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SU(2)f NJL model with Meson Loops:The Gap Equation at Finite Temperature
Renan Pereira
Supervisors: Pedro Costa & Constanca Providencia
Centre for Physics of the University of Coimbra
June 11, 2018
Renan Pereira (CFisUC) June 11, 2018 1 / 4
Motivation
Motivation
The goal is to study the influence of meson degrees of freedom on therestoration of chiral symmetry in a consistent approach.
The effective action formalism is used to calculate the SU(2)f Nambu−Jona-Lasinio gap equation with one-boson loop corrections at finite temperature.
This formalism was only used by (Florkowski and Broniowski, 1996) however,to solve the gap, several approximations were made.
One can obtain the following gap equation:
g−1S (S −m)− 4NcNf Sf0(S)
+ 2NcNf S
∫d4q
(2π)4
{4f1(S , q) + 2f1(S , 0)− 2
[q2 + 4S2
]f2(S , q)
}Kσ(S , q)
+ 6NcNf S
∫d4q
(2π)4
{2f1(S , 0)− 2q2f2(S , q)
}Kπ(S , q) = 0.
Renan Pereira (CFisUC) June 11, 2018 2 / 4
Results
The parameters are fixed to reproduce:⟨
¯⟩ 1
3 = −256 MeV, mπ = 135 MeV and fπ = 93 MeV.
Λb/Λf m[MeV] Λf [MeV] g2SΛf Tc [MeV]
0.00 (MFA) 4.62 690.32 2.01 1880.25 4.62 698.60 2.03 1600.30 4.62 701.78 2.04 1550.50 4.62 717.38 2.07 1390.75 4.62 740.86 2.13 1211.00 4.61 770.92 2.21 104
0.0 0.2 0.4 0.6 0.8 1.0
-250
-240
-230
-220
0
uu
1/3 [M
eV
3]
b/
f
0 100 200 300 4000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0
T [MeV]
b/
f = 0.00
b/
f = 0.25
b/
f = 0.50
b/
f = 0.75
b/
f = 1.00
Renan Pereira (CFisUC) June 11, 2018 3 / 4
Conclusions, Further Work & Acknowledgements
Conclusions
The inclusion of meson fluctuations brings the pseudo criticaltemperature of the chiral transition to lower values;
A set of parameters is found such that Tc ' 155 MeV;
Further Work
Extend the formalism to the SU(3)f and include the Polyakov loop;
Thank you for your attention!
This work is funded by National funds through FCT-Fundacao para a Cienciae Tecnologia under the grant PD/BD/128234/2016 and the project UID/-FIS/04564/2016.
Renan Pereira (CFisUC) June 11, 2018 4 / 4
