Charm hadrons in nuclear medium
S. Yasui(KEK)
K. Sudoh(Nishogakusha Univ.)
“Hadron in nucleus” workshop@YITP, 31 Nov. – 2 Dec. 2013
arXiv:1308:0098 [hep-ph]
Contents
1. Introduction to charm (bottom) nuclei2. Mass formula with 1/mQ expansion3. Anti-D (B) meson in nuclear medium - Heavy meson effective theory with 1/M corretions
4. Summary & perspectives
1. Introduction to charm (bottom) nuclei
1. D (B) meson and nucleon interaction2. Modifications of D (B) meson chiral condensate, gluon condensate, ...3. Modifications of nuclear structure glue-like role?
D(*) (B(*)) meson in nuclear matter
Cf. Kondo effectK.Sudoh, S.Y.,PRC88, 015201(2013)
→ L. Tolos A. Yokota Y. Yamaguchi K. Suzuki
1. Introduction to charm (bottom) nucleiD(*) (B(*)) meson in nuclear matter
Quark-mesoncoupling model QCD sum rules Mean field models
Coupled-channel modelswith contact interactions
Perturbation by pion exchanges
SY and Sudoh, PRC87, 105202 (2013)
Binding energy of D(*) (B(*)) meson in nuclear matter (MeV)
→ L. Tolos A. Yokota Y. Yamaguchi K. Suzuki
1. Introduction to charm (bottom) nuclei
1. D (B) meson and nucleon interaction2. Modifications of D (B) meson chiral condensate, gluon condensate, ...3. Modifications of nuclear structure glue-like role?
D(*) (B(*)) meson in nuclear matter
Cf. Kondo effectK.Sudoh, S.Y.,PRC88, 015201(2013)
→ L. Tolos A. Yokota Y. Yamaguchi K. Suzuki
1. Introduction to charm (bottom) nucleiD(*) (B(*)) meson in nuclear matter
1. D (B) meson and nucleon interaction2. Modifications of D (B) meson chiral condensate, gluon condensate, ...3. Modifications of nuclear structure glue-like role?4. Probe for “gluon dynamics” New from heavy quark!
Cf. Kondo effectK.Sudoh, S.Y.,PRC88, 015201(2013)
→ L. Tolos A. Yokota Y. Yamaguchi K. Suzuki
2. Mass formula with 1/mQ expansion
Heavy Quark Effective Theory (HQET)
2. Mass formula with 1/mQ expansionHeavy quark effective theory (HQET)
Qv
HQET
1/mQ expansionLight quarks & gluons
2. Mass formula with 1/mQ expansionHeavy quark effective theory (HQET)
Mass of heavy meson H containing a heavy quark Q (in vacuum)rest frame
Qv
HQET
1/mQ expansionLight quarks & gluons
2. Mass formula with 1/mQ expansionHeavy quark effective theory (HQET)
Mass of heavy meson H containing a heavy quark Q (in vacuum)
LO
NLO O(1/mQ)
rest frame
Bigi, Shifman, Uraltsev, Vainshtein,PRD52, 196 (1995)
Neubert, PLB322, 419 (1994)“Virial theorem”
Qv
HQET
1/mQ expansion
Matrix elements
scale anomaly
chromoelectric gluon
chromomagnetic gluon
Light quarks & gluons
Heavy Quark Effective Theory (HQET)
3. Anti-D (B) meson in nuclear medium
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)
rest frame
Qv
HQET
1/mQ expansion
Matrix elements
scale anomaly
chromoelectric gluon
chromomagnetic gluon
Light quarks & gluons
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)
rest frame
Qv
HQET
1/mQ expansion
Matrix elements
scale anomaly
chromoelectric gluon
chromomagnetic gluon
Light quarks & gluons
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)
rest frame
Qv
HQET
1/mQ expansion
Matrix elements
scale anomaly
chromoelectric gluon
chromomagnetic gluon
1/mQ
Light quarks & gluons
3. Anti-D (B) meson in nuclear medium
Λ , λ1 and λ2 change in medium.
Gluon fields change in medium.
Q
gluon
Ea, Ba
Heavy meson effective theory (HMET)
3. Anti-D (B) meson in nuclear medium
Non-perturbative dynamics by light quarks and gluons??
LO + NLO
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)
3. Anti-D (B) meson in nuclear mediumHeavy 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
P(*)=(Qq)spin 0 (1)
3. Anti-D (B) meson in nuclear mediumHeavy meson effective theory with 1/M corrections
Axial-currents composed by Hv :
3. Anti-D (B) meson in nuclear mediumHeavy 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. Anti-D (B) meson in nuclear mediumHeavy 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. Anti-D (B) meson in nuclear mediumHeavy 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. Anti-D (B) meson in nuclear mediumHeavy 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. Anti-D (B) meson in nuclear mediumHeavy meson effective theory with 1/M corrections
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
3. Anti-D (B) meson in nuclear mediumHeavy 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
Kitazawa, Kurimoto, PLB323, 65 (1994)
3. Anti-D (B) meson in nuclear mediumHeavy 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 not qualitatively changed.)
