Strong Yukawa Research Articles

Electroweak one-loop contributions to top pair production in hadron colliders

We give a detailed presentation of the electroweak one-loop contributions to the production mechanisms of top quark pairs, q q → t t and gg → t t , for the energy range of future hadron colliders. The full gauge-invariant set of loop diagrams with Higgs, Z 0 and W ± bosons is considered including strong Yukawa couplings. The parton cross sections get sizeable modifications up to 40% and are sensitive to the Higgs boson mass and the Yukawa coupling. Results are also given for the observable hadronic cross section pp → t tX , where the large corrections at the parton level are substantially reduced to the order of a few percent. For the electroweak Standard Model the maximum contribution is about 7% for a light Higgs boson with M η = 60 GeV. For Higgs bosons with M η > 200 GeV, the electroweak contributions are typically (2–3)%.

Phase Structure of the Gauged Yukawa Model

Based on the ladder Schwinger-Dyson equation, we investigate phase struc- ture of the gauged Yukawa model possessing a global $SU(2)_L \times SU(2)_R$ symmetry and an unbroken (vector-like) gauge symmetry. We show that even when we tune the squared mass of the scalar boson in the Lagrangian to be positive, there still exists the dynamical chiral symmetry breaking due to fermion pair condensate (VEV of the composite scalar) triggered by the strong Yukawa coupling larger than a certain critical value. We find a "nontrivial ultraviolet fixed line" and "renormalized trajectories" in the three-dimensional coupling space of the Yukawa coupling, the gauge cou- pling and the "hopping parameter" of the elementary scalar field. Presence of the gauge coupling is crucial to existence of the fixed line. Implications of the result for the lattice calculation and the top quark condensate model are also discussed.

Quantum kinks: Solitons at strong coupling.

We examine solitons in theories with heavy fermions. These "quantum" solitons differ dramatically from semiclassical (perturbative) solitons because fermion loop effects are important when the Yukawa coupling is strong. We focus on kinks in a (1 + 1)-dimensional ${\ensuremath{\varphi}}^{4}$ theory coupled to fermions; a large-$N$ expansion is employed to treat the Yukawa coupling g nonperturbatively. A local expression for the fermion vacuum energy is derived using the WKB approximation for the Dirac eigenvalues. We find that fermion loop corrections increase the energy of the kink and (for large $g$) decrease its size. For large $g$, the energy of the quantum kink is proportional to $g$, and its size scales as $\frac{1}{g}$, unlike the classical kink; we argue that these features are generic to quantum solitons in theories with strong Yukawa couplings. We also discuss the possible instability of fermions to solitons.

Multicritical points in a lattice Yukawa model with the Wilson-Yukawa coupling

For a lattice regularized chiral-invariant SU (2) L×SU (2) R fermion-scalar model with a Yukawa coupling y and a Wilson-Yukawa coupling w, we investigate the phase structure and show in particular the existence of the multicritical line, in the strong Yukawa and/or Wilson-Yukawa coupling region, at which four phases meet. The result is in good agreement with the Monte Carlo simulation. This analytical result is derived from the effective scalar model obtained by integrating out the fermion field where the action is explicitly obtained from the hopping parameter expansion up to next-to-leading order. For estimates on the correlation function of the scalar field we apply the mean-field method.

Spontaneous symmetry breaking on the lattice generated by Yukawa interaction

We study by numerical simulation a lattice Yukawa model with naive fermions at intermediate values of the Yukawa coupling constant y when the nearest-neighbour coupling κ of the scalar field Φ is very weakly ferromagnetic ( κ ≈ 0) or even antiferromagnetic ( κ < 0) and the non-vanishing value of 〈Φ〉 is generated by the Yukawa interaction. The renormalized Yukawa coupling y R achieves here its maximal value and this y-region is thus of particular importance for lattice investigations of strong Yukawa interaction. However, here the scalar field propagators have a very complex structure caused by fermion loop corrections and by the proximity of phases with antiferromagnetic properties. We develop methods for analyzing these propagators and for extracting the physical observables. We find that going into the negative κ region, the scalar field renormalization constant becomes small and y R does not see, to exceed the unitarity bound, making the existence of a non-trivial fixed point in the investigated Yukawa model quite unlikely.

