Abstract
Properly separating and subtracting renormalons in the framework of the op- erator product expansion (OPE) is a way to realize high precision computation of QCD effects in high energy physics. We propose a new method (FTRS method), which enables to subtract multiple renormalons simultaneously from a general observable. It utilizes a property of Fourier transform, and the leading Wilson coefficient is written in a one-parameter integral form whose integrand has suppressed (or vanishing) renormalons. The renormalon subtraction scheme coincides with the usual principal-value prescription at large orders. We perform test analyses and subtract the \( \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}^4\right) \) renormalon from the Adler function, the \( \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}^2\right) \) renormalon from the B → Xul\( \overline{\nu} \) decay width, and the \( \mathcal{O} \)(ΛQCD) and \( \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}^2\right) \) renormalons from the B, D meson masses. The analyses show good consistency with theoretical expectations, such as improved convergence and scale dependence. In particular we obtain \( \overline{\Lambda} \)FTRS = 0.495 ± 0.053 GeV and (\( {\mu}_{\pi}^2 \))FTRS = −0.12 ± 0.23 GeV2 for the non-perturbative parameters of HQET. We explain the formulation and analyses in detail.
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References
M. Beneke, Renormalons, Phys. Rept. 317 (1999) 1 [hep-ph/9807443] [INSPIRE].
K.G. Wilson, Nonlagrangian models of current algebra, Phys. Rev. 179 (1969) 1499 [INSPIRE].
A. Pineda, Heavy Quarkonium And Nonrelativistic Effective Field Theories, Ph.D. Thesis, Barcelona University, Barcelona Spain (1998).
A.H. Hoang, M.C. Smith, T. Stelzer and S. Willenbrock, Quarkonia and the pole mass, Phys. Rev. D 59 (1999) 114014 [hep-ph/9804227] [INSPIRE].
M. Beneke, A Quark mass definition adequate for threshold problems, Phys. Lett. B 434 (1998) 115 [hep-ph/9804241] [INSPIRE].
I.I.Y. Bigi, M.A. Shifman, N.G. Uraltsev and A.I. Vainshtein, The Pole mass of the heavy quark. Perturbation theory and beyond, Phys. Rev. D 50 (1994) 2234 [hep-ph/9402360] [INSPIRE].
M. Neubert and C.T. Sachrajda, Cancellation of renormalon ambiguities in the heavy quark effective theory, Nucl. Phys. B 438 (1995) 235 [hep-ph/9407394] [INSPIRE].
P. Ball, M. Beneke and V.M. Braun, Resummation of running coupling effects in semileptonic B meson decays and extraction of |V(cb)|, Phys. Rev. D 52 (1995) 3929 [hep-ph/9503492] [INSPIRE].
A.A. Penin and N. Zerf, Bottom Quark Mass from Υ Sum Rules to \( \mathcal{O}\left({\alpha}_s^3\right) \), JHEP 04 (2014) 120 [arXiv:1401.7035
Y. Kiyo, G. Mishima and Y. Sumino, Determination of mc and mb from quarkonium 1S energy levels in perturbative QCD, Phys. Lett. B 752 (2016) 122 [Erratum ibid. 772 (2017) 878] [arXiv:1510.07072] [INSPIRE].
M. Beneke, A. Maier, J. Piclum and T. Rauh, NNNLO determination of the bottom-quark mass from non-relativistic sum rules, PoS RADCOR2015 (2016) 035 [arXiv:1601.02949] [INSPIRE].
Fermilab Lattice, MILC, TUMQCD collaboration, Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD, Phys. Rev. D 98 (2018) 054517 [arXiv:1802.04248] [INSPIRE].
C. Peset, A. Pineda and J. Segovia, The charm/bottom quark mass from heavy quarkonium at N3LO, JHEP 09 (2018) 167 [arXiv:1806.05197] [INSPIRE].
A.H. Hoang, Z. Ligeti and A.V. Manohar, B decays in the upsilon expansion, Phys. Rev. D 59 (1999) 074017 [hep-ph/9811239] [INSPIRE].
A. Alberti, P. Gambino, K.J. Healey and S. Nandi, Precision Determination of the Cabibbo-Kobayashi-Maskawa Element Vcb, Phys. Rev. Lett. 114 (2015) 061802 [arXiv:1411.6560] [INSPIRE].
