Fermionic Composites Research Articles

2-index chiral gauge theories

We undertake a systematic study of the 4-dimensional SU(N) 2-index chiral gauge theories and investigate their faithful global symmetries and dynamics. These are a finite set of theories with fermions in the 2-index symmetric and anti-symmetric representations, with no fundamentals, and they do not admit a large-N limit. We employ a combination of perturbative and nonperturbative methods, enabling us to constrain their infrared (IR) phases. Specifically, we leverage the ’t Hooft anomalies associated with continuous and discrete groups to eliminate a few scenarios. In some cases, the anomalies rule out the possibility of fermion composites. In other cases, the interplay between the continuous and discrete anomalies leads to multiple higher-order condensates, which inevitably form to match the anomalies. Further, we pinpoint the most probable symmetry-breaking patterns by searching for condensates that match the full set of anomalies resulting in the smallest number of IR degrees of freedom. Higher-loop β-function analysis suggests that a few theories may flow to a conformal fixed point.

Fermion-axion stars: Static solutions and dynamical stability

We construct spherically symmetric static solutions of the Einstein-Klein-Gordon-Euler system involving a complex scalar field governed by a periodic potential that emerges in models of axionlike particles and fermionic matter modeled by a perfect fluid with a polytropic equation of state. Such solutions describe gravitationally bound composites of fermions and axions, which we dub fermion-axion stars. Sequences of pure axion stars in the existence domain may show the presence of multiple stable branches depending on the value of the decay constant parameter in the potential; this reflects in the appearance of multiple islands of stability in the two-dimensional parameter space of fermion-axion configurations. We investigate the domain of existence for three different values of the decay constant, identifying one or more regions of linear stability, making use of a method we already employed in previous works. We confirm the results from the linear analysis performing fully nonlinear numerical relativity evolutions. In this context, we perform several numerical simulations to identify regions in the parameter space where unstable models face different fates: the collapse to a Schwarzschild black hole, the migration to a stable model, and finally the dispersion of the scalar field together with the dilution of the fermionic matter, which approaches a static fermion star model with very low mass. This latter scenario was never observed in previous models without the periodic potential.

Speed of evolution in entangled fermionic systems

We consider the simplest identical-fermion system that exhibits the phenomenon of entanglement (beyond exchange correlations) to analyze its speed of evolution toward an orthogonal state, and revisit the relation between this latter and the amount of fermionic entanglement. A characterization of the quantum speed limit and the orthogonality times is performed, throwing light into the general structure of the faster and the slower states. Such characterization holds not only for fermionic composites, but apply more generally to a wide family of six-dimensional states, irrespective of the specific nature of the system. Further, it is shown that the connection between speed of evolution and entanglement in the fermionic system, though more subtle than in composites of distinguishable parties, may indeed manifest for certain classes of states.

The SU(8) GUT with composite quarks and leptons

We consider the L-R symmetric composite model for quarks and leptons where constituent preons possessing some local SU(N)MF metaflavor symmetry are bound by the chiral SO(n)L×SO(n)R gauge metacolor forces. The strengthening of the 't Hooft's anomaly matching condition, when the massless fermion composites are required to complete a single representation of the SU(N)MF rather than some set of its representations, allows to fix the number of basic metaflavors N. Particularly, just eight left-handed and eight right-handed preons and their composites preserving the global chiral symmetry SU(8)L×SU(8)R are turned out to underlie the physical world at small distances that uniquely identifies the local metaflavor symmetry SU(8)MF as its effective unified symmetry. We next show that the spontaneous L-R symmetry violation caused by the simultaneously emerged composite scalars reduces this initially vectorlike SU(8)MF theory down to the conventional SU(5) GUT with an extra local family symmetry SU(3)F and three standard families of quarks and leptons. Though the tiny confinement scale for universal preons composing both quarks and leptons makes it impossible to directly confirm their composite nature, simultaneous emergence of several extra SU(5)×SU(3)F multiplets of heavy composite fermions may help with a model verification. Generally, they may be located at scales from O(100) TeV up to the Planck mass scale depending on an interplay between the compositeness scale and scale of the family symmetry SU(3)F. Some of them through a natural see-saw mechanism provide the physical neutrino masses which, in contrast to conventional picture, appear to follow an inverted family hierarchy. Others mix with ordinary quark-lepton families in a way that there may arise a marked violation of unitarity in the CKM matrix for leptons.

