Charmed meson masses in medium based on eﬀec1ve chiral …research.kek.jp/group/hadron10/kek-hn-2017/slides/... · • We include the violation of the heavy quark symmetry by the

Charmedmesonmassesinmediumbasedoneffec1vechiralmodels

MasayasuHarada(NagoyaUniversity)＠ KEKtheorycenterworkshopon

　HadronandNuclearPhysicsin2017(KEK,JAPAN,January9,2017)

Basedon•  M.Harada,Y.L.Ma,D.Suenaga,Y.Takeda,arXiv:1612.03496•  D.Suenaga,M.Harada,Phys.Rev.D93,076005(2016).•  D.Suenga,B.-R.He,Y.L.Ma,M.Harada,Phys.Rev.D91,036001(2015)•  D.Suenaga,B.-R.He,Y.L.Ma,M.Harada,Phys.Rev.C89,068201(2014)•  D.Suenaga,S.Yasui,M.Harada,inprepara1on

2017/1/9 HadronandNuclearPhysicsin2017@KEK 1

1.Introduc,on


OriginofMass ?ofHadrons

ofUs

OneoftheInteres,ngproblemsofQCD=


PhasediagramofQuark-Gluonsystem

Highdensity

NeutronStar

hightemperature

1 trillion kelvin

100 million ton/cm3

• SpontaneousChiralSymmetryBreaking• ConfinementofQuarks

• ChiralSymmetryRestra,on• DeconfinementofQuarks

EarlyUniverse


Q “Light-quark cloud” (Brown Muck) ・・・ made of light quarks and gluons typical energy scale ～ ΛQCD

☆ Heavy-Light Mesons (Qq type) Baryons (Qqq) -

◎ Heavy mesons ・・・ 3 or 3bar, … of SU(3)l ◎ Heavy baryons ・・・ 6, … of SU(3)l

Flavor representations, which do not exist in the light quark sector, give a new clue to understand the hadron structure.

<<MQ

Heavy-lighthadronsasprobesofvacuumstructue

2017/1/9 Hadron and Nuclear Physics in 2017 @ KEK

5

•  In this talk, I will summarize main points of a series of papers, in which we studied spectra of charmed mesons in nuclear matter.

Outline1.  Introduc1on2.  D-D*mixinginspin-isospincorrelatedmaeer

D.Suenaga,B.-R.He,Y.L.MaandM.Harada,Phys.Rev.C89,068201(2014)3.  Dispersionrela1onsofcharmedmesonsinspin-isospin

correlatedmaeerD.Suenaga,M.Harada,PhysicalReviewD93,076005(2016)

4.  Effectsofpar1alchiralsymmetryrestora1oninnuclearmaeertoeffec1vemassesofcharmedmesonsM.Harada,Y.L.Ma,D.Suenaga,Y.Takeda,arXiv:1612.03496D.Suenaga,B.-R.He,Y.L.MaandM.Harada,Phys.Rev.D91,036001(2015)

5.  Modifica1onofspectralfunc1onofcharmedmesonsinnuclearmaeerD.Suenaga,S.Yasui,M.Harada,inprepara1on

6.  Summary


seePosterbyD.Suenaga

2.D-D*mixinginspin-isospincorrelatedmaeerD.Suenaga,B.-R.He,Y.L.MaandM.Harada,Phys.Rev.C89,068201(2014)

7 2017/1/9 HadronandNuclearPhysicsin2017@KEK

dualchiraldensitywave(DCDW)•  NakanoandTatsumishowedtheexistenceoftheDCDWphasewith

inhomogeneouschiralcondensate(Nakano-Tatsumi,PRD71,114006(2005))inthehighdensitymaeer.

qq x!"( ) = σ x

!"( )+ iπ 3 x

!"( )τ 3

=φ cos 2αx( )+ iτ 3φ sin 2αx( )


•  Ananalysisusinganeffec1vehadronmodelin[A.Heinz,F.Giacosa,D.Rischke,NPA93,34(2015)]showedthatthephasetransi1ontotheinhomogeneousphaseoccursatthedensityof2.41mesofnormalnuclearmaeerdensity.

position dependent pion condensation•  Spin-isospin correlation in the nuclear medium will

cause the position dependent pion condensation. •  In the equilibrium case, the pion condensation does

not depend on the time.

