Anti-D and B meson in nuclear medium at zero temperature
description
Transcript of Anti-D and B meson in nuclear medium at zero temperature
Anti-D and B meson in nuclear mediumat zero temperature
Shigehiro YASUI(KEK)
Recent progress in hadron physics -From hadrons to quark and gluon- @Yonsei University, 18-22 Feb. 2013
Hadrons in nuclear medium are useful for study of …
1. Introduction
(i) Interaction between hadron and nucleon
(ii) Modification of properties of hadron
(iii) Change of medium caused by embedded hadron
Hyperon-nucleon interaction, hyperon-hyperon interaction
π, ω, ρ, η(’) meson masses and decay widths in nuclear medium
Kbar-nucleon interaction
Shrink of radii of hypernuclei (“glue” effect by hyperon)Possible high density state in Kbar nuclei
Fundamental questions in QCD:Color confinement, Spontaneous chiral symmetry breaking, …
1. IntroductionCharm & Bottom
→ Change of Mass-scale and Symmetry
up down
strange charm bottom mass
ΛQCD≈2003 5 150 1500 4700
Chiral SymmetryHeavy Quark Symmetry
SU(3)L x SU(3)R SU(2NF)
[MeV]
Change !!
1. IntroductionCharm & Bottom
→ Change of Mass-scale and Symmetry
up down
strange charm bottom mass
ΛQCD≈2003 5 150 1500 4700
Chiral SymmetryHeavy Quark Symmetry
SU(3)L x SU(3)R SU(2NF)
[MeV]
Change !!
D(cq) or D(cq)
D, D (B, B) mesic nuclei- D, D (B, B)-nucleon interaction?- Modification of D, D (B, B) mesons in nuclear matter (χSB)?- Change of nuclear matter?- How is QCD concerned?
1. IntroductionCharm & Bottom
→ Change of Mass-scale and Symmetry
up down
strange charm bottom mass
ΛQCD≈2003 5 150 1500 4700
Chiral SymmetryHeavy Quark Symmetry
SU(3)L x SU(3)R SU(2NF)
[MeV]
Change !!
D(cq) or D(cq)
D, D (B, B) mesic nuclei- D, D (B, B)-nucleon interaction?- Modification of D, D (B, B) mesons in nuclear matter (χSB)?- Change of nuclear matter?- How is QCD concerned?
498 MeV
1870 MeV
5400 MeV
ChargeConjugate
Including u, d antiquark- Annihilation- Absorption
Including u, d quark- NO annihilation- NO absorption
“Particle” ≠ “Antiparticle” in nuclear matter
“Particle”
“Antiparticle”
D*+N (2947 MeV)
D+N (2803 MeV)
Only DN and D*N channel
D and nucleon
`Exotic channel‘
1. Introduction
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
cqqqq
D*+N (2947 MeV)
D+N (2803 MeV)
Only DN and D*N channel
D and nucleon
`Exotic channel‘
1. Introduction
C<0
What is D/D-nucleon interaction ?
cqqqq
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
cqqqq
Strangeness, Charm, Bottom, ...
D BK
K*
D*B*
400 MeV
140 MeV 45 MeV
In cham/bottom, vector meson is also important!
500 MeV 1870 MeV 5280 MeV
Only NG boson (K) is important in dynamics, andvector meson (K*) is almost irrelevant…
pseudo-scalar
vector
1. Introduction
sq cq bq q=u,d
Strangeness, Charm, Bottom, ...
NK
K N
p, ω, ρ
Weinberg-Tomozawa interaction
One-pion exchange potential (OPEP)
ND(*)
D(*) N
NB(*)
B(*) N
One-pion exchange is absent. (short range force)
One-pion exchange is present. (long range force)
p, ω, ρ p, ω, ρ
SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
meson-nucleon interaction
1. Introduction
Strangeness, Charm, Bottom, ...
