arXiv subjects

Riccardo Rattazzi

Publications and source records attributed to Riccardo Rattazzi.

At least 19 recordsLinked to original sources

arXiv2026

Schwinger-Keldysh effective theory of charge transport: redundancies and systematic $ω/T$ expansion

We study Schwinger-Keldysh effective field theories (EFTs) for systems with non-Abelian internal symmetries near thermal equilibrium. We consider two approaches that were put forward in the literature -- one using a redundant Goldstone parameterization, the other employing an adjoint matter field -- and demonstrate their complete equivalence by providing an explicit dictionary and proving their equivalence at the path integral level. Critically, we extend both formalisms to be compatible with the dynamical Kubo-Martin-Schwinger (DKMS) symmetry to all orders in $\hbar ω/T$, classifying all possible invariant kernels satisfying unitarity constraints. We also establish precise power-counting rules, clarifying the interplay between the semiclassical and hydrodynamic expansions. Our work provides a framework for studying non-Abelian charge transport and fluctuations to arbitrary orders in $\hbar ω/T$.

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arXiv2026

Quantum vorticity: a not so effective field theory

We provide a comprehensive picture for the formulation of the perfect fluid in the modern effective field theory formalism at both the classical and quantum level. Due to the necessity of decomposing the hydrodynamical variables $(ρ, p, u^μ)$ into other internal degrees of freedom, the procedure is inherently not unique. We discuss and compare the different inequivalent formulations. These theories possess a peculiarity: the presence of an infinite dimensional symmetry implying a vanishing dispersion relation $ω= 0$ for the transverse modes. This sets the stage for UV-IR mixing in the quantum theory, which we study in the different formulations focussing on the incompressible limit. We observe that the dispersion relation gets modified by quantum effects to become $ω\propto \mathbf{k}^2$, where the fundamental excitations can be viewed as vortex-anti-vortex pairs. The spectrum exhibits infinitely many types of degenerate quanta. The unusual sensitivity to UV quantum fluctuations renders the implementation of the defining infinite symmetry somewhat subtle. However we present a lattice regularization that preserves a deformed version of such symmetry.

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arXiv2025

Exploring the Flavor Symmetry Landscape

We explore flavor dynamics in the broad scenario of a strongly interacting light Higgs (SILH). Our study focuses on the mechanism of partial fermion compositeness, but is otherwise as systematic as possible. Concretely, we classify the options for the underlying flavor (and CP) symmetries, which are necessary in order to bring this scenario safely within the range of present or future explorations. Our main goal in this context is to provide a practical map between the space of hypotheses (the models) and the experimental ground that will be explored in the medium and long term, in both indirect and direct searches, in practice at HL-LHC and Belle II, in EDM searches and eventually at FCC-hh. Our study encompasses scenarios with the maximal possible flavor symmetry, corresponding to minimal flavor violation (MFV), scenarios with no symmetry, corresponding to the so-called flavor anarchy, and various intermediate cases that complete the picture. One main result is that the scenarios that allow for the lowest new physics scale have intermediate flavor symmetry rather than the maximal symmetry of MFV models. Such optimal models are rather resilient to indirect exploration via flavor and CP violating observables, and can only be satisfactorily explored at a future high-energy collider. On the other hand, the next two decades of indirect exploration will significantly stress the parameter space of a large swath of less optimal but more generic models up to mass scales competing with those of the FCC-hh.

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arXiv2025

Superadditivity at Large Charge

The weak gravity conjecture has been invoked to conjecture that the dimensions of charged operators in a CFT should obey a superadditivity relation (sometimes referred to as convexity). In this paper, we study superadditivity of the operator spectrum in theories expanded about the semi-classical saddle point that dominates correlators of large charge operators. We explore this in two contexts. The first is a model with two scalar fields that carry different charges, at a non-trivial Wilson-Fisher fixed point. A careful analysis of the semi-classics for this two field model demonstrates that 'quantum' violations of superadditivity (those not forbidden by the conjecture) persist in the large charge regime. We then turn to study the general properties of CFTs at large charge as bottom-up EFTs. By a trial and error procedure we come up with a seemingly consistent family of examples violating the conjecture. In so doing the presence of a genuine dilaton field appears necessary. On the one hand our result demonstrates that the superadditivity conjecture cannot be proven purely on the basis of a bottom-up analysis. On the other hand, the need for a dilaton, with the corresponding infinite fine tuning, indicates the conjecture-violating EFTs are unlikely to be UV completable.

