arXiv subjects

Maurizio Piai

Publications and source records attributed to Maurizio Piai.

At least 55 records · Page 3Linked to original sources

arXiv2023

$Sp(2N)$ Lattice Gauge Theories and Extensions of the Standard Model of Particle Physics

We review the current status of the long-term programme of numerical investigation of $Sp(2N)$ gauge theories with and without fermionic matter content. We start by introducing the phenomenological as well as theoretical motivations for this research programme, which are related to composite Higgs models, models of partial top compositeness, dark matter models, and in general to the physics of strongly coupled theories and their approach to the large-N limit. We summarise the results of lattice studies conducted so far in the $Sp(2N)$ Yang-Mills theories, measuring the string tension, the mass spectrum of glueballs and the topological susceptibility, and discuss their large-N extrapolation. We then focus our discussion on $Sp(4)$, and summarise numerical measurements of mass and decay constant of mesons in the theories with fermion matter in either the fundamental or the antisymmetric representation, first in the quenched approximation, and then with dynamical fermions. We finally discuss the case of dynamical fermions in mixed representations, and exotic composite fermion states such as the chimera baryons. We conclude by sketching the future stages of the programme. And we describe our approach to open access.

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arXiv2023

Toward minimal composite Higgs models from regular geometries in bottom-up holography

We study a bottom-up, holographic description of a field theory yielding the spontaneous breaking of an approximate SO(5) global symmetry to its SO(4) subgroup. The weakly-coupled, six-dimensional gravity dual has regular geometry. One of the dimensions is compactified on a circle that shrinks smoothly to zero size at a finite value of the holographic direction, hence introducing a physical scale in a way that mimics the effect of confinement in the dual four-dimensional field theory. We study the spectrum of small fluctuations of the bulk fields carrying SO(5) quantum numbers, which can be interpreted as spin-0 and spin-1 bound states in the dual field theory. This work supplements an earlier publication, focused only on the SO(5) singlet states. We explore the parameter space of the theory, paying particular attention to composite states that have the right quantum numbers to be identified as pseudo-Nambu-Goldstone Bosons (PNGBs). We find that in this model the PNGBs are generally heavy, with masses of the same order as other bound states, indicating the presence of a sizeable amount of explicit symmetry breaking in the field theory side. But we also find a qualitatively new, unexpected result. When the dimension of the field-theory operator inducing SO(5) breaking is close to half of the space-time dimensionality, there exists a region of parameter space in which the PNGBs and the lightest scalar are both parametrically light in comparison to all other bound states of the field theory. Although this region is known to yield metastable classical backgrounds, this finding might be relevant to model building in the composite Higgs context.

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arXiv2022

The density of state method for first-order phase transitions in Yang-Mills theories

Lattice Field Theory can be used to study finite temperature first-order phase transitions in new, strongly-coupled gauge theories of phenomenological interest. Metastable dynamics arising in proximity of the phase transition can lead to large, uncontrolled numerical errors when analysed with standard methods. In this contribution, we discuss a prototype lattice calculation in which the first-order deconfinement transition in the strong Yang-Mills sector of the standard model is analysed using a novel lattice method, the logarithmic linear relaxation algorithm. This method provides a determination of the density of states of the system with exponential error suppression.

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arXiv2022

Dilaton Effective Field Theory

We review and extend recent studies of dilaton effective field theory (dEFT) which provide a framework for the description of the Higgs boson as a composite structure. We first describe the dEFT as applied to lattice data for a class of gauge theories with near-conformal infrared behavior. It includes the dilaton associated with the spontaneous breaking of (approximate) scale invariance, and a set of pseudo-Nambu-Goldstone bosons (pNGBs) associated with the spontaneous breaking of an (approximate) internal global symmetry. The theory contains two small symmetry-breaking parameters. We display the leading-order (LO) Lagrangian, and review its fit to lattice data for the $SU(3)$ gauge theory with $N_f = 8$ Dirac fermions in the fundamental representation. We then develop power-counting rules to identify the corrections emerging at next-to-leading order (NLO) in the dEFT action. We list the NLO operators that appear and provide estimates for the coefficients. We comment on implications for composite-Higgs model building.

