The role of the tetraquark at nonzero temperature Francesco Giacosa in collaboration with A. Heinz,...
-
date post
19-Dec-2015 -
Category
Documents
-
view
222 -
download
1
Transcript of The role of the tetraquark at nonzero temperature Francesco Giacosa in collaboration with A. Heinz,...
The role of the tetraquark at nonzero temperature
Francesco Giacosa
in collaboration with A. Heinz, S. Strüber, D. H. Rischke
ITP, Goethe University, Frankfurt am Main
Hadrons@Fias- 26/6/08
Outline
• Scalar mesons below and above 1 GeV at zero T Light scalar mesons (< 1 GeV) as tetraquark states and tetraquark-quarkonia mixing
• A chiral model with pions, light scalar quark-antiquark and tetraquark states Description of the model at zero T, quark and tetraquark condensates and mixing
• Results at nonzero temperature Order of the phase transition, behavior of the condensates and mixing angle, role interchange
Francesco Giacosa Scalar Quest
Francesco Giacosa Scalar Quest
Part I
Spectroscopy in the vacuum
0I)980(
)600(
0
0
f
f
)1710(
)1500(
)1370(
0
0
0
f
f
f2
1I )800(k
1I )980(0a
M < 1 GeV 1 GeV < M < 1.8 GeV
Too many resonances than expected from quark-antiquark states
Francesco Giacosa Scalar Quest
0PCJ
)1450(0a
)1450(K
Scalar resonances below 1.8 GeV reported by PDG:
0I)980(
)600(
0
0
f
f
ss
dduu
)(2/1
2
1I )800(k
1I )980(0a
M < 1 GeV interpretation
Francesco Giacosa Scalar Quest
0PCJ
)(1/2 , , dduuuddu
dssdussu , , ,
Assignment has problems!!!
Francesco Giacosa Scalar Quest
Chiral partner of ?
List of Problems
• Masses: degeneracy of and
• Strong coupling of to
• The scalar quarkonia are p-wave states (L = S = 1), thus expected to be heavier than 1 GeV as tensor and axial-vector mesons
• Some Lattice results find
• Large behavior of light scalar not compatible with quarkonia
)980(0f
Francesco Giacosa Scalar Quest
)980(0a
)980(0a KK
GeVMdu
5.14.1 from: Prelovsek et al., Phys. Rev. D 70 (2004), Burch et al., Phys. Rev. D 73 (2006)
cN-from: Pelaez, Phys. Rev. Lett. (2004), Pelaez and Rios, hep-ph/0610397
Francesco Giacosa Scalar Quest
The light scalars are interpeted as tetraquark state
An example of „good diquark” is:
)(:)(:(:0: BRRBcduudfSpinLSpaceqq
A tetraquark is the bound state of two diquarks
Idea of Jaffe (R.L. Jaffe, Phys. Rev. D 15 (1977)) :
Example: )980(0a du s]][u,s,d[- (and not )
0I)980(
)600(
0
0
f
f ],][,[ dudu
2
1I )800(k
1I )980(0a
M < 1 GeV Tetraquark interpretation
Francesco Giacosa Scalar Quest
0PCJ
]),][,[],][,[(
],,][,[ ,],][,[
sdsdsusu
sdsusdsu
],][,[ ,],][,[
],,][,[ ,],][,[
sudusudu
sddusddu
]),][,[],][,[( sdsdsusu
It is not the chiral partner of !
0I
)1710(
)1500(
)1300(
0
0
0
f
f
f
ss
glueball
dduu
)(2/1
2
1I )1430(0K
1I )1470(0a
M > 1 GeV interpretation
Francesco Giacosa Scalar Quest
0PCJ
)(1/2 , , dduuuddu
dssdussu , , ,
Mixing among the isoscalars is expected
Francesco Giacosa Scalar Quest
Chiral partner of !
Francesco Giacosa Scalar Quest
0PCJ
These are predominantly quarkonia (with glueball-intrusion) (but not only!)
M < 1 GeV 1 GeV < M < 1.8 GeV
0I
)1710(
)1500(
)1370(
0
0
0
f
f
f2
1I
1I )1450(0a
)1450(K
These are predominantlytetraquarks (but not only!)
