scholarly journals Short-distance constraints for HLbL in muon g-2

2022 ◽  
Vol 258 ◽  
pp. 06005
Author(s):  
Johan Bijnens ◽  
Nils Hermansson-Truedsson ◽  
Antonio Rodríguez-Sánchez
Keyword(s):  
Operator Product Expansion ◽  
Short Distance ◽  
Operator Product ◽  
Quark Loop ◽  
Distance Constraints ◽  
Analytic Evaluation ◽  
Power Corrections ◽  
Low Energies ◽  
Model Independent

Model-independent short-distance constraints allow for a reduction of theoretical uncertainties associated to the analytic evaluation of Hadronic Light-by-Light contributions to the muon g-2. In this talk we focus on the region where the three loop virtualities are large. Even when the fourth photon leg is soft, we show how a precise Operator Product Expansion can be applied in that region. The leading contribution is found to be given by the quark loop, while the evaluation of both gluonic and power corrections show how the expansion is well behaved at relatively low energies, where significant contributions to the muon g-2 remain. Numerical values for them are also presented.

scholarly journals The two-loop perturbative correction to the (g − 2)μ HLbL at short distances

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Johan Bijnens ◽  
Nils Hermansson-Truedsson ◽  
Laetitia Laub ◽  
Antonio Rodríguez-Sánchez
Keyword(s):  
Electromagnetic Field ◽  
Perturbative Qcd ◽  
Operator Product Expansion ◽  
Short Distance ◽  
Operator Product ◽  
Quark Loop ◽  
Perturbative Correction ◽  
Massless Quark ◽  
Leading Term ◽  
Perturbative Corrections

Abstract The short-distance behaviour of the hadronic light-by-light (HLbL) contribution to (g − 2)μ has recently been studied by means of an operator product expansion in a background electromagnetic field. The leading term in this expansion has been shown to be given by the massless quark loop, and the non-perturbative corrections are numerically very suppressed. Here, we calculate the perturbative QCD correction to the massless quark loop. The correction is found to be fairly small compared to the quark loop as far as we study energy scales where the perturbative running for the QCD coupling is well-defined, i.e. for scales μ ≳ 1 GeV. This should allow to reduce the large systematic uncertainty associated to high-multiplicity hadronic states.

scholarly journals Effects of longitudinal short-distance constraints on the hadronic light-by-light contribution to the muon $$\mathbf {g-2}$$

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Jan Lüdtke ◽  
Massimiliano Procura
Keyword(s):  
Short Distance ◽  
Independent Method ◽  
Recent Model ◽  
Low Energy ◽  
Muon Anomalous Magnetic Moment ◽  
Distance Constraints ◽  
Independent Information ◽  
Intermediate States ◽  
Model Independent ◽  
Interpolation Functions

AbstractWe present a model-independent method to estimate the effects of short-distance constraints (SDCs) on the hadronic light-by-light contribution to the muon anomalous magnetic moment $$a_\mu ^\text {HLbL}$$ a μ HLbL . The relevant loop integral is evaluated using multi-parameter families of interpolation functions, which satisfy by construction all constraints derived from general principles and smoothly connect the low-energy region with those where either two or all three independent photon virtualities become large. In agreement with other recent model-based analyses, we find that the SDCs and thus the infinite towers of heavy intermediate states that are responsible for saturating them have a rather small effect on $$a_\mu ^\text {HLbL}$$ a μ HLbL . Taking as input the known ground-state pseudoscalar pole contributions, we obtain that the longitudinal SDCs increase $$a_\mu ^\text {HLbL}$$ a μ HLbL by $$(9.1\pm 5.0) \times 10^{-11}$$ ( 9.1 ± 5.0 ) × 10 - 11 , where the isovector channel is responsible for $$(2.6\pm 1.5) \times 10^{-11}$$ ( 2.6 ± 1.5 ) × 10 - 11 . More precise estimates can be obtained with our method as soon as further accurate, model-independent information about important low-energy contributions from hadronic states with masses up to 1–2 GeV become available.

