scholarly journals The strong coupling from $e^+e^-\to$~hadrons

2019 ◽  
Author(s):  
Diogo Boito ◽  
Maarten Golterman ◽  
Alex Keshavarzi ◽  
Kim Maltman ◽  
Daiskuke Nomura ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Strong Coupling ◽  
Sum Rules ◽  
Finite Energy ◽  
Order Perturbation ◽  
Decay Data ◽  
Systematic Effects ◽  
Fixed Order ◽  
Charm Mass ◽  
Good Agreement

We use a new compilation of the hadronic RR-ratio from available data for the process e^+e^-\toe+e−→ hadrons below the charm mass to determine the strong coupling \alpha_sαs, using finite-energy sum rules. Quoting our results at the \tauτ mass to facilitate comparison to the results obtained from similar analyses of hadronic \tauτ-decay data, we find \alpha_s(m_\tau^2)=0.298\pm 0.016\pm 0.006αs(mτ2)=0.298±0.016±0.006 in fixed-order perturbation theory, and \alpha_s(m_\tau^2)=0.304\pm 0.018\pm 0.006αs(mτ2)=0.304±0.018±0.006 in contour-improved perturbation theory, where the first error is statistical, and the second error combines various systematic effects. These values are in good agreement with a recent determination from the OPAL and ALEPH data for hadronic \tauτ decays. We briefly compare the R(s)R(s)-based analysis with the \tauτ-based analysis.

scholarly journals Determination of perturbative QCD coupling from ALEPH $$\tau $$ decay data using pinched Borel–Laplace and Finite Energy Sum Rules

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
César Ayala ◽  
Gorazd Cvetič ◽  
Diego Teca
Keyword(s):  
Perturbation Theory ◽  
Perturbative Qcd ◽  
Sum Rules ◽  
Finite Energy ◽  
Operator Product ◽  
Decay Data ◽  
Fixed Order ◽  
Principal Value ◽  
Adler Function

AbstractWe present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH $$\tau $$ τ -decay data. The determination involves the double-pinched Borel–Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is the Operator Product Expansion (OPE) of the V+A channel Adler function in which the higher order terms of the leading-twist part originate from a model based on the known structure of the leading renormalons of this quantity. The applied evaluation methods are contour-improved perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and Principal Value of the Borel resummation (PV). All the methods involve truncations in the order of the coupling. In contrast to the truncated CIPT method, the truncated FOPT and PV methods account correctly for the suppression of various renormalon contributions of the Adler function in the mentioned sum rules. The extracted value of the $${\overline{\mathrm{MS}}}$$ MS ¯ coupling is $$\alpha _s(m_{\tau }^2) = 0.3116 \pm 0.0073$$ α s ( m τ 2 ) = 0.3116 ± 0.0073 [$$\alpha _s(M_Z^2)=0.1176 \pm 0.0010$$ α s ( M Z 2 ) = 0.1176 ± 0.0010 ] for the average of the FOPT and PV methods, which we regard as our main result. On the other hand, if we include in the average also the CIPT method, the resulting values are significantly higher, $$\alpha _s(m_{\tau }^2) = 0.3194 \pm 0.0167$$ α s ( m τ 2 ) = 0.3194 ± 0.0167 [$$\alpha _s(M_Z^2)=0.1186 \pm 0.0021$$ α s ( M Z 2 ) = 0.1186 ± 0.0021 ].

scholarly journals Improved calculation of the γ*γ → π process at low Q2 using LCSR’s and renormalization-group summation

2022 ◽  
Vol 258 ◽  
pp. 03003
Author(s):  
Sergey Mikhailov ◽  
Alexandr Pimikov ◽  
N.G. Stefanis
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Transition Form Factor ◽  
Sum Rules ◽  
Power Series Expansion ◽  
Transition Form ◽  
Analytic Perturbation Theory ◽  
Fixed Order ◽  
Best Fit ◽  
Good Agreement

We study two versions of lightcone sum rules to calculate the γ*γ → π0 transition form factor (TFF) within QCD. While the standard version is based on fixed-order perturbation theory by means of a power-series expansion in the strong coupling, the new method incorporates radiative corrections by renormalization-group summation and generates an expansion within a generalized fractional analytic perturbation theory involving only analytic couplings. Using this scheme, we determine the relative nonperturbative parameters and the first two Gegenbauer coefficients of the pion distribution amplitude (DA) to obtain TFF predictions in good agreement with the preliminary BESIII data, while the best-fit pion DA satisfies the most recent lattice constraints on the second moment of the pion DA at the three-loop level.

