チャームハドロンの面白さとは何か？

チャームハドロンの面白さとは何か？

安井　繁宏(KEK)

ミニ滞在型研究検討会「チャームバリオンの構造と生成」 @10-13 Sep. 2013

So, what’s interesting in charm hadrons?

Contents

1. Introduction to charm (bottom) hadrons2. Mass spectrum of baryons with a heavy quark 4. Anti-D (B) meson in nuclear medium - Heavy meson effective theory with 1/M corretions

5. Summary & perspectives

Contents

1. Introduction to charm (bottom) hadrons2. Mass spectrum of baryons with a heavy quark 4. Anti-D (B) meson in nuclear medium - Heavy meson effective theory with 1/M corretions


Conclusion

Probe spin dynamics by charm hadrons!Then, we can approach gluon dynamics !!!

1. IntroductionWhat is interesting in hadron physics?

Non-perturbative physics of QCD- Spontaneous breaking of chrial symmetry- Confinement of color- Anomaly (chiral anomaly, scale anomaly, ...)- ...

T

ρColor Superconductivity

Confinement Deconfinement

2x1012 K

NuclearMatter

Gas

ClusterStrangeMatter

Neutron Stars

Early UniverseHeavy Ion Collisions

Quark-Gluon Plasma


Charm (bottom) baryons with a single heavy quark

Quark Model



Quark Model Heavy Quark Effective Theory(QCD)

Heavy quark spin+ Total angular momentum of light quarks and gluons



Quark Model Heavy Quark Effective Theory(QCD)

Heavy quark spin+ Total angular momentum of light quarks and gluons

“Brown Muck”

2. Mass spectrum of baryons with a heavy quark

Heavy quark effective theory　　　　　　 (HQET)

2. Mass spectrum of baryons with a heavy quarkHeavy 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


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


HQET

1/mQ expansion

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


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


HQET

1/mQ expansion

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

scale anomaly

chromoelectric gluon

chromomagnetic gluon

2. Mass spectrum of baryons with a heavy quarkHeavy quark limit (HQL) mQ→∞

Spin decoupling:

Heavy quark

spin

Total angular momentumof light quarks and gluons

SY, Sudoh, Yamaguchi, Ohkoda,Hosaka, Hyodo, arXv:1304.5293

Heavy Quark Symmetry (HQS)


Spin decoupling:

Heavy quark

spin


= +Normal heavy hadron Heavy quark Brown muck




Spin decoupling:

Heavy quark

spin


= +Multiquark heavy hadron Heavy quark Brown muck




Spin decoupling:

Heavy quark

spin


= +Multiquark heavy hadron Heavy quark Brown muck


New!



Spin decoupling:

Heavy quark

spin


= +Hadronic molecular

heavy hadronHeavy quark “Light Spin-Complex”

A complex of light quarks and gluons and light hadrons




Spin decoupling:

Heavy quark

spin






New!!!



Spin decoupling:

Heavy quark

spin






New!!!


Heavy hadron in nuclear medium→ Light Spin-Complex = “quark” + nucleon + hole!


Spin decoupling:

Heavy quark

spin


Ener

gy

mQ → ∞mQ : finiteJ=1/2

J=j-1/2, j+1/2J=j+1/2

J=j-1/2

J=1/2

(j≠0)1/mQ




Spin decoupling:

Heavy quark

spin


Ener

gy

mQ → ∞mQ : finiteJ=1/2

J=j-1/2, j+1/2J=j+1/2

J=j-1/2

J=1/2

(j≠0)1/mQ

HQS Singlet (j=0)



?


Spin decoupling:

Heavy quark

spin


Ener

gy

mQ → ∞mQ : finite

J=j-1/2, j+1/2J=j+1/2

J=j-1/2 (j≠0)1/mQ

J=1/2J=1/2

HQS Doublet (j≠0)



?