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arXiv2024

Tetraquarks at large $M$ and large $N$

We study tetraquarks in large $N$ QCD with heavy quarks, in the domain where non-relativistic quantum mechanics offers an adequate approximation. Within the regime of validity of the Born-Oppenheimer approximation, we systematically study and explicitly construct tetraquark states. At leading order in the $1/N$ expansion, the bound spectrum consists of free mesons, while the $1/N$ corrections give rise to a Born-Oppenheimer potential that can bind the mesons into tetraquarks. We find two different types of tetraquarks, each endowed with distinct color-spatial wavefunctions. These states arise in the presence of an $\mathcal{O}(N)$ mass hierarchy between the quarks and the antiquarks. We provide a quantitative argument indicating that only for such a hierarchy is the ground state of the system a tetraquark. We discuss what the extrapolation of our results to realistic values of the parameters may imply for the QCD tetraquark states.

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arXiv2023

Softening the UV without New Particles

We explore an odd class of QFTs where a hierarchy problem is resolved with new dynamics as opposed to new particles. The essential element of our construction is a $U(1)$ pseudo-NG boson with symmetry breaking interactions all characterized by a large number $N$ of units of the fundamental charge. In the resulting effective theory, quantum corrections, like those to the effective potential and mass, which are normally power divergent and saturated at the UV cut-off, are instead saturated at a much lower scale. This critical scale, which does not involve any new particle, corresponds to the onset of unsuppressed multiparticle production in scattering processes. Remarkably this all happens within the tractable domain of weak coupling. Terms involving arbitrarily high powers of the Goldstone field must however be taken into account. In particular, a truncation to the renormalizable part of the effective Lagrangian would completely miss the physics.

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arXiv2023

The role of the pion in the lineshape of the $X(3872)$

We determine the contribution of long-range pion interactions to the $X(3872)$ dynamics, assuming it is a loosely bound $D^0 \bar{D}^{*0}$ molecule. Our result is based on the distorted wave Born approximation in non-relativistic quantum mechanics. Despite their long-range nature, we find that pion interactions cannot produce a large and negative effective range. Nonetheless, they introduce imaginary parts. In particular, they contribute to the total decay width of the $X(3872)$ with a term associated with, but not precisely corresponding to, the $D^*$ width. Our approach can also be applied to the recently discovered $T_{cc}^+$ states.

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arXiv2023

Flux Correlators and Semiclassics

We consider correlators for the flux of energy and charge in the background of operators with large global $U(1)$ charge in conformal field theory (CFT). It has recently been shown that the corresponding Euclidean correlators generically admit a semiclassical description in terms of the effective field theory (EFT) for a conformal superfluid. We adapt the semiclassical description to Lorentzian observables and compute the leading large charge behavior of the flux correlators in general $U(1)$ symmetric CFTs. We discuss the regime of validity of the large charge EFT for these Lorentzian observables and the subtleties in extending the EFT approach to subleading corrections. We also consider the Wilson-Fisher fixed point in $d=4-ε$ dimensions, which offers a specific weakly coupled realization of the general setup, where the subleading corrections can be systematically computed without relying on an EFT.

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arXiv2022

The Quantum Perfect Fluid in 2D

We consider the field theory that defines a perfect incompressible 2D fluid. One distinctive property of this system is that the quadratic action for fluctuations around the ground state features neither mass nor gradient term. Quantum mechanically this poses a technical puzzle, as it implies the Hilbert space of fluctuations is not a Fock space and perturbation theory is useless. As we show, the proper treatment must instead use that the configuration space is the area preserving Lie group $S\mathrm{Diff}$. Quantum mechanics on Lie groups is basically a group theory problem, but a harder one in our case, since $S\mathrm{Diff}$ is infinite dimensional. Focusing on a fluid on the 2-torus $T^2$, we could however exploit the well known result $S\mathrm{Diff}(T^2)\sim SU(N)$ for $N\to \infty$, reducing for finite $N$ to a tractable case. $SU(N)$ offers a UV-regulation, but physical quantities can be robustly defined in the continuum limit $N\to\infty$. The main result of our study is the existence of ungapped localized excitations, the vortons, satisfying a dispersion $ω\propto k^2$ and carrying a vorticity dipole. The vortons are also characterized by very distinctive derivative interactions whose structure is fixed by symmetry. Departing from the original incompressible fluid, we constructed a class of field theories where the vortons appear, right from the start, as the quanta of either bosonic or fermionic local fields.