•  We are interested in the mass spectrum of charmed

mesons, so that we take the spatial components of the residual momentum of charmed mesons to be zero.

•  Only the space average of α⊥ contributes.

α⊥0A x!"( ) = α||0

A x!"( ) = 0

α⊥iA = d 3x

V∫ α⊥iA x!"( ) : α⊥i

A =1fπ∂iπ

A +# P-wave pion condensation

•α⊥µA =

1fπ∂µπ

A +! ; chiral field for pion

• π 3 x!"( )=φ sin 2αx( ) leads to α⊥i

A =αδi 3δa3

2017/1/9 Hadron and Nuclear Physics in 2017 @ KEK 9

D-D*mixing•  P-wavepioncondensa1ongivesamixingbetweenD(JP=0-)andD*(JP=1-),aswellasamixingbetween2modesofD*.


Lint = �igAMD̄⇤µ ↵

µ? D � igA✏

µ⌫��D̄⇤µ↵?⌫@�D

⇤�

α⊥µ =1fπ∂µπ +!

causesamixingbetweenDandD*mesons

causesamixingbetweendifferentmodesofD*mesons

Mass spectrum in the heavy quark limit

4 states (2 HQ pairs) : (+,+) and (-,-) related by Z2

0 100 200 300 400!150

!100

!50

0

50

100

150

!Α! "MeV#

Mass"Me

V#

U(1)s X U(1)I X Z2 [subgroup of SU(2)spin X SU(2)isospin] exists.

4 states (2 HQ pairs) : (+,-) and (-,+) related by Z2


• α⊥iA =αδi 3δa3

There are 8 states at vacuum, which are degenerated due to the existence of the heavy quark symmetry D+ and D0, D*+ (3 states) and D*0 (3 states)

Inclusion of mass difference at the vacuum

•  We include the violation of the heavy quark symmetry by the mass difference between D and D* mesons at vacuum.

•  Meson spin denoted by SU(2)J together with the isospin SU(2)I is conserved at vacuum.

•  In the spin-isospin correlated matter, the SU(2)J X SU(2)I is broken to a subgroup depending on the symmetry structure of the correlation.


12

Inclusion of mass difference at the vacuum

•  SU(2)J X SU(2)I → U(1)J X U(1)I X Z2 Ø  8 states are split into 4 pairs of Z2 symmetry. Ø  2 D mesons provide 1 pair {(0,+), (0,-) } Ø  6 D* provide 3 pairs :

Ø  {(0,+), (0,-)}, {(+,+), (-,-)}, {(+,-), (-,+)｝. Ø  2 of {(0,+), (0,-)} are mixed with each other

1 pair0 100 200 300 400

1700

1800

1900

2000

2100

2200

!Α! "MeV#

Mass"Me

V#

1 pair1 pair1 pair


3.Dispersionrela1onsofcharmedmesonsinspin-isospincorrelatedmaeerD.Suenaga,M.Harada,PhysicalReviewD93,076005(2016)

14 2017/1/9 HadronandNuclearPhysicsin2017@KEK

Chiralpartnerstructureforcharmedmesons

•  2heavyquarkmul1pletswithJl=1/2areregardedasthechiralpartner:

•  Massdifferenceisgeneratedbythechiralcondensate,andthevalueisroughlyequaltothecons1tuentquarkmass.

•  Experimentalvalueimpliesthatthechiralpartnerstructureseemstowork:

D(0−),D *(1−)"# $% chiral partner← →(((( D0*(0+),D1(1

+)"# $%

•  M.A.Nowak,M.RhoandI.Zahed,PRD48,4370(1993)•  W.A.BardeenandC.T.Hill,PRD49,409(1994)

m 0+( )−m 0−( ) ≈m 1+( )−m 1−( ) ≈ 0.43GeV2017/1/9 HadronandNuclearPhysicsin2017@KEK 15

Aneffec1veLagrangian•  Weconstructedaneffec1veLagrangianoftherela1vis1cformbased

ontheheavyquarksymmetryandthechiralpartnerstructure.•  ThefreeLagrangianandtheinterac1onwithσareexpressedas:

•  Spontaneouschiralsymmetrybreakingatzerodensityleadstothevacuumexpecta1onvalue(VEV)oftheσfieldas<σ>=σ0,whichcausesthemassdifferencebetweenthechiralpartners.