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arXiv2022

The density of states method in Yang-Mills theories and first order phase transitions

Extensions of the standard model that lead to first-order phase transitions in the early universe can produce a stochastic background of gravitational waves, which may be accessible to future detectors. Thermodynamic observables at the transition, such as the latent heat, can be determined by lattice simulations, and then used to predict the expected signatures in a given theory. In lattice calculations, the emergence of metastabilities in proximity of the phase transition may make the precise determination of these observables quite challenging, and may lead to large uncontrolled numerical errors. In this contribution, we discuss as a prototype lattice calculation the first order deconfinement transition that arises in the strong SU(3) Yang-Mills sector. We adopt the novel logarithmic linear relaxation method, which can provide a determination of the density of states of the system with exponential error suppression. Thermodynamic observables can be reconstructed with a controlled error, providing a promising direction for accurate model predictions in the future.

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arXiv2022

Composite dynamics in Sp($2N$) gauge theories

Sp($2N$) gauge theories with fermonic matter provide an ideal laboratory to build extensions of the standard model based on novel composite dynamics. Examples include composite Higgs along with top partial compositeness and composite dark matter. Without fermions, their study also complements those based on SU($N_c$) gauge theories with which they share a common sector in the large $N_c=2N$ limit. We report on our recent progress in the numerical studies of Sp($2N$) gauge theories discretised on a four-dimensional Euclidean lattice. In particular, we present preliminary results for the low-lying mass spectra of mesons and chimera baryons in the theories with $N=2$. We also compute the topological susceptibility for various values of $N$, extrapolate the results to the large $N$ limit, and discuss certain universal properties in Yang-Mills theories.

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arXiv2022

Spectroscopy of chimera baryons in a $Sp(4)$ lattice gauge theory

Chimera baryons are an important element of strongly coupled theories that provide a microscopic origin for UV complete composite Higgs models (CHMs), since they play the role of top partners in top partial compositeness. In a particular interesting realisation of CHMs based upon an underlying $Sp(4)$ gauge theory, such exotic objects are composed of two fermion constituents transforming on the fundamental, and one on the 2-index antisymmetric representations. We perform lattice computations of the chimera baryon spectrum in the quenched approximation. We present preliminary results for the masses of various chimera baryons with different quantum numbers, including the one interpreted as the top partner. We test the technology needed for future calculations with dynamical fermions.

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arXiv2022

Topological susceptibility, scale setting and universality from $Sp(N_c)$ gauge theories

In this contribution, we report on our study of the properties of the Wilson flow and on the calculation of the topological susceptibility of $Sp(N_c)$ gauge theories for $N_c=2,\,4,\,6,\,8$. The Wilson flow is shown to scale according to the quadratic Casimir operator of the gauge group, as was already observed for $SU(N_c)$, and the commonly used scales $t_0$ and $w_0$ are obtained for a large interval of the inverse coupling for each probed value of $N_c$. The continuum limit of the topological susceptibility is computed and we conjecture that it scales with the dimension of the group. The lattice measurements performed in the $SU(N_c)$ Yang-Mills theories by several independent collaborations allow us to test this conjecture and to obtain a universal large-$N_c$ limit of the rescaled topological susceptibility.

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arXiv2022

$Sp(2N)$ Yang-Mills theories on the lattice: scale setting and topology

We study Yang-Mills lattice theories with $Sp(N_c)$ gauge group, with $N_c=2N$, for $N=1,\,\cdots,\,4$. We show that if we divide the renormalised couplings appearing in the Wilson flow by the quadratic Casimir $C_2(F)$ of the $Sp(N_c)$ group, then the resulting quantities display a good agreement among all values of $N_c$ considered, over a finite interval in flow time. We use this scaled version of the Wilson flow as a scale-setting procedure, compute the topological susceptibility of the $Sp(N_c)$ theories, and extrapolate the results to the continuum limit for each $N_c$.