NK
K N
p, ω, ρ
One-pion exchange potential (OPEP)
ND
D* N
NB
B* N
One-pion exchange is absent. (short range force)
One-pion exchange is present. (long range force)
p, ω, ρ p, ω, ρ
meson-nucleon interaction
1. Introduction
SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
Weinberg-Tomozawa interaction
Strangeness, Charm, Bottom, ...
NK
K N
p, ω, ρ
One-pion exchange potential (OPEP)
ND*
D N
NB*
B N
One-pion exchange is absent. (short range force)
One-pion exchange is present. (long range force)
p, ω, ρ p, ω, ρ
meson-nucleon interaction
1. Introduction
SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
Weinberg-Tomozawa interaction
Strangeness, Charm, Bottom, ...
NK
K N
p, ω, ρ
One-pion exchange potential (OPEP)
ND*
D* N
NB*
B* N
One-pion exchange is absent. (short range force)
One-pion exchange is present. (long range force)
p, ω, ρ p, ω, ρ
meson-nucleon interaction
1. Introduction
SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
Weinberg-Tomozawa interaction
Strangeness, Charm, Bottom, ...
NK
K N
p, ω, ρ
One-pion exchange potential (OPEP)
ND(*)
D(*) N
NB(*)
B(*) N
One-pion exchange is absent. (short range force)
One-pion exchange is present. (long range force)
p, ω, ρ p, ω, ρ
meson-nucleon interaction
1. Introduction
SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
Weinberg-Tomozawa interaction
D*+N (2947 MeV)
D+N (2803 MeV)
Only DN and D*N channel
D and nucleon
`Exotic channel‘
1. Introduction
C<0
What is D/D-nucleon interaction ?
cqqqq
D
D
N
N
ND*
S-wave
S-wave
D-wave
・ Mass degeneracy for D and D* MD*-MD = 140 MeV 1/m∝ c
・ π exchange (tensor force) S-D wave mixing (deuteron-like)
π
π
→ New mechanism of DN interaction
SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
→ Some bound/resonant states
“D-D* mixing” via pion exchange
DN2807 MeV
DN state2946 MeV D*N
Λ(1405)
KN
πΣ
1433 MeV
1330 MeV
ΞN
ΛΛ
2255 MeV
2230MeV
H dibaryon
K nuclei
Hypernuclei
BN6217 MeV
BN state6263 MeV
B*N
1. IntroductionFrom hadron-nucleon interactionto a variety of exotic nuclei
K(sq), Ξ(ssq), …
B nuclei ?
D nuclei ?
D nuclei ?DN2807 MeV
DN state2946 MeV D*N
Λ(1405)
KN
πΣ
1433 MeV
1330 MeV
ΞN
ΛΛ
2255 MeV
2230MeV
H dibaryon
K nuclei
Hypernuclei
BN6217 MeV
BN state6263 MeV
B*N
B nuclei ?
1. Introduction
D(cq), B(bq) ??
From hadron-nucleon interactionto a variety of exotic nuclei
From hadron-nucleon interactionto a variety of exotic nuclei
How is Dbar (B) meson bound in nuclear matter?
Dbar (B) meson – nucleon interaction must be very interesting !!
B nuclei ?
D nuclei ?
1. Introduction
Cf. Yamaguchi’s talk on few-body Dbar-nuclear systems in 19
Λ(1405)
KN
πΣ
1433 MeV
1330 MeV
ΞN
ΛΛ
2255 MeV
2230MeV
H dibaryon
K nuclei
Hypernuclei
BN6217 MeV
BN state
DN2807 MeV
DN state2946 MeV
6263 MeV
D*NB*N
Quark-meson coupling model (Quark model)・ K. Tsushima, D. -H. Lu, A. W. Thomas, K. Saito and R. H. Landau, Phys. Rev. C 59, 2824 (1999).・ A. Sibirtsev, K. Tsushima and A. W. Thomas, Eur. Phys. J. A 6, 351 (1999).・ K. Tsushima and F. C. Khanna, Phys. Lett. B 552, 138 (2003).
