Abstract
We present an improved calculation of the light CP-even Higgs boson pole mass in the MSSM based on the FlexibleEFTHiggs hybrid method. The calculation resums large logarithms to all orders and includes power-suppressed terms at fixed order. It uses state-of-the-art 2- and 3-loop matching of the quartic Higgs coupling and renormalization group running up to 4-loop, resulting in a resummation of large logarithmic corrections up to N3LL level. A conceptually novel ingredient is the expansion of the matching conditions in terms of high-scale MSSM parameters instead of SM parameters. In this way leading QCD-enhanced terms in the stop-mixing parameter are effectively resummed, leading to an improved numerical convergence of the perturbative expansion. Furthermore, the avoidance of double counting of loop corrections is more transparent than in other approaches and more independent of the high-scale model. We present numerical results and a detailed discussion of theoretical uncertainties for standard benchmark scenarios.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
ATLAS and CMS collaborations, Combined Measurement of the Higgs Boson Mass in pp Collisions at \( \sqrt{s} \) = 7 and 8 TeV with the ATLAS and CMS Experiments, Phys. Rev. Lett. 114 (2015) 191803 [arXiv:1503.07589] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
ATLAS and CMS collaborations, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \( \sqrt{s} \) = 7 and 8 TeV, JHEP 08 (2016) 045 [arXiv:1606.02266] [INSPIRE].
R. Hempfling and A.H. Hoang, Two loop radiative corrections to the upper limit of the lightest Higgs boson mass in the minimal supersymmetric model, Phys. Lett. B 331 (1994) 99 [hep-ph/9401219] [INSPIRE].
S. Heinemeyer, W. Hollik and G. Weiglein, Precise prediction for the mass of the lightest Higgs boson in the MSSM, Phys. Lett. B 440 (1998) 296 [hep-ph/9807423] [INSPIRE].
S. Heinemeyer, W. Hollik and G. Weiglein, QCD corrections to the masses of the neutral CP-even Higgs bosons in the MSSM, Phys. Rev. D 58 (1998) 091701 [hep-ph/9803277] [INSPIRE].
S. Heinemeyer, W. Hollik and G. Weiglein, The Masses of the neutral CP-even Higgs bosons in the MSSM: Accurate analysis at the two loop level, Eur. Phys. J. C 9 (1999) 343 [hep-ph/9812472] [INSPIRE].
G. Degrassi, P. Slavich and F. Zwirner, On the neutral Higgs boson masses in the MSSM for arbitrary stop mixing, Nucl. Phys. B 611 (2001) 403 [hep-ph/0105096] [INSPIRE].
A. Brignole, G. Degrassi, P. Slavich and F. Zwirner, On the \( O\left({alpha}_t^2\right) \) two loop corrections to the neutral Higgs boson masses in the MSSM, Nucl. Phys. B 631 (2002) 195 [hep-ph/0112177] [INSPIRE].
S.P. Martin, Two Loop Effective Potential for a General Renormalizable Theory and Softly Broken Supersymmetry, Phys. Rev. D 65 (2002) 116003 [hep-ph/0111209] [INSPIRE].
S.P. Martin, Two Loop Effective Potential for the Minimal Supersymmetric Standard Model, Phys. Rev. D 66 (2002) 096001 [hep-ph/0206136] [INSPIRE].
S.P. Martin, Complete Two Loop Effective Potential Approximation to the Lightest Higgs Scalar Boson Mass in Supersymmetry, Phys. Rev. D 67 (2003) 095012 [hep-ph/0211366] [INSPIRE].
A. Dedes and P. Slavich, Two loop corrections to radiative electroweak symmetry breaking in the MSSM, Nucl. Phys. B 657 (2003) 333 [hep-ph/0212132] [INSPIRE].
A. Brignole, G. Degrassi, P. Slavich and F. Zwirner, On the two loop sbottom corrections to the neutral Higgs boson masses in the MSSM, Nucl. Phys. B 643 (2002) 79 [hep-ph/0206101] [INSPIRE].
A. Dedes, G. Degrassi and P. Slavich, On the two loop Yukawa corrections to the MSSM Higgs boson masses at large tan beta, Nucl. Phys. B 672 (2003) 144 [hep-ph/0305127] [INSPIRE].
S.P. Martin, Two loop scalar self energies in a general renormalizable theory at leading order in gauge couplings, Phys. Rev. D 70 (2004) 016005 [hep-ph/0312092] [INSPIRE].