Phase Diagram of Strongly Coupled Lattice Yukawa Theories

Using weak and strong Yukawa coupling expansions combined with the mean field theory, we determine the phase structure of Yukawa models with Z(2), O(2), O(4) scalars. We have taken into account all the terms in the relevant expansions up to eighth order. In the leading order, all the Yukawa models have the four phases and do not possess the ferrimagnetic (FI) phase. This feature persists for Z(2) and O(2) Yukawa models to all orders. In the O(4) Yukawa model, on the other hand, the FI phase appears in the next to leading order and all higher orders, and two symmetric phases are completely separated by the FI phase

Phase Diagram of Strongly Coupled Lattice Yukawa Theories

Using weak and strong Yukawa coupling expansions combined with the mean field theory, we determine the phase structure of Yukawa models with Z(2), O(2), O(4) scalars. We have taken into account all the terms in the relevant expansions up to eighth order. In the leading order, all the Yukawa models have the four phases and do not possess the ferrimagnetic (FI) phase. This feature persists for Z(2) and O(2) Yukawa models to all orders. In the O(4) Yukawa model, on the other hand, the FI phase appears in the next to leading order and all higher orders, and two symmetric phases are completely separated by the FI phase. The result holds irrespective of the choice of fermions; naive or staggered.

Yukawa models with mirror fermions

Scalar-fermion models with mirror pairs of fermion fields on the lattice are discussed. Numerical simulations have been performed both for models with U (1) L ⊗ U (1) R and SU (2) L ⊗ SU (2) R symmetry. For the model with U (1) L ⊗ U (1) R symmetry the phase diagram has been investigated and various phases have been identified. In both the U (1) and the SU (2) case the models appear to allow for strong Yukawa couplings. Results on lower and upper bounds for the Higgs-boson mass and the effect of heavy fermions on these bounds are obtained. In the U (1) L ⊗ U (1) R model the complex fermion determinant has been studied in view of simulations with an odd number of fermion generations.

Phase structure of strongly coupled lattice Yukawa theories

Abstract Using weak and strong Yukawa coupling expansions combined with the mean field theory, we determine the phase structure of Yukawa models with Z (2), U (1), O (4) scalars. We have taken into account all the terms in the relevant expansions up to eighth order. In the leading order, all the Yukawa models have four phases and do not possess the ferrimagnetic (FI) phase. This feature persists for Z (2) and U (1) Yukawa models to all orders. In the O (4) Yukawa model, on the other hand, the FI phase appears in the next to leading order and all higher orders, and two symmetric phases are completely separated by the FI phase. This result suggests that the existence of the FI phase is not a lattice artifact.

Bound states in scalar-fermion Yukawa lattice theory

The U(1) scalar-fermion lattice theory with a strong Yukawa coupling is studied in the mean field approximation. It is shown that for large Yukawa coupling ( Y 2> 1 2 d ) the four-fermion amplitude has poles in some channels which correspond to bound states of a fermion-(anti)fermion pair that are neutral with respect to the U(1) charge and can carry a fermion number equal to 0 or ±2.

A U(1) L ⊗ U(1) R symmetric Yukawa model in the phase with spontaneously broken symmetry

The lattice regularized U(1) L ⊗ U(1) R symmetric scalar-fermion model with a mirror pair of fermion fields is investigated in the phase with spontaneously broken symmetry. The reflection positivity condition, ensuring unitarity in Minkowski space, is proven in this lattice formulation in a wide range of bare parameters. Numerical Monte Carlo calculations with dynamical fermions are performed on 4 3 × 8, 4 3 × 16 and 6 3 × 16 lattices at moderately strong bare Yukawa couplings and at very small and infinite bare quartic scalar coupling. It is shown that not only the lattice fermion doublers but also the mirror fermion can be made heavy, and therefore the light fermion spectrum is “chiral” as in the standard model. The “vacuum stability” bound on the Higgs-boson mass is discussed in lattice perturbation theory and non-perturbatively. It implies that for heavy mirror fermions the Higgs-boson mass has to be close to the non-perturbative upper limit.

Yukawa models with staggered fermions in a expansion at strong Yukawa coupling

Abstract We apply a systematic 1 d expansion to Yukawa models with staggered fermions and radially frozen Higgs fields with a global G L × G R symmetry. We compute the critical line and the two-point functions to the first subleading order in 1 d . The expansion is systematic for Yukawa coupling of order d and thus applies to the strong Yukawa coupling region. There the features found in numerical simulations, most notably the rise of the fermion mass as the critical line is approached from the spontaneously broken phase, are reproduced.

Results from a strong-coupling expansion for a lattice Yukawa model with a real scalar field.