)980(
)600(
0
0
f
f
Indeed, mixing will occur, thus the scenario changes slightly as:
)(21 dduu
],][,[ duduNot the chiral partner of !
)800(k
)980(0a
Chiral partner of !
Francesco Giacosa Scalar Quest
Part II
A chiral model with tetraquark
Francesco Giacosa Scalar Quest
How does this scenario affect finite temperature behavior?
We study this issue in the SU(2) limit within a simple model:
statescalar -extraan is ],][,[2
1)600( resonance The
.pion theofpartner chiral theis )(2
1)1370( resonance The
0
0
duduf
dduuf
Mixing shall play a crucial role:
)(
2
1
],][,[2
1
)cos()sin(
)sin()cos(
)1370(
)600(
00
00
0
0
dduu
dudu
f
f
4545 0
., , :freedom of degrees Five
Francesco Giacosa Scalar Quest
g coupling with piece Tetraquark
22
22
ML theasjust
2222
)(2
1)(
4
gMFλ
V
A simple chiral model with tetraquark
m)(quarkoniu d)duu(2
1 k)(tetraquar ]d,ud][[u,
2
1 triplet,
It emerges as an SU(2) limit of the SU(3) case
0V
V
0)( :minimum absolute for theSearch
20202
2
20 ...,22
1
M
gf
F
Mg
F
condensatek tetraquar
condensatequark
0
0
g,M,F,,
:parametersunknown 5
(A. Heinz, S. Strüber, F. G. and D. H. Rischke: arXiv:0805.1134 [hep-ph] )
(F.G.,Phys.Rev.D75:054007,2007 )
Francesco Giacosa Scalar Quest
)(2
1)(
4 2
222222
2
gMFλ
V
...2
2V
:minimum thearound potential theexpand We
22
21
20
02
21
MMg
gM
0
222
220
2 M ,2
3 where
F
M
gM
diagonal.not ismatrix mass theand potential in the
present is 2 A term .orthogonalnot are and fields that theNotice 0 g
)1370(
)600(
0
0
fS
fHOne must therefore diagonalize the model introducing the mass eigenstates
mixing. quarkonium-k tetraquar thedescribes parameter theThus, g
Francesco Giacosa Scalar Quest
)cos()sin(
)sin()cos(
)1370(
)600(
)2(
00
00
0
0
SOB
fS
fH
That is, the fields H and S, corresponding to the two physical resonances, are introduced in order to diagonalize the potential:
220
21
0
4arctan
MM
g
...2
22
0
02
21
S
HB
Mg
gMBSH t
2
2
20
02
0
0
2
2
S
Ht
M
MB
Mg
gMB
...2
2V 2
0
02
21
Mg
gM
0222
0
222222 4)4( gMMgMMMM HSHS
Francesco Giacosa Scalar Quest
Part III
Results at nonzero T
Francesco Giacosa Scalar Quest
We study this model at nonzero T by using the CJT formalismIn the Hartree approximation. (Only double-bubble diagrams are taken into account)
)( :condensate Tetraquark
)( :condensateQuark
0
0
T
T
)( :angle Mixing 0 T
))1370((S )(MM
))600((H )(MM
)(MM
:Masses
0
0
fT
fT
T
SS
HH
0)0(with T
0)0(with T
0)0( with T
Details in: A. Heinz, S. Strüber, F. G. and D. H. Rischke: arXiv:0805.1134 [hep-ph]
Francesco Giacosa Scalar Quest
MeV 1200M
MeV 400M :esknown valuely approximat 2
MeV 92.4
MeV 139M :esknown valu- well2
,M,F,, :parametersunknown 5
)1370(fS
)600(fH
0
0
0
f
g
)(2
1)(
4 2
222222
2
gMFλ
V
mixing) quarkonium-k(tetraquar gconstant coupling theand
upon them ationsstudy vari shall Weuncertain! are M and M )1370(fS)600(fH 00
Francesco Giacosa Scalar Quest
n transitiophase
chiral theoforder study the weand M and g vary We(fixed). GeV 4.0 SHM
0(T)
)(
)( H
:) ( 0
quarkquark-antiS
tetraquark
decouplingtetraquarkg order 1GeV 948.0
over cross GeV 948.0
S
S
M
M
0805.1134 [hep-ph]0g
Francesco Giacosa Scalar Quest
Quark condensate (order parameter) as function of T for different values of g for MS = 1.0 GeV
Increasing of g (mixing):1) Tc decreases2) First order softened3) Cross-over obtained
for g large enough
Francesco Giacosa Scalar Quest
n transitiophase chiral theoforder study the weand
M and g vary We(fixed). GeV 2.1 HSMSimilar discussion as before
0805.1134 [hep-ph]
Francesco Giacosa Scalar Quest
We now turn to one specific case:
GeV 3.4gstudies Latticewith agreement in
over-cross have order toin gfix We
MeV 1200 M
MeV 400 M :use We
)1370(fS
)600(fH
0
0
We study for this set of parameters all the temperature-dependent quantitites: masses, mixing angle and condensates.
