One-loop renormalization of fermionic currents with the overlap-Dirac operator

Alexandrou, Constantia; Follana, E.; Panagopoulos, H.; Vicari, Ettore

doi:10.1016/s0550-3213(00)00190-5

Cited by 56 publications

(72 citation statements)

References 49 publications

(72 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This conclusion is incorrect, essentially because the instanton gas approximation is not valid due to infrared divergences. The large-N behavior of the coefficients b 2n of the expansion (3.5) can then be easily derived: 16) where C ∞ is the large-N limit of the ratio C = χ/σ 2 . Comparing with Eq.…”

Section: θ Dependence In the Large-n Limitmentioning

confidence: 99%

θ dependence of SU(N) gauge theories in the presence of a topological term

2009

View full text Add to dashboard Cite

We review results concerning the θ dependence of 4D SU (N ) gauge theories and QCD, where θ is the coefficient of the CP-violating topological term in the Lagrangian. In particular, we discuss θ dependence in the large-N limit.Most results have been obtained within the lattice formulation of the theory via numerical simulations. We review results at zero and finite temperature. We show that the results support the scenario obtained by general large-N scaling arguments, and in particular the Witten-Veneziano mechanism to explain the U (1) A problem. We also compare with results obtained by other approaches, especially in the large-N limit, where the issue has been also addressed using, for example, the AdS/CFT correspondence.We discuss issues related to theta dependence in full QCD: the neutron electric dipole moment, the dependence of the topological susceptibility on the quark masses, the U (1) A symmetry breaking at finite temperature.We also review results in the 2D CP N −1 model, which is an interesting theoretical laboratory to study issues related to topology.Finally, we discuss the main features of the two-point correlation function of the topological charge density.

show abstract

Section: θ Dependence In the Large-n Limitmentioning

confidence: 99%

θ dependence of SU(N) gauge theories in the presence of a topological term

2009

View full text Add to dashboard Cite

show abstract

“…Taking into account QCD radiative corrections, the coefficients get modified, but H w can still be written as [27,12] …”

Section: Weak Operators In the Su(3) Chiral Theorymentioning

confidence: 99%

Correlators of left charges and weak operators in finite volume chiral perturbation theory

Hernández

Laine

2003

J. High Energy Phys.

View full text Add to dashboard Cite

We compute the two-point correlator between left-handed flavour charges, and the three-point correlator between two left-handed charges and one strangeness violating ∆I = 3/2 weak operator, at next-to-leading order in finite volume SU(3) L ×SU(3) R chiral perturbation theory, in the so-called ǫ-regime. Matching these results with the corresponding lattice measurements would in principle allow to extract the pion decay constant F , and the effective chiral theory parameter g 27 , which determines the ∆I = 3/2 amplitude of the weak decays K → ππ as well as the kaon mixing parameterB K in the chiral limit. We repeat the calculations in the replica formulation of quenched chiral perturbation theory, finding only mild modifications. In particular, a properly chosen ratio of the three-point and two-point functions is shown to be identical in the full and quenched theories at this order.

show abstract

“…But in fact, already in lattice perturbation theory, the tendency is that the one-loop corrections to Z and Z V are large because of a very large tadpole contribution to the self-energy [37,38] (while g 1 remains close to 1 as we find nonpertubatively). The net effect is already large at 6:0, for the usual s 0:4: Z V 1:247, and still larger for our s 0: Z V 1:444; we use Table 1 of Ref.…”

Section: Comparison With Lattice Perturbation Theorymentioning

confidence: 71%

“…[37] for the analytical expressions (the definition of Z is different, but by a negligible amount); the numbers are quoted assuming a boosted perturbation theory (BPT) boosted coupling with g 2 BPT 1:68 (see Ref. [38] under Eq. (44)).…”

Section: Comparison With Lattice Perturbation Theorymentioning

confidence: 99%

Artifacts and⟨A2⟩power corrections: ReexaminingZψ(p2)
Boucaud
¹
,
Soto
²
,
Leroy
³

et al. 2006
Phys. Rev. D
39
0
19
0
View full text Add to dashboard Cite

The next-to-leading-order (NLO) term in the operator product expansion (OPE) of the quark propagator vector part Z and the vertex function g 1 of the vector current in the Landau gauge should be dominated by the same hA 2 i condensate as in the gluon propagator. On the other hand, the perturbative part has been calculated to a very high precision thanks to Chetyrkin and collaborators. We test this on the lattice, with both clover and overlap fermion actions at 6:0, 6.4, 6.6, 6.8. Elucidation of discretization artifacts appears to be absolutely crucial. First hypercubic artifacts are eliminated by a powerful method, which gives results notably different from the standard democratic method. Then, the presence of unexpected, very large, nonperturbative, O4 symmetric discretization artifacts, increasing towards small momenta, is demonstrated by considering Z MOM V , which should be constant in the absence of such artifacts. They impede in general the analysis of OPE. However, in two special cases with overlap action -(1) for Z ; (2) for g 1 , but only at large p 2 -we are able to identify the hA 2 i condensate; it agrees with the one resulting from gluonic Green functions. We conclude that the OPE analysis of quark and gluon Green function has reached a quite consistent status, and that the power corrections have been correctly identified. A practical consequence of the whole analysis is that the renormalization constant Z ( Z ÿ1 2 of the momentum-subtraction (MOM) scheme) may differ sizably from the one given by democratic selection methods. More generally, the values of the renormalization constants may be seriously affected by the differences in the treatment of the various types of artifacts, and by the subtraction of power corrections.

show abstract

One-loop renormalization of fermionic currents with the overlap-Dirac operator

Cited by 56 publications

References 49 publications

θ dependence of SU(N) gauge theories in the presence of a topological term

θ dependence of SU(N) gauge theories in the presence of a topological term

Correlators of left charges and weak operators in finite volume chiral perturbation theory

Artifacts and⟨A2⟩power corrections: ReexaminingZψ(p2)
Boucaud
¹
,
Soto
²
,
Leroy
³

et al. 2006
Phys. Rev. D
39
0
19
0
View full text Add to dashboard Cite

Contact Info

Product

Resources

About

One-loop renormalization of fermionic currents with the overlap-Dirac operator

Cited by 56 publications

References 49 publications

θ dependence of SU(N) gauge theories in the presence of a topological term

θ dependence of SU(N) gauge theories in the presence of a topological term

Correlators of left charges and weak operators in finite volume chiral perturbation theory

Artifacts and⟨A2⟩power corrections: ReexaminingZψ(p2)Boucaud1, Soto2, Leroy3 et al. 2006Phys. Rev. D390190View full textAdd to dashboardCite

Contact Info

Product

Resources

About

Artifacts and⟨A2⟩power corrections: ReexaminingZψ(p2)
Boucaud
¹
,
Soto
²
,
Leroy
³

et al. 2006
Phys. Rev. D
39
0
19
0
View full text Add to dashboard Cite