Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Parma

The Effective Field Theory of Large-Scale Structure is a formalism that allows us to predict the clustering of Cosmological Large-Scale Structure in the mildly non-linear regime in an accurate and reliable way. In this paper, after validating our technique against several sets of numerical simulations, we perform the analysis for the cosmological parameters of the DR12 BOSS data. We assume <NOBR>Λ</NOBR>CDM, a fixed value of the baryon/dark-matter ratio, <NOBR>Ω<SUB><I>b</I></SUB>/Ω<SUB><I>c</I></SUB></NOBR>, and of the tilt of the primordial power spectrum, <NOBR><I>n</I><SUB><I>s</I></SUB></NOBR>, and no significant input from numerical simulations. By using the one-loop power spectrum multipoles, we measure the primordial amplitude of the power spectrum, <NOBR><I>A</I><SUB><I>s</I></SUB></NOBR>, the abundance of matter, <NOBR>Ω<SUB><I>m</I></SUB></NOBR>, and the Hubble parameter, <NOBR><I>H</I><SUB>0</SUB></NOBR>, {to about <NOBR>13%</NOBR>, <NOBR>3.2%</NOBR> and <NOBR>3.2%</NOBR> respectively, obtaining <NOBR> ln (10<SUP>10</SUP><I>A</I><SUB><I>s</I></SUB>)=2.72± 0.13</NOBR>, <NOBR>0Ω<SUB><I>m</I></SUB>=0.309± 0.01</NOBR>, <NOBR><I>H</I><SUB>0</SUB>=68.5± 2.2</NOBR> km/(s Mpc) at 68% confidence level. If we then add a CMB prior on the sound horizon, the error bar on <NOBR><I>H</I><SUB>0</SUB></NOBR> is reduced to <NOBR>1.6%</NOBR>.} These results are a substantial qualitative and quantitative improvement with respect to former analyses, and suggest that the EFTofLSS is a powerful instrument to extract cosmological information from Large-Scale Structure.

It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the spirit of the stationary phase integration method). In this paper we start to explore this possibility somewhat systematically. A first inspection reveals the presence of many difficulties but---quite surprisingly---most of them have an interesting solution. In particular, it is possible to regularize the lattice theory on a Lefschetz thimble, where the imaginary part of the action is constant and disappears from all observables. This regularization can be justified in terms of symmetries and perturbation theory. Moreover, it is possible to design a Monte Carlo algorithm that samples the configurations in the thimble. This is done by simulating, effectively, a five-dimensional system. We describe the algorithm in detail and analyze its expected cost and stability. Unfortunately, the measure term also produces a phase which is not constant and it is currently very expensive to compute. This residual sign problem is expected to be much milder, as the dominant part of the integral is not affected, but we have still no convincing evidence of this. However, the main goal of this paper is to introduce a new approach to the sign problem, that seems to offer much room for improvements. An appealing feature of this approach is its generality. It is illustrated first in the simple case of a scalar field theory with chemical potential, and then extended to the more challenging case of QCD at finite baryonic density.

Expansion of higher transcendental functions in a small parameter are needed in many areas of science. For certain classes of functions this can be achieved by algebraic means. These algebraic tools are based on nested sums and can be formulated as algorithms suitable for an implementation on a computer. Examples such as expansions of generalized hypergeometric functions or Appell functions are discussed. As a further application, we give the general solution of a two-loop integral, the so-called C-topology, in terms of multiple nested sums. In addition, we discuss some important properties of nested sums, in particular we show that they satisfy a Hopf algebra.

We present a new next-to-leading order calculation for fully differential single-top-quark final states. The calculation is performed using phase space slicing and dipole subtraction methods. The results of the methods are found to be in agreement. The dipole subtraction method calculation retains the full spin dependence of the final state particles. We show a few numerical results to illustrate the utility and consistency of the resulting computer implementations.

We present a computational framework not based on the string hypothesis for the thermodynamics of statistical and quantum field theory models solvable by the Bethe ansatz. In the cases of XXZ Heisenberg chain and the sine-Gordon quantum field theory we derive a single nonlinear integral equation which determines the free energy (or ground-state scaling function). Our approach is very effective at high temperature, and correctly reproduces the low-temperature central charge and the analytic structure of the corrections.

