反D中間子をふくむチャーム原子核
arXiv:1308.0098 [hep-ph]
安井 繁宏
(KEK)
共同研究者
須藤 和敬
(二松学舎大学)
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
Contents
1. Introduction to charm (bottom) nuclei
2. Heavy hadron mass and gluon field
- Heavy quark effective theory (HQET) with 1/mQ corrections
3. Heavy meson effective theory with 1/M corretions
4. Anti-D (B) meson in nuclear medium
5. Discussion
6. Summary & perspectives
チャーム原子核の魅力とは？
課題とは？
1. Introduction
Charm hadrons in medium
D(cq)
- What are charm hadrons in nuclei?
C>0 Λc(cqq) nuclei Bando, Nagata, PTP69, 557
(1983)
Schmidt, Teramond
C=0 J/Ψ(cc) nuclei Brodsky,
PRL64, 1011 (1990)
et al.
C<0 D(cq) nuclei Tsushima
PRC59, 2824 (1999)
Light degrees of freedom “q”
→ Affected by medium effect
(Partial restoration of the chiral symmetry breaking?)
- Questions
・ Are they really stable states?
・ How can be produced in experiments?
・ What are the new and interesting things?
Charmed nuclei
D nuclei (C<0)
No annihilation/absorption
→ Clean probe as mesic nuclei!
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)
1. Introduction
Charm hadrons in medium
D(cq)
- What are charm hadrons in nuclei?
C>0 Λc(cqq) nuclei Bando, Nagata, PTP69, 557
(1983)
Schmidt, Teramond
C=0 J/Ψ(cc) nuclei Brodsky,
PRL64, 1011 (1990)
et al.
C<0 D(cq) nuclei Tsushima
PRC59, 2824 (1999)
Light degrees of freedom “q”
→ Affected by medium effect
(Partial restoration of the chiral symmetry breaking?)
- Questions
・ Are they really stable states?
・ How can be produced in experiments?
・ What are the new and interesting things?
Charmed nuclei
D nuclei (C<0)
No annihilation/absorption
→ Clean probe as mesic nuclei!
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)
1. Introduction
Charm hadrons in medium
D(cq)
- What are charm hadrons in nuclei?
C>0 Λc(cqq) nuclei Bando, Nagata, PTP69, 557
(1983)
Schmidt, Teramond
C=0 J/Ψ(cc) nuclei Brodsky,
PRL64, 1011 (1990)
et al.
C<0 D(cq) nuclei Tsushima
PRC59, 2824 (1999)
Light degrees of freedom “q”
→ Affected by medium effect
Charmed nuclei
(Partial restoration of the chiral symmetry breaking?)
- Questions
Quark-meson
coupling model
D nuclei (C<0)
SY and Sudoh, PRC87, 105202 (2013)
QCD sum rules
No annihilation/absorption
→ Clean
probe as
mesic Perturbation
nuclei! by
Coupled-channel
models
Mean field models
with contact interactions
pion exchanges
1. Introduction
Charm hadrons in medium
D(cq)
- What are charm hadrons in nuclei?
C>0 Λc(cqq) nuclei Bando, Nagata, PTP69, 557
(1983)
Schmidt, Teramond
C=0 J/Ψ(cc) nuclei Brodsky,
PRL64, 1011 (1990)
et al.
C<0 D(cq) nuclei Tsushima
PRC59, 2824 (1999)
Light degrees of freedom “q”
→ Affected by medium effect
(Partial restoration of the chiral symmetry breaking?)
- Questions
・ Are they really stable states?
・ How can be produced in experiments?
・ What are the new and interesting things?
Charmed nuclei
D nuclei (C<0)
No annihilation/absorption
→ Clean probe as mesic nuclei!
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 the “interesting” and “new” roles of heavy hadrons
in medium at finite density?
1. Introduction
Charm hadrons in medium
D(cq)
- What are charm hadrons in nuclei?
C>0 Λc(cqq) nuclei Bando, Nagata, PTP69, 557
(1983)
Schmidt, Teramond
C=0 J/Ψ(cc) nuclei Brodsky,
PRL64, 1011 (1990)
et al.