B.C. Allanach, A. Djouadi, J.L. Kneur, W. Porod and P. Slavich, Precise determination of the neutral Higgs boson masses in the MSSM, JHEP 09 (2004) 044 [hep-ph/0406166] [INSPIRE].
S.P. Martin, Strong and Yukawa two-loop contributions to Higgs scalar boson self-energies and pole masses in supersymmetry, Phys. Rev. D 71 (2005) 016012 [hep-ph/0405022] [INSPIRE].
S. Heinemeyer, W. Hollik, H. Rzehak and G. Weiglein, High-precision predictions for the MSSM Higgs sector at O(αbαs), Eur. Phys. J. C 39 (2005) 465 [hep-ph/0411114] [INSPIRE].
S.P. Martin, Two-loop scalar self-energies and pole masses in a general renormalizable theory with massless gauge bosons, Phys. Rev. D 71 (2005) 116004 [hep-ph/0502168] [INSPIRE].
S.P. Martin, Three-loop corrections to the lightest Higgs scalar boson mass in supersymmetry, Phys. Rev. D 75 (2007) 055005 [hep-ph/0701051] [INSPIRE].
S. Heinemeyer, W. Hollik, H. Rzehak and G. Weiglein, The Higgs sector of the complex MSSM at two-loop order: QCD contributions, Phys. Lett. B 652 (2007) 300 [arXiv:0705.0746] [INSPIRE].
R.V. Harlander, P. Kant, L. Mihaila and M. Steinhauser, Higgs boson mass in supersymmetry to three loops, Phys. Rev. Lett. 100 (2008) 191602 [arXiv:0803.0672] [INSPIRE].
P. Kant, R.V. Harlander, L. Mihaila and M. Steinhauser, Light MSSM Higgs boson mass to three-loop accuracy, JHEP 08 (2010) 104 [arXiv:1005.5709] [INSPIRE].
W. Hollik and S. Paßehr, Two-loop top-Yukawa-coupling corrections to the Higgs boson masses in the complex MSSM, Phys. Lett. B 733 (2014) 144 [arXiv:1401.8275] [INSPIRE].
W. Hollik and S. Paßehr, Higgs boson masses and mixings in the complex MSSM with two-loop top-Yukawa-coupling corrections, JHEP 10 (2014) 171 [arXiv:1409.1687] [INSPIRE].
G. Degrassi, S. Di Vita and P. Slavich, Two-loop QCD corrections to the MSSM Higgs masses beyond the effective-potential approximation, Eur. Phys. J. C 75 (2015) 61 [arXiv:1410.3432] [INSPIRE].
S. Borowka, T. Hahn, S. Heinemeyer, G. Heinrich and W. Hollik, Momentum-dependent two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM, Eur. Phys. J. C 74 (2014) 2994 [arXiv:1404.7074] [INSPIRE].
S. Borowka, T. Hahn, S. Heinemeyer, G. Heinrich and W. Hollik, Renormalization scheme dependence of the two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM, Eur. Phys. J. C 75 (2015) 424 [arXiv:1505.03133] [INSPIRE].
M.D. Goodsell and F. Staub, The Higgs mass in the CP-violating MSSM, NMSSM and beyond, Eur. Phys. J. C 77 (2017) 46 [arXiv:1604.05335] [INSPIRE].
R.V. Harlander, J. Klappert and A. Voigt, Higgs mass prediction in the MSSM at three-loop level in a pure \( \overline{DR} \) context, Eur. Phys. J. C 77 (2017) 814 [arXiv:1708.05720] [INSPIRE].
S. Paßehr and G. Weiglein, Two-loop top and bottom Yukawa corrections to the Higgs-boson masses in the complex MSSM, Eur. Phys. J. C 78 (2018) 222 [arXiv:1705.07909] [INSPIRE].
D. Stöckinger and J. Unger, Three-loop MSSM Higgs-boson mass predictions and regularization by dimensional reduction, Nucl. Phys. B 935 (2018) 1 [arXiv:1804.05619] [INSPIRE].
S. Borowka, S. Paßehr and G. Weiglein, Complete two-loop QCD contributions to the lightest Higgs-boson mass in the MSSM with complex parameters, Eur. Phys. J. C 78 (2018) 576 [arXiv:1802.09886] [INSPIRE].
