Higher-order calculations in the ivSSM - Thomas Biekötter

Higher-order calculations in the µνSSM

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

10/2018

X CPAN Days, Salamanca

1 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Why Supersymmetry?

- Solves the hierarchy problem - Gauge coupling unification - Can provide Dark Matter - Predicted a light Higgs

- Only way to combine spacetime and internal symmetries

(Coleman-Mandula theorem)

Doroshkevich, Lukash, Mikheeva [astro-ph/1209.0388]

Martin [hep-ph/9709356]

Dedes, Heinemeyer, Teixeira-Dias, Weiglein [hep-ph/9912249]

2 / 16

Introduction TheµνSSM 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) - ν-problem: Neutrino masses

Why are they so light?

µνSSM: Simplest extension of the MSSM solving the µ- and the ν-problem at the same time.

Particle content: MSSM +3(1) gauge singlets ˆν^c_j¹

Couplings: Y_ij^νHˆuLˆiνˆ_j^c⇒gauge singlet = right-handed neutrino

→EWSB⇒Dirac masses for neutrinos (Y_ii^ν≈Y₁₁^e) λiνˆ_i^cHˆuHˆd, ¹₃κijkνˆ_i^cνˆ^c_jνˆ_k^c(NMSSM-like)

→EWSB⇒Effectiveµ-term generated at EW scale

→EWSB⇒Additional tree-level contribution to SM-like Higgs mass

→EWSB⇒Majorana masses for R-handed neutrinos

Lopez-Fogliani, Munoz [hep-ph/0508297] Escudero, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/0810.1507] 1Red indices in case of 3 singlets

3 / 16

Introduction TheµνSSM 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) - ν-problem: Neutrino masses

Why are they so light?

µνSSM: Simplest extension of the MSSM solving the µ- and the ν -problem at the same time.

Particle content: MSSM +3(1) gauge singlets ˆν^c_j¹

Couplings: Y_ij^νHˆuLˆiνˆ_j^c⇒gauge singlet = right-handed neutrino

→EWSB⇒Dirac masses for neutrinos (Y_ii^ν≈Y₁₁^e) λiνˆ_i^cHˆuHˆd, ¹₃κijkνˆ_i^cνˆ^c_jνˆ_k^c(NMSSM-like)

→EWSB⇒Effectiveµ-term generated at EW scale

→EWSB⇒Additional tree-level contribution to SM-like Higgs mass

→EWSB⇒Majorana masses for R-handed neutrinos

Lopez-Fogliani, Munoz [hep-ph/0508297] Escudero, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/0810.1507] 1Red indices in case of 3 singlets

3 / 16

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) - ν-problem: Neutrino masses

Why are they so light?

µνSSM: Simplest extension of the MSSM solving the µ- and the ν -problem at the same time.

Particle content: MSSM +3(1) gauge singlets ˆν^c_j¹

Couplings: Y_ij^νHˆuLˆiνˆ_j^c⇒gauge singlet = right-handed neutrino

→EWSB⇒Dirac masses for neutrinos (Y_ii^ν≈Y₁₁^e) λiνˆ_i^cHˆuHˆd, ¹₃κijkνˆ_i^cˆν^c_jνˆ_k^c(NMSSM-like)

→EWSB⇒Effectiveµ-term generated at EW scale

→EWSB⇒Additional tree-level contribution to SM-like Higgs mass

→EWSB⇒Majorana masses for R-handed neutrinos

Lopez-Fogliani, Munoz [hep-ph/0508297]

Escudero, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/0810.1507]

1Red indices in case of 3 singlets 3 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Why higher-order corrections?

- Accurate predictions (∆

≤ ∆

) 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

= 125.09 ± 0.21 (stat.) ± 0.11 (syst.) GeV

Atlas and CMS [hep-ex/1503.07589]

Already a precision observable at the per-mille level!

- While in the SM M

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: ∼ 2 − 3 GeV (MSSM)

Degrassi, Heinemeyer, Hollik, Slavich, Weiglein [hep-ph/0212020] 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 µνSSM.

4 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Why higher-order corrections?

- Accurate predictions (∆

≤ ∆

) 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

= 125.09 ± 0.21 (stat.) ± 0.11 (syst.) GeV

Atlas and CMS [hep-ex/1503.07589]

Already a precision observable at the per-mille level!

- While in the SM M

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: ∼ 2 − 3 GeV (MSSM)

Degrassi, Heinemeyer, Hollik, Slavich, Weiglein [hep-ph/0212020]

Allanach, Voigt [hep-ph/1804.09410]

Bahl, Hollik [hep-ph/1805.00867]

⇒ We present full one-loop + partial MSSM-like two-loop corrections to scalar masses in the µνSSM.