C<0 D(cq) nuclei Tsushima
PRC59, 2824 (1999)
Light degrees of freedom “q”
→ Affected by medium effect
(Partial restoration of the chiral symmetry breaking?)
Charmed nuclei
D nuclei (C<0)
- Questions
・ 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!
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)
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) 1/mQ expansion
HQET
Qv
Effective heavy quark field
(four-velocity v)
Covariant derivative
Tensor field of gluon
(chromoelectric G0i,
chromomagnetic Gij)
Light quarks & gluons
2. Heavy hadron mass and gluon field
Heavy quark effective theory (HQET) 1/mQ expansion
Light quarks & gluons
HQET
Qv
Mass of heavy meson H containing a heavy quark Q (in vacuum)
rest frame
D-D* (B-B*) mass approximate degeneracy
Matrix elements
LO
HQS conserved
HQFS conserved
HQSS conserved
HQFS broken
HQSS conserved
NLO O(1/mQ)
HQS broken
HQFS broken
HQSS broken
HQS = Heavy quark symmetry, HQFS=Heavy quark flavor symmetry, HQSS=Heavy quark spin symmetry
2. Heavy hadron mass and gluon field
Heavy quark effective theory (HQET) 1/mQ expansion
Light quarks & gluons
HQET
Qv
Mass of heavy meson H containing a heavy quark Q (in vacuum)
rest frame
Matrix elements
LO
HQS conserved
NLO O(1/mQ)
HQS broken
HQS = Heavy quark symmetry
Bigi, Shifman, Uraltsev, Vainshtein,
PRD52, 196 (1995)
Neubert, PLB322, 419 (1994)
“the virial theorem”
2. Heavy hadron mass and gluon field
Heavy quark effective theory (HQET) 1/mQ expansion
Light quarks & gluons
HQET
Qv
Mass of heavy meson H containing a heavy quark Q (in medium at T and ρ)
rest frame
Matrix elements
LO
HQS conserved
NLO O(1/mQ)
HQS broken
HQS = Heavy quark symmetry
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
in-medium modifications of ...
LO
HQS conserved
scale anomaly
in QCD
chromoelectric
gluon
NLO O(1/mQ)
HQS broken
chromomagnetic
gluon
Probing gluon dynamics by hadrons with a heavy quark
3. Heavy meson effective theory with 1/M corr.
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?
Point 1. How can we calculate in-medium masses? (LQCD is not applicable.)
Point 2. 1/mQ expansion (mQ=mc, mb).
→ We use the heavy meson effective theory (HMET) with 1/M expansion.
M: heavy hadron mass
3. Heavy meson effective theory with 1/M corr.
How are anti-D (B) mesons are modified in nuclear medium?
Point 1. How can we calculate in-medium masses? (LQCD is not applicable.)
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 1. → Effective degrees of freedom in confinement
phase are hadrons
Point 2. → O(1/mQ0) = O(1/M0)
O(1/mQ1) = O(1/M1)
N
N-1
From M=mQ+Λ+..., we obtain 1/M=1/mQ+...
3. Heavy meson effective theory with 1/M corr.
How are anti-D (B) mesons are modified in nuclear medium?
Point 1. How can we calculate in-medium masses? (LQCD is not applicable.)
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 1. → Effective degrees of freedom in confinement
phase are hadrons
Point 2. → O(1/mQ0) = O(1/M0)
O(1/mQ1) = O(1/M1)
N
N-1
From M=mQ+Λ+..., we obtain 1/M=1/mQ+...
We need the heavy meson effective Lagrangian with 1/M corrections.