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arXiv2022

Identifying Large Charge Operators

The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on $U(1)$ invariant Wilson-Fisher fixed points, we study the spectrum of spinning large charge operators. For sufficiently low spin these correspond to the phonon excitations of the superfluid state. We discuss the organization of these states into conformal multiplets and the form of the corresponding composite operators in the free field theory limit. The latter entails a mapping, built order-by-order in the inverse charge $n^{-1}$, between the Fock space of vacuum fluctuations and the Fock space of fluctuations around the superfluid state. We discuss the limitations of the semiclassical method, and find that the phonon description breaks down for spins of order $n^{1/2}$ while the computation of observables is valid up to spins of order $n$. Finally, we apply the semiclassical method to compute some conformal 3-point and 4-point functions, and analyze the conformal block decomposition of the latter with our knowledge of the operator spectrum.

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arXiv2022

Muon Collider Physics Summary

The perspective of designing muon colliders with high energy and luminosity, which is being investigated by the International Muon Collider Collaboration, has triggered a growing interest in their physics reach. We present a concise summary of the muon colliders potential to explore new physics, leveraging on the unique possibility of combining high available energy with very precise measurements.

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arXiv2022

The physics case of a 3 TeV muon collider stage

In the path towards a muon collider with center of mass energy of 10 TeV or more, a stage at 3 TeV emerges as an appealing option. Reviewing the physics potential of such muon collider is the main purpose of this document. In order to outline the progression of the physics performances across the stages, a few sensitivity projections for higher energy are also presented. There are many opportunities for probing new physics at a 3 TeV muon collider. Some of them are in common with the extensively documented physics case of the CLIC 3 TeV energy stage, and include measuring the Higgs trilinear coupling and testing the possible composite nature of the Higgs boson and of the top quark at the 20 TeV scale. Other opportunities are unique of a 3 TeV muon collider, and stem from the fact that muons are collided rather than electrons. This is exemplified by studying the potential to explore the microscopic origin of the current $g$-2 and $B$-physics anomalies, which are both related with muons.

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arXiv2022

Learning from Radiation at a Very High Energy Lepton Collider

We study the potential of lepton collisions with about $10\text{ TeV}$ center of mass energy to probe Electroweak, Higgs and Top short-distance physics at the $100\text{ TeV}$ scale, pointing out the interplay with the long-distance ($100\text{ GeV}$) phenomenon of Electroweak radiation. On one hand, we find that sufficiently accurate theoretical predictions require the resummed inclusion of radiation effects, which we perform at the double logarithmic order. On the other hand, we notice that short-distance physics does influence the emission of Electroweak radiation. Therefore the investigation of the radiation pattern can enhance the sensitivity to new short-distance physical laws. We illustrate these aspects by studying Effective Field Theory contact interactions in di-fermion and di-boson production, and comparing cross-section measurements that require or that exclude the emission of massive Electroweak bosons. The combination of the two types of measurements is found to enhance the sensitivity to the new interactions. Based on these results, we perform sensitivity projections to Higgs and Top Compositeness and to minimal $Z'$ new physics scenarios at future muon colliders.

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arXiv2021

Positive Moments for Scattering Amplitudes

We find the complete set of conditions satisfied by the forward $2\to2$ scattering amplitude in unitarity and causal theories. These are based on an infinite set of energy dependent quantities -- the arcs -- which are dispersively expressed as moments of a positive measure defined at (arbitrarily) higher energies. We identify optimal finite subsets of constraints, suitable to bound Effective Field Theories (EFTs), at any finite order in the energy expansion. At tree-level arcs are in one-to-one correspondence with Wilson coefficients. We establish under which conditions this approximation applies, identifying seemingly viable EFTs where it never does. In all cases, we discuss the range of validity in both couplings and energy. We also extend our results to the case of small but finite~$t$. A consequence of our study is that EFTs in which the scattering amplitude in some regime grows in energy faster than $E^6$ cannot be UV-completed.