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
Cf. Λ-Σ mixing in nuclear matter
anti-D meson anti-D* meson
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
Cf. Λ-Σ mixing in nuclear matter
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
g →g + (g1+g2)/M
Kitazawa, Kurimoto, PLB323, 65 (1994)
g →g + (g1+g2)/M
g →g + (g1-g2)/M
3. Anti-D (B) meson in nuclear mediumIn-medium masses of anti-D(*) (B(*)) meson in nuclear matter
ρ=0.17 fm-3
3. 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
@ medium
@ vacuum
ρ=0.17 fm-3
about 0.9 suppression in gluon condensate (T. Cohen et al. 1992)
3. 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
@ medium
@ vacuum
ρ=0.17 fm-3
about 0.9 suppression in gluon condensate (T. Cohen et al. 1992)
3. 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
@ medium
@ vacuum
ρ=0.17 fm-3
about 0.9 suppression in gluon condensate (T. Cohen et al. 1992)
3. Anti-D (B) meson in nuclear mediumIn-medium masses of anti-D(*) (B(*)) meson in nuclear matter
scale anomaly in QCD→ suppressed
Energy contribution from gluonsbecomes small. (Suppression ofquantum effects.)
( g, g1/MD, g2/MD ) = (0.5, 0, -0.07)
(0.4, 0, -0.17)
normal density
@ medium
@ vacuum
Λ
3. Anti-D (B) meson in nuclear mediumIn-medium masses of anti-D(*) (B(*)) meson in nuclear matter
scale anomaly in QCD
chromoelectric gluon
→ suppressed
→ enhanced
Energy contribution from gluonsbecomes small. (Suppression ofquantum effects.)
Kinetic energy becomes large,due to the binding energy.
normal density
( g, g1/MD, g2/MD ) = (0.5, 0, -0.07)
(0.4, 0, -0.17)
normal density
@ medium
@ vacuum
Λ
λ1
3. 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
→ 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.
normal density
( g, g1/MD, g2/MD ) = (0.5, 0, -0.07)
(0.4, 0, -0.17)
normal density
@ medium
@ vacuum
Λ
λ1
λ2
3. Anti-D (B) meson in nuclear mediumGluon dynamics in “single particle state” in atomic nuclei with anti-D(*) (Λc)
anti-D12C (Λc
12C)
B.E.
thr.
g.s.
e.s.j-1/2
j+1/2
3. Anti-D (B) meson in nuclear mediumGluon 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, λ1, λ2(mQ) @n2S+1LJ
scale anomaly, chromoelectric gluon, chromomagnetic gluonfor each s.p.s.
Q
gluon
Ea, Ba
g.s.
e.s.j-1/2
j+1/2
Gluon dynamicscan be probed for each s.p.s. !?
3. Anti-D (B) meson in nuclear mediumGluon 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, λ1, λ2(mQ) @n2S+1LJ
scale anomaly, chromoelectric gluon, chromomagnetic gluonfor each s.p.s.
Q
gluon
Ea, Ba
g.s.
e.s.j-1/2
j+1/2
Heavy hadron mass spectrum
Gluon dynamics
Gluon dynamicscan be probed for each s.p.s. !?
3. Anti-D (B) meson in nuclear medium
chromomagnetic gluonchromoelectric gluon→ enhanced → suppressed
Cf. Yamaguchi’s presentation
Few-body calculations
Two-bodyS.Y., K.Sudoh, Phys. Rev. D80, 034008 (2009)Y.Yamaguchi, S.Ohkoda, S.Y., A.Hosaka, Phys. Rev. D84, 014032 (2011); ibid. 85, 054003 (2013)Three-bodyY.Yamaguchi, S.Y., A.Hosaka, arXiv:1309.4324 [nucl-th]
4. Summary & perspectives
We discussed charm (bottom) hadron mass in nuclear medium.
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.
We considered 1/mQ expansion up to O(1/mQ).
Experimental studies for charmed nuclei at J-PARC and GSI-FAIR.
4. Summary & perspectives
We discussed charm (bottom) hadron mass in nuclear medium.
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.
We considered 1/mQ expansion up to O(1/mQ).
Experimental studies for charmed nuclei at J-PARC and GSI-FAIR.
4. Summary & perspectives
We discussed charm (bottom) hadron mass in nuclear medium.
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.
We considered 1/mQ expansion up to O(1/mQ).
Experimental studies for charmed nuclei at J-PARC and GSI-FAIR.
4. Summary & perspectives
We discussed charm (bottom) hadron mass in nuclear medium.
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 and GSI-FAIR.
We considered 1/mQ expansion up to O(1/mQ).
“Gluons” can be researched in charm/bottom systems !!
Quarks & Gluons
Chiralsymmetry
m→0
Chiralsymmetry
Heavyquark
symmetry
Quarks & Gluons
m→0 m→∞
D*+N (2947 MeV)
D+N (2803 MeV)
Only DN and D*N channel
D and nucleon
`Exotic channel‘
π+Σc (2593 MeV)
π+Σc* (2658 MeV)
Λc(2595) 0(1/2-)Λc(2625) 0(3/2-)
Σc(2800) 1(??)
D*+N (2947 MeV)
D+N (2803 MeV)
D and nucleon
`Baryon channel‘
C<0 C>0
different
What is D/D-nucleon interaction ?
cqqqq
cqqqqSY and Sudoh, PRD80, 034008 (2009)
Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
Yamaguchi, Ohkoda, SY, Hosaka, arXiv:1301.4557 [hep-ph]
D*+N (2947 MeV)
D+N (2803 MeV)
Only DN and D*N channel
D and nucleon
`Exotic channel‘
C<0
What is D/D-nucleon interaction ?
cqqqqSY and Sudoh, PRD80, 034008 (2009)
Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
C>0π+Σc (2593 MeV)
π+Σc* (2658 MeV)
Λc(2595) 0(1/2-)Λc(2625) 0(3/2-)
Σc(2800) 1(??)
D*+N (2947 MeV)
D+N (2803 MeV)
D and nucleon
`Baryon channel‘
different
cqqqqYamaguchi, Ohkoda, SY, Hosaka, arXiv:1301.4557 [hep-ph]