•  Then,thecouplingofσtotheheavymesonsarerelatedtothemassdifference(anextendedGoldberger-Treimanrela1on):

heavyquarksymemtry

heavyquarksymemtry

Lfree+� = @µD̄@µD̄† �✓m2��m2

2

�

�0

◆D̄D̄†

+ @µD̄⇤@µD̄⇤† �

✓m2��m2

2

�

�0

◆D̄⇤D̄⇤†

+ @µD̄⇤0@

µD̄⇤†0 �

✓m2+

�m2

2

�

�0

◆D̄⇤

0D̄⇤†0

+ @µD̄1@µD̄†

1 �✓m2+

�m2

2

�

�0

◆D̄1D̄

†1

chiralsymmetry

G�DD =�m2

2�0, . . .2017/1/9 HadronandNuclearPhysicsin2017@KEK 16

Klein-Gordonequa1onsatvacuum•  Wedeterminethedispersionsrela1onsofD,D*,D0*,D1bysolvingthecoupledequa1onsofmo1on.

•  Theequa1onsofmo1onatvacuumareordinaryKlein-Gordonequa1ons.

–  Theheavyquarksymmetryimpliesmassdegeneracy.

–  Thechiralsymmetrybreakinggeneratesthemassdifferences:

MD(0�) = MD⇤(1�) ; MD⇤0 (0

+) = MD1(1+)

2

664�@µ@

µ +m2�

0

BB@

11

11

1

CCA+�m2

2

0

BB@

�1�1

11

1

CCA

3

775

0

BB@

D̄(0�)D̄⇤(1�)D̄⇤

0(0+)

D̄1(1+)

1

CCA = 0

⇥MD⇤

0 (0+)

⇤2 �⇥MD(0�)

⇤2=

⇥MD1(1+)

⇤2 �⇥MD⇤(1�)

⇤2= �m2

2016/07/11 Seminar@RCNP 17

Poten1alintheDCDW

•  Thepoten1alinthematrixformisexpressedas

V =

0

BB@

�V� �iV@⇡ iV⇡ V@�

iV@⇡ �V� V@� iV⇡

�iV⇡ �V@� V� iV@⇡

�V@� �iV⇡ �iV@⇡ V�

1

CCA

– Eachcomponentisgivenby

V� =

�m

2

2

�

�0cos(2fx) , V⇡ =

�m

2

2

�

�0sin(2fx)

V@� = �2fgm

�

�0sin(2fx) , V@⇡ = 2fgm

�

�0cos(2fx)

2016/07/11 Seminar@RCNP 18


•  Theseeffectsareincludedintheequa1onsofmo1onasapoten1alobtainedbyreplacingtheσandπfieldsintheLagrangianas

–  Here,xisoneofthe3direc1onsofthespace,fisafrequencyofthedensitywave,andφisastrengthofthecondensate

Poten1albyσandπmesonsintheDCDW

D

D0*

π

D

D

σ

D0*

D0*

σ…

D

D*

π…

�(x) = � cos(2fx) ; ⇡

3(x) = � sin(2fx)

•  Dmesonsgetmediumcorrec1onsintheDCDWthroughtheexchangeofσandπmesons.

Dispersionrela1onswithnoD*Dπinterac1on•  4modesappearfrom(D,D0

*)sector(2par1clesatvacuum)

E2 = m2 +1

2

⇥(q

x

+ 2f)2 + q2x

⇤+ k2

y

+ k2z

± 1

2

s

[(qx

+ 2f)2 � q2x

]2 + 4�m2�2

�20

E2 = m2 +1

2

⇥q2x

+ (qx

� 2f)2⇤+ k2

y

+ k2z

± 1

2

s

[q2x

� (qx

� 2f)2]2 + 4�m2�2

�20

1.95

2.05

2.15

2.25

2.35

2.45

2.55

2.65

2.75

-1000 -600 -200 200 600 1000

E [GeV]

qx [MeV]

f=400MeV(kx=ky=0)

freeD0*

· Group velocity : vx

=

dE

dqx

��q

x

=k

y

=k

z

=0

vx

=

f

E

2

41± 4f2

q16f4

+

�

2(�m

2)2

�

20

3

5 > 0

vx

= � f

E

2

41± 4f2

q16f4

+

�

2(�m

2)2

�

20

3

5 < 0

•  For-f<qx<0or0<qx<f,vx∝-qx•  Minimumenergyatqx=forqx=-f•  Only4modesinsteadofinfinitemodesfor

usualBloch’streatment.•  Noenergygaps.