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arXiv2022

Spectroscopy of $Sp(4)$ lattice gauge theory with $n_f=3$ antisymmetric fermions

We perform numerical calculations of masses and decay constants of the lightest (flavoured) pseudoscalar, vector and axial vector mesons in the $Sp(4)$ lattice gauge theory with three Dirac fermions in the antisymmetric representation. The corresponding continuum theory plays an important role in certain ultra-violet complete realisations of composite Higgs, partial top compositeness, and composite dark matter models. In addition, we measure the masses of other flavoured mesons in spin-$0$ and $1$ channels, as well as the first excited state of the vector mesons. Using the gradient flow to set the scale, we carry out the continuum extrapolation and show preliminary results for the meson spectrum of the theory.

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arXiv2022

Color dependence of the topological susceptibility in Yang-Mills theories

For Yang-Mills theories in four dimensions, we propose to rescale the ratio between topological susceptibility and string tension squared in a universal way, dependent only on group factors. We apply this suggestion to $SU(N_c)$ and $Sp(N_c)$ groups, and compare lattice measurements performed by several independent collaborations. We show that the two sequences of (rescaled) numerical results in these two families of groups are compatible with each other. We hence perform a combined fit, and extrapolate to the common large-$N_c$ limit.

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arXiv2022

Lattice studies of the $Sp(4)$ gauge theory with two fundamental and three antisymmetric Dirac fermions

We consider the $Sp(4)$ gauge theory coupled to $N_f=2$ fundamental and $n_f=3$ antisymmetric flavours of Dirac fermions in four dimensions. This theory serves as the microscopic origin for composite Higgs models with $SU(4)/Sp(4)$ coset, supplemented by partial top compositeness. We study numerically its lattice realisation, and couple the fundamental plaquette action to Wilson-Dirac fermions in mixed representations, by adopting a (rational) hybrid Monte Carlo method, to perform non-trivial tests of the properties of the resulting lattice theory. We find evidence of a surface (with boundaries) of first-order bulk phase transitions in the three-dimensional space of bare parameters (one coupling and two masses). Explicit evaluation of the Dirac eigenvalues confirms the expected patterns of global symmetry breaking. After investigating finite volume effects in the weak-coupling phase of the theory, for the largest available lattice we study the mass spectra of the lightest spin-0 and spin-1 flavoured mesons composed of fermions in each representation, and of the lightest half-integer spin composite particle made of fermions in different representations -- the chimera baryon. This work sets the stage for future systematical studies of the non-perturbative dynamics in phenomenologically relevant regions of parameter space.

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arXiv2022

Composite two-Higgs doublet model from dilaton effective field theory

We construct a composite two-Higgs-doublet model (2HDM) within the context of dilaton effective field theory. This EFT describes the particle spectrum observed in lattice simulations of a near-conformal $SU(3)$ gauge field theory. A second Higgs doublet is naturally accommodated within the EFT, used previously to construct a one-Higgs-doublet model. We explore the interplay of phenomenological and EFT requirements, supplemented by information from numerical lattice studies of the $SU(3)$ gauge theory with eight fundamental (Dirac) fermions. We build a viable model with moderate parameter tuning. In the relevant portion of parameter space, we match the model to a conventional general description of 2HDMs, and comment on the role of custodial symmetry (breaking) in the scalar potential. Contributions to the precision electroweak parameter $T$ provide a possible explanation for the recent measurement of the W-boson mass by CDF II.

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arXiv2022

Towards top-down holographic composite Higgs: minimal coset from maximal supergravity

Within the context of top-down holography, we study a one-parameter family of regular background solutions of maximal gauged supergravity in seven dimensions, dimensionally reduced on a 2-torus. The dual, four-dimensional confining field theory realises the global (spontaneous as well as explicit) symmetry breaking pattern SO(5)->SO(4). We compute the complete mass spectrum for the fluctuations of the 128 bosonic degrees of freedom of the five-dimensional gravity theory, which correspond to scalar, pseudoscalar, vector, axial-vector, and tensor bound states of the dual field theory, and includes particles with exotic SO(4) quantum numbers. We confirm the existence of tachyonic instabilities near the boundaries of the parameter space. We discuss the interplay between explicit and spontaneous symmetry breaking. The SO(5)/SO(4) coset might provide a first step towards the realisation of a calculable framework and ultraviolet completion of minimal composite Higgs models, if the four pseudo-Nambu-Goldstone bosons are identified with the real components of the Higgs doublet in the standard model (SM), and a subgroup of SO(4) with the SU(2)xU(1) SM gauge group. We exhibit an example with an additional localised boundary term that mimics the effect of a weakly-coupled external sector.

