反 d 中間子をふくむチャーム原子核

反 D 中間子をふくむチャーム原子核安井　繁宏

(KEK)

arXiv:1308.0098 [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 = 」 @5-6 Aug. 2013

共同研究者須藤　和敬( 二松学舎大学 )

1. Introduction to charm (bottom) nuclei2. Heavy hadron mass and gluon field - Heavy quark effective theory (HQET) with 1/mQ corrections

3. Heavy meson effective theory with 1/M corretions4. Anti-D (B) meson in nuclear medium5. Discussion6. 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 nucleiD nuclei (C<0)

SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)SY and Sudoh, PRC87, 105202 (2013)

- What are charm hadrons in nuclei? C>0 Λc(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 nucleiD nuclei (C<0)

SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)SY and Sudoh, PRC87, 105202 (2013)

- What are charm hadrons in nuclei? C>0 Λc(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 nucleiD nuclei (C<0)

- What are charm hadrons in nuclei? C>0 Λc(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-mesoncoupling model QCD sum rules Mean field models

Coupled-channel modelswith contact interactions

Perturbation by pion exchanges

- Questions SY and Sudoh, PRC87, 105202 (2013)

1. Introduction

D(cq)

Charm hadrons in medium

Charmed nucleiD nuclei (C<0)

SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)SY and Sudoh, PRC87, 105202 (2013)

- What are charm hadrons in nuclei? C>0 Λc(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 nucleiD nuclei (C<0)

SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)SY and Sudoh, PRC87, 105202 (2013)

- What are charm hadrons in nuclei? C>0 Λc(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 fieldHeavy quark effective theory (HQET)

Effective heavy quark field (four-velocity v)

Covariant derivative

Tensor field of gluon(chromoelectric G0i, chromomagnetic Gij)

Qv

Light quarks & gluons

HQET

1/mQ expansion

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

Mass of heavy meson H containing a heavy quark Q (in vacuum)

LO

NLO O(1/mQ)

HQS conserved

HQS broken

HQS = Heavy quark symmetry, HQFS=Heavy quark flavor symmetry, HQSS=Heavy quark spin symmetry

rest frame

HQFS conservedHQSS conserved

HQFS brokenHQSS conserved

HQFS brokenHQSS broken

Qv

Light quarks & gluons

HQET

1/mQ expansion

Matrix elementsD-D* (B-B*) mass approximate degeneracy

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

Mass of heavy meson H containing a heavy quark Q (in vacuum)

LO

NLO O(1/mQ)

HQS conserved

HQS broken

HQS = Heavy quark symmetry

rest frame

Bigi, Shifman, Uraltsev, Vainshtein,PRD52, 196 (1995)

Neubert, PLB322, 419 (1994)“the virial theorem”

Qv

Light quarks & gluons

HQET

1/mQ expansion

Matrix elements

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

Mass of heavy meson H containing a heavy quark Q (in medium at T and ρ)

LO

NLO O(1/mQ)

HQS conserved

HQS broken

HQS = Heavy quark symmetry

rest frame

Qv

Light quarks & gluons

HQET

1/mQ expansion

Matrix elements

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

ratios = matrix elements in medium at T and ρ matrix elements in vacuum

LOHQS conserved

NLO O(1/mQ)HQS broken

scale anomalyin QCD

chromomagneticgluon

chromoelectricgluon

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.

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/mQ expansion (mQ=mc, mb).

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/mQ expansion (mQ=mc, mb).

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/mQ0) = O(1/M0)

O(1/mQ1) = O(1/M1) From M=mQ+Λ+..., we obtain 1/M=1/mQ+...

Point 1. → Effective degrees of freedom in confinement phase are hadrons N N-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/mQ expansion (mQ=mc, mb).

→ We use the heavy meson effective theory (HMET) with 1/M expansion.M: heavy hadron mass

Point 2. → O(1/mQ0) = O(1/M0)

O(1/mQ1) = O(1/M1) From M=mQ+Λ+..., we obtain 1/M=1/mQ+...