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
vector meson
pseudoscalar meson
Spin degeneracy at LO
four-velocity + residual momentum
1/M correction (NLO) : uncertainty of four-velocity or residual momentum
(change of frame with v to frame with w)
Hv(x)
Hw(x)
v
w
Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994)
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
vector meson
pseudoscalar meson
Spin degeneracy at LO
four-velocity + residual momentum
1/M correction (NLO) : uncertainty of four-velocity or residual momentum
(change of frame with v to frame with w)
Hv(x)
v
p/M
Hw(x)
w
Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994)
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)
O(1/M0) or 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 :
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 :
HQSS conserved
O(1/M0) or O(1/M1)
HQSS broken
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
Effective Lagrangian for HMET
P-P* mass splitting
Axial-vector current
by pions
Kitazawa, Kurimoto, PLB323, 65 (1994)
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)
Constraint on g1 and g2
We assume g1=0 (conclusion is insensitive to g1)
( 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)
4. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
N
N-1
N
N-1
N
N-1
1/M corrections
from HMET
Cf. Λ-Σ mixing
anti-D meson
anti-D* meson
4. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
N
N-1
N
N-1
N
N-1
1/M corrections
from HMET
Cf. Λ-Σ mixing
anti-D meson
anti-D* meson
4. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
scale anomaly chromoelectric
gluon
in QCD
chromomagnetic
gluon
at normal density
4. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
in-medium modifications of ...
scale anomaly in QCD
chromoelectric gluon
chromomagnetic gluon
at normal density
4. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
in-medium modifications of ...
scale anomaly in QCD
suppressed
chromoelectric gluon
enhanced
chromomagnetic gluon
suppressed
at normal density
4. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
in-medium modifications of ...
(0.4, 0, -0.17)
( g, g1/MD, g2/MD ) = (0.5, 0, -0.07)
scale anomaly in QCD
→ suppressed
normal density
chromoelectric gluon
→ enhanced
chromomagnetic gluon
→ suppressed
normal density
4. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
in-medium modifications of ...
(0.4, 0, -0.17)
( g, g1/MD, g2/MD ) = (0.5, 0, -0.07)
scale anomaly in QCD
→ suppressed
Energy contribution from gluons
becomes small. (Suppression of
quantum effects.)
normal density
chromoelectric gluon
→ enhanced
Kinetic energy becomes large,
due to the binding energy.
chromomagnetic gluon
→ suppressed
D-D* (B-B*) splitting become small.
(Extended brown muck dressed by
nucleon-hole pairs in medium?)
normal density
5. Discussion
Heavy 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. Discussion
Heavy baryon with a heavy quark
Non-exotic baryons (Qqq)
Chromoelectric gluon
Exotic baryons (Qqqqq)
→ enhanced
SY and Sudoh, PRD80, 034008 (2009)
Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011); ibid. 85, 054003 (2012)
5. Discussion
Heavy baryon with a heavy quark
Non-exotic baryons (Qqq)
Chromomagnetic gluon
Exotic baryons (Qqqqq)
→ suppressed
SY and Sudoh, PRD80, 034008 (2009)
Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011); ibid. 85, 054003 (2012)
5. Discussion
Heavy baryon with a heavy quark
Non-exotic baryons (Qqq)
Chromomagnetic gluon
Exotic baryons (Qqqqq)
→ 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 & perspectives
The (personal) path between hadron physics and nuclear physics
D(*)
π
Interaction between an anti-D(*) (B(*)) meson and a nucleon
Heavy quark (spin) symmetry
π exchange interaction
Spin degeneracy
N
SY and Sudoh, PRD80, 034008 (2009)
Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)
Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
Feshbach resonances
Anti-D(*) and B(*) mesons in nuclear medium
Isospin polarization
Kondo effects
SY and Sudoh, PRC87, 105202 (2013)
SY and Sudoh, PRC88, 015201 (2013)
SY, Yamaguchi, Ohkoda, Hosaka, Hyodo, arXv:xxxx.yyyyy.
Spin-Complex
Anti-D(*) (B(*)) meson → Probing gluon dynamics in medium
gluon
SY and Sudoh, arXiv:1308:0098 [hepph]
Chromoelectric & chromomagnetic
gluons probed by a heavy quark
Qv
Ea, Ba
Do heavy quarks connect QCD and nuclear physics?
6. Summary & perspectives
Gluon dynamics in “single particle state” in atomic nuclei with anti-D(*) (Λc)
gluon
12
12
anti-D C (Λc C)
thr.
Qv
Ea, Ba
B.E.
e.s.
J+1/2
J-1/2
g.s.
s.p.s. (n2S+1LJ) of anti-D(*) (Λc)
→ Λ(n2S+1LJ), λ1(n2S+1LJ), λ2(n2S+1LJ,mQ)
scale anomaly, chromoelectric gluon, chromomagnetic gluon
for each s.p.s.
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？