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arXiv2021

Progress in $Sp(2N)$ lattice gauge theories

Lattice studies of gauge theories with symplectic gauge groups provide valuable information about gauge dynamics, and complement the results of lattice investigations focused on unitary gauge groups. These theories play a central role in phenomenological contexts such as composite Higgs and strongly interacting dark matter models. We report on recent progress of our lattice research programme, starting from the glueball mass spectrum and the topology of the pure gauge theory. We present our results on the mass spectrum of mesons in the quenched approximation, by varying the number of colours in the symplectic group. For the $Sp(4)$ theory, we focus on results obtained with dynamical fermion matter content comprising both fundamental and 2-index antisymmetric representations of the gauge group, as dictated by a well known model of composite Higgs with partial top compositeness.

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arXiv2021

Sp(4) gauge theories and beyond the standard model physics

We review numerical results for models with gauge group Sp(2N), discussing the glueball spectrum in the large-N limit, the quenched meson spectrum of Sp(4) with Dirac fermions in the fundamental and in the antisymmetric representation and the Sp(4) gauge model with two dynamical Dirac flavours. We also present preliminary results for the meson spectrum in the Sp(4) gauge theory with two fundamental and three antisymmetric Dirac flavours. The main motivation of our programme is to test whether this latter model is viable as a realisation of Higgs compositeness via the pseudo Nambu Goldstone mechanism and at the same time can provide partial top compositeness. In this respect, we report and briefly discuss preliminary results for the mass of the composite baryon made with two fundamental and one antisymmetric fermion (chimera baryon), whose physical properties are highly constrained if partial top compositeness is at work. Our investigation shows that a fully non-perturbative study of Higgs compositeness and partial top compositeness in Sp(4) is within reach with our current lattice methodology.

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arXiv2021

The Coulomb branch of N=4 SYM and dilatonic scions in supergravity

We find a parametrically light dilaton in special confining theories in three dimensions. Their duals form what we call a scion of solutions to the supergravity associated with the large-N limit of the Coulomb branch of the N=4 Super-Yang-Mills (SYM) theory. The supergravity description contains one scalar with bulk mass that saturates the Breitenlohner-Freedman unitarity bound. The new solutions are defined within supergravity, they break supersymmetry and scale invariance, and one dimension is compactified on a shrinking circle, yet they are completely regular. An approximate dilaton appears in the spectrum of background fluctuations (or composite states in the confining theory), and becomes parametrically light along a metastable portion of the scion of new supergravity solutions, in close proximity of a tachyonic instability. A first-order phase transition separates stable backgrounds, for which the approximate dilaton is not parametrically light, from metastable and unstable backgrounds, for which the dilaton becomes parametrically light, and eventually tachyonic.

hep-th↗

arXiv2021

Dilatonic states near holographic phase transitions

The spectrum of bound states of special strongly coupled confining field theories might include a parametrically light dilaton, associated with the formation of enhanced condensates that break (approximate) scale invariance spontaneously. It has been suggested in the literature that such a state may arise in connection with the theory being close to the unitarity bound in holographic models. We extend these ideas to cases where the background geometry is non-AdS, and the gravity description of the dual confining field theory has a top-down origin in supergravity. We exemplify this programme by studying the circle compactification of Romans six-dimensional half-maximal supergravity. We uncover a rich space of solutions, many of which were previously unknown in the literature. We compute the bosonic spectrum of excitations, and identify a tachyonic instability in a region of parameter space for a class of regular background solutions. A tachyon only exists along an energetically disfavoured (unphysical) branch of solutions of the gravity theory; we find evidence of a first-order phase transition that separates this region of parameter space from the physical one. Along the physical branch of regular solutions, one of the lightest scalar particles is approximately a dilaton, and it is associated with a condensate in the underlying theory. Yet, because of the location of the phase transition, its mass is not parametrically small, and it is, coincidentally, the next-to-lightest scalar bound state, rather than the lightest one.

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