Expansion of higher transcendental functions in a small parameter are needed in many areas of science. For certain classes of functions this can be achieved by algebraic means. These algebraic tools are based on nested sums and can be formulated as algorithms suitable for an implementation on a computer. Examples, such as expansions of generalized hypergeometric functions or Appell functions are discussed. As a further application, we give the general solution of a two-loop integral, the so-called C-topology, in terms of multiple nested sums. In addition, we discuss some important properties of nested sums, in The expansion of higher transcendental functions [1, 2] is a common problem occuring in many areas of science. It is of particular interest in particle physics in the calculation of higher order radiative corrections to scattering amplitudes. There, higher transcendental functions occur frequently in formal solutions for specific loop integrals. The necessary expansions of these

We consider the case of a scalar field, the inflaton, coupled to both lighter scalars and fermions, and study the relaxation of the inflaton via particle production in both the linear and nonlinear regimes. This has an immediate appilcation to the reheating problem in inflationary universe models. The linear regime analysis offers a rationale for the standard approach to the reheating problem, but we make a distinction between relaxation and thermalization. We find that particle production when the inflaton starts in the nonlinear region is typically a far more efficient way of transferring energy out of the inflaton zero mode and into the quanta of the lighter scalar than single particle decay. For the nonlinear regime we takn into account self-consistently the evolution of the expectation value of the inflaton field coupled to the evolution of the quantum fluctuations. An exhaustive numerical analysis of the renormalized equations reveals that the distribution of produced particles is far from thermal, and exhibits the effect associated with open channels. In the fermionic case, Pauli blocking begins to hinder the transfer of energy into the fermion modes very early on in the evolution of the inflaton. We discuss the issue of thermalization and estimate the reheating temperature to be proportional to the inflaton mass. Cosmological implications are discussed in particular for the Polonyi problem. \textcopyright{} 1995 The American Physical Society.

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, ${a}_{\ensuremath{\mu}}^{\mathrm{HVP}}$, in the so-called short and intermediate time-distance windows, ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}$ and ${a}_{\ensuremath{\mu}}^{\mathrm{W}}$, defined by the RBC/UKQCD Collaboration [Phys. Rev. Lett. 121, 022003 (2018)]. We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with ${N}_{f}=2+1+1$ flavors of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavors tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to $\ensuremath{\simeq}0.057$, 0.068 and 0.080 fm with spatial lattice sizes up to $L\ensuremath{\simeq}7.6\text{ }\text{ }\mathrm{fm}$. For the short-distance window we obtain ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}(\mathrm{ETMC})=69.27(34)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which is consistent with the recent dispersive value of ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}({e}^{+}{e}^{\ensuremath{-}})=68.4(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Phys. Lett. B 833, 137313 (2022)]. In the case of the intermediate window we get the value ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{ETMC})=236.3(1.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which is consistent with the result ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{BMW})=236.7(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Nature (London) 593, 51 (2021)] by the BMW Collaboration as well as with the recent determination by the CLS/Mainz group of ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{CLS})=237.30(1.46)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Phys. Rev. D 106, 114502 (2022)]. However, it is larger than the dispersive result of ${a}_{\ensuremath{\mu}}^{\mathrm{W}}({e}^{+}{e}^{\ensuremath{-}})=229.4(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ by approximately 3.6 standard deviations. The tension increases to approximately 4.5 standard deviations if we average our ETMC result with those by BMW and CLS/Mainz. Our accurate lattice results in the short and intermediate windows point to a possible deviation of the ${e}^{+}{e}^{\ensuremath{-}}$ cross section data with respect to Standard Model predictions in the low- and intermediate-energy regions but not in the high-energy region.

In this note we study the correspondence between the ``relativistic spin foam'' model introduced by Barrett, Crane and Baez and the so(4) Plebanski action. We argue that the $so(4)$ Plebanski model is the continuum analog of the relativistic spin foam model. We prove that the Plebanski action possess four phases, one of which is gravity and outline the discrepancy between this model and the model of Euclidean gravity. We also show that the Plebanski model possess another natural dicretisation and can be associate with another, new, spin foam model that appear to be the $so(4)$ counterpart of the spin foam model describing the self dual formulation of gravity.