4 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Why higher-order corrections?

- Accurate predictions (∆

≤ ∆

) 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

= 125.09 ± 0.21 (stat.) ± 0.11 (syst.) GeV

Atlas and CMS [hep-ex/1503.07589]

Already a precision observable at the per-mille level!

- While in the SM M

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: ∼ 2 − 3 GeV (MSSM)

Degrassi, Heinemeyer, Hollik, Slavich, Weiglein [hep-ph/0212020]

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 µνSSM.

4 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Higgs mass prediction in Susy models

Two frameworks:

1. Feynman-diagrammatic (fixed-order) calculation 2. Effective field theory (RG) calculation

Fixed order: SuSpect, H3m, SoftSUSY/FlexibleSUSY, Himalaya

EFT: SusyHd, MhEFT, HSSUSY

Hybrid: FeynHiggs, SPheno/SARAH, FlexibleEFTHiggs

Beyond MSSM models have to catch up! NMSSM:

SoftSUSY/FlexibleSUSY, NMSSM-FeynHiggs, NMSSMCALC, NMSSMTools

µνSSM:

5 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Higgs mass prediction in Susy models

Two frameworks:

1. Feynman-diagrammatic (fixed-order) calculation 2. Effective field theory (RG) calculation

Public codes for theMSSM:

Fixed order: SuSpect, H3m, SoftSUSY/FlexibleSUSY, Himalaya

EFT: SusyHd, MhEFT, HSSUSY

Hybrid: FeynHiggs, SPheno/SARAH, FlexibleEFTHiggs

Beyond MSSM models have to catch up! NMSSM:

SoftSUSY/FlexibleSUSY, NMSSM-FeynHiggs, NMSSMCALC, NMSSMTools

µνSSM:

5 / 16

Higgs mass prediction in Susy models

Two frameworks:

1. Feynman-diagrammatic (fixed-order) calculation 2. Effective field theory (RG) calculation

Public codes for theMSSM:

Fixed order: SuSpect, H3m, SoftSUSY/FlexibleSUSY, Himalaya

EFT: SusyHd, MhEFT, HSSUSY

Hybrid: FeynHiggs, SPheno/SARAH, FlexibleEFTHiggs

Beyond MSSM models have to catch up!

NMSSM:

µνSSM:

5 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Here: Full 1L corrections in the real µνSSM + MSSM-like higher order

TB, Heinemeyer, Munoz [hep-ph/1712.07475]

Conceptuallyas close as possible to MSSM calculation of FeynHiggs:

- Feynman-diagrammatic calculation - Mixed On Shell-DR scheme - Same set of free parameters

⇒ Allows to supplement higher-order corrections from FeynHiggs 2L:O(αsαt, αsαb, α²_t, αtαb)

Resummed contributions of large logs Simplifications:

– NoCP-violation

– No flavor-violation in (s)quark-sector

µνSSM complicated than MSSM:

- More particles - R-parity breaking (and L, L-flavour)

→ - More parameters - More mixing - More VEVs

→

- More diagrams - Larger amplitudes

- Renormalization more complicated

For instance:

MSSM: 112 diagrams

MSSM: 492 diagrams

µνSSM: 377 diagrams

µνSSM: 7813 diagrams

6 / 16

Here: Full 1L corrections in the real µνSSM + MSSM-like higher order

TB, Heinemeyer, Munoz [hep-ph/1712.07475]

Conceptuallyas close as possible to MSSM calculation of FeynHiggs:

- Feynman-diagrammatic calculation - Mixed On Shell-DR scheme - Same set of free parameters

⇒ Allows to supplement higher-order corrections from FeynHiggs 2L:O(αsαt, αsαb, α²_t, αtαb)

Resummed contributions of large logs Simplifications:

– NoCP-violation

– No flavor-violation in (s)quark-sector

µνSSM complicated than MSSM:

- More particles - R-parity breaking (and L, L-flavour)

→ - More parameters - More mixing - More VEVs

→

- More diagrams - Larger amplitudes

- Renormalization more complicated

For instance:

MSSM: 112 diagrams

MSSM: 492 diagrams

µνSSM: 377 diagrams

µνSSM: 7813 diagrams

6 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Lagrangian and Symmetries

W =

Y

H ˆ

L ˆ

e ˆ

+ Y

H ˆ

Q ˆ

d ˆ

+ Y

H ˆ

Q ˆ

u ˆ

+

Y

H ˆ

L ˆ

ν ˆ

− λ

ν ˆ

H ˆ

H ˆ

+ 1

3 κ

ν ˆ

ˆ ν

ν ˆ

– Z₃symmetry forbidsµ-term and Majorana masses→no scale in superpotential – R-parity explicitly broken (via/L)→more complicated particle mixing – Y_ii^ν∼Y₁₁^e ⇒Neutrino masses and mixings provided naturally from EW seesaw – Y_ii^ν→0: R-parity conserved, R-parity violating effects small (Couplings and mixings) – Baryon TrialityB₃to forbid baryon number violation→no proton decay

−Lsoft= _ab

T_ij^eH^a_deL^b_iLee_jR^∗+T_ij^dH_d^aQe_iL^bde_jR^∗+T_ij^uH^b_uQe^a_iLeu_jR^∗+ h.c.

