pseudo-Goldstone Boson Masses Research Articles

Discrete Goldstone bosons

Exact discrete symmetries, if non-linearly realized, can reduce the ultraviolet sensitivity of a given theory. The scalars stemming from spontaneous symmetry breaking are massive without breaking the discrete symmetry, and those masses are protected from divergent quadratic corrections. This is in contrast to non-linearly realized continuous symmetries, for which the masses of pseudo-Goldstone bosons require an explicit breaking mechanism. The symmetry-protected masses and potentials of those discrete Goldstone bosons offer promising physics avenues, both theoretically and in view of the blooming experimental search for ALPs. We develop this theoretical setup using invariant theory and focusing on the maximally natural minima of the potential. For these, we show that typically a subgroup of the ultraviolet discrete symmetry remains explicit in the spectrum, i.e. realized "\`a la Wigner"; this subgroup can be either abelian or non-abelian. This suggests tell-tale experimental signals for those minima: at least two (three) degenerate scalars produced simultaneously if abelian (non-abelian), while the specific ratios of multi-scalar amplitudes provide a hint of the full ultraviolet discrete symmetry. Examples of exact ultraviolet $A_4$ and $A_5$ symmetries are explored in substantial detail.

Limit on Higgs boson trilinear self-coupling in coupled technicolor models

The trilinear self-coupling of the Higgs boson, in a theory in which this boson is composite, is compared to the experimental bound of this quantity obtained by the CMS experiment. In the case of a model where technicolor (TC) is coupled to QCD, we find that the experimental result already constrains the dynamics of the theory, which is represented by an expression of the technifermion self-energy typical of technicolor coupled models, and function of the dynamically generated technifermion mass and two other parameters that describe the technifermion dynamical mass momentum dependence. The limits imposed on this dynamics allow us to make a simple determination of pseudo-Goldstone boson masses that appear in these theories, indicating that these bosons may be expected to be quite massive.

Fermion mass splitting in the technicolor coupled scenario

We discuss fermion mass generation in unified models where QCD and technicolor (or any two strongly interacting theories) have their Schwinger–Dyson equations coupled. In this case the technicolor (TC) and QCD self-energies are modified in comparison with the behavior observed in the isolated theories. In these models the pseudo-Goldstone boson masses are much higher than the ones obtained in different contexts, and phenomenological signals, except from a light scalar composite boson, will be quite difficult to be observed at present collider energies. The most noticeable fact of these models is how the mass splitting between the different ordinary fermions is generated. We discuss how a necessary horizontal (or family) symmetry can be implemented in order to generate the mass splitting between fermions of different generations; how the fermionic mass spectrum may be modified due to GUT interactions, as well as how the mass splitting within the same fermionic generation are generated due to electroweak and GUT interactions.

Technicolor models with coupled systems of Schwinger-Dyson equations

When Technicolor (TC), QCD, Extended Technicolor (ETC) and other interactions become coupled through their different Schwinger-Dyson equations, the solution of these equations are modified in comparison with the ones of the isolated equations. The change in the self-energies is similar to the one obtained in the presence of four-fermion interactions, but without their \textsl{ad hoc} inclusion in the theory. In this case TC and QCD self-energies decrease logarithmically with the momenta, what allow us to build models where ETC boson masses can be pushed to very high energies, and their effects will barely appear at present energies. Here we present a detailed discussion of this class of TC models. We first review the Schwinger-Dyson TC and QCD coupled equations, explaining the origin of the asymptotic self-energies. We develop the basic ideas of how viable TC models may be built along this line, where ordinary lepton masses appear naturally lighter than quark masses. One specific unified TC model associated with a necessary horizontal (or family) symmetry is described. The values of scalar and pseudo-Goldstone boson masses in this class of models are also discussed, as well as the value of the trilinear scalar coupling, and the consistency of the models with the experimental constraints.

Fate of global symmetries in the Universe: QCD axion, quintessential axion and trans-Planckian inflaton decay constant

