^{3}.

The quark-gluon plasma (QGP) equation of state within a minimal length scenario or Generalized Uncertainty Principle (GUP) is studied. The Generalized Uncertainty Principle is implemented on deriving the thermodynamics of ideal QGP at a vanishing chemical potential. We find a significant effect for the GUP term. The main features of QCD lattice results were quantitatively achieved in case of

Essential modifications in Heisenberg’s uncertainty principle are predicted near Planck scale which is called Generalized Uncertainty Principle (GUP). One of the most exciting predictions of some approaches related to quantum gravity [

In other minimal length formalism [

In this paper, the effect of the GUP on QGP equation of state of massless quark flavors at a vanishing chemical potential

In this section, we derive the thermodynamics of QGP in case of bosons and fermions taking into account the GUP impact. Then, the thermodynamical equations such as pressure and energy density of quark-gluon plasma are obtained.

At finite temperature

For simplicity we consider chiral limit (i.e., vanishing mass) and a vanishing chemical potential, which experiments ensure at high energy. Then the dominant excitation in the hadronic phase is a massless pion, while that in the quark-gluon plasma is massless quarks and gluons. For a particle of mass

For the first term,

At finite temperature

For simplicity we consider chiral limit (i.e., vanishing mass) and a vanishing chemical potential, which experiments ensure at high energy. Then the dominant excitation in the hadronic phase is a massless pion, while that in the quark-gluon plasma is massless quarks and gluons. For a particle of mass

For the first term,

Now, the QGP equation of state of free massless quarks and gluons can be derived from the above equations. The total grand canonical partition function of QGP state can be given by adding the grand partition functions coming from the contribution of bosons (gluons), fermions (quarks), and vacuum [

In our case, the vacuum pressure can be represented with the bag constant

Since the value of vacuum partition function equals

The main features of QCD lattice results show a clear

The main problem appears when one starts to adjust the behavior of the energy density, through varying the value of the bag pressure; with the QCD lattice results, one can not obtain a qualitative agreement in case of the pressure using the same bag parameter value [

For overcoming this problem, the bag model was modified [

To adjust the high temperature behavior for

In case of

The theoretical calculation of the pressure and the energy density of the QGP using (^{−1} as taken in [

The symbols show the MC LR for the pressure and the energy density in the

The theoretical calculation of the pressure and the energy density of the QGP using (^{−1} as taken in [

The symbols show the MC LR for the pressure and the energy density in case of

The theoretical calculation of the pressure and the energy density of the QGP using (^{−1} as taken in [

The symbols show the MC LR for the pressure and the energy density in case of

Also, we can calculate the interaction measure

The symbols show the lattice results for the interaction measure in the

In the present work, the effect of the GUP on QGP of massless quark flavors at a vanishing chemical potential,

The authors declare that there is no conflict of interests regarding the publication of this paper.