AN OPERATOR PRODUCT EXPANSION ANALYSIS OF e+e-ANNIHILATION DATA

2013 ◽  
Vol 28 (25) ◽  
pp. 1360009 ◽  
Author(s):  
HUBERT SPIESBERGER
Keyword(s):  
Quantum Chromodynamics ◽  
Cross Section ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Perturbative Quantum Chromodynamics ◽  
Power Corrections ◽  
Perturbative Quantum ◽  
Vacuum Condensates

Perturbative Quantum Chromodynamics combined with the operator product expansion is expected to provide a framework for the description of phenomena in hadron interactions including contributions of nonperturbative origin. Applied to the correlator of two electromagnetic currents, this framework can be confronted with e+e-annihilation into hadrons. Data from the total hadronic e+e-cross-section have become much more precise in recent years and the power corrections in the operator product expansion, i.e. the vacuum condensates are expected to be determined with higher precision than previously. We present an analysis of the condensates of dimensions d = 2, 4 and 6 and find reasonably stable results, though still within rather large errors. Our results are in agreement with values obtained from τ-decay. It also appears that the separation into isovector and isoscalar pieces introduces additional uncertainties and errors.

scholarly journals SHORT DISTANCE REPULSION AMONG BARYONS

2013 ◽  
Vol 22 (05) ◽  
pp. 1330012 ◽  
Author(s):  
SINYA AOKI ◽  
JANOS BALOG ◽  
TAKUMI DOI ◽  
TAKASHI INOUE ◽  
PETER WEISZ
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Lattice Qcd ◽  
Operator Product Expansion ◽  
Short Distance ◽  
Numerical Results ◽  
Wave Functions ◽  
Operator Product ◽  
Distance Behavior

We review recent investigations on the short distance behaviors of potentials among baryons, which are formulated through the Nambu–Bethe–Salpeter (NBS) wave function. After explaining the method to define the potentials, we analyze the short distance behavior of the NBS wave functions and the corresponding potentials by combining the operator product expansion (OPE) and a renormalization group (RG) analysis in the perturbation theory (PT) of QCD. These analytic results are compared with numerical results obtained in lattice QCD simulations.

scholarly journals NEW INSIGHTS CONCERNING DIMENSION EIGHT EFFECTS IN WEAK DECAYS

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 1228-1230
Author(s):  
JOHN F. DONOGHUE
Keyword(s):  
Operator Product Expansion ◽  
Short Distance ◽  
Numerical Estimate ◽  
Dimensional Regularization ◽  
Operator Product ◽  
Higher Dimension ◽  
Matrix Elements ◽  
Weak Decays ◽  
The Matrix ◽  
Weak Operator

Most past work on weak nonleptonic decays has mixed dimensional regularization in the weak operator product expansion with some form of a cutoff regularization in the evaluation of the matrix elements. Even with the usual technique of matching the two schemes, this combination misses physics at short distance which can be described by dimension eight (and higher dimension) operators. I describe some recent work with V. Cirigliano and E. Golowich which clarifies these effects and provides a numerical estimate suggesting that they are important.

scholarly journals New and old about renormalons: In memoriam Kolya Uraltsev

2015 ◽  
Vol 30 (10) ◽  
pp. 1543001 ◽  
Author(s):  
M. Shifman
Keyword(s):  
Operator Product Expansion ◽  
Divergent Series ◽  
Operator Product ◽  
Power Corrections ◽  
Theoretical Status ◽  
In Memoriam

I summarize what we know of renormalons from the 1970s and 80s: their uses and theoretical status. It is emphasized that renormalons in QCD are closely related to the Wilsonean operator product expansion (OPE) — a setup ideally suited for dealing with the factorially divergent series reflecting infrared dynamics. I discuss a breakthrough proposal due to Uraltsev et al. to use renormalons to evaluate nonperturbative (power) corrections in the processes without OPE. Some fresh ideas which were put forward recently are briefly discussed too, with emphasis on a possible relationship between resurgence via trans-series and OPE. This article is devoted to the memory of my friend Kolya Uraltsev. I should emphasize that these are my personal recollections. Other people who closely knew Kolya may or may not agree with my opinions.

scholarly journals Nonperturbative Expansion, Renormalons and τ-Decay

1997 ◽  
Vol 12 (19) ◽  
pp. 1361-1368 ◽  
Author(s):  
H. F. Jones ◽  
A. Ritz ◽  
I. L. Solovtsov
Keyword(s):  
Renormalization Group ◽  
Physical Quantity ◽  
Operator Product Expansion ◽  
Spectral Representation ◽  
Infrared Region ◽  
Operator Product ◽  
Effective Coupling ◽  
Power Corrections

We analyze inclusive τ-decay using a modified version of the a expansion, a nonperturbative technique in which the effective coupling is analytic in the infrared region. The modification involves renormalization group improvement of the integrand in a spectral representation for the D-function prior to implementing the a expansion. The advantage of this approach is that it enables us to monitor the structure of the induced power corrections and to ensure that these are consistent with the operator product expansion. Numerically the method agrees well with experiment: the comparison is made with the physical quantity RZ using Rτ as input.

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