Pseudoscalars appearing in particle physics are reviewed systematically. From the fundamental point of view at an ultraviolet completed theory, they can be light if they are realized as pseudo-Goldstone bosons of some spontaneously broken global symmetries. The spontaneous breaking scale is parametrized by the decay constant [Formula: see text]. The global symmetry is defined by the lowest order terms allowed in the effective theory consistent with the gauge symmetry in question. Since any global symmetry is known to be broken at least by quantum gravitational effects, all pseudoscalars should be massive. The mass scale is determined by [Formula: see text] and the explicit breaking terms [Formula: see text] in the effective potential and also anomaly terms [Formula: see text] for some non-Abelian gauge groups [Formula: see text]. The well-known example by non-Abelian gauge group breaking is the potential for the “invisible” QCD axion, via the Peccei–Quinn symmetry, which constitutes a major part of this review. Even if there is no breaking terms from gauge anomalies, there can be explicit breaking terms [Formula: see text] in the potential in which case the leading term suppressed by [Formula: see text] determines the pseudoscalar mass scale. If the breaking term is extremely small and the decay constant is trans-Planckian, the corresponding pseudoscalar can be a candidate for a “quintessential axion.” In general, [Formula: see text] is considered to be smaller than [Formula: see text], and hence the pseudo-Goldstone boson mass scales are considered to be smaller than the decay constants. In such a case, the potential of the pseudo-Goldstone boson at the grand unification scale is sufficiently flat near the top of the potential that it can be a good candidate for an inflationary model, which is known as “natural inflation.” We review all these ideas in the bosonic collective motion framework.

Dark Energy, QCD Axion, and Trans-Planckian-Inflaton Decay Constant

Pseudoscalars appear frequently in particle spectra. They can be light if they appear as pseudo-Goldstone bosons from some spontaneously broken global symmetries with the decay constant f. Since any global symmetry is broken at least by quantum gravitational effects, all pseudoscalars are massive. The mass scale of a pseudoscalar is determined by the spontaneous symmetry breaking scale f of the corresponding global symmetry and the explicit breaking terms in the effective potential. The explicit breaking terms can arise from anomaly terms with some non-Abelian gauge groups among which the best-known example is the potential of the QCD axion. Even if there is no breaking terms from gauge anomalies, there can be explicit breaking terms in the potential in which case the leading term suppressed by f determines the pseudoscalar mass scale. If the breaking term is extremely small and the decay constant is trans-Planckian, the corresponding pseudoscalar can be a candidate for a quintessential axion. In the other extreme that the breaking scales are large, still the pseudo-Goldstone boson mass scales are in general smaller than the decay constants. In such a case, still the potential of the pseudo-Goldstone boson at the grand unification scale is sufficiently flat near the top of the potential that it can be a good candidate for an inflationary model. We review these ideas in the bosonic collective motion framework.

The vacuum component of the Universe (cosmological constant) should evolve

The evolution of the vacuum component of the Universe is studied in both the quantum and classical regimes. Our Universe has emerged as a result of a tunneling process, beginning with an oscillating mode and passing on to a Friedmann mode, and it very probably had a high symmetry for the Planck parameters. In the first fractions of a second (the quantum regime), as it cooled, the vacuum component of the Universe lost its high degree of symmetry due to phase transitions; i.e., its positive energy density was subject to negative contributions from quantum field condensates (by 78 orders of magnitude). After the last (quark-hadron) phase transition, the vacuum energy “froze.” At this time (10−6 s), the vacuum energy density can be calculated using the formula of Zel’dovich and substituting the mean values of the pseudo-Goldstone boson (π-mesons) masses characterizing the chromodynamic vacuum. Chiral symmetrywas lost at that time. The dynamics of the equilibrium vacuum after its “hardening” is considered using the holographic principle. During the next 4 × 1017 s (the classical regime), the vacuum component of the Universe was reduced by 45 orders of magnitude due to the creation of new quantum states during its expansion. It is possible to solve the cosmological-constant problem using the holographic principle, since the 123 problematic orders of magnitude disappear in usual physical processes. The vacuum energy density is also calculated in the classical regime to a redshift of 1011 using a “cosmological calculator.”

Taste non-Goldstone, flavor-charged pseudo-Goldstone boson masses in staggered chiral perturbation theory

We calculate the masses of taste non-Goldstone pions and kaons in staggered chiral perturbation theory through next-to-leading order in the standard power counting. The results can be used to quantitatively understand taste violations in existing lattice data generated with staggered fermions and to extract the $u$, $d$, and $s$ quark masses and Gasser-Leutwyler parameters from the experimentally observed spectrum. The expressions for the non-Goldstone masses contain low-energy couplings unique to the non-Goldstone sector. With two exceptions these enter as coefficients of analytic terms; all the new couplings can be fixed by performing spectrum calculations. We report one-loop results for the quenched case and the fully dynamical and partially quenched 1+1+1 and 2+1 flavor cases in the chiral SU(3) and SU(2) theories.

