Dynamical symmetry breaking with a fourth generation

Dynamical symmetry breaking can happen through a Higgs mechanism but also spontaneously within a strongly-enough coupled theory. We treat a field-theoretical quark model of QCD based on a linear+Coulomb Cornell potential (to account for the longitudinal interaction), together with a transverse interaction (to account for Coulomb-gauge gluons) in BCS approximation. After extracting the well-known BCS ground state on which abundant hadron phenomenology implementing dynamical chiral symmetry breaking has been built, we find two excited replica vacuum like states shown in figure 1. At the BCS level they are classically unstable, but second quantization blocks transitions between them in volumes much larger than a hadron size. Mesons built over the replica vacua have relative masses similar to normal mesons on the ordinary vacuum; we find no negative-mass mode, confirming their stability found earlier with a harmonic oscillator potential.

We address the problem of accounting for light neutrino masses in theories with dynamical electroweak symmetry breaking. We discuss this in the context of a class of extended technicolor (ETC) models. As a possible solution, we propose a combination of suppressed Dirac masses and a seesaw involving dynamically generated condensates of standard‐model singlet, ETC‐nonsinglet fermions. We show how this can be realized in an explicit ETC model. An important feature of this proposal is that, because of the suppression of Dirac neutrino mass terms, a seesaw yielding realistic neutrino masses does not require superheavy Majorana masses. We then generalize this mechanism to theories with extended strong‐electroweak gauge symmetries.

A modification of perturbation theory, known as the delta expansion (variationally improved perturbation), gave rigorously convergent series in some D=1 models (oscillator energy levels) with factorially divergent ordinary perturbative expansions. In a generalization of the variationally improved perturbation technique appropriate to renormalizable asymptotically free theories, we show that the large expansion orders of certain physical quantities are similarly improved, and prove the Borel convergence of the corresponding series for $m_{\mathrm {v}} \lessim 0$ , with $m_{\mathrm {v}}$ the new (arbitrary) mass perturbation parameter. We argue that non-ambiguous estimates of quantities relevant to dynamical (chiral) symmetry breaking in QCD are possible in this resummation framework.

In supersymmetric models with minimal particle content and without large left-right squarks mixing, the conventional knowledge is that the Higgs Boson mass around 125 GeV leads to top squark masses O(10) TeV, far beyond the reach of colliders. Here, we pointed out that this conclusion is subject to several theoretical uncertainties. We find that electroweak symmetry breaking and evaluation of Higgs mass at a scale far away from the true electroweak symmetry breaking scale introduce a large uncertainty in Higgs mass calculation. We show that the electroweak symmetry breaking at the scale near the true vacuum expectation value of Higgs field can increase the Higgs Boson mass about 4–5 GeV and can lower the bounds on squarks and slepton masses to 1 TeV. Here we pointed out that the Higgs mass even with inclusion of radiative corrections can vary with electroweak symmetry breaking scale. We calculate it at two loop level and show that it varies substantially. We argue that Higgs mass like other coupling parameters can vary with energy scale and the Higgs potential with all orders loop corrections is scale invariant. This uncertainty to the Higgs mass calculation due to electroweak symmetry breaking around the supersymmetry breaking scale, normally taken as mt˜Lmt˜R, to minimize the 1-loop radiative corrections can be removed if one considers all significant radiative contributions to make Higgs potential renormalization group evolution scale invariant and evaluates electroweak symmetry breaking at the scale near the electroweak symmetry breaking scale. A large parameter space becomes allowed when one considers electroweak symmetry breaking at its true scale not only for producing correct values of the Higgs masses, but also for providing successful breaking of this symmetry in more parameter spaces.

