BES III Collaboration has recently observed a vector resonance in the χc0ω channel, at a mass of about 4220 MeV, named Y (4220). Hints of a similar structure appear in the hcπ + π − channel. We find that the two observations are likely due to the same state, which we identify with one of the expected diquark-antidiquark resonances with orbital quantum number L = 1. This assignment fulfills heavy quark spin conservation. The measured branching ratio of the Y (4220) into χc0ω and hcπ + π − is compatible with the prediction for such a tetraquark state. PACS numbers: 14.40.Rt, 12.39.Jh, 13.25.Gv In a very recent paper, the BES III Collaboration reports the e + e − → χ cJ ω (J = 0, 1, 2) production cross section as a function of √ s [1]. Hints of a resonant structure are present in the χ c0 ω channel at ∼ 30 MeV above threshold (i.e. at about 4220 MeV), whereas no evident structure appears in the χ c1,2 ω channels. Some theoretical interpretations for this peak have been proposed [2]. BES Collaboration also reported the measurement of e + e − → h c π + π − production cross section as a function of √ s [3]. Hints of structures not compatible with the Y (4260) have been found [4, 5]: in particular a narrow peak at ∼ 4220 MeV. Heavy quark spin symmetry prevents any ordinary charmonium from decaying into both χ c and h c . Violations of this symmetry have already been observed in the bottomonium sector, and are explained in [6][7][8]. In the charmonium mass region, many exotic charmonium-like states have been identified according to the diquark-antidiquark model [9] (for a review, see [10]). In particular, the latest model [11] predicts a tetraquark state, named Y 3 , with quantum numbers J P C = 1 −− , and mass and decay modes compatible with a Y (4220) resonance. The wave function of this tetraquark state contains both heavy quark spin states, so it can naturally decay into both χ c0 ω and h c π + π − with no violation of the heavy quark spin. Since the Breit-Wigner parameters of the peaks measured in the two channels χ c0 ω and h c π + π − are very similar, we test the hypothesis that the two observed structures may coincide.We fit data with two different models (I and II in the following) similar to those considered in Refs. [1,5]. In the h c π + π − invariant mass distribution, we add to the BES dataset the experimental point σ hcπ + π − (4.17 GeV) = (15.6 ± 4.2) pb 1 by , with statistical and systematic errors added in quadrature. For the BES data, we take into account only statistical errors, since the systematic ones are common to all points and are not expected to modify the shape of the distribution.Following model-I, we fit the h c π + π − and χ c0 ω data with the sum of a Breit-Wigner corrected for the energy dependence given by PCAC, and a pure phase-space background. To test our hypothesis, the mass and the width of the resonance are constrained to be the same in both channels. Thus, the fitting functions are:where m 0 and Γ are the mass and width of the resonance, m is the invariant mass of the system, B...

Numerical Stochastic Perturbation Theory (NSPT) allows for perturbative computations in quantum field theory. We present an implementation of NSPT that yields results for high orders in the perturbative expansion of lattice gauge theories coupled to fermions. The zero-momentum mode is removed by imposing twisted boundary conditions; in turn, twisted boundary conditions require us to introduce a smell degree of freedom in order to include fermions in the fundamental representation. As a first application, we compute the critical mass of two flavours of Wilson fermions up to order in a gauge theory. We also implement, for the first time, staggered fermions in NSPT. The residual chiral symmetry of staggered fermions protects the theory from an additive mass renormalisation. We compute the perturbative expansion of the plaquette with two flavours of massless staggered fermions up to order in a gauge theory, and investigate the renormalon behaviour of such series. We are able to subtract the power divergence in the Operator Product Expansion (OPE) for the plaquette and estimate the gluon condensate in massless QCD. Our results confirm that NSPT provides a viable way to probe systematically the asymptotic behaviour of perturbative series in QCD and, eventually, gauge theories with fermions in higher representations.

We discuss a substantial update to the Grid software library for Lattice QCD, enabling it to port to multiple GPU architectures while retaining CPU vectorisation and SIMD execution within OpenMP threads. The GPU environments supported include vendor specific Nvidia CUDA and AMD HIP environments and a (mostly) standards based SYCL implementation. This is performed by an internal abstraction interface giving single source cross-platform performance portability across all number of planned Exascale architectures, and all those planned by the US Department of Energy.

Abstract. We investigate the possibility of using numerical stochastic perturbation theory (NSPT) to probe high orders in the perturbative expansion of lattice gauge theories with massless Wilson fermions. Twisted boundary conditions are used to regularise the gauge zero-mode; the extension of these boundary conditions to include fermions in the fundamental representation requires to introduce a smell degree of freedom. Moreover, the mass of Wilson fermions is affected by an additive renormalisation: we study how to determine the mass counterterms consistently in finite volume. The knowledge of the critical masses will enable high-order perturbative computations in massless QCD, e.g. (as a first application) for the plaquette.

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