Functions Π(q2), R(s), and D(Q2) Within Dispersive Approach

132

The product of the gluon dressing function and the square of the ghost dressing function in the Landau gauge can be regarded to represent, apart from the inverse power corrections 1/Q 2n , a nonperturbative generalization A(Q 2 ) of the perturbative QCD running coupling a(Q 2 ) (≡ αs(Q 2 )/π). Recent large volume lattice calculations for these dressing functions indicate that the coupling defined in such a way goes to zero as A(Q 2 ) ∼ Q 2 when the squared momenta Q 2 go to zero (Q 2 1 GeV 2 ). In this work we construct such a QCD coupling A(Q 2 ) which fulfills also various other physically motivated conditions. At high momenta it becomes the underlying perturbative coupling a(Q 2 ) to a very high precision. And at intermediate low squared momenta Q 2 ∼ 1 GeV 2 it gives results consistent with the data of the semihadronic τ lepton decays as measured by OPAL and ALEPH. The coupling is constructed in a dispersive way, resulting as a byproduct in the holomorphic behavior of A(Q 2 ) in the complex Q 2 -plane which reflects the holomorphic behavior of the spacelike QCD observables. Application of the Borel sum rules to τ -decay V + A spectral functions allows us to obtain values for the gluon (dimension-4) condensate and the dimension-6 condensate, which reproduce the measured OPAL and ALEPH data to a significantly better precision than the perturbative MS coupling approach.3 It is possible to show that pQCD renormalization schemes exist in which pQCD coupling a(Q 2 ) is holomorphic for Q 2 ∈ C\(−∞, −M 2 thr ] and at the same time reproduces the high-energy QCD phenomenology as well as the semihadronic τ -lepton decay physics [23][24][25]. 4 MiniMOM scheme is known at present to four loops [18][19][20]. 5 In this scheme, however, we rescale Q 2 from the Λ MM to the usual Λ MS convention. 6 In Ref. [29], the matching of A(Q 2 ) and dA(Q 2 )/d ln Q 2 at an IR/UV transition scale Q 2 0 ∼ 1 GeV 2 is imposed, fixing the values of A(0) > 0 and Q 2 0 . On the other hand, our coupling A(Q 2 ) will be holomorphic, no explicit IR/UV matching scale will exist. Instead of the matching, we will impose various physically motivated conditions which will affect simultaneously the behavior of A(Q 2 ) in the UV and IR regimes.10 In principle, we could construct A in any other scheme, e.g., in MS scheme, but then it would not be clear how such a coupling compares with A latt of Ref.[32] in the deep IR regime. For an application and discussion of the MiniMOM scheme in pQCD, see Ref.[56].

Section: Construction Of the Coupling ðQ 2 þmentioning

confidence: 99%

Section: Construction Of the Coupling ðQ 2 þmentioning

confidence: 99%

“…. Analogously to the dispersive relation (17), the Cauchy integral formula applied in this case to the function…”

Section: < ~)mentioning

confidence: 99%

Section: Varying Parameters Of the Coupling And Of Sum Rulesmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Nearly perturbative lattice-motivated QCD coupling with zero IR limit

Ayala

Cvetič

Kögerler

et al. 2018

132

Lattice-motivated holomorphic nearly perturbative QCD

Ayala¹,

Cvetič²,

Kögerler³

2017

Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite nonzero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of Quantum Field Theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with small higher-twist effects. Subsequent application of the Borel sum rules to the V+A spectral functions of tau lepton decays, as measured by OPAL Collaboration, determines the values of the gluon condensate and of the V+A 6-dimensional condensate, and reproduces the data to a significantly higher precision than the usual MS running coupling.

Lattice-motivated QCD coupling and hadronic contribution to muon g − 2

Cvetič

Kögerler

2021

We present an updated version of a QCD coupling which fulfills various physically motivated conditions: at high momenta it practically coincides with the perturbative QCD coupling; at intermediate momenta it reproduces correctly the physics of the semihadronic tau decay; and at very low momenta it is suppressed as suggested by large-volume lattice calculations. An earlier presented analysis is updated here in the sense that the Adler function, in the regime |Q 2|≲ 1 GeV2, is evaluated by a renormalon-motivated resummation method. This Adler function is then used here in the evaluation of the quantities related with the semihadronic (strangeless) τ-decay spectral functions, including Borel–Laplace sum rules in the (V + A)-channel. The analysis is then extended to the evaluation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, a μ had ( 1 ) , where we include in the Adler function the V-channel higher-twist OPE terms which are regulated in the infrared (IR) by mass parameters which are expected to be ≲1 GeV. The correct value of a μ had ( 1 ) can be reproduced with the mentioned IR-regulating mass parameters if the value of the condensate ⟨ O 4 ⟩ V + A is positive (and thus the gluon condensate value is positive). This restriction and the requirement of the acceptable quality of the fits to the various mentioned sum rules then lead us to the restriction