Francesco Giacosa Scalar Quest
Finite Temperature behavior of quark and tetraquark condensates:
increase tostarts )(then
TTfor holds )()( T nonzeroAt c2
2
T
TM
gT
2020 :T zero that Remind
M
g
This property depends on the characteristics of the model. However,It does not influence other quantities
0805.1134 [hep-ph]
Francesco Giacosa Scalar Quest
454/)( :as defined
))(cos())(sin(
))(sin())(cos(
)1370(
)600(
0
0
ss TT
TT
TT
fS
fH
Finite Temperature behavior of masses and angles:
Two ‘critical temperatures’:
MeV 170140 :example In this cs TT
The mixing angle grows with T up to theMaximal value. Then, it changes sign at Ts and becomes negative. (Second change at higher T)
antiquark-quarkmostly is statelighter theTTFor
e)interchang role mixing, (maximal
s
0805.1134 [hep-ph]
Francesco Giacosa Scalar Quest
Summary and outlook
• Spectroscopy of light scalars at zero T: if the light scalars are not quark-antiquark, how does chiral restoration change?
• Description of a model with pions, scalar quark-antiquark and tetraquark. Mixing at zero T: f0(600) is predominantly tetraquark and f0(1370) pred. quark-antiquark
• Tetraquark-quarkonium mixing implies: (i) decreasing of the critical temperature, (ii) softer first order, and, if the mixing is large enough, cross over. The latter can be obtained also for a mass of the chiral partner above 1 GeV
• The mixing increases with T. At a certain Ts the mixing angle is maximal and a role interchange takes place. Then, chiral restoration takes place in the standard form.
• This was the first step! One shall go further and include more resonances.
Francesco Giacosa Scalar Quest
g=2 GeV. Ts>Tc
Francesco Giacosa Scalar Quest
8.14.1 GM GeV
0
0
I
J PC
lightest predicted glueball
Lattice:
Morningstar (1999)
ssS
ggG
nnN
f
f
f
97.006.026.0
06.089.049.0
26.045.086.0
)1710(
)1500(
)1370(
0
0
0
Result for the mixed states:Obtained upon fit to the known results of PDG
Francesco Giacosa Scalar Quest
has the largest gluonic amount!!!)1500(f0
F.G. et al, Phys.Rev.D72:094006, 2005 (hep-ph/0509247)
F.G. et al, Phys.Lett.B622:277-285,2005 (hep-ph/0504033)
F.G. et al, Phys.Rev.C71:025202,2005 (hep-ph/0408085 )
)1370(0f19.046.0
500200
)1500(
)1500(
0
0
f
KKf
MeVstatenn
)1500(0f05.024.0
5109
)1500(
)1500(
0
0
f
KKf
MeV
)1710(0f 2.05
10140
)1500(
)1500(
0
0
f
KKf
MeV
Compatible with a dominant:
)( glueballinert
stategg
statess
Francesco Giacosa Scsalar Quest
Francesco Giacosa Scalar Quest
Strong decays of a tetraquark state:
Subdominant
P
P
[4q]S
P
P
Dominant
[4q]S
}',,,{ K
}',,,{ K
}',,,{ K
}',,,{ K
Previous works and motivations
Original paper:
Jaffe, Phys. Rev. D 15 (1977),
Revival in:
Maiani et al, Phys. Rev. Lett. (2004)