Chiral vacuum alignment and spontaneousCPviolation by four-Fermi operators

In models where there is a global chiral symmetry which spontaneously breaks to its vectorial subgroup, the introduction of an explicit symmetry breaking perturbation will define the true vacuum of the theory. This true vacuum is found via the minimization of the expectation value of the perturbing Hamiltonian between different vacua as prescribed by Dashen. The procedure of finding the correct vacuum of the theory may result in the spontaneous breaking of CP symmetry even if one initially demands CP invariance on the perturbation. In this work we study, in detail, models where the perturbation is provided by four-Fermi operators. We present the exact treatment for models with two fermion flavors and study the three flavor case in depth numerically. We show that after the Dashen procedure is applied the solutions for the true vacuum fall in three classes with different CP breaking patterns. Critical transitions are possible between these classes as one varies the parameters of the perturbation. We rigorously show that at these transitions a pseudo-Goldstone boson mass vanishes. We also advocate, and substantiate with numerical statistical analysis for various types of models, that if one imposes CP invariance on the perturbation before solving the vacuum alignment, themore » resulting vacuum structure will have a sizable probability for a light pseudo-Goldstone boson mass. That is a statistical variant of Peccei-Quinn mechanism can be speculated to operate.« less

Staggered chiral perturbation theory at next-to-leading order

We study taste and Euclidean rotational symmetry violation for staggered fermions at nonzero lattice spacing using staggered chiral perturbation theory. We extend the staggered chiral Lagrangian to $\mathcal{O}({a}^{2}{p}^{2})$, $\mathcal{O}({a}^{4})$, and $\mathcal{O}({a}^{2}m)$, the orders necessary for a full next-to-leading order calculation of pseudo-Goldstone boson masses and decay constants including analytic terms. We then calculate a number of $SO(4)$ taste-breaking quantities, which involve only a small subset of these next-to-leading order operators. We predict relationships between $SO(4)$ taste-breaking splittings in masses, pseudoscalar decay constants, and dispersion relations. We also find predictions for a few quantities that are not $SO(4)$ breaking. All these results hold also for theories in which the fourth root of the fermionic determinant is taken to reduce the number of quark tastes; testing them will therefore provide evidence for or against the validity of this trick.

Next-to-Leading-Order Staggered Chiral Perturbation Theory

We have extended staggered chiral perturbation theory (S χ PT) to O ( a 2 p 2 ) , O ( a 4 ) , and O ( a 2 m ) , the orders necessary for a full next-to-leading order (NLO) calculation of pseudo-Goldstone boson (PGB) masses and decay constants including taste-symmetry violations. We present predictions relating S O ( 4 ) taste-breaking splittings in masses, pseudoscalar decay constants, and dispersion relations. These can be used to test the D e t 4 trick.

Phenomenological constraints on the Jaffe-Wilczek model of pentaquarks

A model recently introduced by Jaffe and Wilczek based on the quarks being dynamically bound into diquarks has been used to predict that the recently observed exotic baryons (pentaquarks) fall into a nearly ideally mixed combination of the 8 and $\overline{10}$ representations of $\mathrm{S}\mathrm{U}(3)$ flavor. The model predicts two states with nucleon quantum numbers which have tentatively been identified with the ${\mathrm{N}}^{*}(1440)$ and the ${\mathrm{N}}^{*}(1710)$. This paper examines the viability of this model by focusing on the decay width of the nucleon members of the multiplet. An inequality relating the partial widths of these nucleon states in the $\ensuremath{\pi}+\mathrm{\text{nucleon}}$ channel to the width of the ${\ensuremath{\theta}}^{+}$ is derived for this model assuming ideal mixing and that the only significant exact $\mathrm{S}\mathrm{U}(3)$ symmetry violations are the result of ideal mixing, threshold effects, and the masses of pseudo-Goldstone bosons. This inequality is badly violated if the states in the multiplet are the ${\mathrm{N}}^{*}(1440)$ and the ${\mathrm{N}}^{*}(1710)$ and if the recent bounds extracted for the ${\ensuremath{\theta}}^{+}$ width are reliable. Thus, the model appears to require a scenario with the existence of at least one presently unknown resonance with nucleon quantum numbers.

Lattice QCD data versus chiral perturbation theory: the case of Mπ

I present a selection of recent lattice data by major collaborations for the pseudo-Goldstone boson masses in full ( N f = 2) QCD, where the valence quarks are chosen exactly degenerate with the sea quarks. At least the more chiral points should be consistent with Chiral Perturbation Theory for the latter to be useful in extrapolating to physical masses. Perspectives to reliably determine NLO Gasser-Leutwyler coefficients are discussed.