Proper vertex in studies of dynamical chiral symmetry breaking

The precision electroweak data in warped extra-dimension models

In the Standard Model (SM) of the elementary particles, the interactions among the known fundamental fermions (leptons and quarks) are mediated through gauge bosons which obey the symmetry: SU(3) Ⓧ SU(2) Ⓧ U(1). More precisely, the electroweak interaction [4-6] is described by a gauge symmetry SU(2) Ⓧ U(1) which is broken spontaneously. The electroweak symmetry breaking is implemented by the introduction of a complex scalar Higgs field which has a non-zero vacuum expectation value (vev). This way, the lagrangian of the theory remains invariant under SU(2) transformations, but quantization of the fields must start from a ground state which does not exhibit this symmetry, and therefore the full symmetry of the lagrangian is not manifest. Invariance of the theory under local SU(2) transformations implies the presence of vectorial gauge fields which mediate the electroweak interactions. The so called spontaneous symmetry breaking allows the quanta of these gauge fields, the W and Z bosons, to acquire a finite mass. The photon, the particle which mediates the electromagnetic interaction, remains massless. The Higgs boson is one of only two particles in the SM which have not yet been directly observed (the other is the vτ, although there is indirect evidence of its existence). Although the SM does not predict the Higgs mass, a lower limit ~ 100 GeV/c2 is set by LEPII data, and theoretical considerations prefer Higgs masses not higher than a few hundred GeV/c2. At the Tevatron, a search for the Higgs boson is hard due to the small production cross section and the huge backgrounds that do not allow to see the signal clearly. It is still interesting, however, to perform sensitivity studies at the Tevatron. The easiest production channel to observe at the Tevatron is the associated production of Higgs with weak (W or Z) bosons. The Higgs boson coupling to the fermions increases with fermion mass, so the most likely decay in the mass range they are interested, M(H0) ~ 100 GeV/c2, in is H → b$\bar{b}$. There are different possible final states depending on the decay of the associated vector boson: two jets plus lepton plus missing transverse energy (leptonic channel) and four jets (hadronic channel). In the former, the presence of a highly energetic, isolated lepton makes it relatively easy to reduce the background, while the latter has a larger production cross section times branching fraction, but it also has a huge amount of irreducible QCD background. CDF has searched for the Higgs boson in both final states, setting upper limits on the production cross sections.

Not only the top-quark condensate appears to be the natural significant source of dynamical electroweak symmetry breaking. Provided the seesaw scenario, the neutrinos can have their Dirac masses large enough so that their condensates contribute significantly to the electroweak scale as well. We address the question of a phenomenological feasibility of the top-quark and neutrino condensation conspiracy against the electroweak symmetry within the simplifying two-composite-Higgs-doublet model. Mandatory is to reproduce the masses of electroweak gauge bosons, the top-quark mass and the recently observed scalar mass of 125 GeV, and to satisfy the upper limits on absolute value of active neutrino masses. To accomplish that, the number of right-handed neutrinos participating on the seesaw mechanism turns out to be rather large, O(100–1000).

Dynamical electroweak symmetry breaking with a heavy fourth generation

Lectures on flavor physics presented at the 2012 CERN HEP Summer School. Content: 1) flavor physics within the Standard Model, 2) phenomenology of B andD decays, 3) flavor physics beyond the Standard Model. In the limit of unbroken electroweak symmetry none of the basic constituent of matter could have a non-vanishing mass. The problem of quark and lepton masses is therefore intimately related to the other big open question in particle physics: which is the mechanism behind the breaking of the electroweak symmetry, or which is the mechanism responsible for the non-vanishing masses of the weak force carriers (theW andZ bosons). Within the SM these two problems are both addressed by the Higgs mechanism: the masses of quarks and leptons, as well as the masses ofW andZ bosons, are the result of the interaction of these basic fields (both matter constituents and force carriers) with a new type of field, the Higgs scalar field, whose ground state breaks spontaneously the electroweak symmetry. The recent observation by the ATLAS and CMS experiments of a new state compatible with the properties of the Higgs boson (or the spin-0 excitation of the Higgs field) has significantly reinforced the evidences in favor of the Higgs mechanisms and the validity of the SM. However, we have also clear indications that this theory is not complete: the phenomenon of neutrino oscillations and the evidence for dark matter cannot be explained within the SM. The SM is also affected by a serious theoretical problem because of the instability of the Higgs sector under quantum corrections. We have not yet enough information to unambiguously determine how this theory should be extended; however, most realistic proposals point toward the existence of new degrees of freedom in the TeV range, possibly accessible at the high-pT experiments at the LHC. The description of quark and lepton masses in terms of the Higgs mechanism is particularly un- satisfactory since the corresponding interactions is not controlled by any symmetry principle, contrary to all other known interactions, resulting in a large number of free parameters. Beside determining quark masses, the interaction of the quarks with the Higgs is responsible for the peculiar pattern of mixing of

A radiative electroweak symmetry breaking in the minimal supergravity model is discussed, with assumptions of an 0(10 TeV) gravitino and the Nambu-Goldstone Higgs bosons. The electroweak symmetry is broken if a fine tuning of initial parameters for the renormalization group equations is made. This model predicts one light (::;; 0(10 GeV)) neutral Higgs boson. 23 Supergravity theories necessarily involve a massive spin 3/2 particle, the gravitino, and the mass of a gravitino is expected to be 0(100 GeV) in many models/} in order to relate the supersymmetry (SUSY) breaking to the electroweak gauge symmetry breaking. However, the garvitino with a mass between 0(1 ke V) and 0(10 TeV) is forbidden in the standard big bang cosmology/} since such a gravitino has a lifetime longer than the cosmic time at the primordial nucleosynthesis, and disastrously alter the abundances of light elements. Although some works in antici­ pation of solving this problem (the gravitino problem) by changing the cosmological scenario (inflation, for example) exist,3} a satisfactory solution is not obtained yet. If the gravitino is assumed to be sufficiently heavy, one may expect that all sparticles and Higgs bosons are very heavy and such a model is not phenome­ nologically appealing at all. However if an assumption that Higgs scalars are (pseudo-) Nambu-Goldstone bosons of a certain broken global symmetry4} is added, one might hope the existence of some light Higgs bosons. In this paper, we analyze a possibility of the electroweak symmetry breaking under the two assumptions, namely, the gravitino mass m3/2=0(10 TeV) and the Nambu-Goldstone hypothesis. We find that the electroweak symmetry can be broken successfully by renormalization effects if a fine tuning of some parameters is allowed, and there exists indeed one light Higgs scalar while other scalar paticles, namely, squarks, sleptons and other Higgs bosons are quite heavy. The model used in our calculation is the minimal supersymmetric 5U(3) X 5U(2) X U(l) gauge model with soft and explicit SUSY breaking terms which are obtained from a spontaneous local SUSY breaking in a hidden sector as usua1. 5

