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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 Presentation
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Scalar D mesons in nuclear matter
Taesoo Song, Woosung Park,
Kie Sang Jeong and Su Houng Lee
(Yonsei Univ.)
Procedure
1. Motivation
2. QCD sum rule in vacuum & in nuclear matter
3. Application to Scalar D mesons
4. Conclusions
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-).
2. QCD sum rule
1. OPE (operator product expansion)
2. Phenomenological side
3. Dispersion relation
4. Borel transformation
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
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
Perturbative quark propagator in a weak gluonic background field(The gluons are supposed to emerge from the ground state)
:)()( xSxSTr cq : ~ gConsiderin (0)
Perturbative part I : dimension 0
Gluon condensates<G2> : dimension 4
and more condensateswith higher dimensionor more strong couplings
:)(......:!
)(
)...(...!
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)
y graphicall is )1(
Quark condensate <qq> : dimension 3
Quark-gluon mixed condensates<qGq> : dimension 5
and more condensateswith higher dimensionor more strong couplings
OPE up to dimension 5 in vacuum
, where C0 (q2) is perturbative part
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
List of employed condensate parameters
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
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
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
Dispersion relation (in nuclear matter)
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
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
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
Borel windowThe range of M2 satisfying below two conditions
1) continuum/total < 0.3
/ < 0.3
2) Power correction/total < 0.3
/ <0.3
Borel curve for D0*(2400) in vacuum
(adjust s0 to obtain flattest curve within Borel window)
S0=7.7 GeV2
3.2. Charm scalar meson D0* in nuclear matter
• Two dispersion relations for πe and πo exist
• ≡f(s0+,s0
-)
• ≡g(s0+,s0
-)
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
Mass shift of D0*±(2400) in nuclear matter
(The conditions for Borel window are continuum/total<0.5 & power correction/total <0.5)
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
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
Borel curves for Ds0 (2317) in vacuum
(The conditions for Borel window are continuum/total<0.5 & power correction/total <0.5)
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)
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.
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.
