The Euclidean Adler function and its interplay with $ \Delta {\alpha}_{\textrm{QED}}^{\textrm{had}} $ and α$_{s}$

Davier, M.; Díaz-Calderón, D.; Malaescu, B.; Pich, A.; Rodríguez-Sánchez, A.; Zhang, Z.

doi:10.1007/JHEP04(2023)067

The Euclidean Adler function and its interplay with $\Delta {\alpha}_{\textrm{QED}}^{\textrm{had}}$ and α $_{s}$

M. Davier
(
- IJCLab, Orsay
)
,
D. Díaz-Calderón
(
- Valencia U., IFIC
)
,
B. Malaescu
(
- LPNHE, Paris
)
,
A. Pich
(
- Valencia U., IFIC
)
,
A. Rodríguez-Sánchez
(
- LPNHE, Paris and
- Paris, LPTHE and
- SISSA, Trieste
)

Feb 2, 2023

55 pages

Published in:

JHEP 04 (2023) 067

Published: Apr 17, 2023

e-Print:

2302.01359 [hep-ph]

DOI:

10.1007/JHEP04(2023)067

View in:

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Abstract: (Springer)

Three different approaches to precisely describe the Adler function in the Euclidean regime at around 2 GeVs are available: dispersion relations based on the hadronic production data in e

^{+}

e

^{−}

annihilation, lattice simulations and perturbative QCD (pQCD). We make a comprehensive study of the perturbative approach, supplemented with the leading power corrections in the operator product expansion. All known contributions are included, with a careful assessment of uncertainties. The pQCD predictions are compared with the Adler functions extracted from

\Delta {\alpha}_{\textrm{QED}}^{\textrm{had}}

(Q

^{2}

), using both the DHMZ compilation of e

^{+}

e

^{−}

data and published lattice results. Taking as input the FLAG value of α

_{s}

, the pQCD Adler function turns out to be in good agreement with the lattice data, while the dispersive results lie systematically below them. Finally, we explore the sensitivity to α

_{s}

of the direct comparison between the data-driven, lattice and QCD Euclidean Adler functions. The precision with which the renormalisation group equation can be tested is also evaluated.

Note:

56 pages, 22 figures, 14 tables. Published version

Correlation Functions
Effective Field Theories of QCD
The Strong Coupling
quantum chromodynamics: perturbation theory
quantum chromodynamics: Euclidean
lattice
quantum electrodynamics
dispersion
operator product expansion
GeV

References(164)

Figures(39)

Nonlagrangian models of current algebra

Kenneth G. Wilson
(
- Cornell U., LNS
)

- Phys.Rev. 179 (1969) 1499-1512
•
DOI:
- 10.1103/PhysRev.179.1499

[2]

QCD and Resonance Physics. Theoretical Foundations

- Nucl.Phys.B 147 (1979) 385-447
•
DOI:
- 10.1016/0550-3213(79)90022-1

[3]

QCD and Resonance Physics: Applications

- Nucl.Phys.B 147 (1979) 448-518
•
DOI:
- 10.1016/0550-3213(79)90023-3

[4]

Some Simple Vacuum Polarization Phenomenology: $e^+ e^- \to$ Hadrons: The $\mu$ - Mesic Atom x-Ray Discrepancy and $g_{\mu}^{-2}$

Stephen L. Adler
(
- Fermilab and
- Princeton, Inst. Advanced Study
)

- Phys.Rev.D 10 (1974) 3714,
•
DOI:
- 10.1103/PhysRevD.10.3714

[5]

Chiral Perturbation Theory to One Loop

J. Gasser
(
- Bern U.
)
,
H. Leutwyler
(
- CERN
)

- Annals Phys. 158 (1984) 142
•
DOI:
- 10.1016/0003-4916(84)90242-2

[6]

Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark

J. Gasser
(
- Bern U.
)
,
H. Leutwyler
(
- CERN
)

- Nucl.Phys.B 250 (1985) 465-516
•
DOI:
- 10.1016/0550-3213(85)90492-4

Two point functions at two loops in three flavor chiral perturbation theory

- Nucl.Phys.B 568 (2000) 319-363
•
e-Print:
- hep-ph/9907264
•
DOI:
- 10.1016/S0550-3213(99)00674-4

Charmonium and Gluons: Basic Experimental Facts and Theoretical Introduction

et al.

- Phys.Rept. 41 (1978) 1-133
•
DOI:
- 10.1016/0370-1573(78)90120-5

[9]

GLUON CONDENSATE AND LEPTON DECAYS OF VECTOR MESONS. (IN RUSSIAN)

A.I. Vainshtein
(
- Moscow, ITEP
)
,
Valentin I. Zakharov
(
- Moscow, ITEP
)
,
Mikhail A. Shifman
(
- Moscow, ITEP
)

- JETP Lett. 27 (1978) 55-58,
- Pisma Zh.Eksp.Teor.Fiz. 27 (1978) 60-64

[10]

Precise Charm- and Bottom-Quark Masses: Theoretical and Experimental Uncertainties

et al.

- Theor.Math.Phys. 170 (2012) 217-228
•
e-Print:
- 1010.6157
•
DOI:
- 10.1007/s11232-012-0024-7

Addendum to “Charm and bottom quark masses: An update”

Konstantin G. Chetyrkin
(
- Hamburg U., Inst. Theor. Phys. II
)
,
Johann H. Kuhn
(
- KIT, Karlsruhe
)
,
Andreas Maier
(
- Durham U., IPPP
)
,
Philipp Maierhofer
(
- Freiburg U.
)
,
Peter Marquard
(
- DESY, Zeuthen
)

et al.

- Phys.Rev.D 96 (2017) 11, 116007 (addendum)
•
e-Print:
- 1710.04249
•
DOI:
- 10.1103/PhysRevD.96.116007

Confinement of Quarks

Kenneth G. Wilson
(
- Cornell U., LNS
)

- Phys.Rev.D 10 (1974) 2445-2459,
- In *Rebbi, C. ( Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 45-59. ( Phys. Rev. D10 ( 1974) 2445-2459) and Cornell Univ. Ithaca - CLNS-74-262 (74,REC.MAR.) 47p,
•
DOI:
- 10.1103/PhysRevD.10.2445