Point 1. → Effective degrees of freedom in confinement phase are hadrons N N-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

Hv(x)

Hw(x)

Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994)

vector meson pseudoscalar meson Spin 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

Hv(x)

Hw(x)

p/M

Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994)

vector meson pseudoscalar meson Spin degeneracy at LO

3. Heavy meson effective theory with 1/M corr.Heavy meson effective theory with 1/M corrections

Axial-currents composed by Hv :

3. Heavy meson effective theory with 1/M corr.Heavy meson effective theory with 1/M corrections

Axial-currents composed by Hv :

HQSS conserved (Γ=1, iγ5, γμ) HQSS=Heavy quark spin symmetryO(1/M0) or O(1/M1)

3. Heavy meson effective theory with 1/M corr.Heavy meson effective theory with 1/M corrections

Axial-currents composed by Hv :

HQSS broken (Γ=γμγ5, σμν) smaller than or equal to O(1/M1) 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 Hv :

O(1/M0) or O(1/M1)

HQSS conserved

O(1/M1)

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 currentby 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, g1 and g2? ---

LO NLO NLO

Lattice QCD simulations by Detmold, Lin, Meinel, PRD.85, 114508 (2012)

g

g=0.4-0.5

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, g1 and g2? ---

LO NLO NLO

Decay width of D* → Dπ (PDG2012)

( g, g1/MD, g2/MD ) = (0.5, 0, -0.07) for g=0.5 (Set 1) (0.4, 0, -0.17) for g=0.4 (Set 2)

Constraint on g1 and g2

We assume g1=0 (conclusion is insensitive to g1)

4. Anti-D (B) meson in nuclear mediumIn-medium masses of anti-D(*) (B(*)) meson in nuclear matter

N N NN-1 N-1 N-1

anti-D meson anti-D* meson

1/M correctionsfrom HMET

Cf. Λ-Σ mixing

4. Anti-D (B) meson in nuclear mediumIn-medium masses of anti-D(*) (B(*)) meson in nuclear matter

N N NN-1 N-1 N-1

1/M correctionsfrom HMET

anti-D meson anti-D* meson

Cf. Λ-Σ mixing

4. Anti-D (B) meson in nuclear mediumIn-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 mediumIn-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 mediumIn-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 mediumIn-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, g1/MD, g2/MD ) = (0.5, 0, -0.07)

(0.4, 0, -0.17)

normal density

4. Anti-D (B) meson in nuclear mediumIn-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 gluonsbecomes small. (Suppression ofquantum 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, g1/MD, g2/MD ) = (0.5, 0, -0.07)

(0.4, 0, -0.17)

normal density

5. DiscussionHeavy baryon with a heavy quark

Non-exotic baryons (Qqq)

Exotic baryons (Qqqqq)

SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011); ibid. 85, 054003 (2012)

5. DiscussionHeavy baryon with a heavy quark

Non-exotic baryons (Qqq)

Exotic baryons (Qqqqq)Chromoelectric gluon→ enhanced

SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011); ibid. 85, 054003 (2012)

5. DiscussionHeavy baryon with a heavy quark

Non-exotic baryons (Qqq)

Exotic baryons (Qqqqq)Chromomagnetic gluon→ suppressed

SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011); ibid. 85, 054003 (2012)

5. DiscussionHeavy baryon with a heavy quark

Non-exotic baryons (Qqq)

Exotic baryons (Qqqqq)Chromomagnetic gluon→ suppressed

SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011); ibid. 85, 054003 (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 & perspectivesThe (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, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)

SY and Sudoh, PRC87, 105202 (2013)SY and Sudoh, PRC88, 015201 (2013)SY, Yamaguchi, Ohkoda, Hosaka, Hyodo, arXv:xxxx.yyyyy.

Heavy quark (spin) symmetryπ 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(*)

π

Spin-Complex

Spin degeneracy

Qv

gluon

Ea, Ba

6. Summary & perspectivesGluon dynamics in “single particle state” in atomic nuclei with anti-D(*) (Λc)

B.E.

thr.anti-D12C (Λc

12C)

s.p.s. (n2S+1LJ) of anti-D(*) (Λc)→ Λ(n2S+1LJ), λ1(n2S+1LJ), λ2(n2S+1LJ,mQ)

scale anomaly, chromoelectric gluon, chromomagnetic gluonfor each s.p.s.

Qv

gluon

Ea, Ba

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？