A concrete composite 2-Higgs doublet model

We consider a Composite Higgs Model (CHM) with two isospin doublet Higgs fields arising as pseudo Nambu-Goldstone bosons from a SO(6) → SO(4) × SO(2) breaking. The main focus of this work is to explicitly compute the properties of these Higgses in terms of the fundamental parameters of the composite sector such as masses, Yukawa and gauge couplings of the new spin-1 and spin-1/2 resonances. Concretely, we calculate the Higgs potential at one-loop level through the Coleman-Weinberg mechanism from the explicit breaking of the SO(6) global symmetry by the partial compositeness of fermions and gauge bosons. We derive then the phenomenological properties of the Higgs states and highlight the main signatures of this Composite 2-Higgs Doublet Model at the Large Hadron Collider, including modifications to the SM-like Higgs couplings as well as production and decay channels of heavier Higgs bosons. We also consider flavour bounds that are typical of CHMs with more than one Higgs doublet.

The other effective fermion compositeness

We discuss the only two viable realizations of fermion compositeness described by a calculable relativistic effective field theory consistent with unitarity, crossing symmetry and analyticity: chiral-compositeness vs goldstino-compositeness. We construct the effective theory of mathcal{N} Goldstini and show how the Standard Model can emerge from this dynamics. We present new bounds on either type of compositeness, for quarks and leptons, using dilepton searches at LEP, dijets at the LHC, as well as low-energy observables and precision measurements. Remarkably, a scale of compositeness for Goldstino-like electrons in the 2 TeV range is compatible with present data, and so are Goldstino-like first generation quarks with a compositeness scale in the 10 TeV range. Moreover, assuming maximal R-symmetry, goldstino-compositeness of both right- and left-handed quarks predicts exotic spin-1/2 colored sextet particles that are potentially within the reach of the LHC.

Composites and Quasiparticles in a Number Conserving Bosonization Method

A method of bosonization is presented in which fermion composites and fermionic quasiparticles are treated on the same footing respecting fermion number conservation and avoiding double counting.

Signature of short distance physics on inflation power spectrum and CMB anisotropy

The inflaton field responsible for inflation may not be a canonical fundamental scalar. It is possible that the inflaton is a composite of fermions or it may have a decay width. In these cases the standard procedure for calculating the power spectrum is not applicable and a new formalism needs to be developed to determine the effect of short range interactions of the inflaton on the power spectrum and the CMB anisotropy. We develop a general formalism for computing the power spectrum of curvature perturbations for such non-canonical cases by using the flat space Källén-Lehmann spectral function in curved quasi-de Sitter space assuming implicitly that the Bunch-Davis boundary conditions enforces the inflaton mode functions to be plane wave in the short wavelength limit and a complete set of mode functions exists in quasi-de Sitter space. It is observed that the inflaton with a decay width suppresses the power at large scale while a composite inflaton's power spectrum oscillates at large scales. These observations may be vindicated in the WMAP data and confirmed by future observations with PLANCK.

Semivariational approach to QCD at finite temperature and baryon density

Recently a new bosonization method has been used to derive, at zero fermion density, an effective action for relativistic field theories whose partition function is dominated by fermionic composites, chiral mesons in the case of QCD. This approach shares two important features with variational methods: the restriction to the subspace of the composites, and the determination of their structure functions by a variational calculation. But unlike standard variational methods it treats excited states on the same footing as the ground state. I show that this bosonization method is an approximation of an exact procedure in which composites are introduced in the presence of fermionic states with the quantum numbers of the constituents (quasiparticles). This procedure consists of an independent Bogoliubov transformation at each time slice. The time-dependent parameters of the transformation are then associated with composite fields. In this way states of nonvanishing fermion (baryon) number (neglected in the bosonization approach) are retained. By the exact procedure I derive an effective action for QCD at finite temperature and baryon density. I test the result on a four-fermion interaction model.

Composite boson dominance in many-fermion systems

I recently proposed a method of bosonization based on the use of coherent states of fermion composites, whose validity was restricted to smooth structure functions. In the present paper I remove this limitation and derive results which hold for arbitrary interactions and structure functions. The method respects all symmetries and in particular fermion number conservation. It reproduces exactly the results of the pairing model of atomic nuclei and of the BCS model of superconductivity in the number conserving form of the quasi-chemical equilibrium theory.

