1 Nuclear Binding and QCD ( with G. Chanfray) Magda Ericson, IPNL, Lyon SCADRON70 Lisbon February...
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Transcript of 1 Nuclear Binding and QCD ( with G. Chanfray) Magda Ericson, IPNL, Lyon SCADRON70 Lisbon February...
1
Nuclear Binding and QCD
( with G. Chanfray)
Magda Ericson, IPNL, Lyon
SCADRON70 Lisbon February 2008
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Nuclear Binding and QCD
The existence of a scalar meson coupled to nucleons has consequences for nuclear binding
• Basis of relativistic theories of nuclei(Walecka, Serot) : (attraction) and exchange (repulsion)
•What new developments and perspectives?
-Quark-Meson-Coupling model (QMC) : introduction of nucleonic response to (Guichon, Thomas et al.)
-Link to QCD parameters (Chanfray, M.E.)
3
BUT : this identification is not allowed ! It violates chiral constraints! (Birse)Additional exchanges needed to cancel violating terms.
Feasible, but cumbersome
Identification with natural.Would make life simple ; mass would follow condensate evolution
Nuclear scalar field in the - model
(Here is the nucleon sigma commutator and sN the nucleon scalar density)
Use of effective theories : -model andchiral
partners
In vacuum <> = f . In medium <> = f +
4SHORT CUT : introduce another scalar field (Chanfray, Guichon, M. E.)
go from cartesian (linear representation) to polar coordinates (non-linear)
In nuclear medium : allow for a change in radius :
Satisfies all chiral constraints
Associate nuclear scalar field with the radial mode by the identification with
Loss of previous simplicity : MN and evolve differently
Pion cloud influence should be removed from to extract
model dependence introduced
5
Nuclear Binding in model
The model is not a viable theory of nuclear matter.
The tadpole problem can be phenomenologically cured with introduction of the response, N , of the nucleon to the scalar field
The introduction of this nucleonic response is the basis of Quark-Meson-Coupling model, QMC (Guichon, Thomas, ..) .
Large effect (about 30% decrease of m at 0)Produces collapse instead of saturation (Kerman,Miller)
s
3s coupling lowers mass in medium :
ss
N
Potential :
6
But phenomenology is not our aim!Where is the link to QCD??
It goes through the study of the
For us, in a purely phenomenological description, saturation can be obtained, for N > 0 , with a cancellation of about 2/3
of the tadpole scattering amplitude
QCD scalar susceptibility
Definition :
Scalar susceptibility
= order parameter
explicit symmetry breaking parameter
Nuclear susceptibility defined as
(vacuum value is subtracted)
7 is the propagator of the fluctuations of the order parameter,
In the model, the simulation of by (x) leads to
D(0) is the propagator at q=0
(vacuum value)
For the nuclear medium
In medium, modification of mby tadpole diagram
Expanding sA in density :
8The term linear in density of sA represents the contribution of the
individual nucleons, sN N
s , to the nuclear response
In the model we thus find :
This contribution is proportional to the tadpole scattering amplitude
Introducing Qs = scalar quark number of the nucleonProportionality factor :
9In summary : the model predicts the existence of a non-pionic component in s
N linked to the scalar meson. Its sign is negative
Any indication in favor of its existence?
Maybe!In lattice results on the evolution of MN with the quark mass (equivalently with m
2) : MN (m)
Lattice data are available only for m >0.1 (GeV)2
Extrapolation needed to reach the physical MN
MN(m
Nucleon mass GeV
Lattice data for MN(m versus m
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Lattice data of interest : successive derivatives of MN (m
) provide Qs and sN !
But these are total values which include the pionic contribution
Fortunately,
The pion loop contribution to MN(m2) has been separated out (Thomas et al.)
(It contains non-analytical terms in mq , which prevents a small mq expansion) .The separation introduces model dependence
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Method of Thomas, Leinweber et al. :
a2 = +1.5 GeV-1 ; a4 = -0.5 GeV-3
The pionic loop contribution to MN depends on the N form factor.Different forms are used (monopole, dipole, gaussian)
with an adjustable parameter .The rest is expanded in m
MN(mmpionic term + apionic term + a0 0 + a+ a22mm
2 2 + a+ a44mm4 4 +… +…
The parameters a are practically insensitive to the choice of the form factor
(dominated by a(dominated by a22 term) term)
From this we deduce :
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Sign of a4<0 is as predicted in the model
This magnitude is more than 10 times too large!!This magnitude is more than 10 times too large!!The The model is contradicted by the parameter model is contradicted by the parameter a4 !