We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign problem that afflicts Monte Carlo calculations of models with complex actions can be softened significantly by changing the domain of integration to the Lefschetz thimble or approximations thereof. We study the interacting complex scalar field theory (relativistic Bose gas) in lattices of size up to ${8}^{4}$ using a computationally inexpensive approximation of the Lefschetz thimble. Our results are in excellent agreement with known results. We show that---at least in the case of the relativistic Bose gas---the thimble can be systematically approached and the remaining residual phase leads to a much more tractable sign problem (if at all) than the original formulation. This is especially encouraging in view of the wide applicability---in principle---of our method to quantum field theories with a sign problem. We believe that this opens up new possibilities for accurate Monte Carlo calculations in strongly interacting systems of sizes much larger that previously possible.

An accurate theoretical template for the galaxy power spectrum is key for the success of ongoing and future spectroscopic surveys. We examine to what extent the effective field theory (EFT) of large-scale structure is able to provide such a template and correctly estimate cosmological parameters. To that end, we initiate a blinded challenge to infer cosmological parameters from the redshift-space power spectrum of high-resolution mock catalogs mimicking the BOSS galaxy sample but covering a 100 times larger cumulative volume. This gigantic simulation volume allows us to separate systematic bias due to theoretical modeling from the statistical error due to sample variance. The challenge is to measure three unknown input parameters used in the simulation: the Hubble constant, the matter density fraction, and the clustering amplitude. We present analyses done by two independent teams, who have fitted the mock simulation data generated by yet another independent group. This allows us to avoid any confirmation bias by analyzers and to pin down possible tuning of the specific EFT implementations. Both independent teams have recovered the true values of the input parameters within subpercent statistical errors corresponding to the total simulation volume.

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We apply the Effective Field Theory of Large-Scale Structure to analyze the $w$CDM cosmological model. By using the full shape of the power spectrum and the BAO post-reconstruction measurements from BOSS, the Supernovae from Pantheon, and a prior from BBN, we set the competitive CMB-independent limit $w=-1.046_{-0.052}^{+0.055}$ at $68\%$ C.L.. After adding the Planck CMB data, we find $w=-1.023_{-0.030}^{+0.033}$ at $68\%$ C.L.. Our results are obtained using PyBird, a new, fast Python-based code which we make publicly available.

Abstract The disagreement between direct late-time measurements of the Hubble constant from the SH0ES collaboration, and early-universe measurements based on the ΛCDM model from the Planck collaboration might, at least in principle, be explained by new physics in the early universe. Recently, the application of the Effective Field Theory of Large-Scale Structure to the full shape of the power spectrum of the SDSS/BOSS data has revealed a new, rather powerful, way to measure the Hubble constant and the other cosmological parameters from Large-Scale Structure surveys. In light of this, we analyze two models for early universe physics, Early Dark Energy and Rock 'n' Roll, that were designed to significantly ameliorate the Hubble tension. Upon including the information from the full shape to the Planck, BAO, and Supernovae measurements, we find that the degeneracies in the cosmological parameters that were introduced by these models are well broken by the data, so that these two models do not significantly ameliorate the tension.

We introduce a bipartite, diluted and frustrated, network as a sparse restricted Boltzmann machine and we show its thermodynamical equivalence to an associative working memory able to retrieve several patterns in parallel without falling into spurious states typical of classical neural networks. We focus on systems processing in parallel a finite (up to logarithmic growth in the volume) amount of patterns, mirroring the low-level storage of standard Amit-Gutfreund-Sompolinsky theory. Results obtained through statistical mechanics, the signal-to-noise technique, and Monte Carlo simulations are overall in perfect agreement and carry interesting biological insights. Indeed, these associative networks pave new perspectives in the understanding of multitasking features expressed by complex systems, e.g., neural and immune networks.

