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Charm hadrons in nuclear medium
arXiv:1308:0098 [hep-ph]
S. Yasui
(KEK)
K. Sudoh
(Nishogakusha Univ.)
“Hadron in nucleus” workshop@YITP, 31 Nov. – 2 Dec. 2013
Contents
1. Introduction to charm (bottom) nuclei
2. Mass formula with 1/mQ expansion
3. Anti-D (B) meson in nuclear medium
- Heavy meson effective theory with 1/M corretions
4. Summary & perspectives
1. Introduction to charm (bottom) nuclei
D(*) (B(*)) meson in nuclear matter
1. D (B) meson and nucleon interaction
2. Modifications of D (B) meson
chiral condensate, gluon condensate, ...
3. Modifications of nuclear structure
glue-like role?
→ L. Tolos
A. Yokota
Y. Yamaguchi
K. Suzuki
Cf. Kondo effect
K.Sudoh, S.Y.,
PRC88, 015201
(2013)
1. Introduction to charm (bottom) nuclei
D(*) (B(*)) meson in nuclear matter
→ L. Tolos
A. Yokota
Y. Yamaguchi
K. Suzuki
SY and Sudoh, PRC87, 105202 (2013)
Binding energy of D(*) (B(*)) meson in nuclear matter (MeV)
Quark-meson
coupling model
QCD sum rules
Mean field models
Coupled-channel models
with contact interactions
Perturbation by
pion exchanges
1. Introduction to charm (bottom) nuclei
D(*) (B(*)) meson in nuclear matter
1. D (B) meson and nucleon interaction
2. Modifications of D (B) meson
chiral condensate, gluon condensate, ...
3. Modifications of nuclear structure
glue-like role?
→ L. Tolos
A. Yokota
Y. Yamaguchi
K. Suzuki
Cf. Kondo effect
K.Sudoh, S.Y.,
PRC88, 015201
(2013)
1. Introduction to charm (bottom) nuclei
D(*) (B(*)) meson in nuclear matter
→ L. Tolos
A. Yokota
Y. Yamaguchi
K. Suzuki
1. D (B) meson and nucleon interaction
2. Modifications of D (B) meson
chiral condensate, gluon condensate, ...
Cf. Kondo effect
K.Sudoh, S.Y.,
PRC88, 015201
(2013)
3. Modifications of nuclear structure
glue-like role?
4. Probe for “gluon dynamics”
New from heavy quark!
2. Mass formula with 1/mQ expansion
Heavy Quark Effective Theory
(HQET)
2. Mass formula with 1/mQ expansion
Heavy quark effective theory (HQET) 1/mQ expansion
Light quarks
& gluons
HQET
Qv
2. Mass formula with 1/mQ expansion
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
2. Mass formula with 1/mQ expansion
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
scale anomaly
NLO O(1/mQ)
chromoelectric gluon
chromomagnetic gluon
Bigi, Shifman, Uraltsev, Vainshtein,
PRD52, 196 (1995)
Neubert, PLB322, 419 (1994)
“Virial theorem”
3. Anti-D (B) meson in nuclear medium
In-medium
Heavy Quark Effective Theory
(HQET)
3. Anti-D (B) meson in nuclear medium
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
scale anomaly
NLO O(1/mQ)
chromoelectric gluon
chromomagnetic gluon
3. Anti-D (B) meson in nuclear medium
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
scale anomaly
NLO O(1/mQ)
chromoelectric gluon
chromomagnetic gluon
3. Anti-D (B) meson in nuclear medium
Heavy quark effective theory (HQET) 1/mQ expansion
Light quarks
& gluons
HQET
Qv
1/mQ
Mass of heavy meson H containing a heavy quark Q (in medium at T and ρ)
rest frame
Matrix elements
LO
scale anomaly
NLO O(1/mQ)
chromoelectric gluon
chromomagnetic gluon
3. Anti-D (B) meson in nuclear medium
Λ , λ1 and λ2 change in medium.
Gluon fields change in medium.
gluon
Q
Ea, Ba
3. Anti-D (B) meson in nuclear medium
Non-perturbative dynamics by light quarks and gluons??