Model-dependent axion as quintessence with almost massless hidden sector quarks

A pseudo-Goldstone boson for {\it quintessence} is known to require the decay constant $F_q\sim M_P$ and the height of the potential $(0.003 {\rm eV})^4$, and hence the pseudo-Goldstone boson mass of order $10^{-33}$ eV. The model-dependent axion in some superstring models is suggested as a good candidate for the quintessence. We realize this idea with a hidden-sector gauge group $SU(3)_H\times U(1)_H$. The hidden-sector instanton contribution to the quintessence potential is suppressed by the almost massless hidden-sector quarks. The model-independent axion is the QCD axion required for the strong CP solution.

Semilepton decay of B mesons into in a technicolour model

The O corrections to the inclusive semitauonic B decay are calculated in a one-generation technicolour model. Comparing the theoretical prediction with the recent experimental results, we present a stronger constraint on the masses of the charged colour-singlet pseudo-Goldstone bosons, at 95% confidence level.

PGB corrections to top-quark production at the Fermilab Tevatron in technicolor models.

We calculate the pseudo Goldstone boson (PGB) corrections to {ital q{bar q}}{r_arrow}{ital t{bar t}} of order {alpha}{ital m}{sup 2}{sub {ital t}} at the Fermilab Tevatron in the framework of the one-generation technicolor model (OGTC) and a minimal technicolor model (MTC) with a massless weak doublet recently presented by Carone and Georgi. The PGB correction can decrease the total {ital t{bar t}} production cross section by as much as {minus}38{percent} for a top-quark mass of 176 GeV and color octet PGB mass of 150 GeV in the OGTC model, which is potentially observable at the Tevatron. However, the results show that the process is unmeasurably small in the MTC model. {copyright} {ital 1996 The American Physical Society.}

Remarks on flavor-changing neutral currents in walking technicolor.

We point out that since the running coupling $\overline{\ensuremath{\alpha}}({q}^{2})$ in walking technicolor (WTC) can be rather strong at the extended technicolor (ETC) scale ${q}^{2}\ensuremath{\sim}{\ensuremath{\Lambda}}_{\mathrm{ETC}}^{2}$, the standard consideration of flavor-changing neutral currents (FCNCs) in WTC based on the lowest order in perturbation theory in $\ensuremath{\alpha}$ is not fully conclusive. We reanalyze this problem and conclude that FCNCs can indeed be suppressed in WTC if ETC interactions are chosen in an appropriate way. The crucial point is that the factor of enhancement of the masses of pseudo Goldstone bosons in WTC is just that which is sufficient to suppress FCNCs. FCNCs in the so-called strong ETC are also briefly discussed.

Enhanced mass spectrum of pseudo-Goldstone bosons?

In an attempt to clarify recent claims by Lusignoli, Masiero and Roncadelli, we study possibilities of enhanced pseudo-Goldstone boson masses through three examples in which a global symmetry is intrinsically as well as spontaneously broken: lepton number in a variant of the triplet Majoron model, Peccei-Quinn symmetry in low-energy supersymmetric standard models or two Higgs doublet standard models and chiral symmetries in extended walking technicolor models. We obviate the claims by Lusignoli et al. by pointing our that the size of intrinsic global symmetry breaking depends on hierarchies of the vacuum expectation values. The notions of approximate global symmetry and pseudo-Goldstone bosons hold only when the hierarchy is not too large.

On spontaneous versus explicit breaking of continuous global symmetries

Pseudo-Goldstone boson masses are considered in models with very slightly explicitly broken continuous global symmetries. These masses are compared with the size of the explicit symmetry breaking and with the masses of other scalars. The lepton number violation in some extensions of the standard model is discussed as an example.

Mixing in Dynamically Broken Theory11This work was supported by the U.S. Department of Energy, Contract No. W-7405-Eng-82, Office of Energy Research (KA-01-01), Division of High Energy and Nuclear Physics. ZHU was also partially supported by the National Science Foundation of China and CCAST (World Laboratory).

The mixing is investigated in a dynamically broken electroweak theory such as the minimal technicolor theory with a monophagic coupling of quarks and pseudo-Goldstone bosons. The contrbutions of the technicolor pseudo-Goldstone bosons, enhanced by QCD color factors, dominate the process for a wide range of parameters. If the top-down quark Kobayashi-Maskawa matrix element is not near the minimal allowed value, the pseudo-Goldstone bosons plus W boson can adequately account for the observed mixing large of the pseudo-Goldstone boson and top quark mass.