Results are presented from a strong bare Yukawa coupling expansion for a lattice Yukawa theory with a real scalar field. It is found the effective action involves competing interactions, consistent with the existence of a ferrimagnetic phase at intermediate Yukawa coupling $y$. We also give evidence that the (bosonic) continuum theory defined at the ferromagnetic-paramagnetic phase boundary at large $y$ is free.

Unquenched investigation of fermion masses in a chiral fermion theory on the lattice

Using dynamical fermions we study the decoupling of the fermion doublers of chiral lattice fermions in the broken symmetry phase of a scalar-fermion model. The model uses a chiral invariant Wilson term, called a Wilson-Yukawa term with coupling strength w, in addition to the usual Yukawa coupling y. We find qualitative agreement with our results obtained before in the quenched approximation. First in the w = 0 case we establish a strong Yukawa coupling region. Then for relatively large but fixed w we confirm that the fermion doublers can be easily decoupled by giving them masses of the order of the cutoff as the symmetry restoring transition is approached.

Non-perturbative lattice study of the electroweak model with dynamical fermions

Recent non-perturbative lattice studies of the Electroweak Model with dynamical fermions are reviewed. Important non-perturbative issues are introduced and the potential of lattice investigations is emphasized. Implications of unitarity bounds on electroweak S-matrix elements and early renormalization group arguments for mass bounds are presented for comparison with new lattice work on related questions. The Higgs sector with strong Yukawa coupling to heavy fermions will be discussed in two simple models. The effects of dynamical fermion loops on the SU(2) W phase diagram of the Electroweak Model will be reviewed. The lattice approach to the strongly coupled Standard Model will be discussed as a first warm-up study to investigate composite models on supercomputers.

Non-perturbative Yukawa coupling in scalar-fermion systems

We summarize our results of the 1-component real and complex scalar-fermion models. We show that the perturbative predictions are not valid for strong Yukawa coupling and investigate the possibility of a non-trivial tricritical fixed point.

New heavy-quark physics in the strongly Yukawa-coupled standard model.

We show that for strong enough Yukawa coupling the electroweak standard-model quark finds it energetically advantageous to transform itself into a bound state in a Skyrme background. This picture implies a maximum mass for the quark and predicts the existence of an excited spin-(3/2 quark. Moreover, two-quark, color-antitriplet, and three-quark, color-singlet, bound states, which can be very deeply bound, are shown to occur. The spectrum is studied in the semiclassical approximation. On including the one-loop Casimir effect in the exponential background approximation one loses the present picture for the single-quark case. The leading decays of the excited states are estimated, which should provide clear experimental signatures of this scheme. For the quarkonium, surprisingly, the attractive potential is found to be dominated by QCD around the Bohr radius.

Strongly coupled quarks in the standard model.

For sufficiently strong Yukawa couplings the standard model goes over to the linear \ensuremath{\sigma} model. We point out that the associated heavy quarks may behave like strongly interacting low-energy u and d quarks so one cannot argue that very-heavy-quark systems will provide an easy test of QCD. An upper-quark-mass bound of about 1.5 TeV is found. (This should also apply to techniquarks.) Experimental confirmation of the scheme might come from the observation of very tightly bound baryons made from three heavy quarks.

A theory of elementary couplings III

We further develop a recent method, based on compensation between Feynman diagrams, for obtaining a priori information on the spectrum and interactions (weak and strong) of the elementary particles. The theory is based on hadron octets or nonets of spin zero and one half, together with vector bosons including photons. It has the necessary ingredients of a realistic broken-symmetry gauge theory, the compensation method giving the rules for breaking the symmetry. In this article, the scope of the compensation principle is greatly enlarged, thanks to the inclusion of scalar mesons. The main point of this paper is to show in detail how the strong (Yukawa) couplings may be completely determined by the compensation relations. The numerical results are worked out in the limit of exact SU(3) for the weak couplings. The eta and charged kaon lifetimes can now be computed, and come out in fair agreement with the data. The strong ΣΛπ coupling is no longer zero, as in parts I and II, but is still smaller than the current experimental estimates. The accurate mass formula N −1+ Ξ −1+ Σ −1 = 6( N+ Ξ) −1 is rederived in a new framework, and appears to be connected with a simple SU(3)-breaking weak or superweak interaction.

Potential Theory Calculations by the Quasiparticle Method

The quasiparticle method is used to find binding energies, scattering lengths, and cross sections for one particle in a strong Yukawa, Hulth\'en, or exponential potential. The results are excellent in the lowest approximation.