Higher-order calculations in the µ ν SSM Thomas Biek¨ otter in collaboration with Sven Heinemeyer and Carlos Mu˜ noz [hep-ph/1712.07475] Instituto de F´ ısica Te´ orica (UAM-CSIC) Universidad Aut´ onoma de Madrid 07/2018 SUSY18 Barcelona 1 / 20
Introduction The µ ν SSM Scalar potential Renormalization Results Conclusion Why higher-order corrections? - Accurate predictions ( ∆ theo. < ∆ exp. ) for precisely measured observables need to take into account quantum corrections - Every model has to incorporate a SM-like Higgs boson with the properties measured at LHC M e xp = 125 . 09 ± 0 . 21 (stat.) ± 0 . 11 (syst.) GeV H Atlas and CMS [hep-ex/1503.07589] Already a precision observable at the per-mille level! 2 / 20
Introduction The µ ν SSM Scalar potential Renormalization Results Conclusion Why higher-order corrections? - Accurate predictions ( ∆ theo. < ∆ exp. ) for precisely measured observables need to take into account quantum corrections - Every model has to incorporate a SM-like Higgs boson with the properties measured at LHC M e xp = 125 . 09 ± 0 . 21 (stat.) ± 0 . 11 (syst.) GeV H Atlas and CMS [hep-ex/1503.07589] Already a precision observable at the per-mille level! - While in the SM M H is a free parameter, SUSY models predict the Higgs boson mass dependent on the parameters of the model - Higher-order corrections to scalar masses give substantial contributions, in some cases of the order of the tree-level mass ⇒ Large theoretical uncertainties: ∼ 3 GeV (MSSM) Degrassi, Heinemeyer, Hollik, Slavich, Weiglein [hep-ph/0212020] Maybe now ∼ 2 GeV ? Allanach, Voigt [hep-ph/1804.09410] Bahl, Hollik [hep-ph/1805.00867] 2 / 20
Introduction The µ ν SSM Scalar potential Renormalization Results Conclusion Why higher-order corrections? - Accurate predictions ( ∆ theo. < ∆ exp. ) for precisely measured observables need to take into account quantum corrections - Every model has to incorporate a SM-like Higgs boson with the properties measured at LHC M e xp = 125 . 09 ± 0 . 21 (stat.) ± 0 . 11 (syst.) GeV H Atlas and CMS [hep-ex/1503.07589] Already a precision observable at the per-mille level! - While in the SM M H is a free parameter, SUSY models predict the Higgs boson mass dependent on the parameters of the model - Higher-order corrections to scalar masses give substantial contributions, in some cases of the order of the tree-level mass ⇒ Large theoretical uncertainties: ∼ 3 GeV (MSSM) Degrassi, Heinemeyer, Hollik, Slavich, Weiglein [hep-ph/0212020] Maybe now ∼ 2 GeV ? Allanach, Voigt [hep-ph/1804.09410] Bahl, Hollik [hep-ph/1805.00867] Any model beyond the MSSM potentially has even larger uncertainty ⇒ We present full one-loop + partial MSSM-like two-loop corrections to scalar masses in the µ ⌫ SSM. 2 / 20
Introduction The µ ν SSM Scalar potential Renormalization Results Conclusion Why go beyond MSSM? – No new physics at LHC (so far) – Big loop-corrections to Higgs mass needed (fine-tuning) – µ -problem (MSSM superpotential has a scale) – ⌫ -problem: Neutrino masses Why are they so light? from 2013 J. Phys.: Conf. Ser. 408 012015 3 / 20
Introduction The µ ν SSM Scalar potential Renormalization Results Conclusion Why go beyond MSSM? – No new physics at LHC (so far) – Big loop-corrections to Higgs mass needed (fine-tuning) – µ -problem (MSSM superpotential has a scale) – ⌫ -problem: Neutrino masses Why are they so light? from 2013 J. Phys.: Conf. Ser. 408 012015 µ ν SSM: Simplest extension of the MSSM solving the µ - and the ν -problem at the same time. 3 / 20
Introduction The µ ν SSM Scalar potential Renormalization Results Conclusion Why go beyond MSSM? – No new physics at LHC (so far) – Big loop-corrections to Higgs mass needed (fine-tuning) – µ -problem (MSSM superpotential has a scale) – ⌫ -problem: Neutrino masses Why are they so light? from 2013 J. Phys.: Conf. Ser. 408 012015 µ ν SSM: Simplest extension of the MSSM solving the µ - and the ν -problem at the same time. ⌫ c Particle content: MSSM + 3 (1) gauge singlets ˆ j ij ˆ H u ˆ Couplings: Y ν ⌫ c L i ˆ j ) gauge singlet = right-handed neutrino ! EWSB ) Dirac masses for neutrinos ( Y ν ii ⇡ Y e 11 ) i ˆ H u ˆ ⌫ c H d , 1 ⌫ c ⌫ c ⌫ c � i ˆ 3 ijk ˆ i ˆ j ˆ k (NMSSM-like) ! EWSB ) E ff ective µ -term generated at EW scale ! EWSB ) Majorana masses for R-handed neutrinos Lopez-Fogliani, Munoz [hep-ph/0508297] Escudero, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/0810.1507] 3 / 20
Introduction The µ ν SSM Scalar potential Renormalization Results Conclusion Lagrangian and Symmetries ⇣ ⌘ Y e ij ˆ H a d ˆ L b e c j + Y d ij ˆ H a d ˆ Q b i ˆ d c j + Y u ij ˆ H b u ˆ Q a u c W = ✏ ab i ˆ i ˆ j + 1 ⇣ ⌘ ij ˆ H b u ˆ L a ⌫ c ⌫ c i ˆ H b u ˆ H a ⌫ c ⌫ c ⌫ c Y ν + ✏ ab i ˆ j − � i ˆ 3 ijk ˆ i ˆ j ˆ d k – Z 3 symmetry forbids µ -term and Majorana masses ! no scale in superpotential – R -parity explicitly broken (via / L ) ! more complicated particle mixing – Additinal sources of LFV after EWSB – Baryon Triality B 3 to forbid baryon number violation ! no proton decay 4 / 20
Introduction The µ ν SSM Scalar potential Renormalization Results Conclusion Lagrangian and Symmetries ⇣ ⌘ Y e ij ˆ H a d ˆ L b e c j + Y d ij ˆ H a d ˆ Q b i ˆ d c j + Y u ij ˆ H b u ˆ Q a u c W = ✏ ab i ˆ i ˆ j + 1 ⇣ ⌘ ij ˆ H b u ˆ L a ⌫ c ⌫ c i ˆ H b u ˆ H a ⌫ c ⌫ c ⌫ c Y ν + ✏ ab i ˆ j − � i ˆ 3 ijk ˆ i ˆ j ˆ d k – Z 3 symmetry forbids µ -term and Majorana masses ! no scale in superpotential – R -parity explicitly broken (via / L ) ! more complicated particle mixing – Additinal sources of LFV after EWSB – Baryon Triality B 3 to forbid baryon number violation ! no proton decay ⇣ ⌘ T e ij H a d e L b e ⇤ jR + T d ij H a d e Q b iL e d ⇤ jR + T u ij H b u e Q a u ⇤ � L soft = ✏ ab iL e iL e jR + h.c. ✓ ◆ u + 1 T ν ij H b u e L a ⌫ ⇤ jR � T λ ⌫ ⇤ iR H a d H b 3 T κ ⌫ ⇤ ⌫ ⇤ ⌫ ⇤ + iL e e ijk e iR e jR e kR + h.c. ✏ ab i ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ m 2 Q a ⇤ e iL e Q a m 2 u ⇤ m 2 d ⇤ e iR e m 2 e L a ⇤ iL e L a + jL + ij e iR e u jR + d jR + e e e e QL uR dR LL jL ij ij ij ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ m 2 i H a ⇤ d e L a m 2 ⌫ ⇤ m 2 e ⇤ e jR + m 2 Hd H a ⇤ H a d + m 2 Hu H a ⇤ H a + iL + ij e iR e ⌫ jR + ij e iR e Hd e e ν R e eR d u u LL ⇣ ⌘ 1 B 0 e B 0 + h.c. g + M 2 f W f W + M 1 e + M 3 e g e 2 We put soft masses mixing di ff erent fields to zero at tree-level, explained by diagonal K¨ ahler metric in certain Sugra models Brignole, Ibanez, Munoz [hep-ph/9707209] Ghosh, Lara, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/1707.02471] 4 / 20
Introduction The µ ν SSM Scalar potential Renormalization Results Conclusion Particle Spectrum and Phenomenology 8 (6) CP-even neutral scalars: ' T = ( H R d , H R ⌫ R ⌫ R u , e iR , e jL ) Left and right sneutrinos can be lighter than 125GeV Mixing of left sneutrinos to H suppressed by Y ν and v L 8 (6) CP-odd neutral scalars: � T = ( H I d , H I ⌫ I ⌫ I u , e iR , e jL ) Includes the neutral Goldstone boson Mixing of left sneutrinos to H suppressed by Y ν and v L 8 charged sleptons: C T = ( H � ⇤ , H + e ⇤ e ⇤ u , e iL , e jR ) d Includes the charged Goldstone boson Mixing of sleptons to H suppressed by Y ν and v L 5 charginos: ( � � ) T = (( e iL ) c ⇤ , f d ) , ( � + ) T = (( e jR ) c , f W � , e W + , e H � H + u ) Three light states corresponding to e , µ and ⌧ Mixing of leptons to gauginos suppressed by Y ν and v L 10 (8) Majorana fermions: ( � 0 ) T = (( ⌫ iL ) c ⇤ , e B 0 , f W 0 , e H 0 d , e H 0 u , ⌫ ⇤ jR ) Type-I seesaw at EW scale Mass matrix of rank 10 (6) ) 0 (2) massless states at tree-level 3 (1) neutrino masses of O ( < eV) at tree-level 3 (1) heavy right-handed neutrinos of O ( < TeV) 5 / 20
Introduction The µ ν SSM Scalar potential Renormalization Results Conclusion Particle Spectrum and Phenomenology Collider: MSSM-bounds from Atlas/CMS usually do not hold in the µ ⌫ SSM The LSP 1 can be charged or colored ! Opens distinct regions of parameter space ! Di ff erent decay channels Displaced vertices: Sneutrino: O (mm), Singlino: O (m) Ghosh, Lara, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/1707.02471] Lara, Lopez-Fogliani, Munoz, Nagata, Otono, Ruiz de Austri [hep-ph/1804.00067] Novel signals: FS with multi-/leptons/jets, �� + leptons/ / E T Ghosh, Lara, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/1707.02471] Ghosh, Lopez-Fogliani, Mitsou, Munoz, Ruiz de Austri [hep-ph/1410.2070] Ghosh, Lopez-Fogliani, Mitsou, Munoz, Ruiz de Austri [hep-ph/1211.3177] Ghosh, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/1107.4614] 1 Forgetting about the gravitino because it is not relevant for colliders 6 / 20
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