Abstract
The m W − m Z interdependence in the Standard Model is studied in the \( \overline{M\ S} \) scheme at the two-loop level, including the known higher-order contributions. The relevant radiative parameters, \( \varDelta \widehat{\alpha}\left(\mu \right) \) , \( \varDelta {\widehat{r}}_W \) , \( \widehat{\rho} \) are computed at O(α 2) taking into account higherorder QCD corrections and the resummation of the reducible contributions. We obtain m W = 80.357 ± 0.009 ± 0.003 GeV where the errors refer to the parametric and theoretical uncertainties, respectively. A comparison with the known result in the On-Shell scheme gives a difference of ≈ 6 MeV. As a byproduct of our calculation we also obtain the \( \overline{M\ S} \) electromagnetic coupling and the weak mixing angle at the top mass scale, \( \widehat{\alpha}\left({M}_t\right)={(127.73)}^{-1}\pm 0.0000003 \) and \( { \sin}^2{\widehat{\theta}}_W\left({M}_t\right)=0.23462\pm 0.00012 \).
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ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
A. Sirlin and W.J. Marciano, Radiative Corrections to ν μ + N → μ − + X and their Effect on the Determination of ρ 2 and sin 2 θ W , Nucl. Phys. B 189 (1981) 442 [INSPIRE].
A. Sirlin, Radiative Corrections in the SU(2) L × U (1) Theory: A Simple Renormalization Framework, Phys. Rev. D 22 (1980) 971 [INSPIRE].
A. Sirlin, On the O(α 2) Corrections to τ μ , m W , m Z in the SU(2) L × U(1) Theory, Phys. Rev. D 29 (1984) 89 [INSPIRE].
A. Djouadi and C. Verzegnassi, Virtual Very Heavy Top Effects in LEP / SLC Precision Measurements, Phys. Lett. B 195 (1987) 265 [INSPIRE].
L. Avdeev, J. Fleischer, S. Mikhailov and O. Tarasov, \( \mathcal{O}\left(\alpha {\alpha}_s^2\right) \) correction to the electroweak ρ parameter, Phys. Lett. B 336 (1994) 560 [hep-ph/9406363] [INSPIRE].
K.G. Chetyrkin, J.H. Kuhn and M. Steinhauser, Corrections of order \( \mathcal{O}\left({G}_F{M}_t^2{\alpha}_s^2\right) \) to the ρ parameter, Phys. Lett. B 351 (1995) 331 [hep-ph/9502291] [INSPIRE].
K.G. Chetyrkin, J.H. Kuhn and M. Steinhauser, QCD corrections from top quark to relations between electroweak parameters to order α 2 S , Phys. Rev. Lett. 75 (1995) 3394 [hep-ph/9504413] [INSPIRE].
J.J. van der Bij and F. Hoogeveen, Two Loop Correction to Weak Interaction Parameters Due to a Heavy Fermion Doublet, Nucl. Phys. B 283 (1987) 477 [INSPIRE].
R. Barbieri, M. Beccaria, P. Ciafaloni, G. Curci and A. Vicere, Radiative correction effects of a very heavy top, Phys. Lett. B 288 (1992) 95 [hep-ph/9205238] [INSPIRE].
R. Barbieri, M. Beccaria, P. Ciafaloni, G. Curci and A. Vicere, Two loop heavy top effects in the Standard Model, Nucl. Phys. B 409 (1993) 105 [INSPIRE].
J. Fleischer, O.V. Tarasov and F. Jegerlehner, Two loop heavy top corrections to the ρ parameter: A Simple formula valid for arbitrary Higgs mass, Phys. Lett. B 319 (1993) 249 [INSPIRE].
M. Consoli, W. Hollik and F. Jegerlehner, The Effect of the Top Quark on the M W − M Z Interdependence and Possible Decoupling of Heavy Fermions from Low-Energy Physics, Phys. Lett. B 227 (1989) 167 [INSPIRE].
G. Degrassi, P. Gambino and A. Vicini, Two loop heavy top effects on the m Z − m W interdependence, Phys. Lett. B 383 (1996) 219 [hep-ph/9603374] [INSPIRE].
G. Degrassi, P. Gambino and A. Sirlin, Precise calculation of M W , sin 2 θ W (M Z ) and sin 2 θ lept eff , Phys. Lett. B 394 (1997) 188 [hep-ph/9611363] [INSPIRE].
M. Faisst, J.H. Kuhn, T. Seidensticker and O. Veretin, Three loop top quark contributions to the ρ parameter, Nucl. Phys. B 665 (2003) 649 [hep-ph/0302275] [INSPIRE].
J.J. van der Bij, K.G. Chetyrkin, M. Faisst, G. Jikia and T. Seidensticker, Three loop leading top mass contributions to the ρ parameter, Phys. Lett. B 498 (2001) 156 [hep-ph/0011373] [INSPIRE].
K.G. Chetyrkin, M. Faisst, J.H. Kuhn, P. Maierhofer and C. Sturm, Four-Loop QCD Corrections to the ρ Parameter, Phys. Rev. Lett. 97 (2006) 102003 [hep-ph/0605201] [INSPIRE].
R. Boughezal and M. Czakon, Single scale tadpoles and O(G F m 2 t α 3 s ) corrections to the ρ parameter, Nucl. Phys. B 755 (2006) 221 [hep-ph/0606232] [INSPIRE].
A. Djouadi, O(αα s ) Vacuum Polarization Functions of the Standard Model Gauge Bosons, Nuovo Cim. A 100 (1988) 357 [INSPIRE].
B.A. Kniehl, Two Loop Corrections to the Vacuum Polarizations in Perturbative QCD, Nucl. Phys. B 347 (1990) 86 [INSPIRE].
A. Djouadi and P. Gambino, Electroweak gauge bosons selfenergies: Complete QCD corrections, Phys. Rev. D 49 (1994) 3499 [hep-ph/9309298] [INSPIRE].
F. Halzen and B.A. Kniehl, Δr beyond one loop, Nucl. Phys. B 353 (1991) 567 [INSPIRE].
A. Freitas, W. Hollik, W. Walter and G. Weiglein, Complete fermionic two loop results for the M W − M Z interdependence, Phys. Lett. B 495 (2000) 338 [hep-ph/0007091] [INSPIRE].
A. Freitas, W. Hollik, W. Walter and G. Weiglein, Electroweak two loop corrections to the M W − M Z mass correlation in the standard model, Nucl. Phys. B 632 (2002) 189 [hep-ph/0202131] [INSPIRE].
M. Awramik and M. Czakon, Complete two loop electroweak contributions to the muon lifetime in the standard model, Phys. Lett. B 568 (2003) 48 [hep-ph/0305248] [INSPIRE].
M. Awramik and M. Czakon, Complete two loop bosonic contributions to the muon lifetime in the standard model, Phys. Rev. Lett. 89 (2002) 241801 [hep-ph/0208113] [INSPIRE].
A. Onishchenko and O. Veretin, Two loop bosonic electroweak corrections to the muon lifetime and M Z − M W interdependence, Phys. Lett. B 551 (2003) 111 [hep-ph/0209010] [INSPIRE].
M. Awramik, M. Czakon, A. Onishchenko and O. Veretin, Bosonic corrections to Δr at the two loop level, Phys. Rev. D 68 (2003) 053004 [hep-ph/0209084] [INSPIRE].
M. Awramik, M. Czakon, A. Freitas and G. Weiglein, Precise prediction for the W boson mass in the standard model, Phys. Rev. D 69 (2004) 053006 [hep-ph/0311148] [INSPIRE].
D.Y. Bardin, P. Christova, M. Jack, L. Kalinovskaya, A. Olchevski et al., ZFITTER v.6.21: A Semianalytical program for fermion pair production in e + e − annihilation, Comput. Phys. Commun. 133 (2001) 229 [hep-ph/9908433] [INSPIRE].
H. Flacher, M. Goebel, J. Haller, A. Hocker, K. Monig et al., Revisiting the Global Electroweak Fit of the Standard Model and Beyond with Gfitter, Eur. Phys. J. C 60 (2009) 543 [arXiv:0811.0009] [INSPIRE].
M. Baak, M. Goebel, J. Haller, A. Hoecker, D. Kennedy et al., The Electroweak Fit of the Standard Model after the Discovery of a New Boson at the LHC, Eur. Phys. J. C 72 (2012) 2205 [arXiv:1209.2716] [INSPIRE].
M. Ciuchini, E. Franco, S. Mishima and L. Silvestrini, Electroweak Precision Observables, New Physics and the Nature of a 126 GeV Higgs Boson, JHEP 08 (2013) 106 [arXiv:1306.4644] [INSPIRE].
A. Sirlin, Role of sin2 θ W (m Z ) at the Z 0 Peak, Phys. Lett. B 232 (1989) 123 [INSPIRE].
S. Fanchiotti and A. Sirlin, Accurate Determination of sin2 θ W (M z ), Phys. Rev. D 41 (1990) 319 [INSPIRE].
G. Degrassi, S. Fanchiotti and A. Sirlin, Relations Between the On-shell and \( \overline{M\;S} \) Frameworks and the M W − M Z Interdependence, Nucl. Phys. B 351 (1991) 49 [INSPIRE].
G. Degrassi and A. Vicini, Two loop renormalization of the electric charge in the standard model, Phys. Rev. D 69 (2004) 073007 [hep-ph/0307122] [INSPIRE].
A. Sirlin, Theoretical considerations concerning the Z 0 mass, Phys. Rev. Lett. 67 (1991) 2127 [INSPIRE].
S. Willenbrock and G. Valencia, On the definition of the Z boson mass, Phys. Lett. B 259 (1991) 373 [INSPIRE].
M. Passera and A. Sirlin, Analysis of the Z 0 resonant amplitude in the general R ξ gauges, Phys. Rev. Lett. 77 (1996) 4146 [hep-ph/9607253] [INSPIRE].
D.Y. Bardin, A. Leike, T. Riemann and M. Sachwitz, Energy Dependent Width Effects in e + e − Annihilation Near the Z Boson Pole, Phys. Lett. B 206 (1988) 539 [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001.
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
R. Mertig and R. Scharf, TARCER: A Mathematica program for the reduction of two loop propagator integrals, Comput. Phys. Commun. 111 (1998) 265 [hep-ph/9801383] [INSPIRE].
O.V. Tarasov, Generalized recurrence relations for two loop propagator integrals with arbitrary masses, Nucl. Phys. B 502 (1997) 455 [hep-ph/9703319] [INSPIRE].
R. Mertig, M. Böhm and A. Denner, FEYN CALC: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
A.I. Davydychev and J.B. Tausk, Two loop selfenergy diagrams with different masses and the momentum expansion, Nucl. Phys. B 397 (1993) 123 [INSPIRE].
S.P. Martin, Evaluation of two loop selfenergy basis integrals using differential equations, Phys. Rev. D 68 (2003) 075002 [hep-ph/0307101] [INSPIRE].
S.P. Martin and D.G. Robertson, TSIL: A Program for the calculation of two-loop self-energy integrals, Comput. Phys. Commun. 174 (2006) 133 [hep-ph/0501132] [INSPIRE].
M. Davier, A. Hoecker, B. Malaescu and Z. Zhang, Reevaluation of the Hadronic Contributions to the Muon g-2 and to α(M Z ), Eur. Phys. J. C 71 (2011) 1515 [arXiv:1010.4180] [INSPIRE].
H. Burkhardt and B. Pietrzyk, Recent BES measurements and the hadronic contribution to the QED vacuum polarization, Phys. Rev. D 84 (2011) 037502 [arXiv:1106.2991] [INSPIRE].
K.G. Chetyrkin, J.H. Kuhn and M. Steinhauser, Three loop polarization function and O(α 2 S ) corrections to the production of heavy quarks, Nucl. Phys. B 482 (1996) 213 [hep-ph/9606230] [INSPIRE].
T. Kinoshita and A. Sirlin, Radiative corrections to Fermi interactions, Phys. Rev. 113 (1959) 1652 [INSPIRE].
T. van Ritbergen and R.G. Stuart, On the precise determination of the Fermi coupling constant from the muon lifetime, Nucl. Phys. B 564 (2000) 343 [hep-ph/9904240] [INSPIRE].
D. Buttazzo, G. Degrassi, P.P. Giardino, G.F. Giudice, F. Sala et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 [arXiv:1307.3536] [INSPIRE].
A.H. Hoang and I.W. Stewart, Top Mass Measurements from Jets and the Tevatron Top-Quark Mass, Nucl. Phys. Proc. Suppl. 185 (2008) 220 [arXiv:0808.0222] [INSPIRE].
S. Moch, S. Weinzierl, S. Alekhin, J. Blumlein, L. de la Cruz et al., High precision fundamental constants at the TeV scale, arXiv:1405.4781 [INSPIRE].
G. Degrassi, S. Di Vita, J. Elias-Miro, J.R. Espinosa, G.F. Giudice et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
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Degrassi, G., Gambino, P. & Giardino, P.P. The m W − m Z interdependence in the Standard Model: a new scrutiny. J. High Energ. Phys. 2015, 154 (2015). https://doi.org/10.1007/JHEP05(2015)154
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DOI: https://doi.org/10.1007/JHEP05(2015)154