A. Bazavov, N. Brambilla, X. Garcia i Tormo, P. Petreczky, J. Soto and A. Vairo, Determination of αs from the QCD static energy, Phys. Rev. D 86 (2012) 114031 [arXiv:1205.6155] [INSPIRE].
Y. Sumino, QCD potential as a ’Coulomb plus linear’ potential, Phys. Lett. B 571 (2003) 173 [hep-ph/0303120] [INSPIRE].
Y. Sumino, Static QCD potential at r < \( {\Lambda}_{\mathrm{QCD}}^{-1} \): Perturbative expansion and operator-product expansion, Phys. Rev. D 76 (2007) 114009 [hep-ph/0505034] [INSPIRE].
Y. Sumino, ’Coulomb + linear’ form of the static QCD potential in operator product expansion, Phys. Lett. B 595 (2004) 387 [hep-ph/0403242] [INSPIRE].
Y. Sumino, Understanding Interquark Force and Quark Masses in Perturbative QCD, arXiv:1411.7853 [INSPIRE].
H. Takaura, T. Kaneko, Y. Kiyo and Y. Sumino, Determination of αs from static QCD potential with renormalon subtraction, Phys. Lett. B 789 (2019) 598 [arXiv:1808.01632] [INSPIRE].
H. Takaura, T. Kaneko, Y. Kiyo and Y. Sumino, Determination of αs from static QCD potential: OPE with renormalon subtraction and lattice QCD, JHEP 04 (2019) 155 [arXiv:1808.01643] [INSPIRE].
C. Ayala, X. Lobregat and A. Pineda, Hyperasymptotic approximation to the plaquette and determination of the gluon condensate, JHEP 12 (2020) 093 [arXiv:2009.01285] [INSPIRE].
Y. Sumino and H. Takaura, On renormalons of static QCD potential at u = 1/2 and 3/2, JHEP 05 (2020) 116 [arXiv:2001.00770] [INSPIRE].
Y. Hayashi, Y. Sumino and H. Takaura, New method for renormalon subtraction using Fourier transform, Phys. Lett. B 819 (2021) 136414 [arXiv:2012.15670] [INSPIRE].
A.H. Mueller, On the Structure of Infrared Renormalons in Physical Processes at High-Energies, Nucl. Phys. B 250 (1985) 327 [INSPIRE].
C. Ayala, X. Lobregat and A. Pineda, Superasymptotic and hyperasymptotic approximation to the operator product expansion, Phys. Rev. D 99 (2019) 074019 [arXiv:1902.07736] [INSPIRE].
C. Ayala, X. Lobregat and A. Pineda, Hyperasymptotic approximation to the top, bottom and charm pole mass, Phys. Rev. D 101 (2020) 034002 [arXiv:1909.01370] [INSPIRE].
C. Ayala, X. Lobregat and A. Pineda, Determination of α(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair, JHEP 09 (2020) 016 [arXiv:2005.12301] [INSPIRE].
H. Takaura, Formulation for renormalon-free perturbative predictions beyond large-β0 approximation, JHEP 10 (2020) 039 [arXiv:2002.00428] [INSPIRE].
T. Lee, Normalization constants of large order behavior, Phys. Lett. B 462 (1999) 1 [hep-ph/9908225] [INSPIRE].
N. Brambilla, A. Pineda, J. Soto and A. Vairo, The Infrared behavior of the static potential in perturbative QCD, Phys. Rev. D 60 (1999) 091502 [hep-ph/9903355] [INSPIRE].
T. Lee, Surviving the renormalon in heavy quark potential, Phys. Rev. D 67 (2003) 014020 [hep-ph/0210032] [INSPIRE].
P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order \( {\alpha}_s^4 \) in a General Gauge Theory, Phys. Rev. Lett. 104 (2010) 132004 [arXiv:1001.3606] [INSPIRE].
P.A. Baikov, K.G. Chetyrkin, J.H. Kühn and J. Rittinger, Adler Function, Sum Rules and Crewther Relation of Order \( \mathcal{O}\left({\alpha}_s^4\right) \): the Singlet Case, Phys. Lett. B 714 (2012) 62 [arXiv:1206.1288] [INSPIRE].
D. Bernecker and H.B. Meyer, Vector Correlators in Lattice QCD: Methods and applications, Eur. Phys. J. A 47 (2011) 148 [arXiv:1107.4388] [INSPIRE].
P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, Higgs Decay, Z Decay and the QCD β-function, Acta Phys. Polon. B 48 (2017) 2135 [arXiv:1711.05592] [INSPIRE].