Examples1. Non-exotic baryons2. Exotic baryons3. Heavy meson in nuclear matter



Quark ModelRoberts and Pervin, Int. J. Mod. Phys. 23, 2817 (2008)

1. Non-exotic baryons (charm baryons) 野海・安井 “ J-PARC 高運動量ビームラインで拓く新しいハドロン・原子核物理” 原子核研究


Quark ModelRoberts and Pervin, Int. J. Mod. Phys. 23, 2817 (2008)


HQS Singlet


PDG2012 Quark ModelRoberts and Pervin, Int. J. Mod. Phys. 23, 2817 (2008)


HQS Singlet


PDG2012 Quark ModelRoberts and Pervin, Int. J. Mod. Phys. 23, 2817 (2008)


多数の未知の状態 !!

HQS Singlet

2. Mass spectrum of baryons with a heavy quark2. Exotic baryons (P(*)N molecule state; JP=1/2-, 3/2-) P(*)=(Qq)spin 0 (1)

N

P(*)

π

SY, Sudoh, Yamaguchi, Ohkoda, Hosaka, Hyodo, arXv:1304.5293


N

P(*)

π

Unitary transformation




N

P(*)

π





N

P(*)

π





N

P(*)

π





N

P(*)

π



P(*)N(1/2-) is degenerate with P(*)N(3/2-).



N

P(*)

π



P(*)N(1/2-) is degenerate with P(*)N(3/2-).HQS Doublet



N

P(*)

π



P(*)N(1/2-) is degenerate with P(*)N(3/2-).Light Spin-Complex “qN” (1+) is commonly contained.

HQS Doublet


2. Mass spectrum of baryons with a heavy quark3. P(*) meson in nuclear matter P(*)=(Qq)spin 0 (1)



3 2 1Degrees ofdegeneracy =



In-medium mass of P = In medium mass of P*




In-medium mass of P = In medium mass of P*


HQS Doublet



In-medium mass of P = In medium mass of P*HQS Doublet



Light Spin-Complex “qNN-1” (1/2+) is commonly contained.

In-medium mass of P = In medium mass of P*HQS Doublet



T



2x1012 K

NuclearMatter

Gas


Neutron Stars


Quark-Gluon Plasma



T



2x1012 K

NuclearMatter

Gas


Neutron Stars


Quark-Gluon Plasma

Colored Object ?in quarkyoic phase,color superconductivity, ...



T



2x1012 K

NuclearMatter

Gas


Neutron Stars


Quark-Gluon Plasma

Light Spin-Complexin heavy hadron



T



2x1012 K

NuclearMatter

Gas


Neutron Stars


Quark-Gluon Plasma

Light Spin-Complexin heavy hadron


Connection by charm (bottom) quark?

3. Anti-D (B) meson in nuclear medium

Let us talk more about 1/M expansionfor heavy meson P(*) in nuclear matter!

P(*)=(Qq)spin 0 (1)

SY and Sudoh, arXiv:1308:0098 [hep-ph]

Heavy Quark Effective Theory　　　　　　 (HQET)


In-medium

3. Anti-D (B) meson in nuclear mediumHeavy 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


rest frame

Qv


HQET

1/mQ expansion

Matrix elements

scale anomaly




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


rest frame

Qv


HQET

1/mQ expansion

Matrix elements

scale anomaly




mQ

vacuum medium

Mass

Λ : O(mQ0) + λ1 : O(1/mQ)

Λ : O(mQ0) + λ1 : O(1/mQ)

λ2 : O(1/mQ)

λ2 : O(1/mQ)

j-1/2

j-1/2

j-1/2

j-1/2

1/mQ expansion


mQ

vacuum medium

Mass

Λ : O(mQ0) + λ1 : O(1/mQ)

Λ : O(mQ0) + λ1 : O(1/mQ)

λ2 : O(1/mQ)

λ2 : O(1/mQ)

j-1/2

j-1/2

j-1/2

j-1/2

Λ , λ1 and λ2 change in medium.

1/mQ expansion


mQ

vacuum medium

Mass

Λ : O(mQ0) + λ1 : O(1/mQ)

Λ : O(mQ0) + λ1 : O(1/mQ)

λ2 : O(1/mQ)

λ2 : O(1/mQ)

j-1/2

j-1/2

j-1/2

j-1/2

Λ , λ1 and λ2 change in medium.

Gluon fields change in medium.