QCD sum rule・ F. Klingl, S. -s. Kim, S. H. Lee, P. Morath and W. Weise, Phys. Rev. Lett. 82, 3396 (1999.・ Y. -H. Song, S. H. Lee and K. Morita, Phys. Rev. C 79, 014907 (2009).・ K. Morita and S. H. Lee, Phys. Rev. C 85, 044917 (2012).・ A. Hayashigaki, Phys. Lett. B 487, 96 (2000).・ B. Friman, S. H. Lee and T. Song, Phys. Lett. B 548, 153 (2002).・ T. Hilger, R. Thomas and B. Kampfer, Phys. Rev. C 79, 025202 (2009).・ T. Hilger, R. Schulze and B. Kampfer, J. Phys. G G 37, 094054 (2010).・ Z. -G. Wang and T. Huang, Phys. Rev. C 84, 048201 (2011).
Hadron dynamics I (W-T interaction from SU(4) symmetry with breaking term)・ A. Mishra, E. L. Bratkovskaya, J. Schaner-Bielich, S. Schramm and H. Stoecker, Phys. Rev. C 69, 015202 (2004).・ M. F. M. Lutz and C. L. Korpa, Phys. Lett. B 633, 43 (2006).・ L. Tolos, A. Ramos and T. Mizutani, Phys. Rev. C 77, 015207 (2008).・ A. Mishra and A. Mazumdar, Phys. Rev. C 79, 024908 (2009).・ A. Kumar and A. Mishra, Phys. Rev. C 81, 065204 (2010).・ C. E. Jimenez-Tejero, A. Ramos, L. Tolos and I. Vidana, Phys. Rev. C 84, 015208 (2011).・ A. Kumar and A. Mishra, Eur. Phys. J. A 47, 164 (2011).・ C. Garcia-Recio, J. Nieves, L. L. Salcedo and L. Tolos, Phys. Rev. C 85, 025203 (2012).
Hadron dynamics II (π exchange interaction)・ S. Yasui, K. Sudoh, Phys. Rev. C87, 015202 (2013). ← Heavy Quark Symmetry + π exchange
1. Introduction2. Dbar and B mesons bound in nuclear matter3. “Strong coupling problem“ in heavy mass limit4. Summary & perspectives
Heavy meson Lagrangian (heavy quark symmetry & chiral symmetry)G. Burdman and J.F. Donoghue (1992)M.B. Wise (1992)T.-M. Yan, H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y.C. Lin and H.-L. Yu (1997)
vector + pseudoscalarP*=D*bar P=Dbar
Multiplet field
Coupling const. from experimental value of deacy width of D*→Dπ
Self-energy of D in nuclear matter at order of two pion exchange
D
D D
D
D*ΛcN
π
π N N Nin-medium nucleon propagator(Pauli exclusion principle)
suppressed by 1/mD, 1/mD*, 1/mN
Cf. Nuclear matterKaiser, Fritsch, Weise, NPB697, 255 (2002); ibid. A750, 259 (2005)Fiorilla, Kaiser, Weise, Prog. Part. Nucl. Phys. 67, 317 (2012)Hypernuclear matterKaiser, Weise, PRC71, 015203 (2005)Kaiser, PRC71, 068201 (2005)
SY and Sudoh, PRC87, 015202 (2013)
2. Dbar and B mesons in nuclear matter
・ Mass degeneracy of Dbar and D*bar in heavy quark limit
・ Vertex strength: gπDD*=gπD*D* (spin symmetry)
D
D
N
N
ND*
π
πD
D
ND*
π
π
DN scattering in vacuum D self-energy in matter
2. Dbar and B mesons in nuclear matterSelf-energy of D in nuclear matter
D
D*
Dπ
πN
D
D*
D
SY and Sudoh, PRC87, 015202 (2013)
Free Pauli exclusion in Fermi surface
In-medium fermion propagator (kF: Fermi momentum)
“particle” “hole” “particle” “hole”
2. Dbar and B mesons in nuclear matterSelf-energy of D* in nuclear matter
D*
D*
D*
D*
D
D*
D*
D*
D*
D*
D
D*π
πN