A.R. Fazio and E.A. Reyes R., The Lightest Higgs Boson Mass of the MSSM at Three-Loop Accuracy, Nucl. Phys. B 942 (2019) 164 [arXiv:1901.03651] [INSPIRE].
M.D. Goodsell and S. Paßehr, All two-loop scalar self-energies and tadpoles in general renormalisable field theories, Eur. Phys. J. C 80 (2020) 417 [arXiv:1910.02094] [INSPIRE].
P. Draper and H. Rzehak, A Review of Higgs Mass Calculations in Supersymmetric Models, Phys. Rept. 619 (2016) 1 [arXiv:1601.01890] [INSPIRE].
P. Draper, G. Lee and C.E.M. Wagner, Precise estimates of the Higgs mass in heavy supersymmetry, Phys. Rev. D 89 (2014) 055023 [arXiv:1312.5743] [INSPIRE].
E. Bagnaschi, G.F. Giudice, P. Slavich and A. Strumia, Higgs Mass and Unnatural Supersymmetry, JHEP 09 (2014) 092 [arXiv:1407.4081] [INSPIRE].
J. Pardo Vega and G. Villadoro, SusyHD: Higgs mass Determination in Supersymmetry, JHEP 07 (2015) 159 [arXiv:1504.05200] [INSPIRE].
G. Lee and C.E.M. Wagner, Higgs bosons in heavy supersymmetry with an intermediate mA, Phys. Rev. D 92 (2015) 075032 [arXiv:1508.00576] [INSPIRE].
E. Bagnaschi, J. Pardo Vega and P. Slavich, Improved determination of the Higgs mass in the MSSM with heavy superpartners, Eur. Phys. J. C 77 (2017) 334 [arXiv:1703.08166] [INSPIRE].
J. Braathen, M.D. Goodsell and P. Slavich, Matching renormalisable couplings: simple schemes and a plot, Eur. Phys. J. C 79 (2019) 669 [arXiv:1810.09388] [INSPIRE].
M. Gabelmann, M. Mühlleitner and F. Staub, Automatised matching between two scalar sectors at the one-loop level, Eur. Phys. J. C 79 (2019) 163 [arXiv:1810.12326] [INSPIRE].
B.C. Allanach and A. Voigt, Uncertainties in the Lightest C P Even Higgs Boson Mass Prediction in the Minimal Supersymmetric Standard Model: Fixed Order Versus Effective Field Theory Prediction, Eur. Phys. J. C 78 (2018) 573 [arXiv:1804.09410] [INSPIRE].
R.V. Harlander, J. Klappert, A.D. Ochoa Franco and A. Voigt, The light CP-even MSSM Higgs mass resummed to fourth logarithmic order, Eur. Phys. J. C 78 (2018) 874 [arXiv:1807.03509] [INSPIRE].
E. Bagnaschi, G. Degrassi, S. Paßehr and P. Slavich, Full two-loop QCD corrections to the Higgs mass in the MSSM with heavy superpartners, Eur. Phys. J. C 79 (2019) 910 [arXiv:1908.01670] [INSPIRE].
M. Krämer, B. Summ and A. Voigt, Completing the scalar and fermionic Universal One-Loop Effective Action, JHEP 01 (2020) 079 [arXiv:1908.04798] [INSPIRE].
H. Bahl, I. Sobolev and G. Weiglein, Precise prediction for the mass of the light MSSM Higgs boson for the case of a heavy gluino, arXiv:1912.10002 [INSPIRE].
T. Hahn, S. Heinemeyer, W. Hollik, H. Rzehak and G. Weiglein, High-Precision Predictions for the Light CP-Even Higgs Boson Mass of the Minimal Supersymmetric Standard Model, Phys. Rev. Lett. 112 (2014) 141801 [arXiv:1312.4937] [INSPIRE].
H. Bahl and W. Hollik, Precise prediction for the light MSSM Higgs boson mass combining effective field theory and fixed-order calculations, Eur. Phys. J. C 76 (2016) 499 [arXiv:1608.01880] [INSPIRE].
P. Athron, J.-h. Park, T. Steudtner, D. Stöckinger and A. Voigt, Precise Higgs mass calculations in (non-)minimal supersymmetry at both high and low scales, JHEP 01 (2017) 079 [arXiv:1609.00371] [INSPIRE].
F. Staub and W. Porod, Improved predictions for intermediate and heavy Supersymmetry in the MSSM and beyond, Eur. Phys. J. C 77 (2017) 338 [arXiv:1703.03267] [INSPIRE].
