scalar d mesons in nuclear matter
DESCRIPTION
Scalar D mesons in nuclear matter. Taesoo Song, Woosung Park, Kie Sang Jeong and Su Houng Lee (Yonsei Univ.). Procedure. Motivation 2. QCD sum rule in vacuum & in nuclear matter 3. Application to Scalar D mesons 4. Conclusions. 1. Motivation. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/1.jpg)
Scalar D mesons in nuclear matter
Taesoo Song, Woosung Park,
Kie Sang Jeong and Su Houng Lee
(Yonsei Univ.)
![Page 2: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/2.jpg)
Procedure
1. Motivation
2. QCD sum rule in vacuum & in nuclear matter
3. Application to Scalar D mesons
4. Conclusions
![Page 3: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/3.jpg)
1. Motivation
• Charm-strange scalar meson Ds0+(2317) was
discovered in 2003• Its mass is too lower than the expected values in
quark models and other theoretical predictions.• It has been interpreted as the isosinglet state
(conventional scalar meson), a four-quark state, a mixed state of both, a DK molecule, …
• Later charm scalar meson D0*(2400) with broad width was discovered in 2004
• Its mass is similar to or larger than that of D+
s0(2317), even though Ds(0-) is 100 MeV higher than D(0-).
![Page 4: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/4.jpg)
2. QCD sum rule
1. OPE (operator product expansion)
2. Phenomenological side
3. Dispersion relation
4. Borel transformation
![Page 5: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/5.jpg)
2. 1. OPE (operator product expansion)
effect) range (long
ndimension ith operator wr Nonsingula :
effect) range(short t Coefficien Wilson :
)0(
)(
)0()()0()(lim0
n
n
nnn
x
O
xC
OxCBxA
![Page 6: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/6.jpg)
As an example,
sduq
xccqxqxcxSc
qxSxqxSxSTrxedi
qcxcxqTxedi
jxjTxedi
q
ccqxiq
xiq
xiq
,,
:)()0()0()(::)()()0(
:)0()()(::)()(:
)0()0(),()(
)0(),(
)3()2()1()0(
4
4
4
where,
:
iscurrent scalar charm offunction on polarizati The
may be ignored
![Page 7: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/7.jpg)
Perturbative quark propagator in a weak gluonic background field(The gluons are supposed to emerge from the ground state)
![Page 8: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/8.jpg)
:)()( xSxSTr cq : ~ gConsiderin (0)
Perturbative part I : dimension 0
Gluon condensates<G2> : dimension 4
and more condensateswith higher dimensionor more strong couplings
![Page 9: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/9.jpg)
:)(......:!
)(
)...(...!
1)(
)...(...)2(!
)(
0)(
11
011
011
qqSDDqn
i
DDxxn
x
FDDxxnn
xxA
xAx
cn
nn
n
nxn
n
nxn
n
and
GaugeSchwinger Fock in
(1)
![Page 10: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/10.jpg)
y graphicall is )1(
Quark condensate <qq> : dimension 3
Quark-gluon mixed condensates<qGq> : dimension 5
and more condensateswith higher dimensionor more strong couplings
![Page 11: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/11.jpg)
OPE up to dimension 5 in vacuum
, where C0 (q2) is perturbative part
![Page 12: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/12.jpg)
OPE up to dimension 5 in nuclear matter
where
at meson scalar gconsiderin and
, matter, theof framerest in the
),()()(
),0,(
)0,1(
200
200
0
qqqq
v
oe
![Page 13: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/13.jpg)
List of employed condensate parameters
![Page 14: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/14.jpg)
2.2. Phenomenological side
.
, function step of definition theand
, operatorson translatiusing and
,
operatorscurrent obetween twoperator identity Inserting
iqEE
jo
iqEE
joq
iw
edw
ix
joexjo
dpI
oxjjoxojxjoxxedi
ojxjToxediq
q
q
iwx
pxip
p
ppp
xiq
xiq
0
2
0
2
0
3
3
004
42
2
|)0(|
2
|)0(|)(
2
1)(
|)0(||)(|
||2)2(
|)()0(|)(|)0()(|)(
|)]0(),([|)(
0
![Page 15: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/15.jpg)
Ansatz' ContinuumPole' called so is which
!!function spectral
, If
2
1
, usingby extracted ispart imaginary Its
,
)(Im)(
)(||Im
||||
)(||2
)(||22
1Im
)(1
0222
220
2
22
220
2022
0
20
222
sqmqF
Eqjo
jojo
EqjoE
qEqjo
E
q
xix
P
ix
h
qqq
qqq
![Page 16: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/16.jpg)
2.3. Dispersion relation(in vacuum)
L.H.S .is a function of QCD parameters such as g, mq, <qq>, <G2>…, obtained from OPE.