SY and Sudoh, PRC87, 015202 (2013)
“hole” “hole”“particle” “particle”
Numerical results
self-energy of D, B mesons in nuclear matter
momentum cutoff : 1.27 × 0.7 GeV for Dbar
1.22 × 0.7 GeV for B
-35 MeV
-107 MeV
Negative self-energies
Bound in nuclear matter
D
B
2. Dbar and B mesons in nuclear matter
Normal nuclear matter density
radius ratio × hyperon cutoff
Numerical results
self-energy of D*, B* mesons in nuclear matter
2. Dbar and B mesons in nuclear mattermomentum cutoff : 1.27 × 0.7 GeV for Dbar
1.22 × 0.7 GeV for B
Negative self-energies (real),but large imaginary parts
Bound but unstable in nuclear matter
-150 – i160 MeV
-200 – i120 MeV
D*
B*
radius ratio × hyperon cutoff
Normal nuclear matter density
・ Atomic nuclei with D meson
2. Dbar and B mesons in nuclear matter
Fine splittings (≈ten MeV)
Applications SY and Sudoh, PRC87, 015202 (2013)
V0=-35 MeV
δ : density difference between p and n
Cf. “Isovector deformation” in Kbar nuclei Dote, Akaishi, Horiuchi, Yamazaki, PLB590, 51 (2004)
・ Isospin polarization
embedded in symmetric nuclear matter
“Stable” distribution of isospin density
→ “Unstable” distribution of isospin density
2. Dbar and B mesons in nuclear matter
Dbar (0-) : Qbar + q + qbarqq + gq + …
D*bar (1-) : Qbar + q + qbarqq + gq + …
↑↓
↑ ↑
Discussion on spin in heavy quark limit in QCD
Dbar and D*bar should be degenerate in vacuum.(Bottom is much better.)
in vacuum
“brown muck” - everything that is not the heavy quark (Isgur)degenerate
Dbar (0-) : Qbar + q + qbarqq + gq + … + matter
D*bar (1-) : Qbar + q + qbarqq + gq + … + matter
↑↓
↑ ↑
in medium
Discussion on spin in heavy quark limit in QCD2. Dbar and B mesons in nuclear matter
Dbar and D*bar should be degenerate in vacuum.(Bottom is much better.)
“in-medium brown muck”degenerate
Dbar (0-) : Qbar + q + qbarqq + gq + … + matter
D*bar (1-) : Qbar + q + qbarqq + gq + … + matter
↑↓
↑ ↑
Dbar and D*bar should be degenerate also in matter.(Bottom is much better.)
in medium
degenerate“in-medium brown muck”
QCD-based resultDiscussion on spin in heavy quark limit in QCD
2. Dbar and B mesons in nuclear matter
A. Yes. Dbar and D*bar in matter are degeneratein heavy mass limit (Δ m∝ D*-mD→0).
1. Introduction2. Dbar and B mesons bound in nuclear matter3. “Strong coupling problem“ in heavy mass limit4. Summary & perspectives
3. “Strong coupling problem” in heavy mass limit
We critically discuss heavy mass limit in matter at zero temperature.
Heavy quark limit exists in matter as well as in vacuum.
BUT always so?
Fermi gas by fermion ψ
Heavy “flavorerd” particle Φ (mass: MB→∞)
Assumptions SY and Sudoh, arXiv.1301.6830 ・ Fundamental representation of SU(n) symmetry (isospin doublet for n=2) ・ Current-current interaction with λf ・ λB factor (λf/B: generator of SU(n) group) ・ Small coupling constant GB (so that perturbation can be applied.)