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arXiv2021

Gapped Goldstones at the cut-off scale: a non-relativistic EFT

At finite density, the spontaneous breakdown of an internal non-Abelian symmetry dictates, along with gapless modes, modes whose gap is fixed by the algebra and proportional to the chemical potential: the gapped Goldstones. Generically the gap of these states is comparable to that of other non-universal excitations or to the energy scale where the dynamics is strongly coupled. This makes it non-straightforward to derive a universal ef effective field theory (EFT) description realizing all the symmetries. Focusing on the illustrative example of a fully broken SU (2) group, we demonstrate that such an EFT can be constructed by carving out around the Goldstones, gapless and gapped, at small 3-momentum. The rules governing the EFT, where the gapless Goldstones are soft while the gapped ones are slow, are those of standard nonrelativistic EFTs, like for instance nonrelativistic QED. In particular, the EFT Lagrangian formally preserves gapped Goldstone number, and processes where such number is not conserved are described inclusively by allowing for imaginary parts in the Wilson coefficients. Thus, while the symmetry is manifestly realized in the EFT, unitarity is not. We comment on the application of our construction to the study of the large charge sector of conformal field theories with non-Abelian symmetries.

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arXiv2020

Feynman diagrams and the large charge expansion in $3-\varepsilon$ dimensions

In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge $n$ operator in the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-\varepsilon$ can be computed semiclassically for arbitrary values of $λn$, where $λ$ is the perturbatively small fixed point coupling. Here we generalize this result to the fixed point of the $U(1)$ model in $3-\varepsilon$ dimensions. The result interpolates continuously between diagrammatic calculations and the universal conformal superfluid regime for CFTs at large charge. In particular it reproduces the expectedly universal $O(n^0)$ contribution to the scaling dimension of large charge operators in $3d$ CFTs.

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arXiv2019

The Epsilon Expansion Meets Semiclassics

We study the scaling dimension $Δ_{ϕ^n}$ of the operator $ϕ^n$ where $ϕ$ is the fundamental complex field of the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-\varepsilon$. Even for a perturbatively small fixed point coupling $λ_*$, standard perturbation theory breaks down for sufficiently large $λ_*n$. Treating $λ_* n$ as fixed for small $λ_*$ we show that $Δ_{ϕ^n}$ can be successfully computed through a semiclassical expansion around a non-trivial trajectory, resulting in $$ Δ_{ϕ^n}=\frac{1}{λ_*}Δ_{-1}(λ_* n)+Δ_{0}(λ_* n)+λ_* Δ_{1}(λ_* n)+\ldots $$ We explicitly compute the first two orders in the expansion, $Δ_{-1}(λ_* n)$ and $Δ_{0}(λ_* n)$. The result, when expanded at small $λ_* n$, perfectly agrees with all available diagrammatic computations. The asymptotic at large $λ_* n$ reproduces instead the systematic large charge expansion, recently derived in CFT. Comparison with Monte Carlo simulations in $d=3$ is compatible with the obvious limitations of taking $\varepsilon=1$, but encouraging.

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arXiv2019

Which EFT

We classify effective field theory (EFT) deformations of the Standard Model (SM) according to the analyticity property of the Lagrangian as a function of the Higgs doublet H. Our distinction in analytic and non-analytic corresponds to the more familiar one between linearly and non-linearly realized electroweak symmetry, but offers deeper physical insight. From the UV perspective, non-analyticity occurs when the new states acquire mass from electroweak symmetry breaking, and thus cannot be decoupled to arbitrarily high scales. This is reflected in the IR by the anomalous growth of the interaction strength for processes involving many Higgs bosons and longitudinally polarized massive vectors, with a breakdown of the EFT description below a scale $O(4 πv)$. Conversely, analyticity occurs when new physics can be pushed parametrically above the electroweak scale. We illustrate the physical distinction between these two EFT families by discussing Higgs boson self-interactions. In the analytic case, at the price of some unnaturalness in the Higgs potential, there exists space for $O(1)$ deviations of the cubic coupling, compatible with single Higgs and electroweak precision measurements, and with new particles out of the direct LHC reach. Larger deviations are possible, but subject to less robust assumptions about higher-dimensional operators in the Higgs potential. On the other hand, when the cubic coupling is produced by a non-analytic deformation of the SM, we show by an explicit calculation that the theory reaches strong coupling at $O(4 πv)$, quite independently of the magnitude of the cubic enhancement.

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