Publications

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An overview of lattice results for parton distribution functions

Luigi Del Debbio

SciPost Phys. Proc. 15, 028 (2024) · published 3 April 2024 | · pdf

Following a ground-breaking proposal by Ji [Phys. Rev. Lett. 110, 262002 (2013)], numerical simulations of Quantum Chromo Dynamics (QCD) on a Euclidean lattice have provided new, valuable information on the structure of hadrons. In this talk, we briefly review the lattice approach to the reconstruction of parton densities, highlighting the connection between lattice observables and parton densities, with a focus on theoretical issues. Since parton distributions are extracted from lattice data by solving an inverse problem, we discuss some of the difficulties that affect these determinations and how they can be formulated in a Bayesian framework.
All about the neutron from lattice QCD

Rajan Gupta

SciPost Phys. Proc. 15, 021 (2024) · published 3 April 2024 | · pdf

I describe how simulations of lattice QCD using the path integral formulation provide the two basic quantum mechanical properties of QCD, its ground state in which correlation functions are calculated, and Fock state wavefunctions between which matrix elements of operators are calculated. Both constructs are stochastic, so unfortunately one gets no intuitive picture or even qualitative understanding of what they look like, nevertheless they contain and display all the subtleties of the quantum field theory. Today, these simulations provide many quantities that are impacting phenomenology and experiments. I illustrate the methods and the steps in the analysis using, as examples, three observables: the isovector charges of the nucleon, the contribution of the quark's intrinsic spin to the nucleon spin, and the pion-nucleon sigma term.
Towards the computation of inclusive decay rates using lattice QCD

Paolo Gambino, Shoji Hashimoto, Sandro Mächler, Marco Panero, Francesco Sanfilippo, Silvano Simula, Antonio Smecca, Nazario Tantalo

SciPost Phys. Proc. 15, 004 (2024) · published 2 April 2024 | · pdf

We present a non-perturbative computation of inclusive rates of semileptonic decays of heavy mesons from lattice QCD simulations. The calculation is based on the extraction of smeared spectral functions obtained from four-point Euclidean correlation functions computed on configuration ensembles of the JLQCD and ETM collaborations. We compare our results for the inclusive decay rates with analytical predictions from the operator-product expansion, finding a good agreement for the calculation of the inclusive decay rate. This opens the path to the theoretical determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $V_{cb}$ to a level of precision competitive with the present experimental uncertainty.
NLO finite system size corrections to $2\to2$ scattering in $\phi^4$ theory using newly derived sum of sinc functions

Jean F. Du Plessis, William A. Horowitz

SciPost Phys. Proc. 15, 002 (2024) · published 2 April 2024 | · pdf

Previously an equation of state for the relativistic hydrodynamics encountered in heavy-ion collisions at the LHC and RHIC has been calculated using lattice gauge theory methods. This leads to a prediction of very low viscosity, due to the calculated trace anomaly. Finite system corrections to this trace anomaly could challenge this calculation, since the lattice calculation was done in an effectively infinite system. In order to verify this trace anomaly it is sensible to add phenomenologically relevant finite system corrections. We investigate massive $\phi^4$ theory with periodic boundary conditions on $n$ of the 3 spatial dimensions. $2\to2$ NLO scattering is then computed. Using a newly derived formula for an arbitrary dimensional sum of sinc functions, we show that the NLO finite size corrections preserve unitarity.
A coupling prescription for post-Newtonian corrections in quantum mechanics

Jelle Hartong, Emil Have, Niels A. Obers, Igor Pikovski

SciPost Phys. 16, 088 (2024) · published 27 March 2024 | · pdf

The interplay between quantum theory and general relativity remains one of the main challenges of modern physics. A renewed interest in the low-energy limit is driven by the prospect of new experiments that could probe this interface. Here we develop a covariant framework for expressing post-Newtonian corrections to Schrödinger's equation on arbitrary gravitational backgrounds based on a $1/c^2$ expansion of Lorentzian geometry, where $c$ is the speed of light. Our framework provides a generic coupling prescription of quantum systems to gravity that is valid in the intermediate regime between Newtonian gravity and General Relativity, and that retains the focus on geometry. At each order in $1/c^2$ this produces a nonrelativistic geometry to which quantum systems at that order couple. By considering the gauge symmetries of both the nonrelativistic geometries and the $1/c^2$ expansion of the complex Klein-Gordon field, we devise a prescription that allows us to derive the Schrödinger equation and its post-Newtonian corrections on a gravitational background order-by-order in $1/c^2$. We also demonstrate that these results can be obtained from a $1/c^2$ expansion of the complex Klein-Gordon Lagrangian. We illustrate our methods by performing the $1/c^2$ expansion of the Kerr metric up to $\mathcal{O}(c^{-2})$, which leads to a special case of the Hartle-Thorne metric. The associated Schrödinger equation captures novel and potentially measurable effects.