“Dbar, B meson”
“Nuclear matter”
3. “Strong coupling problem” in heavy mass limitScattering amplitude for fermion ψ and heavy boson Φ
SY and Sudoh, arXiv.1301.6830
Heavy boson Φwith mass MB
Fermion ψ (matter)
+ += + …
1st order (tree)
2nd order(one-loop)
Heavy boson Φ in matter
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
particle
hole
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
1st order (tree)
2nd order(one-loop)
Heavy boson Φ in matter
Logarithmic enhancement in loop diagramin heavy mass limit (MB→∞)
Scattering amplitude for fermion ψ and heavy boson Φ
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Heavy boson Φwith mass MB
Fermion ψ (matter)
hole
particle
≈ GBMB λf ・ λB ≈ GB2MB Log(MB) λf ・ λB
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
Heavy boson Φ in matter
Scattering amplitude for fermion ψ and heavy boson Φ
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Heavy boson Φwith mass MB
Fermion ψ (matter)
hole
particle
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
Heavy boson Φ in matter
Scattering amplitude for fermion ψ and heavy boson Φ
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Heavy boson Φwith mass MB
Fermion ψ (matter)
hole
particle
Fermi surface MB: heavy boson mass, m: fermion mass
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
Heavy boson Φ in matter
Scattering amplitude for fermion ψ and heavy boson Φ
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Heavy boson Φwith mass MB
Fermion ψ (matter)
hole
particle
Fermi surface
Singularity on Fermi surfacedenominator = 0 for
MB = ∞ case
MB: heavy boson mass, m: fermion mass
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
Heavy boson Φ in matter
Scattering amplitude for fermion ψ and heavy boson Φ
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Heavy boson Φwith mass MB
Fermion ψ (matter)
hole
particle
Fermi surface
No singularity on Fermi surfacedenominator = 0 for
MB = finite case
MB: heavy boson mass, m: fermion mass
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
Heavy boson Φ in matter
Scattering amplitude for fermion ψ and heavy boson Φ
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Heavy boson Φwith mass MB
Fermion ψ (matter)
hole
particle
Fermi surface
MB= ∞MB = finite
SingularityNo singularityLog MB
Logarithmic
MB: heavy boson mass, m: fermion mass
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
Heavy boson Φ in matter
Scattering amplitude for fermion ψ and heavy boson Φ
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Heavy boson Φwith mass MB
Fermion ψ (matter)
hole
particle
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
Heavy boson Φ in matter
Scattering amplitude for fermion ψ and heavy boson Φ
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Heavy boson Φwith mass MB
Fermion ψ (matter)
hole
particle↑
↑
↑
↑
↑
↑
↑
↑
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
Heavy boson Φ in matter
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Scattering amplitude for fermion ψ and heavy boson Φ
Fermion ψ (matter)
Heavy boson Φwith mass MB
particle
hole
↑
↑
↑ ↑ ↑ ↑
↑ ↑↑ ↑ ↑
↑
1. Spin non-flip in intermediate state
→ Logarithmic singularity at Fermi surface is canceled.
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
Heavy boson Φ in matter
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Scattering amplitude for fermion ψ and heavy boson Φ
Fermion ψ (matter)
Heavy boson Φwith mass MB
particle
hole
↑
↑↓ ↑ ↑ ↑
↓ ↑↑ ↓ ↑
↓
2. Spin flip in intermediate state
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
Heavy boson Φ in matter
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Scattering amplitude for fermion ψ and heavy boson Φ
Fermion ψ (matter)
Heavy boson Φwith mass MB
particle
hole
↑
↑↓ ↑ ↑ ↑
↓ ↑↑ ↓ ↑
↓
2. Spin flip in intermediate state
→ Logarithmic singularity at Fermi surface is NOT canceled.
