon dynamics in heavy baryons. Experimental studies for charmed nuclei are important at J-PARC.

6. Summary & perspectives The (personal) path between hadron physics and nuclear physics Interaction between an anti-D ( * ) (B ( * ) ) meson and a nucleon Anti-D ( * ) and B ( * ) mesons in nuclear medium Anti-D ( * ) (B ( * ) ) meson → Probing gluon dynamics in medium SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) SY and Sudoh, PRC87, (2013) SY and Sudoh, PRC88, (2013) SY, Yamaguchi, Ohkoda, Hosaka, Hyodo, arXv:xxxx.yyyyy. Heavy quark (spin) symmetry π exchange interaction Isospin polarization Feshbach resonances Kondo effects Chromoelectric & chromomagnetic gluons probed by a heavy quark SY and Sudoh, arXiv:1308:0098 [hep- ph] Do heavy quarks connect QCD and nuclear physics? N D(*)D(*) π Spin-Complex Spin degeneracy QvQv gluon E a, B a

6. Summary & perspectives Gluon dynamics in “single particle state” in atomic nuclei with anti-D ( * ) (Λc) B.E. thr. anti-D 12 C ( Λc 12 C) s.p.s. (n 2S+1 L J ) of anti-D ( * ) (Λc) → Λ(n 2S+1 L J ), λ 1 (n 2S+1 L J ), λ 2 (n 2S+1 L J,m Q ) scale anomaly, chromoelectric gluon, chromomagnetic gluon for each s.p.s. QvQv gluon E a, B a g.s. e.s. J-1/2 J+1/2 魅力 = チャームクォーク、グルーオン、原子核を結ぶ 課題 = で、どうやって作るの？