We study charmonium properties at non-zero temperature in the temperature range 153 MeV $<T<$ 305 MeV using lattice QCD. We use HISQ action for dynamical quarks and Wilson clover action for valence charm quarks and calculate the correlation function of extended meson operators. Our lattice QCD results are consistent with the existence of all charmonium states below the open charm threshold in this temperature region. However, charmonium states acquire sizable thermal width, which increases with increasing temperature. The size of the thermal width follows the hierarchy of charmonium sizes, i.e. the smaller ground state charmonium has a smaller thermal width than the larger excited charmonia.

In this paper, we attempt to test whether Euclidean lattice quantum field theory can be analytically continued into Minkowski space via the inverse Wick rotation. Our discussion indicates that such an analytical continuation is impossible without first taking the lattice theory to the continuum limit. The obstacle is that discretization of spacetime converts local quantum field theory into a theory with a nonlocal form factor, for which the Wick rotation is infeasible.

This paper discusses a paradox encountered when employing the canonical approach, particularly in the high-temperature region where the Roberge-Weiss transition exists at finite imaginary chemical potential. The paradox is that the results obtained using the canonical approach cannot match the correct results in that region. We show that the paradox originates from the Roberge-Weiss transition in the infinite-size system, which is linked to the non-trivial Polyakov-loop sectors. Furthermore, it is shown that this paradox disappears in finite-size systems because of the smearing effect for the Roberge-Weiss transition, which validates the use of the canonical approach in lattice QCD simulations.

While we have several complementary models of confinement, some of which are phenomenologically appealing, we do not have the ability to calculate analytically even simple aspects of confinement, let alone have a framework to eventually prove confinement. The problem we are facing is to evolve the theory from the perturbative regime to the long distance confining regime. This is generally achieved by renormalization group transformations. With the gradient flow we now have a technique to address the problem from first principles. The primary focus is on the running coupling $\alpha_S(\mu)$, from which confinement can be concluded alone. A central point is that the gluon condensate is scale invariant, which reflects its self-similar behavior across different scales. Building on that, we derive $\alpha_S(\mu) \simeq \Lambda_S^2/\mu^2$, which evolves to the infrared fixed point $1/\alpha_S = 0$ in accordance with infrared slavery. The only important factor appears to be the presence of the gluon condensate, which is a universal feature that QCD shares with many other models. The analytical results are supported by numerical simulations.

In this work, we present a first-principles lattice-QCD calculation of the unpolarized quark PDF for the pion and the kaon. The lattice data rely on matrix elements calculated for boosted mesons coupled to non-local operators containing a Wilson line. The calculations on this lattice ensemble correspond to two degenerate light, a strange, and a charm quark ($N_f=2+1+1$), using maximally twisted mass fermions with a clover term. The lattice volume is $32^3\times 64$, with a lattice spacing of 0.0934 fm, and a pion mass of 260 MeV. Matrix elements are calculated for hadron boosts of $|P_3| = 0,~0.41,~0.83,~1.25,~1.66,$ and 2.07 GeV. To match lattice QCD results to their light-cone counterparts, we employ two complementary frameworks: the large-momentum effective theory (LaMET) and the short-distance factorization (SDF). Using these approaches in parallel, we also test the lattice data to identify methodology-driven systematics. Results are presented for the standard quark PDFs, as well as the valence sector. Beyond obtaining the PDFs, we also explore the possibility of extracting information on SU(3) flavor-symmetry-breaking effects. For LaMET, we also parametrize the momentum dependence to obtain the infinite-momentum PDFs.