Flavour Lattice Averaging Group collaboration, FLAG Review 2019: Flavour Lattice Averaging Group (FLAG), Eur. Phys. J. C 80 (2020) 113 [arXiv:1902.08191] [INSPIRE].
M. Beneke, Large order perturbation theory for a physical quantity, Nucl. Phys. B 405 (1993) 424 [INSPIRE].
A.V. Manohar and M.B. Wise, Heavy quark physics, vol. 10 (2000) [INSPIRE].
A. Pak and A. Czarnecki, Heavy-to-heavy quark decays at NNLO, Phys. Rev. D 78 (2008) 114015 [arXiv:0808.3509] [INSPIRE].
M. Fael, K. Schönwald and M. Steinhauser, Third order corrections to the semileptonic b → c and the muon decays, Phys. Rev. D 104 (2021) 016003 [arXiv:2011.13654] [INSPIRE].
T. Becher, H. Boos and E. Lunghi, Kinetic corrections to B → Xcℓ\( \overline{\nu} \) at one loop, JHEP 12 (2007) 062 [arXiv:0708.0855] [INSPIRE].
A. Alberti, P. Gambino and S. Nandi, Perturbative corrections to power suppressed effects in semileptonic B decays, JHEP 01 (2014) 147 [arXiv:1311.7381] [INSPIRE].
A.F. Falk and M. Neubert, Second order power corrections in the heavy quark effective theory. 1. Formalism and meson form-factors, Phys. Rev. D 47 (1993) 2965 [hep-ph/9209268] [INSPIRE].
P. Marquard, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Quark Mass Relations to Four-Loop Order in Perturbative QCD, Phys. Rev. Lett. 114 (2015) 142002 [arXiv:1502.01030] [INSPIRE].
P. Marquard, A.V. Smirnov, V.A. Smirnov, M. Steinhauser and D. Wellmann, \( \overline{\mathrm{MS}} \)-on-shell quark mass relation up to four loops in QCD and a general SU(N) gauge group, Phys. Rev. D 94 (2016) 074025 [arXiv:1606.06754] [INSPIRE].
A.G. Grozin, P. Marquard, J.H. Piclum and M. Steinhauser, Three-Loop Chromomagnetic Interaction in HQET, Nucl. Phys. B 789 (2008) 277 [arXiv:0707.1388] [INSPIRE].
P. Ball, M. Beneke and V.M. Braun, Resummation of (β0αs)n corrections in QCD: Techniques and applications to the tau hadronic width and the heavy quark pole mass, Nucl. Phys. B 452 (1995) 563 [hep-ph/9502300] [INSPIRE].
C. Ayala, G. Cvetič and A. Pineda, The bottom quark mass from the Υ(1S) system at NNNLO, JHEP 09 (2014) 045 [arXiv:1407.2128] [INSPIRE].
M. Fael, K. Schönwald and M. Steinhauser, Exact results for \( {Z}_m^{\mathrm{OS}} \) and \( {Z}_2^{\mathrm{OS}} \) with two mass scales and up to three loops, JHEP 10 (2020) 087 [arXiv:2008.01102] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
T. Lee, Estimation of the large order behavior of the Plaquette, Phys. Lett. B 711 (2012) 360 [arXiv:1112.4433] [INSPIRE].
K.G. Chetyrkin, V.P. Spiridonov and S.G. Gorishnii, Wilson expansion for correlators of vector currents at the two loop level: dimension four operators, Phys. Lett. B 160 (1985) 149 [INSPIRE].
G.S. Bali, C. Bauer and A. Pineda, Model-independent determination of the gluon condensate in four-dimensional SU(3) gauge theory, Phys. Rev. Lett. 113 (2014) 092001 [arXiv:1403.6477] [INSPIRE].
T. Lee, Extracting gluon condensate from the average plaquette, Nucl. Part. Phys. Proc. 258-259 (2015) 181 [arXiv:1503.07988] [INSPIRE].
A.H. Hoang and C. Regner, Borel Representation of τ Hadronic Spectral Function Moments in Contour-Improved Perturbation Theory, arXiv:2008.00578 [INSPIRE].
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Hayashi, Y., Sumino, Y. & Takaura, H. Renormalon subtraction in OPE using Fourier transform: formulation and application to various observables. J. High Energ. Phys. 2022, 16 (2022). https://doi.org/10.1007/JHEP02(2022)016
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DOI: https://doi.org/10.1007/JHEP02(2022)016