Heavy meson effective theory
(HMET)
LO + NLO
3. Anti-D (B) meson in nuclear medium
Heavy meson effective theory with 1/M corrections
Heavy-meson effective field and separation of momentum
P(*)=(Qq)spin 0 (1)
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. Anti-D (B) meson in nuclear medium
Heavy meson effective theory with 1/M corrections
Heavy-meson effective field and separation of momentum
P(*)=(Qq)spin 0 (1)
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. Anti-D (B) meson in nuclear medium
Heavy meson effective theory with 1/M corrections
Axial-currents composed by Hv :
3. Anti-D (B) meson in nuclear medium
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. Anti-D (B) meson in nuclear medium
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. Anti-D (B) meson in nuclear medium
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. Anti-D (B) meson in nuclear medium
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. Anti-D (B) meson in nuclear medium
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
H
pion
axial-current coupling g1, g1/M, g2/M
H
3. Anti-D (B) meson in nuclear medium
Heavy meson effective theory with 1/M corrections
Effective Lagrangian for HMET --- How to fix couplings g, g1 and g2? --Kitazawa, Kurimoto, PLB323, 65 (1994)
LO
NLO
NLO
Lattice QCD simulations by Detmold, Lin, Meinel, PRD.85, 114508 (2012)
g
g=0.4-0.5
3. Anti-D (B) meson in nuclear medium
Heavy meson effective theory with 1/M corrections
Effective Lagrangian for HMET --- How to fix couplings g, g1 and g2? --Kitazawa, Kurimoto, PLB323, 65 (1994)
LO
NLO
NLO
Decay width of D* → Dπ (PDG2012)
Constraint on g1 and g2
We assume g1=0. (Conclusion is not qualitatively changed.)
( 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)
3. 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
Cf. Λ-Σ mixing in
nuclear matter
anti-D meson
anti-D* meson
3. 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
Cf. Λ-Σ mixing in
nuclear matter
anti-D meson
anti-D* meson
Kitazawa, Kurimoto,
PLB323, 65 (1994)
3. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
g →g + (g1-g2)/M
N
N-1
N
N-1
1/M corrections
from HMET
g →g + (g1+g2)/M
N
N-1
g →g + (g1+g2)/M
Cf. Λ-Σ mixing in
nuclear matter
anti-D meson
anti-D* meson
Kitazawa, Kurimoto,
PLB323, 65 (1994)
3. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
ρ=0.17 fm-3
3. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
@
mediu
m
@ vacuum
ρ=0.17 fm-3
scale anomaly in QCD
about 0.9 suppression in gluon
condensate (T. Cohen et al. 1992)
chromoelectric gluon
chromomagnetic gluon
3. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
@
mediu
m
@ vacuum
ρ=0.17 fm-3
scale anomaly in QCD
about 0.9 suppression in gluon
condensate (T. Cohen et al. 1992)
chromoelectric gluon
chromomagnetic gluon
3. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
@
mediu
m
@ vacuum
ρ=0.17 fm-3
scale anomaly in QCD
about 0.9 suppression in gluon
condensate (T. Cohen et al. 1992)
chromoelectric gluon
chromomagnetic gluon
3. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
@
mediu
m
@ vacuum
(0.4, 0, -0.17)
( g, g1/MD, g2/MD ) = (0.5, 0, -0.07)
scale anomaly in QCD
Λ
→ suppressed
Energy contribution from gluons
becomes small. (Suppression of
quantum effects.)
normal density
3. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
@
mediu
m
@ vacuum
(0.4, 0, -0.17)
( g, g1/MD, g2/MD ) = (0.5, 0, -0.07)
scale anomaly in QCD
Λ
→ suppressed
Energy contribution from gluons
becomes small. (Suppression of
quantum effects.)
normal density
chromoelectric gluon
λ1
→ enhanced
Kinetic energy becomes large,
due to the binding energy.
normal density
3. Anti-D (B) meson in nuclear medium
In-medium masses of anti-D(*) (B(*)) meson in nuclear matter
@
mediu
m
@ vacuum
(0.4, 0, -0.17)
( g, g1/MD, g2/MD ) = (0.5, 0, -0.07)
scale anomaly in QCD
Λ
→ suppressed
Energy contribution from gluons
becomes small. (Suppression of
quantum effects.)
normal density
chromoelectric gluon
λ1
→ enhanced
Kinetic energy becomes large,
due to the binding energy.
chromomagnetic gluon
λ2
→ suppressed
D-D* (B-B*) splitting become small.
normal density
3. Anti-D (B) meson in nuclear medium
Gluon dynamics in “single particle state” in atomic nuclei with anti-D(*) (Λc)
12
12
anti-D C (Λc C)
thr.