Experimental study:
D. V. Bugg, EPJC47 (2006)
Systematic evaluation of amplitudes: my work
Phys.Rev.D74:014028,2006
Francesco Giacosa Scalar Quest
I studied the strong decays with a hadronic model
(never see quarks and gluons, only hadrons)
6
2
3
632
632
ˆ
800
0800
800
KK
K
K
PP aa
Nonet of pseduoscalar states:
Nonet of scalar tetraquark states:
]4[
2
)980(]4[)980(
)980(2
)980(]4[
0
000
0
0
00
]4[
qkk
kaqf
a
kaaqf
S
B
B
B
q
]d,ud][[u,2
1]4[
22
])s,ds][[d,]s,us][([u,]4[
q
qf
B
B
The phys. resonances result from mixing
Francesco Giacosa Scalar Quest
Write the flavor, P, C invariant interaction Lagrangian for the scalar 4q decays:
PPAATrScPAPATrScL
SPP
jjqij
itjqij
qaa
ˆˆˆˆ
nonetscalar -4q nonet, pseud. ˆ
]4[2
]4[1int
]4[
)(with ijkjkiA
]4[ qS
1c}',,,{ K
}',,,{ K]4[ qS
2c}',,,{ K
}',,,{ K
P
P
Dominant
[4q]
S
Sumdominant
P
P
[4q]
S
The trace structure corresponds to the microscopic diagrams:
• Scalar tetraquark and quarkonia states can mix Black et al, Phys. Rev. D 64 (2001), F.G., Phys.Rev.D 75,(2007)
• Extension of the model: ; consider scalar and pseudoscalar quarkonia meson and scalar tetraquark states
Francesco Giacosa Scalar Quest
)3()3()3( RLV SUSUSU
)(4
1L , 0
2][ SBqq VVTriPS
Spontaneous symmetry breaking takes place, but no need to specify the potential. The pions emerge as Golstone bosons..
22,
2,
20
][min
FF
FFdiagS K
Going further: tetraquark-quarkonia mixing
Francesco Giacosa Scalar Quest
:obtained is mixing around expandingWhen
.)(22
0
]4[2*]4[1int
jjqij
ijitjqij AATrS
cAAAATrS
cL
TcNTNcNcTNcTNL
fNN SN
S T
shift
q]q[
q][
200
22
00
4
2
with NN :Shift .quarkoniumd)duu(2
1
tetraquark]d,ud][[u,2
1
decay mixing tq-condensate
:dimension oneIn
Francesco Giacosa Scalar Quest
10%)(sin :Result
][
]4[
)cos()sin(
)sin()cos(
)1450(
)980(
2
0
0
0
0
qqa
qa
a
a
One relates the tetraquark-decay parameters to the mixing strenght by using the decay widths of PDG; then, one can evaluate the mixing:
Result in the isovector sector
The mixing is small !!!
Francesco Giacosa Scalar Quest
Consider flavor: 3 antisymmetric combinations
d][u, s][u,- ],[ sd
Under SU(3)-flavor the 3 diquarks behave like antiquarks:
q
s
d
u
],[
],[
],[
du
su
sd
jii
i
U )(qq
qU)(q
j
jij
)3(SUU
)3(SUU
jiji
ji
U
)(
)U( ji
Francesco Giacosa Scalar Quest
We have the correspondences:
and: ]d,u[ ]s,u[- ],[ sd
s d u
d][u, s][u,- ],[ sd
s d u
Compose a diquark and an antidiquark: full 4-q nonet
Example: du s]][u,s,d[- )980(0a
Francesco Giacosa Scalar Quest
A tetraquark condensate is generated:
22
]4[
2122
]4[
21 )()(2]4[ F
M
cc
M
ccqσ
qσu
qσb
bb
22,
2,
2,,0
FF
FFdiagdiag Ksuu
55
5
GeV 10)42(
]4[],][,[2
1
qdudu bQCD
Francesco Giacosa Scalar Quest