FERMION-SECTOR FRUSTRATED SU(4) AS A PREONIC PRECURSOR OF THE STANDARD MODEL

We give a model for composite quarks and leptons based on the semisimple gauge group SU(4), with the preons in the 10 representation; this choice of gauge gluon and preon multiplets is motivated by the possibility of embedding them in an N=6 supergravity multiplet, with the preons and antipreons both in the 20 of SU(6). Hypercolor singlets are forbidden in the fermionic sector of this theory; we propose that the SU(4) symmetry spontaneously breaks to SU (3)× U (1), with the binding of triality nonzero preons and gluons into composites, and with the formation of a color singlet condensate that breaks the initial Z12 vacuum symmetry to Z6. The spin ½ fermionic composites have the triality structure of a quark–lepton family, and the initial Z12 symmetry implies that there are six massless families, which mix to give three distinct families below the scale of the condensate. The spin 1 triality zero composites of the color triplet SU(4) gluons, when coupled to the condensate and with the color singlet representation of the 10 acting as a doorway state, lead to weak interactions of the fermionic composites through an SU(2) gauge algebra. The initial Z12 symmetry implies that this SU(2) gauge algebra structure is doubled, which in turn permits the corresponding independent gauge bosons to couple to chiral components of the composite fermions. Since the U(1) couples to the 10 representation as B-L, an effective SU (2)L× SU (2)R × U (1)B-L electroweak theory arises at the condensate scale, with all composites having the correct electric charge structure. Assuming a mechanism for forming composite Higgs bosons, the Z12→ Z6 symmetry breaking chain implies that below the condensate scale there can be two sets of discrete chiral Z6 triplets of Higgs doublets, as required by a phenomenological model for the CKM matrix that we have analyzed in detail elsewhere. A renormalization group analysis of the SU(4) model shows that the conversion by binding of one 10 of SU(4) to 12 triplets of SU(3) can give a very large, calculable hierarchy ratio between the SU(4) and the hadronic mass scales.

New excitations in the Thirring model

The quantization of the massless Thirring model in the light-cone using functional methods is considered. The need to compactify the coordinate x − in the light-cone spacetime implies that the quantum effective action for left-handed fermions contains excitations similar to abelian instantons produced by composite of left-handed fermions. Right-handed fermions don't have a similar effective action. Thus, quantum mechanically, chiral symmetry must be broken as a result of the topological excitations. The conserved charge associated to the topological states is quantized. Different cases with only fermionic excitations or bosonic excitations or both can occur depending on the boundary conditions and the value of the coupling.

Model-independent limits on four-fermion contact interactions at LC with polarization

Fermion compositeness, and other types of new physics that can be described by the exchange of very massive particles, can manifest themselves as the result of an effective four-fermion contact interaction. In the case of the processes e +e −→μ +μ −,τ +τ −, b ̄ b and c ̄ c at future e + e − colliders with s =0.5 –1 TeV, we examine the sensitivity to four-fermion contact interactions of two new integrated observables, σ + and σ −, conveniently defined for such kind of analysis. We find that, if longitudinal polarization of the electron beam were available, these observables would offer the opportunity to separate the helicity cross sections and, in this way, to derive model-independent bounds on the relevant parameters.

Use of even grassmann variables to construct effective actions for mesons

In the framework of an approach to bosonization based on the use of fermionic composites as fundamental variables, a quadratic action in even Grassmann variables with the quantum numbers of the pions has been constructed. It includes the σ-field in order to be invariant under [ SU(2)] L ⊗ [ SU(2)] R tranfformations over the quarks. This action exhibits the Goldstone phenomenon reducing its symmetry to the O(3) isospin invariance. The model has been investigated in the Stratonovitch-Hubbard representation, in which form it is reminiscent of the Gell-Mann-Lévy model. By the saddle point method a renormalizable expansion in inverse powers of the index of nilpotency of the mesonic fields (which is 24), is generated. The way it might be used in a new perturbative approach to QCD is outlined.

A free action for pions as quark composites

In the framework of an approach to bosonization based on the use of fermionic composites as fundamental variables, a quadratic action in even Grassmann variables with the quantum numbers of the pions has been constructed. It includes the σ-field in order to be invariant under [ SU(2)] L ⊗ [ SU(2)] R transformations over the quarks. This action exhibits the Goldstone phenomenon reducing its symmetry to the O(3) isospin invariance. A squared mass for the pions is generated according to PCAC. The model has been investigated in the Stratonovitch-Hubbard representation, in which form it is reminiscent of the Gell-Mann-Lévy model. By the saddle-point method a renormalizable expansion in inverse powers of the index of nilpotency of the mesonic fields (which is 24), is generated. The way it might be used in a new perturbative approach to QCD is outlined.