2017/1/9 HadronandNuclearPhysicsin2017@KEK 20graycurve:freeD

Effectsofchiralsymmetryrestora1on•  Weconsidertheeffectsofchiralsymmetryrestora1onbyreducingφ:


qq x!"( ) = σ x

!"( )+ iπ a x

!"( )τ a =φ cos 2 f x( )+ iτ 3φ sin 2f x( )

1.95

2.05

2.15

2.25

2.35

2.45

2.55

-1000 -600 -200 200 600 1000

E [GeV]

qx [MeV]

1.95

2.05

2.15

2.25

2.35

2.45

-1000 -600 -200 200 600 1000

E [GeV]

qx [MeV]

1.95

2.05

2.15

2.25

2.35

2.45

-1000 -600 -200 200 600 1000E [GeV]

qx [MeV]

1.95

2.05

2.15

2.25

2.35

2.45

-1000 -600 -200 200 600 1000

E [GeV]

qx [MeV]

f = 200MeV ;�

�0= 1

�

�0= 0.6

�

�0= 0.3

�

�0= 0f = 200MeV ;

�

�0= 1

�

�0= 0.6

�

�0= 0.3

�

�0= 0f = 200MeV ;

�

�0= 1

�

�0= 0.6

�

�0= 0.3

�

�0= 0f = 200MeV ;

�

�0= 1

�

�0= 0.6

�

�0= 0.3

�

�0= 0

•  Asthevalueofφbecomessmall,theredandgreencurvesmoveup,andtheorangeandbluecurvesmovedown.

•  Forφ=0,thereareonly2modeswhichhaveadegeneratedispersionrela1on,reflec1ngthechiralsymmetryrestora1on.Notethat2modesdisappearsincetheeigenvectorsvanish.

Dispersionrela1onswithD*Dπinterac1onincluded•  Allof(D,D*,D0*,D1)mix.WecansolvethecoupledEoManaly1cally.•  8modesappear,whichiscomparedwith4modesatvacuum.


1.85

1.95

2.05

2.15

2.25

2.35

2.45

2.55

2.65

-1000 -600 -200 200 600 1000

E [GeV]

qx [MeV]•  f=200MeV(g=0.5)•  Forallthemodes,vx∝-qx.•  Minimumenergyisrealizedatqx=for

qx=-f.

1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80

-1000 -600 -200 200 600 1000

E [GeV]

qx [MeV]•  f=400MeV(g=0.5)•  Levelcrossingoccursbetweenred

doeedandorangesolidcurves

•  ThespliungbetweenasolidcurveandadoeedcurvewiththesamecoloriscausedbythemixingbetweenDandD*mesonsaswellasthemixingbetweenD0*andD1mesons.

4.Effectsofpar,alchiralsymmetryrestora,oninnuclearmaKertoeffec,vemassesofcharmedmesons

M.Harada,Y.L.Ma,D.Suenaga,Y.Takeda,arXiv:1612.03496D.Suenaga,B.-R.He,Y.L.MaandM.Harada,Phys.Rev.D91,036001(2015)


Par1alchiralsymmetryrestora1oninnuclearmaeer

•  Itisexpectedthatthechiralsymmetryispar1allyrestoredinnuclearmaeer:–  e.g.inlineardensityapproxima1on


f⇤⇡

f⇡= 1� �⇡N

m2⇡f

2⇡

⇢B0 1

⇢B/⇢0

•  Anexperimentshowedthedecreasingoffπinmaeer–  K.Suzukietal.,PRL92,072302(2004)

f⇤⇡(⇢B)

f⇡

�2' 0.64 at ⇢B = ⇢0

Massesofcharmedmesonsinnuclearmaeer

2017/1/9HadronandNuclearPhysicsin2017@KEK

25

•  Effec1vemassesforD(JP=0-),D(JP=0+)innuclearmaeer

m(e↵)D(�) = m� 1

2�M

h�if⇡

+ g!DD h!0i

m(e↵)D(+) = m+

1

2�M

h�if⇡

+ g!DD h!0i

•  Effec1vemassesforan1-charmedmesons

D

D

σD

D

ω

m(e↵)D̄(�)