P. Athron et al., FlexibleSUSY 2.0: Extensions to investigate the phenomenology of SUSY and non-SUSY models, Comput. Phys. Commun. 230 (2018) 145 [arXiv:1710.03760] [INSPIRE].
H. Bahl, S. Heinemeyer, W. Hollik and G. Weiglein, Reconciling EFT and hybrid calculations of the light MSSM Higgs-boson mass, Eur. Phys. J. C 78 (2018) 57 [arXiv:1706.00346] [INSPIRE].
H. Bahl and W. Hollik, Precise prediction of the MSSM Higgs boson masses for low MA, JHEP 07 (2018) 182 [arXiv:1805.00867] [INSPIRE].
E.A. Reyes R. and A.R. Fazio, Comparison of the EFT Hybrid and Three-Loop Fixed-Order Calculations of the Lightest MSSM Higgs Boson Mass, Phys. Rev. D 100 (2019) 115017 [arXiv:1908.00693] [INSPIRE].
R.V. Harlander, J. Klappert and A. Voigt, The light CP-even MSSM Higgs mass including N3LO+N3LL QCD corrections, Eur. Phys. J. C 80 (2020) 186 [arXiv:1910.03595] [INSPIRE].
H. Bahl, S. Heinemeyer, W. Hollik and G. Weiglein, Theoretical uncertainties in the MSSM Higgs boson mass calculation, Eur. Phys. J. C 80 (2020) 497 [arXiv:1912.04199] [INSPIRE].
P. Athron, J.-h. Park, D. Stöckinger and A. Voigt, FlexibleSUSY — A spectrum generator generator for supersymmetric models, Comput. Phys. Commun. 190 (2015) 139 [arXiv:1406.2319] [INSPIRE].
H. Bahl, Pole mass determination in presence of heavy particles, JHEP 02 (2019) 121 [arXiv:1812.06452] [INSPIRE].
J. Fleischer, F. Jegerlehner, O.V. Tarasov and O.L. Veretin, Two loop QCD corrections of the massive fermion propagator, Nucl. Phys. B 539 (1999) 671 [Erratum ibid. 571 (2000) 511] [hep-ph/9803493] [INSPIRE].
A.V. Bednyakov, Running mass of the b-quark in QCD and SUSY QCD, Int. J. Mod. Phys. A 22 (2007) 5245 [arXiv:0707.0650] [INSPIRE].
A. Bednyakov, A. Onishchenko, V. Velizhanin and O. Veretin, Two loop \( O\left({\alpha}_s^2\right) \) MSSM corrections to the pole masses of heavy quarks, Eur. Phys. J. C 29 (2003) 87 [hep-ph/0210258] [INSPIRE].
A. Bednyakov, D.I. Kazakov and A. Sheplyakov, On the two-loop \( O\left({\alpha}_s^2\right) \) corrections to the pole mass of the t-quark in the MSSM, Phys. Atom. Nucl. 71 (2008) 343 [hep-ph/0507139] [INSPIRE].
J.R. Espinosa and R.-J. Zhang, Complete two loop dominant corrections to the mass of the lightest CP even Higgs boson in the minimal supersymmetric standard model, Nucl. Phys. B 586 (2000) 3 [hep-ph/0003246] [INSPIRE].
G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
S.P. Martin and D.G. Robertson, Higgs boson mass in the Standard Model at two-loop order and beyond, Phys. Rev. D 90 (2014) 073010 [arXiv:1407.4336] [INSPIRE].
C. Ford, I. Jack and D.R.T. Jones, The Standard model effective potential at two loops, Nucl. Phys. B 387 (1992) 373 [Erratum ibid. 504 (1997) ] [hep-ph/0111190] [INSPIRE].
D.M. Pierce, J.A. Bagger, K.T. Matchev and R.-j. Zhang, Precision corrections in the minimal supersymmetric standard model, Nucl. Phys. B 491 (1997) 3 [hep-ph/9606211] [INSPIRE].
L.J. Hall, R. Rattazzi and U. Sarid, The Top quark mass in supersymmetric SO(10) unification, Phys. Rev. D 50 (1994) 7048 [hep-ph/9306309] [INSPIRE].
M. Carena, M. Olechowski, S. Pokorski and C.E.M. Wagner, Electroweak symmetry breaking and bottom-top Yukawa unification, Nucl. Phys. B 426 (1994) 269 [hep-ph/9402253] [INSPIRE].
