The electromagnetic form factors of the proton and the neutron are computed within lattice QCD using simulations with quarks masses fixed to their physical values. Both connected and disconnected contributions are computed. We analyze two new ensembles of N f = 2 and N f = 2 + 1 + 1 twisted mass clover-improved fermions and determine the proton and neutron form factors, the electric and magnetic radii, and the magnetic moments. We use several values of the sink-source time separation in the range of 1.0 fm to 1.6 fm to ensure ground state identification. Disconnected contributions are calculated to an unprecedented accuracy at the physical point. Although they constitute a small correction, they are non-negligible and contribute up to 15% for the case of the neutron electric charge radius.

We evaluate the gluon and quark contributions to the spin of the proton using an ensemble of gauge configurations generated at physical pion mass. We compute all valence and sea quark contributions to high accuracy. We perform a nonperturbative renormalization for both quark and gluon matrix elements. We find that the contribution of the up, down, strange, and charm quarks to the proton intrinsic spin is 1 2 P q¼u;d;s;c ΔΣ q þ ¼ 0.191ð15Þ and to the total spin P q¼u;d;s;c J q þ ¼ 0.285ð45Þð10Þ. The gluon contribution to the spin is J g ¼ 0.187ð46Þð10Þ yielding J ¼ J q þ J g ¼ 0.473ð71Þð14Þ confirming the spin sum. The momentum fraction carried by quarks in the proton is found to be 0.618(60) and by gluons 0.427(92), the sum of which gives 1.045(118) confirming the momentum sum rule. All scale and scheme dependent quantities are given in the MS scheme at 2 GeV.

We present the QCD simulation of the first gauge ensemble of two degenerate light quarks, a strange and a charm quark with all quark masses tuned to their physical values within the twisted mass fermion formulation. Results for the pseudoscalar masses and decay constants confirm that the produced ensemble is indeed at the physical parameters of the theory. This conclusion is corroborated by a complementary analysis in the baryon sector. We examine cutoff and isospin breaking effects and demonstrate that they are suppressed through the presence of a clover term in the action. arXiv:1807.00495v1 [hep-lat]

Effects of heavy sea quarks on the low energy physics are described by an effective theory where the expansion parameter is the inverse quark mass, 1/M . At leading order in 1/M (and neglecting light quark masses) the dependence of any low energy quantity on the heavy quark mass is given in terms of the ratio of Λ parameters of the effective and the fundamental theory. We define a function describing the scaling with the mass M . Our study of perturbation theory suggests that its perturbative expansion is very reliable for the bottom quark and also seems to work very well at the charm quark mass. The same is then true for the ratios of Λ (4) /Λ (5) and Λ (3) /Λ (4) , which play a major rôle in connecting (almost all) lattice determinations of αMS from the three-flavor theory with α (5) MS (M Z ). Also the charm quark content of the nucleon, relevant for dark matter searches, can be computed accurately from perturbation theory.In order to further test perturbation theory in this situation, we investigate a very closely related model, namely QCD with N f = 2 heavy quarks. Our non-perturbative information is derived from simulations on the lattice, with masses up to the charm quark mass and lattice spacings down to about 0.023 fm followed by a continuum extrapolation. The non-perturbative mass dependence agrees within rather small errors with the perturbative prediction at masses around the charm quark mass. Surprisingly, from studying solely the massive theory we can make a prediction for the ratio Qwhich refers to the chiral limit in N f = 2. Here t 0 is the Gradient Flow scale of [1]. The uncertainty for Q is estimated to be 2.5%. For the phenomenologically interesting Λ (3) /Λ (4) , we conclude that perturbation theory introduces errors which are at most at the 1.5% level, smaller than other current uncertainties.

We present a factorization formula for the dependence of light hadron masses and low energy hadronic scales on the mass M of a heavy quark: apart from an overall mass-independent factor Q, ratios such as r 0 ðMÞ=r 0 ð0Þ are computable in perturbation theory at large M. The perturbation theory part is stable concerning different loop orders. Our nonperturbative Monte Carlo results obtained in a model calculation, where a doublet of heavy quarks is decoupled, match quantitatively to the perturbative prediction. Upon taking ratios of different hadronic scales at the same mass, the perturbative function drops out and the ratios are given by the decoupled theory up to M −2 corrections. We verify-in the continuum limit-that the sea quark effects of quarks with masses around the charm mass are very small in such ratios. Introduction.-One usually presumes that the low energy dynamics of QCD, such as the hadron mass spectrum, is rather insensitive to the physics of heavy quarks. One can then work with QCD with just the three or four light quarks in order to understand it [1]. While large N c (color) arguments suggest a general suppression of quark loop effects, and then a particular one for heavy quarks, so far there has not been any nonperturbative investigation determining the typical magnitude of these effects. This is understandable, since lattice gauge theory with heavy quarks generically has enhanced discretization errors and it is a nontrivial task to separate the physical effects from those unwanted errors. It is thus of high interest for the lattice community to understand whether it is already time to include a charm sea quark in the simulations. Note that one has to be precise about the meaning of the decoupling of heavy quarks [2,3]. They do leave traces through renormalization, which we discuss below.The theoretical tool to understand these questions is the low energy effective theory [3,4] describing the physics with one or more heavy quarks decoupled. We denote this theory by decQCD. The leading order effective theory is just QCD with one or more quark flavors less. The gauge couplingḡ dec and quark masses of decQCD are adjusted such that decQCD (approximately) reproduces the physics of the (more) fundamental theory at an energy sufficiently below the mass of the decoupled quark [5]. This adjustment is referred to as matching.We consider the situation with N l light quarks and N q quarks in total. Indicating the flavor content N f of the theory by a subscript, the fundamental theory is QCD N q .