Quantum Statistical Mechanics of an Ideal Gas with Fractional Exclusion Statistics in Arbitrary Dimensions

The quantum statistical mechanics of an ideal gas with fractional exclusion (i.e., Haldane-Wu) statistics in arbitrary dimensions is discussed. The general formulation for pressure and density of the system is obtained in a closed form in terms of the $D$-dimensional momentum representation, which can be regarded as a natural generalization of the classic results for Fermi and Bose gases. Using this, it is shown that ideal gases with fractional exclusion statistics can be regarded as composites of fermions and bosons, and that no condensation occurs at low temperature except for the pure boson case.

Bosonization and even Grassmann variables

We test a new approach to bosonization in relativistic field theories and many-body systems, whose purpose is to set up a perturbative scheme where the unperturbed action is the free action of the composites. The method is of practical relevance since the free propagators of the composites can be evaluated in a number of interesting cases. This is achieved by performing a generalized change of variables in the Berezin integral which defines the partition function of the system, whereby one assumes the composites as new integration variables. Still to be established, however, is a general procedure for deriving the free action of the composites starting from the one of the constituents. To shed light on this problem and to explore further features of the method we study a simplified version of the BCS model, whose spectrum consists of the excitations of the composite field associated to a Cooper pair. We are able to obtain the free action of this field, which displays a peculiar feature which we conjecture to characterize all the actions of quadratic fermionic composites, namely it does not contain a time derivative. Nevertheless it yields the right propagator, because, due to the properties of the integral over even elements of a Grassmann algebra, the propagator turns out not to be the inverse of the wave operator.

Even Grassmann fields in momentum space

We extend previous results about fields whose Fourier components are even elements of a Grassmann algebra. Their main interest is related to the possibility that they describe fermionic composites. We evaluate the free propagators for arbitrary index of nilpotency and investigate to one loop a φ 4 model. Due to the nature of the integral over even Grassmann fields such a model exists for repulsive as well as attractive selfinteraction. In the first case the β -function is equal to that of the ordinary theory while in the second one the model is asymptotically free. The renormalized mass has a peculiar dependence on the cut off, being quadratically increasing/decreasing for attractive/repulsive selfinteraction.

Nonstandard gamma gamma -->l+l- processes in relativistic heavy-ion collisions.

We study lepton pair production in heavy-ion collisions with emphasis on nonstandard contributions to the QED subprocess {gamma}{gamma}{r arrow}{ital l}{sup +}{ital l{minus}}. The existence of compositeness of fermions and/or bosons can be tested in this reaction up to the TeV mass scale. We show that for some processes the capabilities of relativistic heavy-ion colliders to disclose new physics surpass the possibilities of {ital e}{sup +}{ital e{minus}} or {ital p{bar p}} machines. In particular, spin-zero composite particles which couple predominantly to two photons, predicted in composite models, can be studied in a broad range of masses.

The equation of state and critical exponents in quenched strongly coupled QED

We study the equation of state of quenched strongly coupled QED with fine structure constant α, extended by a chirally invariant four-Fermi interaction with strength parametrized by G, along the entire critical line in the ( α, G) plane as described by the Schwinger-Dyson equation for the fermion self-mass. From there we extract the critical indices β, δ, ν and γ as functions of the two couplings and find that they vary continuously from their mean field values at α = 0, G = 4 to those corresponding to the essential singularity behaviour at α = π 3 , G = 1 . At each point on the critical line, the critical exponents satisfy hyperscaling. We extract the critical exponents δ and β from quenched lattice QED simulations by studying the bare fermion mass dependence of the chiral condensate and the λ-dependence of the density of states ϱ(λ) of the spectrum of the Dirac operator at the critical point. We find that the effective δ obtained from numerical fits depends sensitively on the value of β c taken as the critical coupling. Our best fits favor β c = 0.257(1), δ = 2.2(1), and the exponent β = 0.8(1). For the particular value of the critical exponents obtained from the lattice simulations we find a point on the critical line. Since the exponent δ depends on the anomalous dimensions of the fermion composites, we make a connection between lattice measurements and Schwinger-Dyson equation results.