B.E.
e.s.
j+1/2
j-1/2
g.s.
3. Anti-D (B) meson in nuclear medium
Gluon dynamics in “single particle state” in atomic nuclei with anti-D(*) (Λc)
gluon
Gluon dynamics
12C ( 12C)
thr.
anti-D
Λc
can be probed
Q
for each s.p.s. !?
a
a
E ,B
B.E.
j+1/2
e.s.
s.p.s. (n2S+1L ) of anti-D(*) (Λc)
j-1/2
g.s.
J
→ Λ, λ1, λ2(mQ) @n2S+1LJ
scale anomaly, chromoelectric gluon, chromomagnetic gluon
for each s.p.s.
3. Anti-D (B) meson in nuclear medium
Gluon dynamics in “single particle state” in atomic nuclei with anti-D(*) (Λc)
gluon
Gluon dynamics
12C ( 12C)
thr.
anti-D
Λc
can be probed
Q
for each s.p.s. !?
a
a
E ,B
B.E.
j+1/2
e.s.
s.p.s. (n2S+1L ) of anti-D(*) (Λc)
j-1/2
g.s.
J
→ Λ, λ1, λ2(mQ) @n2S+1LJ
scale anomaly, chromoelectric gluon, chromomagnetic gluon
for each s.p.s.
Heavy hadron mass spectrum
Gluon dynamics
3. Anti-D (B) meson in nuclear medium
Cf. Yamaguchi’s presentation
Few-body calculations
chromoelectric gluon chromomagnetic gluon
→ enhanced
→ suppressed
Two-body
S.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-body
Y.Yamaguchi, S.Y., A.Hosaka, arXiv:1309.4324 [nucl-th]
4. Summary & perspectives
We considered 1/mQ expansion up to O(1/mQ).
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.
4. Summary & perspectives
We considered 1/mQ expansion up to O(1/mQ).
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.
4. Summary & perspectives
We considered 1/mQ expansion up to O(1/mQ).
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.
4. Summary & perspectives
We considered 1/mQ expansion up to O(1/mQ).
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.
“Gluons” can be researched in charm/bottom systems !!
Quarks & Gluons
Chiral
symmetry
m→0
Quarks & Gluons
Heavy
Chiral
quark
symmetry symmetry
m→0
m→∞
What is D/D-nucleon interaction ?
D and nucleon
D*+N (2947 MeV)
D+N (2803 MeV)
Only DN and D*N channel
C<0
differen
t
D and nucleon
D*+N (2947 MeV)
D+N (2803 MeV)
Σc(2800) 1(??)
π+Σc* (2658 MeV)
Λc(2625) 0(3/2-)
Λc(2595) 0(1/2-)
C>0
π+Σc (2593 MeV)
`Exotic channel‘
cqqq
SY and Sudoh, PRD80, 034008 (2009)
q
Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)
Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
`Baryon channel‘
cqqq
q Hosaka, arXiv:1301.4557 [hep-ph]
Yamaguchi, Ohkoda, SY,
What is D/D-nucleon interaction ?
D and nucleon
D*+N (2947 MeV)
D+N (2803 MeV)
Only DN and D*N channel
C<0
differen
t
D and nucleon
D*+N (2947 MeV)
D+N (2803 MeV)
Σc(2800) 1(??)
π+Σc* (2658 MeV)
Λc(2625) 0(3/2-)
Λc(2595) 0(1/2-)
C>0
π+Σc (2593 MeV)
`Exotic channel‘
cqqq
SY and Sudoh, PRD80, 034008 (2009)
q
Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)
Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
`Baryon channel‘
cqqq
q Hosaka, arXiv:1301.4557 [hep-ph]
Yamaguchi, Ohkoda, SY,