Anti-D and B meson in nuclear medium at zero temperature Shigehiro YASUI (KEK) Recent progress in hadron physics -From hadrons to quark and gluon- @Yonsei

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 !!



up down


ΛQCD≈2003 5 150 1500 4700



[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?



up down


ΛQCD≈2003 5 150 1500 4700



[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

Èxotic 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)


D and nucleon

Èxotic channel‘

1. Introduction

C<0


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


NK

K N

, ω, ρp

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)

, ω, ρp , ω, ρp

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


NK

K N

, ω, ρp


ND

D* N

NB

B* N



, ω, ρp , ω, ρp


1. Introduction




NK

K N

, ω, ρp


ND*

D N

NB*

B N



, ω, ρp , ω, ρp


1. Introduction




NK

K N

, ω, ρp


ND*

D* N

NB*

B* N



, ω, ρp , ω, ρp


1. Introduction




NK

K N

, ω, ρp


ND(*)

D(*) N

NB(*)

B(*) N



, ω, ρp , ω, ρp


1. Introduction



D*+N (2947 MeV)

D+N (2803 MeV)


D and nucleon

Èxotic channel‘

1. Introduction

C<0


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


→ 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


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


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


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 result

Discussion on spin in heavy quark limit in QCD2. 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)


Logarithmic enhancement in loop diagramin heavy mass limit (MB→∞)

Scattering amplitude for fermion ψ and heavy boson Φ



Fermion ψ (matter)

hole

particle

≈ GBMB λf ・ λB ≈ GB2MB Log(MB) λf ・ λB


+ += + …





Fermion ψ (matter)

hole

particle


+ += + …





Fermion ψ (matter)

hole

particle

Fermi surface MB: heavy boson mass, m: fermion mass


+ += + …





Fermion ψ (matter)

hole

particle

Fermi surface

Singularity on Fermi surface

denominator = 0 for

MB = ∞ case

MB: heavy boson mass, m: fermion mass


+ += + …





Fermion ψ (matter)

hole

particle

Fermi surface

No singularity on Fermi surface

denominator = 0 for

MB = finite case



+ += + …





Fermion ψ (matter)

hole

particle

Fermi surface

MB= ∞MB = finite

SingularityNo singularityLog MB

Logarithmic



+ += + …





Fermion ψ (matter)

hole

particle


+ += + …





Fermion ψ (matter)

hole

particle↑

↑

↑

↑

↑

↑

↑

↑


+ += + …




Fermion ψ (matter)


particle

hole

↑

↑

↑ ↑ ↑ ↑

↑ ↑↑ ↑ ↑

↑

1. Spin non-flip in intermediate state

→ Logarithmic singularity at Fermi surface is canceled.


+ += + …




Fermion ψ (matter)


particle

hole

↑

↑↓ ↑ ↑ ↑

↓ ↑↑ ↓ ↑

↓

2. Spin flip in intermediate state


+ += + …




Fermion ψ (matter)


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=∞.


+ += + …

1st order (tree)

2nd order(one-loop)






Fermion ψ (matter)

hole

particle



+ += + …

1st order (tree)

2nd order(one-loop)


“Strong coupling problem” in λf ・ λB-dependent interaction in MB→∞ (isospin)



Fermion ψ (matter)


particle

hole



Heavy fermion Ψ in matter

Scattering amplitude for fermion ψ and heavy fermion Ψ

Fermion ψ (matter)

Heavy fermion Ψwith mass MF


+ += + …

1st order (tree)

2nd order(one-loop)


“Strong coupling problem” in λf ・ λF-dependent interaction in MF→∞


Fermion ψ (matter)


particle

hole

≈ GF λf ・ λF ≈ GF2

Log(MF) λf ・ λF


+ += + …

1st order (tree)

2nd order(one-loop)



Log(MF) λf ・ λF


Nuclear matter with isospin SU(2) ψ: nucleon Ψ: Λc baryon ???Not applicable, because Λc is NOT doublet in SU(2) !!



Fermion ψ (matter)

particle

hole


+ += + …

1st order (tree)

2nd order(one-loop)



Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark→ 3c representation of color SU(3)

(color)



Fermion ψ (matter)

particle

hole


Log(MF) λf ・ λF


+ += + …

1st order (tree)

2nd order(one-loop)




(color)



Fermion ψ (matter)

particle

hole


Log(MF) λf ・ λF

R

R

R R

R R

R

R

RR R

R

“color non-flip”


+ += + …

1st order (tree)

2nd order(one-loop)




(color)



Fermion ψ (matter)

particle

hole


Log(MF) λf ・ λF

R

R

R R

R R

R

R

BB B

B

“color flip”


+ += + …

1st order (tree)

2nd order(one-loop)




Quark matter with charm (bottom) quark at zero temperaturemay not be perturbative system, but be strongly coupled one!!

particle


Fermion ψ (matter)

hole


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


a(’), b(’)=1, …, n


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


2nd order (one-loop level)

GBMB GBMB

GBMB GBMB

(Log MB)/MB(Log MB)/MB


≈ GB2MB Log(MB)

Logarithmic enhancementin heavy mass limit (MB→∞) !!

Log MB from loop contributionwith particles and holes


Fermion ψ(matter)



GBMB GBMB

GBMB GBMB

(Log MB)/MB(Log MB)/MB

λf ・ λB-independent term → Log MB

λf ・ λB-dependent term → Log MB


Fermion ψ(matter)


2nd order (one-loop level) ≈ GB2MB Log(MB)




λf ・ λB λf ・ λB λf ・ λB λf ・ λB

Opposite signs in λf ・ λB are important for presence of Log(MB).

< 0 > 0


Fermion ψ(matter)


2nd order (one-loop level) ≈ GB2MB Log(MB)


3. “Strong coupling problem” in heavy mass limitBrief summary

Heavy boson in matter

≈ GB2MB Log(MB)

≈ GBMB



Fermion ψ (matter)

Nuclear matter with isospin SU(n=2) ψ: nucleon Φ: Dbar (B) meson

+ +


“Strong coupling problem” in λf ・ λB-dependent interaction(isospin)

λf ・ λB

λf ・ λB λf ・ λB

λf ・ λB λf ・ λB


Heavy fermion in matter

≈ GF

Brief summary

Heavy flavorfermion Ψwith mass MF

Fermion ψ (matter)

Logarithmic enhancement in loop diagramin heavy mass limit (MF→∞)

++


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


“Strong coupling problem” in λf ・ λF-dependent interaction(isospin)

≈ GF2

Log(MF)


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→∞)

++


Quark matter with color SU(n=3) ψ: light quark Ψ: charm (bottom) quark→ 3c representation of color SU(3)


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


Èxotic channel‘


Heavy quark symmetry+ π exchange (tensor force)

C<0

cqqqq

Documents

Anti-D and B meson in nuclear medium at zero temperature Shigehiro YASUI (KEK) Recent progress in hadron physics -From hadrons to quark and gluon- @Yonsei