Cf. “Kondo problem” by J. Kondo (1964); log|q-kF| for q→kF, MB=∞.
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
1st order (tree)
2nd order(one-loop)
Heavy boson Φ in matter
Logarithmic enhancement in loop diagramin heavy mass limit (MB→∞)
Scattering amplitude for fermion ψ and heavy boson Φ
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Heavy boson Φwith mass MB
Fermion ψ (matter)
hole
particle
≈ GBMB λf ・ λB ≈ GB2MB Log(MB) λf ・ λB
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
1st order (tree)
2nd order(one-loop)
Heavy boson Φ in matter
“Strong coupling problem” in λf ・ λB-dependent interaction in MB→∞ (isospin)
Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson
Scattering amplitude for fermion ψ and heavy boson Φ
Fermion ψ (matter)
Heavy boson Φwith mass MB
particle
hole
≈ GBMB λf ・ λB ≈ GB2MB Log(MB) λf ・ λB
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
Heavy fermion Ψ in matter
Scattering amplitude for fermion ψ and heavy fermion Ψ
Fermion ψ (matter)
Heavy fermion Ψwith mass MF
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
1st order (tree)
2nd order(one-loop)
Heavy fermion Ψ in matter
“Strong coupling problem” in λf ・ λF-dependent interaction in MF→∞
Scattering amplitude for fermion ψ and heavy fermion Ψ
Fermion ψ (matter)
Heavy fermion Ψwith mass MF
particle
hole
≈ GF λf ・ λF ≈ GF2
Log(MF) λf ・ λF
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
1st order (tree)
2nd order(one-loop)
Heavy fermion Ψ in matter
≈ GF λf ・ λF ≈ GF2
Log(MF) λf ・ λF
“Strong coupling problem” in λf ・ λF-dependent interaction in MF→∞
Nuclear matter with isospin SU(2) ψ: nucleon Ψ: Λc baryon ???Not applicable, because Λc is NOT doublet in SU(2) !!
Scattering amplitude for fermion ψ and heavy fermion Ψ
Heavy fermion Ψwith mass MF
Fermion ψ (matter)
particle
hole
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
1st order (tree)
2nd order(one-loop)
Heavy fermion Ψ in matter
“Strong coupling problem” in λf ・ λF-dependent interaction in MF→∞
Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark→ 3c representation of color SU(3)
(color)
Scattering amplitude for fermion ψ and heavy fermion Ψ
Heavy fermion Ψwith mass MF
Fermion ψ (matter)
particle
hole
≈ GF λf ・ λF ≈ GF2
Log(MF) λf ・ λF
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
1st order (tree)
2nd order(one-loop)
Heavy fermion Ψ in matter
“Strong coupling problem” in λf ・ λF-dependent interaction in MF→∞
Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark→ 3c representation of color SU(3)
(color)
Scattering amplitude for fermion ψ and heavy fermion Ψ
Heavy fermion Ψwith mass MF
Fermion ψ (matter)
particle
hole
≈ GF λf ・ λF ≈ GF2
Log(MF) λf ・ λF
R
R
R R
R R
R
R
RR R
R
“color non-flip”
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
1st order (tree)
2nd order(one-loop)
Heavy fermion Ψ in matter
“Strong coupling problem” in λf ・ λF-dependent interaction in MF→∞
Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark→ 3c representation of color SU(3)
(color)
Scattering amplitude for fermion ψ and heavy fermion Ψ
Heavy fermion Ψwith mass MF
Fermion ψ (matter)
particle
hole
≈ GF λf ・ λF ≈ GF2
Log(MF) λf ・ λF
R
R
R R
R R
R
R
BB B
B
“color flip”
3. “Strong coupling problem” in heavy mass limitSY and Sudoh, arXiv.1301.6830
+ += + …
1st order (tree)
2nd order(one-loop)
Heavy fermion Ψ in matter
Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark→ 3c representation of color SU(3)
Scattering amplitude for fermion ψ and heavy fermion Ψ
Quark matter with charm (bottom) quark at zero temperaturemay not be perturbative system, but be strongly coupled one!!
particle
Heavy fermion Ψwith mass MF
Fermion ψ (matter)
hole
≈ GF λf ・ λF ≈ GF2
Log(MF) λf ・ λF
R
R R R
RR
R
R
BB B
B
4. Summary & perspectives・ Heavy quark symmetry & chiral symmetry is important to understand open charm and bottom mesons in nuclear medium.