R.H.S. is a function of physical parameters such as mλ and s0
![Page 17: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/17.jpg)
Dispersion relation (in nuclear matter)
![Page 18: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/18.jpg)
2.4. Borel transformation
dsesdsQs
sB
MNQB
qQdQ
dQ
nB
C
Ms
C
NN
n
n
MnQnQ
2
22
2
/2
22
222
2
/
)(Im)(Imˆ
1
)!1(
11ˆ
)()!1(
1limˆ
part continuum gsuppressinby side ogicalphenomenol theimproves 2)
termscondensate ldimensiona-high gsuppressinby side OPE improves 1)
where, ation transformBorel
![Page 19: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/19.jpg)
3. Application to scalar D mesons
1. Charm scalar meson D0* in vacuum
2. Charm scalar meson D0* in nuclear matter
3. Charm-strange scalar meson Ds0 in vacuum & in nuclear matter
![Page 20: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/20.jpg)
3.1. Charm scalar meson D0* in vacuum
From the dispersion relation
,
the mass of scalar D meson is
22
22
/~
2/~
2~
/1/~
~Mm
Mm
eF
MeFm
![Page 21: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/21.jpg)
Borel windowThe range of M2 satisfying below two conditions
1) continuum/total < 0.3
/ < 0.3
2) Power correction/total < 0.3
/ <0.3
![Page 22: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/22.jpg)
Borel curve for D0*(2400) in vacuum
(adjust s0 to obtain flattest curve within Borel window)
S0=7.7 GeV2
![Page 23: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/23.jpg)
3.2. Charm scalar meson D0* in nuclear matter
• Two dispersion relations for πe and πo exist
• ≡f(s0+,s0
-)
• ≡g(s0+,s0
-)
![Page 24: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/24.jpg)
density, saturationnuclear times0.1 of case in the example,For
method. iterativeby solved are they and
,
is,That
functions, twoofion recombinatproper After
),,(
),,(
.),(),(
),()/1(
),()/1(
),(),(
),()/1(
),()/1(
00
00
0000
0020022
0000
0020022
ssmmm
ssmmm
ssgmssf
ssgMdd
mssfMdd
m
ssgmssf
ssgMdd
mssfMdd
m
iteration No. D+ s0 D+ mass D- s0 D- mass
0 7.7 2.392
1 7.55 2.373 2 7.8 2.391
3 7.5 2.371 4 7.8 2.391
![Page 25: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/25.jpg)
Mass shift of D0*±(2400) in nuclear matter
(The conditions for Borel window are continuum/total<0.5 & power correction/total <0.5)
![Page 26: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/26.jpg)
Physical interpretation of the result
matter.nuclear in ofthat
than more decreases of mass thereason why theisThat
. than attractive more is result, a As
quarks. and in rich ismatter Nuclear
. is of that and , is ofcomponent quark The
*0
*0
*0
*0
*0
*0
D
D
DdcDcd
du
dcDcdD
![Page 27: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/27.jpg)
3.3. Charm-strange scalar meson Ds0 in vacuum & in nuclear matter
ns.calculatio lattice from and
GeV
GeV
belows. as changed are parameters Condensate
.simplicityfor ignored isquark strange of mass The
2
36.0
8
1
8
1
8
1
018.0
0
8.0
8.0
20
20
20
20
20
20
00
y
FdgdyFsgsFdgd
dDdysDsdDd
dFgDdysFgDsdFgDd
nsiDsdiDd
ssdd
ssFsgsFdgd
ddyddssddmattervacuum
![Page 28: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/28.jpg)
Borel curves for Ds0 (2317) in vacuum
(The conditions for Borel window are continuum/total<0.5 & power correction/total <0.5)
![Page 29: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/29.jpg)
Mass shift of Ds0±(2317) in nuclear
matter (The conditions for Borel window are
continuum/total<0.5 & power correction/total <0.5)
Nuclear density (0.17 nucleon/fm3) Nuclear density (0.17 nucleon/fm3)
![Page 30: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/30.jpg)
4. Conclusion1. We successfully reproduced the mass of charm scalar
meson D0* in vacuum and that of charm-strange scalar meson Ds0 by using QCD sum rule
2. Based on this success, their mass shifts in the nuclear matter are estimated by considering the change of condensate parameters and adding new condensate parameters which do not exist in vacuum state.
3. The mass of D0*+ decreases in the nuclear matter more than that of D0*-, as naively expected.
4. But the mass of Ds0+ increases a little in the nuclear matter,
while that of Ds0- decreases.
5. The quark component of these scalar particles are still in question, whether they are conventional mesons or quark-quark states or their combinations or others.
6. We expect that the behavior of their masses in nuclear matter serves to determine the exact quark component of those scalar particles.
![Page 31: Scalar D mesons in nuclear matter](https://reader035.vdocuments.site/reader035/viewer/2022081504/5681308f550346895d966c8b/html5/thumbnails/31.jpg)
4.1. Future work
• QCD sum rule for pseudoscalar D meson, which is the chiral partner of charm scalar meson – the mass difference between scalar and pseudoscalar meson is expected to decrease in nuclear matter due to the partial restoration of chiral symmetry.
• QCD sum rule for charm scalar meson as four quark state – The comparison of its mass shift in nuclear matter with that of conventional meson will reveal the exact component of charm scalar meson.