Are the magnitudes of the expansion parameters also compatible with the model?
In the In the model : model :
13Another failure of the model ?No, the same one as before,
sN and TN are related !
Our approach : MN is partly from condensate, partly from confinement.
Keep assumption : The nuclear scalar field affects the quark condensate, as in the model
Need for compensating term !Need for compensating term !Common cure found in confinement
Introduces a positive nucleon response to the scalar field, as in QMC
Quark Meson Coupling Model : : Bag model : MN totally from confinementNo relation of nuclear field to chiral field
With confinement :What is the link between s
N and TN ?
14Illustration in a hybrid model of the nucleon (introduced by Shen, Toki)
-Scalar susceptibility :
-Scalar nucleon charge :
-Nucleon mass : MN = 3E(M) > 3M ;
Three constituent quarks (mass M) kept together by a central harmonic potential V(r)
Susceptibility of constituent quark <0Confinement term >0
15Two terms of opposite sign contribute to sN
Compensation possible
Similar compensation in N scattering amplitude T N?
Two components contribute as well to T
i) Tadpole scattering amplitude on constituent quarks
tadpole amplitude on a constituent quarkg
q == -quark coupling constant= scalar number of constituent quarks
Note : the coupling of the nuclear field to the constituent quarks is linked to the assumption that acts on the quark condensate, i. e., on the constituent quark mass :
q
16ii) Amplitude N from nucleon structure (confinement)
Sign : >0 compensation possible
ii) Chiral parts
Compare term by term :i) Confinement part
as in model
confinement chiral
17In the NJL model which describes the constituent quark, we recover at the quark level the previous results of the model :
Note : numerically our simple model fails to produce enough compensation.
But it is important to illustrate the role of confinement.
Overall
Same amount of compensation by confinement as in sN and TN
The ratio rchiral becomes
and
18Our approach
Use QCD lattice expansion to fix the scalar parameters of nuclear physicsExpansion provides Qs and N
s
From the expressions of Qs and sN and the relation :
instead of 3 for the tadpole alone
we can write the in-medium propagator :
m stabilized !
ii)
i)
193-body forces
repulsive 3-body forces
m stable. But the introduction of response, N , is important
Make field transformation :
For C>1 overcompensation repulsive 3-body forces, important for saturation
The chiral potential V(s) transforms :
In our fit the energy per nucleon from the 3-body force is :
20
Our fit parameters
M*N
m*
Mass MeV
m*with N=0
Density dependence of M*N and m*
s in our fit
Pion contribution: not at Hartree level but through Fock term and correlation terms (with or without ). Dependence on N form factor. Short range interaction added through Landau-Migdal parameters g’.
• Vector potential : m =783 MeV, g: free (gfit close to VDM value)
• N form factor : dipole with =0.98 GeV (Npion=21 MeV or N
total =50 MeV )
• g’ values : from spin-isospin physics g’NN=0.7, g’N=0.3, g’=0.5
• gs/m2 =a2 /f =15 GeV-2
(gives mean scalar field about 20 MeV at 0)with gs= MN/f =10 ( model value), m= 800 MeV
• C ( = N f/gs ) : allowed to vary near the lattice value Clattice =2.5 :
Cfit =2
Lead to successful description of nuclear binding !
21Summary
Full consistency between QCD lattice expansion and nuclear binding!
•linear model fails for both•proper description must include nucleon structure and confinement
• origin of nucleon mass mixed : - in part from condensate- in part from confinement
•nuclear scalar field identified with chiral invariant field, linked to quark condensate
Description of nuclear binding successful with parameters close to those extracted from QCD
Consistency favors existence of link between the scalar nuclear potential and
the modification of the QCD vacuum!
it is possible to link the parameters of QCD lattice expansion
to the scalar parameters of the nuclear potential
(Near model independence but separation of pion cloud effect necessary)
With the assumptions: