Abstract
We use the \( \mathcal{O}\left( {\alpha_s^3} \right) \) approximation of the heavy-quark vacuum polarization function in the threshold region to determine the bottom quark mass from nonrelativistic \( \varUpsilon \) sum rules. We find very good stability and convergence of the perturbative series for the bottom quark mass in \( \overline{\mathrm{MS}} \) renormalization scheme. Our final result is \( {{\overline{m}}_b}\left( {{{\overline{m}}_b}} \right)=4.169\pm 0.00{8_{\mathrm{th}}}\pm 0.00{2_{{{\alpha_s}}}}\pm 0.00{2_{\exp }} \).
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References
M.B. Voloshin, On Dynamics of Heavy Quarks in Nonperturbative QCD Vacuum, Nucl. Phys. B 154 (1979) 365 [INSPIRE].
H. Leutwyler, How to Use Heavy Quarks to Probe the QCD Vacuum, Phys. Lett. B 98 (1981) 447 [INSPIRE].
N. Brambilla, A. Pineda, J. Soto and A. Vairo, The Heavy quarkonium spectrum at order \( m\alpha_s^5\ln\,{\alpha_s} \) , Phys. Lett. B 470 (1999) 215 [hep-ph/9910238] [INSPIRE].
A.A. Penin and M. Steinhauser, Heavy quarkonium spectrum at \( O\left( {\alpha_s^5{m_q}} \right) \) and bottom/top quark mass determination, Phys. Lett. B 538 (2002) 335 [hep-ph/0204290] [INSPIRE].
B.A. Kniehl and A.A. Penin, Order \( \alpha_s^3{\ln^2}\left( {{1 \left/ {{{\alpha_s}}} \right.}} \right) \) corrections to heavy quarkonium creation and annihilation, Nucl. Phys. B 577 (2000) 197 [hep-ph/9911414] [INSPIRE].
B.A. Kniehl, A.A. Penin, M. Steinhauser and V.A. Smirnov, Heavy quarkonium creation and annihilation with \( \alpha_s^3\ln \left( {{1 \left/ {{{\alpha_s}}} \right.}} \right) \) accuracy, Phys. Rev. Lett. 90 (2003) 212001 [hep-ph/0210161] [INSPIRE].
M. Beneke, Y. Kiyo, P. Marquard, A. Penin, J. Piclum et al., Leptonic decay of the Upsilon(1S) meson at third order in QCD, arXiv:1401.3005 [INSPIRE].
V.A. Novikov, L.B. Okun, M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, Sum Rules for Charmonium and Charmed Mesons Decay Rates in Quantum Chromodynamics, Phys. Rev. Lett. 38 (1977) 626 [Erratum ibid. 38 (1977) 791] [INSPIRE].
V.A. Novikov, L.B. Okun, M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, Charmonium and Gluons: Basic Experimental Facts and Theoretical Introduction, Phys. Rept. 41 (1978) 1 [INSPIRE].
J.H. Kuhn, M. Steinhauser and C. Sturm, Heavy Quark Masses from Sum Rules in Four-Loop Approximation, Nucl. Phys. B 778 (2007) 192 [hep-ph/0702103] [INSPIRE].
K. Chetyrkin et al., Precise Charm- and Bottom-Quark Masses: Theoretical and Experimental Uncertainties, Theor. Math. Phys. 170 (2012) 217 [arXiv:1010.6157] [INSPIRE].
K.G. Chetyrkin et al., Charm and Bottom Quark Masses: An Update, Phys. Rev. D 80 (2009) 074010 [arXiv:0907.2110] [INSPIRE].
M.B. Voloshin and Y. Zaitsev, Physics of upsilon resonances: Ten years later, Sov. Phys. Usp. 30 (1987) 553 [INSPIRE].
M.B. Voloshin, Precision determination of α s and m b from QCD sum rules for \( b\overline{b} \), Int. J. Mod. Phys. A 10 (1995) 2865 [hep-ph/9502224] [INSPIRE].
J.H. Kuhn, A.A. Penin and A.A. Pivovarov, Coulomb resummation for \( b\overline{b} \) system near threshold and precision determination of αs and m b, Nucl. Phys. B 534 (1998) 356 [hep-ph/9801356] [INSPIRE].
A.A. Penin and A.A. Pivovarov, Next-to-next-to leading order vacuum polarization function of heavy quark near threshold and sum rules for \( b\overline{b} \) system, Phys. Lett. B 435 (1998) 413 [hep-ph/9803363] [INSPIRE].
A.H. Hoang, Bottom quark mass from Upsilon mesons, Phys. Rev. D 59 (1999) 014039 [hep-ph/9803454] [INSPIRE].
K. Melnikov and A. Yelkhovsky, The b quark low scale running mass from Upsilon sum rules, Phys. Rev. D 59 (1999) 114009 [hep-ph/9805270] [INSPIRE].
A.A. Penin and A.A. Pivovarov, Bottom quark pole mass and |V cb | matrix element from R(e + e − → \( b\overline{b} \)) and Γsl(b → clν l ) in the next to next-to-leading order, Nucl. Phys. B 549 (1999) 217 [hep-ph/9807421] [INSPIRE].
A.H. Hoang, 1S and MS-bar bottom quark masses from Upsilon sum rules, Phys. Rev. D 61 (2000) 034005 [hep-ph/9905550] [INSPIRE].
M. Beneke and A. Signer, The Bottom MS-bar quark mass from sum rules at next-to-next-to-leading order, Phys. Lett. B 471 (1999) 233 [hep-ph/9906475] [INSPIRE].
A. Pineda and A. Signer, Renormalization group improved sum rule analysis for the bottom quark mass, Phys. Rev. D 73 (2006) 111501 [hep-ph/0601185] [INSPIRE].
A. Hoang, P. Ruiz-Femenia and M. Stahlhofen, Renormalization Group Improved Bottom Mass from Upsilon Sum Rules at NNLL Order, JHEP 10 (2012) 188 [arXiv:1209.0450] [INSPIRE].
W.E. Caswell and G.P. Lepage, Effective Lagrangians for Bound State Problems in QED, QCD and Other Field Theories, Phys. Lett. B 167 (1986) 437 [INSPIRE].
G.T. Bodwin, E. Braaten and G.P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev. D 51 (1995) 1125 [Erratum ibid. D 55 (1997) 5853] [hep-ph/9407339] [INSPIRE].
A. Pineda and J. Soto, Effective field theory for ultrasoft momenta in NRQCD and NRQED, Nucl. Phys. Proc. Suppl. 64 (1998) 428 [hep-ph/9707481] [INSPIRE].
N. Brambilla, A. Pineda, J. Soto and A. Vairo, Potential NRQCD: An Effective theory for heavy quarkonium, Nucl. Phys. B 566 (2000) 275 [hep-ph/9907240] [INSPIRE].
B.A. Kniehl and A.A. Penin, Ultrasoft effects in heavy quarkonium physics, Nucl. Phys. B 563 (1999) 200 [hep-ph/9907489] [INSPIRE].
M. Beneke, New results on heavy quarks near threshold, hep-ph/9806429 [INSPIRE].
A. Pineda and F.J. Yndurain, Calculation of quarkonium spectrum and m b , m c to order \( \alpha_s^4 \) , Phys. Rev. D 58 (1998) 094022 [hep-ph/9711287] [INSPIRE].
A.A. Penin, V.A. Smirnov and M. Steinhauser, Heavy quarkonium spectrum and production/annihilation rates to order \( \beta_0^3\alpha_s^3 \) , Nucl. Phys. B 716 (2005) 303 [hep-ph/0501042] [INSPIRE].
M. Beneke, Y. Kiyo and K. Schuller, Third-order Coulomb corrections to the S-wave Green function, energy levels and wave functions at the origin, Nucl. Phys. B 714 (2005) 67 [hep-ph/0501289] [INSPIRE].
C. Anzai, Y. Kiyo and Y. Sumino, Static QCD potential at three-loop order, Phys. Rev. Lett. 104 (2010) 112003 [arXiv:0911.4335] [INSPIRE].
A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Three-loop static potential, Phys. Rev. Lett. 104 (2010) 112002 [arXiv:0911.4742] [INSPIRE].
A. Czarnecki and K. Melnikov, Two loop QCD corrections to the heavy quark pair production cross-section in e + e − annihilation near the threshold, Phys. Rev. Lett. 80 (1998) 2531 [hep-ph/9712222] [INSPIRE].
M. Beneke, A. Signer and V.A. Smirnov, Two loop correction to the leptonic decay of quarkonium, Phys. Rev. Lett. 80 (1998) 2535 [hep-ph/9712302] [INSPIRE].
A.H. Hoang, Three loop anomalous dimension of the heavy quark pair production current in nonrelativistic QCD, Phys. Rev. D 69 (2004) 034009 [hep-ph/0307376] [INSPIRE].
M.E. Luke and M.J. Savage, Power counting in dimensionally regularized NRQCD, Phys. Rev. D 57 (1998) 413 [hep-ph/9707313] [INSPIRE].
P. Marquard, J.H. Piclum, D. Seidel and M. Steinhauser, Fermionic corrections to the three-loop matching coefficient of the vector current, Nucl. Phys. B 758 (2006) 144 [hep-ph/0607168] [INSPIRE].
P. Marquard, J.H. Piclum, D. Seidel and M. Steinhauser, Completely automated computation of the heavy-fermion corrections to the three-loop matching coefficient of the vector current, Phys. Lett. B 678 (2009) 269 [arXiv:0904.0920] [INSPIRE].
P. Marquard, J.H. Piclum, D. Seidel and M. Steinhauser, Three-loop matching of the vector current, Phys. Rev. D 89 (2014) 034027 [arXiv:1401.3004] [INSPIRE].
M. Beneke, Y. Kiyo and K. Schuller, Third-order non-Coulomb correction to the S-wave quarkonium wave functions at the origin, Phys. Lett. B 658 (2008) 222 [arXiv:0705.4518] [INSPIRE].
M. Beneke, Y. Kiyo and K. Schuller, Third-order correction to top-quark pair production near threshold I. Effective theory set-up and matching coefficients, arXiv:1312.4791 [INSPIRE].
B.A. Kniehl, A.A. Penin, M. Steinhauser and V.A. Smirnov, Non-Abelian \( {{{\alpha_s^3}} \left/ {{\left( {{m_q}{r^2}} \right)}} \right.} \) heavy quark anti-quark potential, Phys. Rev. D 65 (2002) 091503 [hep-ph/0106135] [INSPIRE].
B.A. Kniehl, A.A. Penin, V.A. Smirnov and M. Steinhauser, Potential NRQCD and heavy quarkonium spectrum at next-to-next-to-next-to-leading order, Nucl. Phys. B 635 (2002) 357 [hep-ph/0203166] [INSPIRE].
M. Beneke, Y. Kiyo and A.A. Penin, Ultrasoft contribution to quarkonium production and annihilation, Phys. Lett. B 653 (2007) 53 [arXiv:0706.2733] [INSPIRE].
Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
F. Jegerlehner, alphaQED: Fortran package for calculation of the hadronic contribution and the effective fine structure constant. Nuovo Cim. C 034S1 (2011) 31
M. Beneke, Renormalons, Phys. Rept. 317 (1999) 1 [hep-ph/9807443] [INSPIRE].
C. Bauer, G.S. Bali and A. Pineda, Compelling Evidence of Renormalons in QCD from High Order Perturbative Expansions, Phys. Rev. Lett. 108 (2012) 242002 [arXiv:1111.3946] [INSPIRE].
K.G. Chetyrkin and M. Steinhauser, The Relation between the MS-bar and the on-shell quark mass at order \( \alpha_s^3 \), Nucl. Phys. B 573 (2000) 617 [hep-ph/9911434] [INSPIRE].
K. Melnikov and T.v. Ritbergen, The three loop relation between the MS-bar and the pole quark masses, Phys. Lett. B 482 (2000) 99 [hep-ph/9912391] [INSPIRE].
A.H. Hoang, Z. Ligeti and A.V. Manohar, B decay and the Upsilon mass, Phys. Rev. Lett. 82 (1999) 277 [hep-ph/9809423] [INSPIRE].
Y. Kiyo and Y. Sumino, \( \mathcal{O}\left( {\alpha_s^5m} \right) \) quarkonium 1S spectrum in large β 0 approximation and renormalon cancellation, Phys. Lett. B 496 (2000) 83 [hep-ph/0007251] [INSPIRE].
A. Pineda, Determination of the bottom quark mass from the Upsilon(1S) system, JHEP 06 (2001) 022 [hep-ph/0105008] [INSPIRE].
K.G. Chetyrkin, J.H. Kuhn and M. Steinhauser, RunDec: A Mathematica package for running and decoupling of the strong coupling and quark masses, Comput. Phys. Commun. 133 (2000) 43 [hep-ph/0004189] [INSPIRE].
A.A. Penin, A. Pineda, V.A. Smirnov and M. Steinhauser, Spin dependence of heavy quarkonium production and annihilation rates: Complete next-to-next-to-leading logarithmic result, Nucl. Phys. B 699 (2004) 183 [Erratum ibid. 829 (2010) 398-399] [hep-ph/0406175] [INSPIRE].
D. Eiras and J. Soto, Light fermion finite mass effects in non-relativistic bound states, Phys. Lett. B 491 (2000) 101 [hep-ph/0005066] [INSPIRE].
M. Melles, The static QCD potential in coordinate space with quark masses through two loops, Phys. Rev. D 62 (2000) 074019 [hep-ph/0001295] [INSPIRE].
A.H. Hoang, Bottom quark mass from Upsilon mesons: Charm mass effects, hep-ph/0008102 [INSPIRE].
A. Pineda, Next-to-leading nonperturbative calculation in heavy quarkonium, Nucl. Phys. B 494 (1997) 213 [hep-ph/9611388] [INSPIRE].
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Penin, A.A., Zerf, N. Bottom quark mass from \( \varUpsilon \) sum rules to \( \mathcal{O}\left( {\alpha_s^3} \right) \) . J. High Energ. Phys. 2014, 120 (2014). https://doi.org/10.1007/JHEP04(2014)120
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DOI: https://doi.org/10.1007/JHEP04(2014)120