3 citations
Anomalies of generalized symmetries from solitonic defects

Lakshya Bhardwaj, Mathew Bullimore, Andrea E. V. Ferrari, Sakura Schäfer-Nameki

SciPost Phys. 16, 087 (2024) · published 26 March 2024 | · pdf

We propose the general idea that 't Hooft anomalies of generalized global symmetries can be understood in terms of the properties of solitonic defects, which generically are non-topological defects. The defining property of such defects is that they act as sources for background fields of generalized symmetries. 't Hooft anomalies arise when solitonic defects are charged under these generalized symmetries. We illustrate this idea for several kinds of anomalies in various spacetime dimensions. A systematic exploration is performed in 3d for 0-form, 1-form, and 2-group symmetries, whose 't Hooft anomalies are related to two special types of solitonic defects, namely vortex line defects and monopole operators. This analysis is supplemented with detailed computations of such anomalies in a large class of 3d gauge theories. Central to this computation is the determination of the gauge and 0-form charges of a variety of monopole operators: these involve standard gauge monopole operators, but also fractional gauge monopole operators, as well as monopole operators for 0-form symmetries. The charges of these monopole operators mainly receive contributions from Chern-Simons terms and fermions in the matter content. Along the way, we interpret the vanishing of the global gauge and ABJ anomalies, which are anomalies not captured by local anomaly polynomials, as the requirement that gauge monopole operators and mixed monopole operators for 0-form and gauge symmetries have non-fractional integer charges.

4 citations
Generalized symmetries and anomalies of 3d $\mathcal{N}=4$ SCFTs

Lakshya Bhardwaj, Mathew Bullimore, Andrea E. V. Ferrari, Sakura Schäfer-Nameki

SciPost Phys. 16, 080 (2024) · published 20 March 2024 | · pdf

We study generalized global symmetries and their 't Hooft anomalies in 3d $\mathcal{N}=4$ superconformal field theories (SCFTs). Following some general considerations, we focus on good quiver gauge theories, comprised of balanced unitary nodes and unbalanced unitary and special unitary nodes. While the global form of the Higgs branch symmetry group may be determined from the UV Lagrangian, the global form of Coulomb branch symmetry groups and associated mixed 't Hooft anomalies are more subtle due to potential symmetry enhancement in the IR. We describe how Coulomb branch symmetry groups and their mixed 't Hooft anomalies can be deduced from the UV Lagrangian by studying center charges of various types of monopole operators, providing a concrete and unambiguous way to implement 't Hooft anomaly matching. The final expression for the symmetry group and 't Hooft anomalies has a concise form that can be easily read off from the quiver data, specifically from the positions of the unbalanced and flavor nodes with respect to the positions of the balanced nodes. We provide consistency checks by applying our method to compute symmetry groups of 3d $\mathcal{N}=4$ theories corresponding to magnetic quivers of 4d Class S theories and 5d SCFTs. We are able to match these results against the flavor symmetry groups of the 4d and 5d theories computed using independent methods. Another strong consistency check is provided by comparing symmetry groups and anomalies of two theories related by 3d mirror symmetry.

3 citations
Non-perturbative topological string theory on compact Calabi-Yau 3-folds

Jie Gu, Amir-Kian Kashani-Poor, Albrecht Klemm, Marcos Mariño

SciPost Phys. 16, 079 (2024) · published 19 March 2024 | · pdf

We obtain analytic and numerical results for the non-perturbative amplitudes of topological string theory on arbitrary, compact Calabi-Yau manifolds. Our approach is based on the theory of resurgence and extends previous special results to the more general case. In particular, we obtain explicit trans-series solutions of the holomorphic anomaly equations. Our results predict the all orders, large genus asymptotics of the topological string free energies, which we test in detail against high genus perturbative series obtained recently in the compact case. We also provide additional evidence that the Stokes constants appearing in the resurgent structure are closely related to integer BPS invariants.

2 citations
EFT matching from analyticity and unitarity

Stefano De Angelis, Gauthier Durieux

SciPost Phys. 16, 071 (2024) · published 12 March 2024 | · pdf

We present a new on-shell method for the matching of ultraviolet models featuring massive states onto their massless effective field theory. We employ a dispersion relation in the space of complex momentum dilations to capture, in a single variable, the relevant analytic structure of scattering amplitudes at any multiplicity. Multivariate complex analysis and crossing considerations are therefore avoided. Remarkably, no knowledge about the infrared effective field theory is required in dimensional regularisation. All matching information is extracted from the residues and iscontinuities of the ultraviolet scattering amplitudes, which unitarity expresses in terms of lower-point and lower-loop results, respectively. This decomposition into simpler building blocks could deliver new insight in the structure of the effective field theories obtained from classes of ultraviolet scenarios and facilitate computations at higher loop orders.

1 citation
The functional generalization of the Boltzmann-Vlasov equation and its gauge-like symmetry

Giorgio Torrieri

SciPost Phys. 16, 070 (2024) · published 11 March 2024 | · pdf

We argue that one can model deviations from the ensemble average in non-equilibrium statistical mechanics by promoting the Boltzmann equation to an equation in terms of functionals , representing possible candidates for phase space distributions inferred from a finite observed number of degrees of freedom. We find that, provided the collision term and the Vlasov drift term are both included, a gauge-like redundancy arises which does not go away even if the functional is narrow. We argue that this effect is linked to the gauge-like symmetry found in relativistic hydrodynamics [Ann. Phys. 442, 168902 (2022)] and that it could be part of the explanation for the apparent fluid-like behavior in small systems in hadronic collisions and other strongly-coupled small systems [Annu. Rev. Nucl. Part. Sci. 68, 211 (2018)]. When causality and Lorentz invariance are omitted this problem can be look at via random matrix theory show, and we show that in such a case thermalization happens much more quickly than the Boltzmann equation would infer. We also sketch an algorithm to study this problem numerically.

1 citation

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