= m� 1

2�M

h�if⇡

� g!DD h!0i

m(e↵)D̄(+)

= m+1

2�M

h�if⇡

� g!DD h!0i

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.41900

2000

2100

2200

2300

2400

2500

ΡB!Ρ0

EffectiveMass"MeV#

mG"eff#

mH"eff#

mG"eff#

mH"eff#

g!DDg!NN > 0

g!DDg!NN < 0

Effec1vemassesinlineardensityapproxima1on

26

h!0i =g!NN

m2!

⇢B ,h�ih�i0

= 1� �⇡N

m2⇡f

2⇡

⇢Bm(e↵)

D(�) = m� 1

2�M

h�if⇡

+ g!DD h!0i

m(e↵)D(+) = m+

1

2�M

h�if⇡

+ g!DD h!0i

Anexample

g!DDg!NN > 0

g!DDg!NN < 0

⇢B/⇢0

m(e↵)D̄(�)

= m� 1

2�M

h�if⇡

� g!DD h!0i

m(e↵)D̄(+)

= m+1

2�M

h�if⇡

� g!DD h!0i

2017/1/9 HadronandNuclearPhysicsin2017@KEK

|g!DD| = 3.7 , |g!NN | = 6.23 , �⇡N = 45MeV

D̄(+) D(+)

D(+) D̄(+)

D̄(�) D(�)

D(�) D̄(�)

Increasingordecreasingofpseudo-scalarD(-)mesonmassonlyisnotenoughformeasuringthepar1alchiralsymmetryrestora1on.

Par1alchiralsymmetryrestora1on


m(e↵)D(�) = m� 1

2�M

h�if⇡

+ g!DD h!0i

m(e↵)D(+) = m+

1

2�M

h�if⇡

+ g!DD h!0i

m(e↵)D̄(�)

= m� 1

2�M

h�if⇡

� g!DD h!0i

m(e↵)D̄(+)

= m+1

2�M

h�if⇡

� g!DD h!0i

h!0i =g!NN

m2!

⇢B ,h�ih�i0

= 1� �⇡N

m2⇡f

2⇡

⇢B

D(+)�D(�)

•  Inaddi1ontostudythemassdifferenceofchiralpartners,takingaverageofpar1cleandan1-par1clewillgiveaclueforpar1alchiralsymmetryrestora1on.

•  Thresholdenergyforproduc1onofDandan1-Dmesonpairinmediumislargerthanvacuumreflec1ngthepar1alchiralsymmetryrestora1on.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40

100

200

300

400

500

ΡB!Ρ

EffectiveM

assDifference"MeV#

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.41900

2000

2100

2200

2300

2400

2500

ΡB!Ρ0

EffectiveM

ass"MeV#

"mG"eff#"m

G"eff##!2

"mH"eff#"m

H"eff##!2

D(+) + D̄(+)

D(�) + D̄(�)

Nuclearmaeerfromaparitydoubletmodel


•  In[Y.Motohiro,Y.Kim,M.Harada,Phys.Rev.C92,025201(2015)],weconstructedameanfieldmodelofWaleckatype,usingaparitydoubletmodelfornucleon,whichreproducestheproper1esofnuclearmaeeratnormalnuclearmaeerdensity.

•  Hereweusethemodeltodeterminethemeanfieldsofsigmaandomega. g!DD < 0

m(e↵)D(�) = m� 1

2�M

h�if⇡

+ g!DD h!0i

m(e↵)D(+) = m+

1

2�M

h�if⇡

+ g!DD h!0i

m(e↵)D̄(�)

= m� 1

2�M

h�if⇡

� g!DD h!0i

m(e↵)D̄(+)

= m+1

2�M

h�if⇡

� g!DD h!0i

g!DD > 0

Densitydependenceisquitesimilartotheoneinthelineardensityapproxima1on.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.41800

2000

2200

2400

2600

ΡB!Ρ0

EffectiveM

ass"Me

V#

mG"eff#

mH"eff#

mG"eff#

mH"eff#

D̄(+) D(+)

D(+) D̄(+)

D̄(�) D(�)

D(�) D̄(�)