Comparison of Numerical and Perturbation Solutions of Two-Dimensional Nonlinear Water-Wave Problems

1976 ◽  
Vol 20 (03) ◽  
pp. 160-170
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Perturbation Theory ◽  
Numerical Solutions ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Wave System ◽  
Two Dimensional ◽  
Third Order ◽  
Flow Past ◽  
Wave Problems ◽  
Good Agreement

Numerical solutions of the nonlinear problem of the steady two-dimensional potential flow past a submerged line vortex are obtained using the finite-difference iterative technique previously presented by the authors. These solutions are compared in detail with third-order perturbation theory solutions. It is found that very good agreement is obtained for cases of positive circulation of the vortex with strength large enough to produce downstream waves whose steepness is within 15 percent of the maximum possible steepness of irrotational free waves. These computed waves are as steep as the steepest waves obtained in a certain experiment involving the flow past a two-dimensional hydrofoil. For negative circulation, there is substantial difference between the numerical results and third-order perturbation theory. The failure of the perturbation theory is discussed. Details of the far-downstream wave system obtained by the numerical method are compared with other numerical solutions and very high-order perturbation theory solutions of the free-wave problem. Very good agreement is obtained in most cases.

scholarly journals STATUS OF THE HADRONIC τ DETERMINATION OF Vus

2008 ◽  
Vol 23 (21) ◽  
pp. 3191-3195 ◽  
Author(s):  
K. MALTMAN ◽  
C. E. WOLFE ◽  
S. BANERJEE ◽  
M. RONEY ◽  
I. NUGENT
Keyword(s):  
Sum Rules ◽  
Branching Fractions ◽  
Sum Rule ◽  
Slow Convergence ◽  
Decay Data ◽  
Decay Modes ◽  
Good Agreement

We update the extraction of Vus from hadronic τ decay data in light of recent BaBar and Belle results on the branching fractions of a number of important strange decay modes. A range of sum rule analyses is employed, particular attention being paid to those based on “non-spectral weights”, developed previously to bring the slow convergence of the relevant integrated D = 2 OPE series under improved control. Results from the various sum rules are in good agreement with one another, but ~ 3σ below expectations based on 3-family unitarity.

scholarly journals Modelling the post-reionization neutral hydrogen (H i) 21-cm bispectrum

2019 ◽  
Vol 490 (2) ◽  
pp. 2880-2889 ◽  
Author(s):  
Debanjan Sarkar ◽  
Suman Majumdar ◽  
Somnath Bharadwaj
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Cosmological Parameters ◽  
Neutral Hydrogen ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Intensity Mapping ◽  
High Level ◽  
Second Order Perturbation Theory ◽  
Good Agreement

ABSTRACT Measurements of the post-reionization 21-cm bispectrum $B_{{\rm H\,{\small I}}\, }(\boldsymbol {k_1},\boldsymbol {k_2},\boldsymbol {k_3})$ using various upcoming intensity mapping experiments hold the potential for determining the cosmological parameters at a high level of precision. In this paper, we have estimated the 21-cm bispectrum in the z range 1 ≤ z ≤ 6 using seminumerical simulations of the neutral hydrogen (H i) distribution. We determine the k and z range where the 21-cm bispectrum can be adequately modelled using the predictions of second-order perturbation theory, and we use this to predict the redshift evolution of the linear and quadratic H i bias parameters b1 and b2, respectively. The b1 values are found to decrease nearly linearly with decreasing z, and are in good agreement with earlier predictions obtained by modelling the 21-cm power spectrum $P_{{\rm H\,{\small I}}\, }(k)$. The b2 values fall sharply with decreasing z, becomes zero at z ∼ 3 and attains a nearly constant value b2 ≈ −0.36 at z < 2. We provide polynomial fitting formulas for b1 and b2 as functions of z. The modelling presented here is expected to be useful in future efforts to determine cosmological parameters and constrain primordial non-Gaussianity using the 21-cm bispectrum.

Fixed order perturbation theory and leading logarithms in energy-energy correlations

1984 ◽  
Vol 136 (1-2) ◽  
pp. 99-104 ◽  
Author(s):  
S.D. Ellis ◽  
D.G. Richards ◽  
W.J. Stirling
Keyword(s):  
Perturbation Theory ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Fixed Order

scholarly journals Current Status of inclusive hadronic tau determinations of |V_us|

2019 ◽  
Author(s):  
Kim Maltman ◽  
P. A. Boyle ◽  
R. J. Hudspith ◽  
T. Izubuchi ◽  
A. Juttner ◽  
...  
Keyword(s):  
Sum Rules ◽  
Branching Fractions ◽  
Finite Energy ◽  
Current Status ◽  
Decay Data ◽  
The Status ◽  
Hadronic Tau

We review the status of the determination of \vert V_{us}\vert|Vus| from both flavor-breaking finite-energy sum rules based on inclusive non-strange and strange hadronic \tauτ decay data and the recent lattice-based analysis of inclusive strange hadronic \tauτ decay data. In particular, we update the results from these analysis frameworks taking into account recent improvements to a number of strange branching fractions reported by HFLAV at CKM2018 and this meeting. We find that inclusive \tauτ decay data yields results for \vert V_{us}\vert|Vus| compatible within errors with the expectations of three-family unitarity.

THE CHIRAL LIMIT K → ππ MATRIX ELEMENTS OF THE ELECTROWEAK PENGUIN OPERATORS Q7,8

2003 ◽  
Vol 18 (02n06) ◽  
pp. 366-369
Author(s):  
K. MALTMAN ◽  
V. CIRIGLIANO ◽  
J. F. DONOGHUE ◽  
E. GOLOWICH
Keyword(s):  
Sum Rules ◽  
Chiral Limit ◽  
Finite Energy ◽  
Matrix Elements ◽  
Decay Data ◽  
Electroweak Penguin

The SU(3) chiral limit K → ππ matrix elements of the electroweak penguin operators, Q7,8, are determined using hadronic τ decay data, and dispersive and finite energy sum rules.

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