Charm hadrons in nuclear medium

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)


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



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!



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


Mass of heavy meson H containing a heavy quark Q (in vacuum)rest frame

Qv

HQET

1/mQ expansionLight quarks & gluons


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






LO

NLO O(1/mQ)

rest frame

Qv

HQET

1/mQ expansion

Matrix elements

scale anomaly






LO

NLO O(1/mQ)

rest frame

Qv

HQET

1/mQ expansion

Matrix elements

scale anomaly



1/mQ



Λ , λ1 and λ2 change in medium.

Gluon fields change in medium.

Q

gluon

Ea, Ba

Heavy meson effective theory　　　　　　 (HMET)


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)


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)


Axial-currents composed by Hv :



HQSS conserved (Γ=1, iγ5, γμ) HQSS=Heavy quark spin symmetryO(1/M0) or O(1/M1)



HQSS broken (Γ=γμγ5, σμν) smaller than or equal to O(1/M1) HQSS=Heavy quark spin symmetry



HQSS broken (Γ=γμγ5, σμν) smaller than or equal to O(1/M1) HQSS=Heavy quark spin symmetry



O(1/M0) or O(1/M1)

HQSS conserved

O(1/M1)

HQSS broken

HQSS=Heavy quark spin symmetry


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


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)


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.)


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


N N NN-1 N-1 N-1





N N NN-1 N-1 N-1


1/M correctionsfrom HMET


g →g + (g1+g2)/M


g →g + (g1+g2)/M

g →g + (g1-g2)/M


ρ=0.17 fm-3


scale anomaly in QCD



@ medium

@ vacuum

ρ=0.17 fm-3

about 0.9 suppression in gluon condensate (T. Cohen et al. 1992)





@ medium

@ vacuum

ρ=0.17 fm-3






@ medium

@ vacuum

ρ=0.17 fm-3



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




→ suppressed

→ enhanced


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





→ suppressed

→ enhanced

→ suppressed


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


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. !?


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. !?


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]


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.
















“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]

Documents

Charm hadrons in nuclear medium