・ Pseudoscalar (Dbar, B) mesons are bound in nuclear matter. Vector (Dbar*, B*) mesons are bound, but with large widths.
・ For embedded particle, λf ・ λB/F-dependent interaction will become strong by logarithmic enhancement in heavy mass limit.
・ How to deal with “strong coupling problem”? Application to nuclear matter and quark matter?
・ Charmed nuclei are interesting for experiments at J-PARC. → Dbar, D, J/Ψ, Λc, Σc
(*) embedded in atomic nuclei
To study “new” physics in charmed (bottom) nuclear systemswill be important for J-PARC (and others).
[6] K. Tsushima, D. -H. Lu, A. W. Thomas, K. Saito and R. H. Landau, Phys. Rev. C 59, 2824 (1999).[7] A. Sibirtsev, K. Tsushima and A. W. Thomas, Eur. Phys. J. A 6, 351 (1999).[15] T. Hilger, R. Thomas and B. Kampfer, Phys. Rev. C 79, 025202 (2009).[16] T. Hilger, R. Schulze and B. Kampfer, J. Phys. G G 37, 094054 (2010).[17] Z. -G. Wang and T. Huang, Phys. Rev. C 84, 048201 (2011).[18] A. Mishra, E. L. Bratkovskaya, J. Schaner-Bielich, S. Schramm and H. Stoecker, Phys. Rev. C 69, 015202 (2004).[19] M. F. M. Lutz and C. L. Korpa, Phys. Lett. B 633, 43 (2006).[20] L. Tolos, A. Ramos and T. Mizutani, Phys. Rev. C 77, 015207 (2008).[21] A. Mishra and A. Mazumdar, Phys. Rev. C 79, 024908 (2009).[22] A. Kumar and A. Mishra, Phys. Rev. C 81, 065204 (2010).[23] C. E. Jimenez-Tejero, A. Ramos, L. Tolos and I. Vidana, Phys. Rev. C 84, 015208 (2011).[24] A. Kumar and A. Mishra, Eur. Phys. J. A 47, 164 (2011).[25] C. Garcia-Recio, J. Nieves, L. L. Salcedo and L. Tolos, Phys. Rev. C 85, 025203 (2012).
2. Dbar and B mesons in nuclear matterComparison with other works
Quark-meson coupling model QCD rum ruleMean field
Channel-coupling(w/o π exchange)
Hadron dynamics
π exchange
Binding energy [MeV]
3. “Strong coupling problem” in heavy mass limitScattering amplitude for fermion and heavy flavor boson
1st order (tree level) ≈ GBMB
Fermion ψ(matter)
Heavy flavorboson Φwith mass MB GBMB
SY and Sudoh, arXiv.1301.6830
a(’), b(’)=1, …, n
3. “Strong coupling problem” in heavy mass limit
2nd order (one-loop level)
GBMB GBMB
GBMB GBMB
SY and Sudoh, arXiv.1301.6830Scattering amplitude for fermion and heavy flavor boson
Fermion ψ(matter)
Heavy flavorboson Φwith mass MB
3. “Strong coupling problem” in heavy mass limit
2nd order (one-loop level)
GBMB GBMB
GBMB GBMB
(Log MB)/MB(Log MB)/MB
MB: heavy boson mass, m: fermion mass
≈ GB2MB Log(MB)
Logarithmic enhancementin heavy mass limit (MB→∞) !!