Models of dynamical electroweak symmetry breaking usually include new spin-1 resonances, whose couplings and masses have to satisfy electroweak precision tests. We propose to use dilepton searches to probe the underlying structure responsible for satisfying these. Using the invariant mass spectrum and charge asymmetry, we can determine the number, parity, and isospin of these resonances. We pick three models of strong/warped symmetry breaking, and show that each model produces specific features that reflect this underlying structure of electroweak symmetry breaking and cancellations.

I discuss the impact of the discovery of a Higgs-like state on composite dynamics starting by critically examining the reasons in favour of either an elementary or composite nature of this state. Accepting the standard model interpretation I re-address the standard model vacuum stability within a Weyl-consistent computation. I will carefully examine the fundamental reasons why what has been discovered might not be the standard model Higgs. Dynamical electroweak breaking naturally addresses a number of the fundamental issues unsolved by the standard model interpretation. However this paradigm has been challenged by the discovery of a not-so-heavy Higgslike state. I will therefore review the recent discovery1 that the standard model topinduced radiative corrections naturally reduce the intrinsic non-perturbative mass of the composite Higgs state towards the desired experimental value. Not only we have a natural and testable working framework but we have also suggested specific gauge theories that can realise, at the fundamental level, these minimal models of dynamical electroweak symmetry breaking. These strongly coupled gauge theories are now being heavily investigated via first principle lattice simulations with encouraging results. The new findings show that the recent naive claims made about new strong dynamics at the electroweak scale being disfavoured by the discovery of a not-so-heavy composite Higgs are unwarranted. I will then introduce the more speculative idea of extreme compositeness according to which not only the Higgs sector of the standard model is composite but also quarks and leptons, and provide a toy example in the form of gauge-gauge duality.

We investigate the dynamical mass generation resulted from interaction terms with four chiral superfields. The kind of interactions maybe considered a supersymmetric generalization of the four-fermion interactions of the classic Nambu--Jona-Lasinio model. A four-superfield interaction that contains a four-fermion interaction as one of its component terms has been the standard supersymmetrization of the NJL model for decades. Recently, we introduced a holomorphic variant with a dimension five interaction term instead. The latter is a main target of the present analysis. With the introduction of a new perspective on the superfield gap equation, we derive it for each one of the four-superfield interactions, using the supergraph technique. Through analyzing solutions to the gap equations, we illustrate the dynamical generation of superfield Dirac mass, including a supersymmetry breaking part. A dynamical symmetry breaking generally goes along with the dynamical mass generation, for which a bi-superfield condensate is responsible. The explicit illustration of dynamical symmetry breaking from the holomorphic dimension five interaction is reported for the first time. It has rich and novel features, which would be easily missed without the superfield approach developed here. We also discuss the nature of the bi-superfield condensate and its role of the effective Higgs superfield picture for both cases, illustrating their difference. Note that such a holomorphic quark superfield interaction term can successful account for the electroweak symmetry breaking with Higgs superfields as composites.

We propose a model of a confining dark sector, dark technicolor, that communicates with the Standard Model (SM) through the Higgs portal. In this model electroweak (EW) symmetry breaking and dark matter (DM) share a common origin, and the EW scale is generated dynamically. Our motivation to suggest this model is the absence of evidence for new physics from recent Large Hadron Collider (LHC) data. Although the conclusion is far from certain at this point, this lack of evidence may suggest that no mechanism exists at the EW scale to stabilize the Higgs mass against radiative corrections from ultraviolet (UV) physics. The usual reaction to this puzzling situation is to conclude that the stabilizing new physics is either hidden from us by accident, or that it appears at energies that are currently inaccessible, such that nature is indeed fine-tuned. In order to re-examine the arguments that have led to this dichotomy, we review the concept of naturalness in effective field theories, discussing in particular the role of quadratic divergences in relation to different energy scales. This leads us to suggest classical scale invariance as a guideline for model building, implying that explicit mass scales are absent in the underlying theory.