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Register a new userTesting a non-perturbative mechanism for elementary fermion mass generation: lattice setup
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In this contribution we lay down a lattice setup that allows for the non-perturbative study of a field theoretical model where a SU(2) fermion doublet, subjected to non-Abelian gauge interactions, is also coupled to a complex scalar field doublet via a Yukawa and an irrelevant Wilson-like term. Using naive fermions in quenched approximation and based on the renormalized Ward identities induced by purely fermionic chiral transformations, lattice observables are discussed that enable: a) in the Wigner phase, the determinations of the critical Yukawa coupling value where the purely fermionic chiral transformation become a symmetry up to lattice artifacts; b) in the Nambu-Goldstone phase of the resulting critical theory, a stringent test of the actual generation of a fermion mass term of non-perturbative origin. A soft twisted fermion mass term is introduced to circumvent the problem of exceptional configurations, and observables are then calculated in the limit of vanishing twisted mass.
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Based on a recent proposal according to which elementary particle masses could be generated by a non-perturbative dynamical phenomenon, alternative to the Higgs mechanism, we carry out lattice simulations of a model where a non-abelian strongly interacting fermion doublet is also coupled to a doublet of complex scalar fields via a Yukawa and an irrelevant Wilson-like term. In this pioneering study we use naive fermions and work in the quenched approximation. We present preliminary numerical results both in the Wigner and in the Nambu-Goldstone phase, focusing on the observables relevant to check the occurrence of the conjectured dynamical fermion mass generation effect in the continuum limit of the critical theory in its spontaneously broken phase.
We consider a field theoretical model where a SU(2) fermion doublet, subjected to non-Abelian gauge interactions, is also coupled to a complex scalar field doublet via a Yukawa and an irrelevant Wilson-like term. Despite the presence of these two chiral breaking operators in the Lagrangian, an exact symmetry acting on fermions and scalars prevents perturbative mass corrections. In the phase where fermions are massless (Wigner phase) the Yukawa coupling can be tuned to a critical value at which chiral transformations acting on fermions only become a symmetry of the theory (up to cutoff effects). In the Nambu-Goldstone phase of the critical theory a fermion mass term of dynamical origin is expected to arise in the Ward identities of the purely fermionic chiral transformations. Such a non-perturbative mechanism of dynamical mass generation can provide a natural (`a la t Hooft) alternative to the Higgs mechanism adopted in the Standard Model. Here we lay down the theoretical framework necessary to demonstrate the existence of this mechanism by means of lattice simulations.
In this talk we present a numerical lattice study of an SU(3) gauge model where an SU(2) doublet of non-Abelian strongly interacting fermions is coupled to a complex scalar field doublet via a Yukawa and a Wilson-like term. The model enjoys an exact symmetry, acting on all fields, which prevents UV power divergent fermion mass corrections, despite the presence of these two chiral breaking operators in the Lagrangian. In the phase where the scalar potential is non-degenerate and fermions are massless, the bare Yukawa coupling can be set at a critical value at which chiral fermion transformations become symmetries of the theory. Numerical simulations in the Nambu-Goldstone phase of the critical theory, for which the renormalized Yukawa coupling by construction vanishes, give evidence for non-perturbative generation of a UV finite fermion mass term in the effective action.
Recent developments in non-perturbative renormalization for lattice QCD are reviewed with a particular emphasis on RI/MOM scheme and its variants, RI/SMOM schemes. Summary of recent developments in Schroedinger functional scheme, as well as the summary of related topics are presented. Comparison of strong coupling constant and the strange quark mass from various methods are made.
We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $Delta F = 1$ and $Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with quenched Wilson quarks, we compute non-perturbatively the renormalization group running of these operators in the continuum limit in a large range of renormalization scales. Continuum limit extrapolations are well controlled thanks to the implementation of two fermionic actions (Wilson and Clover). The ratio of the renormalization group invariant operator to its renormalized counterpart at a low energy scale, as well as the renormalization constant at this scale, is obtained for all schemes.
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