σ

density

d 3x∫ σ

NuclearmaeerfromSkyrmecrystal


•  Y. –L. Ma, M. Harada, H.K. Lee, Y. Oh, B. –Y. Park, M. Rho, PRD88 (2013) 014016 •  Y. –L. Ma, M. Harada, H.K. Lee, Y. Oh, B. –Y. Park, M. Rho, PRD90 (2014) 34105 •  M. Harada, H.K. Lee, Y.-L. Ma, M. Rho, PRD91, (2015) 096011 •  D.Suenga, B.R.He, Y.L.Ma. M.Harada, PRD 91, 036001 (2015)

•  IntheSkyrmecrystalmodel,thereexiststhe“half-Skyrmionphase”,wherethespaceaverageofthesigmacondensatevanishes.

g!DD < 0g!DD > 0

Chiralpartnersaredegeneratewitheachotherinthehalf-Skyrmionphase.Proper1esinthenormalnuclearmaeeraresimilartotheothercases.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.41900

2000

2100

2200

2300

2400

2500

ΡB!Ρ0

EffectiveM

ass"Me

V#

mG"eff#

mH"eff#

mG"eff#

mH"eff#

D̄(+) D(+)

D̄(�) D(�)

D(+) D̄(+)

D(�) D̄(�)

5.Modifica,onofspectralfunc,onofcharmedmesonsinnuclearmaKer

D.Suenaga,S.Yasui,M.Harada,inprepara1on


Inclusionoffluctua1onmodes•  Weincludethefluctua1onmodesofσandπtostudythespectralfunc1onofcharmedmesons.


- modifications of and are calculated by following diagrams

tree level one loop corrections

- meson propagators must be resummed ones to maintain chiral symmetry:

Modifica1onofmasses


� � � � ��

� � � � ��

� � � � � �

� � � � � �

0.02 0.04 0.06 0.08 0.10� [/fm3]

1900

2000

2100

2200

2300

Mass [MeV]

- Mass of and are not changed from mean field level

D̄ D̄⇤0

or : or meson mass with mean fieldD̄or : or meson mass with one loops

D̄⇤0

D̄ D̄⇤0

Spectralfunc1on

①  LandaudampingPosi1onmovestohigherenergyregion.Hightisenhanced

②  ThresholdenhancementPosi1onmovestohigherenergyregion.Hightisenhanced.

③  DecayofD*0→DπCollisionalbroadening.Posi1onmovestolowerenergyregion.


1900 2000 2100 2200 2300 24000.00000

2.×10-6

4.×10-6

6.×10-6

8.×10-6

0.00001

q0 [MeV]

�(q 0,0�

)[/MeV

2 ]

1900 2000 2100 2200 2300 24000.00000

2.×10-6

4.×10-6

6.×10-6

8.×10-6

0.00001

q0 [MeV]

�(q 0,0�)[/MeV

2 ]1900 2000 2100 2200 2300 2400

0.00000

2.×10-6

4.×10-6

6.×10-6

8.×10-6

0.00001

q0 [MeV]

�(q 0,0�

)[/MeV

2 ]

① ①①

②

② ②③

③③

ρB/ρ0=0.23ρB/ρ0=0.41 ρB/ρ0=0.51

6.Summary•  Weproposedtostudythemassspectrumofheavy-light

mesonstoprobethesymmetrystructureofnuclearmaeer.•  Existenceofspin-isospincorrela1ongeneratesamixing

amongDandD*mesons.•  Inaddi1ontostudythemassdifferenceofchiralpartners,

takingaverageofpar1cleandan1-par1clewillgiveaclueforpar1alchiralsymmetryrestora1on.

•  Thresholdenergyforproduc1onofDandan1-Dmesonpairinmediumislargerthanvacuumreflec1ngthepar1alchiralsymmetryrestora1on.

•  Spectralfunc1onisalsomodifiedbytheeffectofpar1alchiralsymmetryrestora1on.

•  Ourresultsimplythatstudyingcharmedmesonspectrumwillgivecluestounderstandthechiralsymmetrystructureofnuclearmaeer.



35

Documents

Charmed meson masses in medium based on eﬀec1ve chiral …research.kek.jp/group/hadron10/kek-hn-2017/slides/... · • We include the violation of the heavy quark symmetry by the