We determine the curvature of the pseudocritical line of ${N}_{f}=2+1$ QCD with physical quark masses via Taylor expansion in the quark chemical potentials. We adopt a discretization based on stout improved staggered fermions and the tree level Symanzik gauge action; the location of the pseudocritical temperature is based on chiral symmetry restoration. Simulations are performed on lattices with different temporal extent (${N}_{t}=6$, 8, 10), leading to a continuum extrapolated curvature $\ensuremath{\kappa}=0.0145(25)$, which is in very good agreement with the continuum extrapolation obtained via analytic continuation and the same discretization, $\ensuremath{\kappa}=0.0135(20)$. This result eliminates the possible tension emerging when comparing analytic continuation with earlier results obtained via Taylor expansion.

The big-jump principle is a well-established mathematical result for sums of independent and identically distributed random variables extracted from a fat-tailed distribution. It states that the tail of the distribution of the sum is the same as the distribution of the largest summand. In practice, it means that when in a stochastic process the relevant quantity is a sum of variables, the mechanism leading to rare events is peculiar: Instead of being caused by a set of many small deviations all in the same direction, one jump, the biggest of the lot, provides the main contribution to the rare large fluctuation. We reformulate and elevate the big-jump principle beyond its current status to allow it to deal with correlations, finite cutoffs, continuous paths, memory, and quenched disorder. Doing so we are able to predict rare events using the extended big-jump principle in Lévy walks, in a model of laser cooling, in a scattering process on a heterogeneous structure, and in a class of Lévy walks with memory. We argue that the generalized big-jump principle can serve as an excellent guideline for reliable estimates of risk and probabilities of rare events in many complex processes featuring heavy-tailed distributions, ranging from contamination spreading to active transport in the cell.

Abstract After calibrating the predictions of the Effective Field Theory of Large-Scale Structure against several sets of simulations, as well as implementing a new method to assert the scale cut of the theory without the use of any simulation, we analyze the Full Shape of the BOSS Correlation Function. Imposing a prior from Big Bang Nucleosynthesis on the baryon density, we are able to measure all the parameters in ΛCDM + massive neutrinos in normal hierarchy, except for the total neutrino mass, which is just bounded. When combining the BOSS Full Shape with the Baryon Acoustic Oscillation measurements from BOSS, 6DF/MGS and eBOSS, we determine the present day Hubble constant, H 0 , the present day matter fraction, Ω m , the amplitude of the primordial power spectrum, A s , and the tilt of the primordial power spectrum, n s , to 1.4 %, 4.5 %, 23.5% and 7.6% precision, respectively, at 68 %-confidence level, finding H 0 =68.19 ± 0.99 (km/s)/Mpc, Q m =0.309± 0.014, ln (10 10 A s )=3.12 +0.21 -0.26 and n s =0.963 +0.062 -0.085 , and we bound the total neutrino mass to 0.87 eV at 95 %-confidence level. These constraints are fully consistent with Planck results and the ones obtained from BOSS power spectrum analysis. In particular, we find no tension in H 0 or σ 8 with Planck measurements, finding consistency at 1.2σ and 0.6σ, respectively.

We present two new families of Wilson loop operators in N=6 supersymmetric Chern–Simons theory. The first one is defined for an arbitrary contour on the three dimensional space and it resembles the Zarembo construction in N=4 SYM. The second one involves arbitrary curves on the two dimensional sphere. In both cases one can add certain scalar and fermionic couplings to the Wilson loop so it preserves at least two supercharges. Some previously known loops, notably the 1/2 BPS circle, belong to this class, but we point out more special cases which were not known before. They could provide further tests of the gauge/gravity correspondence in the ABJ(M) case and interesting observables, exactly computable by localization techniques.

The problem of constructing a quantum theory of gravity has been tackled with very different strategies, most of which rely on the interplay between ideas from physics and from advanced mathematics. On the mathematical side, a central role is played by combinatorial topology, often used to recover the space–time manifold from the other structures involved. An extremely attractive possibility is that of encoding all possible space–times as specific Feynman diagrams of a suitable field theory. In this work we analyze how exactly one can associate combinatorial four-manifolds with the Feynman diagrams of certain tensor theories.