M. Carena, D. Garcia, U. Nierste and C.E.M. Wagner, Effective Lagrangian for the \( \overline{t}{bH}^{+} \) interaction in the MSSM and charged Higgs phenomenology, Nucl. Phys. B 577 (2000) 88 [hep-ph/9912516] [INSPIRE].
L. Hofer, U. Nierste and D. Scherer, Resummation of tan-beta-enhanced supersymmetric loop corrections beyond the decoupling limit, JHEP 10 (2009) 081 [arXiv:0907.5408] [INSPIRE].
T. Kwasnitza and D. Stöckinger, Resummation of QCD-enhanced squark-mixing contributions in Higgs mass calculations, in preparation.
L.N. Mihaila, J. Salomon and M. Steinhauser, Gauge Coupling β-functions in the Standard Model to Three Loops, Phys. Rev. Lett. 108 (2012) 151602 [arXiv:1201.5868] [INSPIRE].
A.V. Bednyakov, A.F. Pikelner and V.N. Velizhanin, Anomalous dimensions of gauge fields and gauge coupling β-functions in the Standard Model at three loops, JHEP 01 (2013) 017 [arXiv:1210.6873] [INSPIRE].
A.V. Bednyakov, A.F. Pikelner and V.N. Velizhanin, Yukawa coupling β-functions in the Standard Model at three loops, Phys. Lett. B 722 (2013) 336 [arXiv:1212.6829] [INSPIRE].
K.G. Chetyrkin and M.F. Zoller, Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the Standard Model, JHEP 06 (2012) 033 [arXiv:1205.2892] [INSPIRE].
A.V. Bednyakov, A.F. Pikelner and V.N. Velizhanin, Higgs self-coupling β-function in the Standard Model at three loops, Nucl. Phys. B 875 (2013) 552 [arXiv:1303.4364] [INSPIRE].
K.G. Chetyrkin and M.F. Zoller, Leading QCD-induced four-loop contributions to the β-function of the Higgs self-coupling in the SM and vacuum stability, JHEP 06 (2016) 175 [arXiv:1604.00853] [INSPIRE].
S.P. Martin, Four-Loop Standard Model Effective Potential at Leading Order in QCD, Phys. Rev. D 92 (2015) 054029 [arXiv:1508.00912] [INSPIRE].
A.V. Bednyakov and A.F. Pikelner, Four-loop strong coupling β-function in the Standard Model, Phys. Lett. B 762 (2016) 151 [arXiv:1508.02680] [INSPIRE].
I. Jack, D.R.T. Jones and A.F. Kord, Three loop soft running, benchmark points and semiperturbative unification, Phys. Lett. B 579 (2004) 180 [hep-ph/0308231] [INSPIRE].
I. Jack, D.R.T. Jones and A.F. Kord, Snowmass benchmark points and three-loop running, Annals Phys. 316 (2005) 213 [hep-ph/0408128] [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].
S.P. Martin, Top-quark pole mass in the tadpole-free \( \overline{MS} \) scheme, Phys. Rev. D 93 (2016) 094017 [arXiv:1604.01134] [INSPIRE].
S. Fanchiotti, B.A. Kniehl and A. Sirlin, Incorporation of QCD effects in basic corrections of the electroweak theory, Phys. Rev. D 48 (1993) 307 [hep-ph/9212285] [INSPIRE].
S. Bethke, The 2009 World Average of αs, Eur. Phys. J. C 64 (2009) 689 [arXiv:0908.1135] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
ATLAS, CDF, CMS and D0 collaborations, First combination of Tevatron and LHC measurements of the top-quark mass, arXiv:1403.4427 [INSPIRE].
S.P. Martin and M.T. Vaughn, Two loop renormalization group equations for soft supersymmetry breaking couplings, Phys. Rev. D 50 (1994) 2282 [Erratum ibid. 78 (2008) 039903] [hep-ph/9311340] [INSPIRE].
J.R. Espinosa and R.-J. Zhang, MSSM lightest CP even Higgs boson mass to O(αsαt): The Effective potential approach, JHEP 03 (2000) 026 [hep-ph/9912236] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2003.04639
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Kwasnitza, T., Stöckinger, D. & Voigt, A. Improved MSSM Higgs mass calculation using the 3-loop FlexibleEFTHiggs approach including xt-resummation. J. High Energ. Phys. 2020, 197 (2020). https://doi.org/10.1007/JHEP07(2020)197
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2020)197