1/mQ expansion

Heavy meson effective theory　　　　　　 (HMET)



HQET HMET 1/mQ expansion(mQ : heavy quark mass)

1/M expansion(M : heavy meson mass)










3. Anti-D (B) meson in nuclear mediumHeavy 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)

P(*)=(Qq)spin 0 (1)


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

P(*)=(Qq)spin 0 (1)


Axial-currents composed by Hv :



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



HQSS broken (Γ=γμγ5, σμν) smaller than or equal to O(1/M1) HQSS=Heavy quark spin symmetry



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

HQSS conserved

O(1/M1)

HQSS broken

HQSS=Heavy quark spin symmetry


Effective Lagrangian for HMETKitazawa, Kurimoto, PLB323, 65 (1994)

P-P* mass splitting

Axial-vector currentby pions

H

H pion

axial-current coupling g1, g1/M, g2/M


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

Kitazawa, Kurimoto, PLB323, 65 (1994)


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)

Kitazawa, Kurimoto, PLB323, 65 (1994)

3. 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 in nuclear matter


N N NN-1 N-1 N-1





N N NN-1 N-1 N-1





N N NN-1 N-1 N-1





N N NN-1 N-1 N-1





scale anomaly in QCD



at normal density





in-medium modifications of ... at normal density

@ medium

@ vacuum






@ medium

@ vacuum






@ medium

@ vacuum





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

@ medium

@ vacuum






→ 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

@ medium

@ vacuum






→ 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

@ medium

@ vacuum

about 0.9 suppression in gluon condensate (Cohen et al. 1992)

4. 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)



Exotic baryons (Qqqqq)Chromoelectric gluon → enhanced




Exotic baryons (Qqqqq)Chromomagnetic gluon → suppressed



We discussed charm baryon mass spectrum.



Heavy quark symmetry is important for (approximately) degeneratemass levels. - Non-exotic baryons - Exotic baryons (P(*)N) - P(*) meson in nuclear matter




By probing of P(*) meson mass in nuclear matter, we find ... (1) Scale anomaly from QCD is suppressed. (2) Chromoelectric gluons are enhanced. (3) Chromomagnetic gluons are suppressed.




By probing of P(*) meson mass in nuclear matter, we find ... (1) Scale anomaly from QCD is suppressed. (2) Chromoelectric gluons are enhanced. (3) Chromomagnetic gluons are suppressed.

Experimental studies for charmed nuclei at J-PARC are important.

5. Summary & perspectivesPath between hadron physics and nuclear physics

Interaction between an anti-D(*) (B(*)) meson and a nucleonSY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)

Heavy quark (spin) symmetry

π exchange interaction Feshbach resonancesN

D(*)

π


Interaction between an anti-D(*) (B(*)) meson and a nucleon

Anti-D(*) and B(*) mesons in nuclear 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, Sudoh, Yamaguchi, Ohkoda, Hosaka, Hyodo, arXv:1304.5293 [hep-ph]


π exchange interaction

Isospin polarization

Feshbach resonances

Kondo effects

N

D(*)

π

Spin-ComplexSpin degeneracy




Anti-D(*) (B(*)) meson → Probing gluon dynamics in medium






Feshbach resonances

Kondo effects

Chromoelectric & chromomagnetic gluons probed by a heavy quark


N

D(*)

π


Qv

gluon

Ea, Ba




Anti-D(*) (B(*)) meson → Probing gluon dynamics in medium






Feshbach resonances

Kondo effects

Chromoelectric & chromomagnetic gluons probed by a heavy quark


Heavy quarks connect QCD and nuclear physics!!

N

D(*)

π


Qv

gluon

Ea, Ba

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

B.E.

thr.anti-D12C (Λc

12C)

g.s.

e.s.J-1/2

J+1/2s.p.s. (n2S+1LJ) of anti-D(*) (Λc)

5. 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

Let’s probe spin dynamics by charm hadrons!


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

Then, we can approach gluon dynamics !!!

Gluon dynamics in “single particle state” in atomic nuclei with anti-D(*) (Λc)

Documents

チャームハドロンの 面白さとは何か？

チャームハドロンの面白さとは何か？