Log MB from loop contributionwith particles and holes
SY and Sudoh, arXiv.1301.6830Scattering amplitude for fermion and heavy flavor boson
Fermion ψ(matter)
Heavy flavorboson Φwith mass MB
3. “Strong coupling problem” in heavy mass limit
GBMB GBMB
GBMB GBMB
(Log MB)/MB(Log MB)/MB
λf ・ λB-independent term → Log MB
λf ・ λB-dependent term → Log MB
SY and Sudoh, arXiv.1301.6830Scattering amplitude for fermion and heavy flavor boson
Fermion ψ(matter)
Heavy flavorboson Φwith mass MB
2nd order (one-loop level) ≈ GB2MB Log(MB)
Logarithmic enhancementin heavy mass limit (MB→∞) !!
MB: heavy boson mass, m: fermion mass
3. “Strong coupling problem” in heavy mass limit
λf ・ λB λf ・ λB λf ・ λB λf ・ λB
Opposite signs in λf ・ λB are important for presence of Log(MB).
< 0 > 0
SY and Sudoh, arXiv.1301.6830Scattering amplitude for fermion and heavy flavor boson
Fermion ψ(matter)
Heavy flavorboson Φwith mass MB
2nd order (one-loop level) ≈ GB2MB Log(MB)
Logarithmic enhancementin heavy mass limit (MB→∞) !!
3. “Strong coupling problem” in heavy mass limitBrief summary
Heavy boson in matter
≈ GB2MB Log(MB)
≈ GBMB
Logarithmic enhancement in loop diagramin heavy mass limit (MB→∞)
Heavy flavorboson Φwith mass MB
Fermion ψ (matter)
Nuclear matter with isospin SU(n=2) ψ: nucleon Φ: Dbar (B) meson
+ +
SY and Sudoh, arXiv.1301.6830
“Strong coupling problem” in λf ・ λB-dependent interaction(isospin)
λf ・ λB
λf ・ λB λf ・ λB
λf ・ λB λf ・ λB
3. “Strong coupling problem” in heavy mass limit
Heavy fermion in matter
≈ GF
Brief summary
Heavy flavorfermion Ψwith mass MF
Fermion ψ (matter)
Logarithmic enhancement in loop diagramin heavy mass limit (MF→∞)
++
SY and Sudoh, arXiv.1301.6830
Nuclear matter with isospin SU(n=2) ψ: nucleon Ψ: Λc and Σc
(*) baryon ???Not applicable, because Λc and Σc
(*) are NOT doublet in SU(2) !!
+ +λf ・ λF
λf ・ λF λf ・ λF
λf ・ λF λf ・ λF
“Strong coupling problem” in λf ・ λF-dependent interaction(isospin)
≈ GF2
Log(MF)
3. “Strong coupling problem” in heavy mass limit
Heavy fermion in matter
≈ GF2
Log(MF)
≈ GF
Brief summary
Heavy flavorfermion Ψwith mass MF
Fermion ψ (matter)
Logarithmic enhancement in loop diagramin heavy mass limit (MF→∞)
++
SY and Sudoh, arXiv.1301.6830
Quark matter with color SU(n=3) ψ: light quark Ψ: charm (bottom) quark→ 3c representation of color SU(3)
λf ・ λF λf ・ λF
λf ・ λF λf ・ λFλf ・ λF
“Strong coupling problem” in λf ・ λF-dependent interaction(color)
Quark matter with charm (bottom) quark at zero temperaturemay not be perturbative system, but be strongly coupled one!!
What is D/D-nucleon interaction ?1. Introduction
D*+N (2947 MeV)
D+N (2803 MeV)
D and nucleonD*+N
D+Nbound state
resonant states
SY and Sudoh, PRD80, 034008 (2009)Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011)Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)
`Exotic channel‘
Only DN and D*N channel
Heavy quark symmetry+ π exchange (tensor force)
C<0
cqqqq