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Register a new userPath Integration in QCD with Arbitrary Space-Dependent Static Color Potential
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Authors
Gouranga C. Nayak
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We perform path integral for a quark (antiquark) in the presence of an arbitrary space-dependent static color potential A^a_0(x)(=-int dx E^a(x)) with arbitrary color index a=1,2,...8 in SU(3) and obtain an exact non-perturbative expression for the generating functional. We show that such a path integration is possible even if one can not solve the Dirac equation in the presence of arbitrary space-dependent potential. It may be possible to further explore this path integral technique to study non-perturbative bound state formation.
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We determine the strong coupling constant $alpha_s(M_Z)$ from the static QCD potential by matching a lattice result and a theoretical calculation. We use a new theoretical framework based on operator product expansion (OPE), where renormalons are subtracted from the leading Wilson coefficient. We find that our OPE prediction can explain the lattice data at $Lambda_{rm QCD} r lesssim 0.8$. This allows us to use a larger window in matching, which leads to a more reliable determination. We obtain $alpha_s(M_Z)=0.1179^{+0.0015}_{-0.0014}$.
We determine the strong coupling constant $alpha_s$ from the static QCD potential by matching a theoretical calculation with a lattice QCD computation. We employ a new theoretical formulation based on the operator product expansion, in which renormalons are subtracted from the leading Wilson coefficient. We remove not only the leading renormalon uncertainty of $mathcal{O}(Lambda_{rm QCD})$ but also the first $r$-dependent uncertainty of $mathcal{O}(Lambda_{rm QCD}^3 r^2)$. The theoretical prediction for the potential turns out to be valid at the static color charge distance $Lambda_{rm overline{MS}} r lesssim 0.8$ ($r lesssim 0.4$ fm), which is significantly larger than ordinary perturbation theory. With lattice data down to $Lambda_{rm overline{MS}} r sim 0.09$ ($r sim 0.05$ fm), we perform the matching in a wide region of $r$, which has been difficult in previous determinations of $alpha_s$ from the potential. Our final result is $alpha_s(M_Z^2) = 0.1179^{+0.0015}_{-0.0014}$ with 1.3 % accuracy. The dominant uncertainty comes from higher order corrections to the perturbative prediction and can be straightforwardly reduced by simulating finer lattices.
We investigate the phase diagram of QCD-like gauge theories at strong coupling at finite magnetic field $B$, temperature $T$ and baryon chemical potential $mu$ using the improved holographic QCD model including the full backreaction of the quarks in the plasma. In addition to the phase diagram we study the behavior of the quark condensate as a function of $T$, $B$ and $mu$ and discuss the fate of (inverse) magnetic catalysis at finite $mu$. In particular we observe that inverse magnetic catalysis exists only for small values of the baryon chemical potential. The speed of sound in this holographic quark-gluon plasma exhibits interesting dependence on the thermodynamic parameters.
Using state of the art lattice techniques we investigate the static baryon potential. We employ the multi-hit procedure for the time links and a variational approach to determine the ground state with sufficient accuracy that, for distances up to $sim 1.2$ fm, we can distinguish the $Y$- and $Delta$- Ansatze for the baryonic Wilson area law. Our analysis shows that the $Delta$-Ansatz is favoured. This result is also supported by the gauge-invariant nucleon wave function which we measure for the first time.
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schrodinger equation modified with the Gaussian and the mean curvature.
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