+ _ab

T_ij^νH_u^beL^a_iLeν_jR^∗−T_i^λeν_iR^∗H_d^aH^b_u+1

3T_ijk^κeν^∗_iReν^∗_jReν_kR^∗ + h.c.

+

m²

QLe

ijQe^a∗_iLQe^a_jL+ m²

euR

ijue^∗_iRuejR+ m²

dRe

ijde_iR^∗dejR+ m²

eLL

ijeL^a∗_iLLe^a_jL

+

m²

HdeLL

iH_d^a∗eL^a_iL+ m²

νeR

ijeν_iR^∗νejR+ m²

eeR

ijee_iR^∗eejR+m²_HdH_d^a∗H_d^a+m²_HuH_u^a∗H_u^a

+ 1

2

M₃egge+M₂WfWf+M₁Be⁰Be⁰+ h.c.

We put soft masses mixing different 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]

7 / 16

Lagrangian and Symmetries

W =

Y

H ˆ

L ˆ

e ˆ

+ Y

H ˆ

Q ˆ

d ˆ

+ Y

H ˆ

Q ˆ

u ˆ

+

Y

H ˆ

L ˆ

ν ˆ

− λ

ν ˆ

H ˆ

H ˆ

+ 1

3 κ

ν ˆ

ˆ ν

ν ˆ

– Z₃symmetry forbidsµ-term and Majorana masses→no scale in superpotential – R-parity explicitly broken (via/L)→more complicated particle mixing – Y_ii^ν∼Y₁₁^e ⇒Neutrino masses and mixings provided naturally from EW seesaw – Y_ii^ν→0: R-parity conserved, R-parity violating effects small (Couplings and mixings) – Baryon TrialityB₃to forbid baryon number violation→no proton decay

−Lsoft= _ab

T_ij^eH^a_deL^b_iLee_jR^∗+T_ij^dH_d^aQe_iL^bde_jR^∗+T_ij^uH^b_uQe^a_iLeu_jR^∗+ h.c.

+ _ab

T_ij^νH_u^beL^a_iLeν_jR^∗−T_i^λeν_iR^∗H_d^aH_u^b+1

3T_ijk^κeν^∗_iReν^∗_jReν_kR^∗ + h.c.

+

m²

QLe

ijQe_iL^a∗Qe^a_jL+ m²

euR

ijue^∗_iRuejR+ m²

edR

ijde_iR^∗dejR+ m²

eLL

ijeL^a∗_iLLe^a_jL

+

m²

HdeLL

iH^a∗_d eL^a_iL+ m²

νeR

ijeν_iR^∗eν_jR+ m²

eeR

ijee_iR^∗ee_jR+m²_HdH^a_d^∗H_d^a+m²_HuH_u^a∗H^a_u

+ 1

2

M₃egge+M₂WfWf+M₁Be⁰Be⁰+ h.c.

We put soft masses mixing different 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]

7 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Particle spectrum

”Higgses”:

CP-even: (H_d^R,H_u^R,νe_iR^R,νe_jL^R)

⇒Includesh^SM CP-odd: (H_d^I,H_u^I,eν_iR^I,eν^I_jL)

⇒Includes one unphysical GB Charged: (H_d^−∗,H_u⁺,ee_iL^∗,ee^∗_jR)

⇒Includes one unphysical GB

”Neutralinos”:

((νiL)^c∗,Be⁰,Wf⁰,He⁰_d,He⁰_u, ν^∗_jR)

⇒3 light neutrinos, MSSM-like neutralinos, 3 heavy sterile neutrinos

”Charginos”:

((e_jR)^c,Wf⁺,He_u⁺)

⇒e,µ,τ, gaugino, Higgsino

Quarks and squarks practically like in MSSM.

Phenomenology

Collider: MSSM-bounds from Atlas/CMS usually do not hold in theµνSSM The LSP can be charged or colored

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,γγ+ 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]

Talk tomorrow, Inaki Lara Perez:µνSSM and stealth bosons at the LHC Dark Matter: Gravitino (one possiblity) with lifetime longer than age of universe

Albert, Gomez-Vargas, Grefe, Munoz, Weniger, Bloom, Charles, Mazziotta, Morselli [hep-ph/1406.3430] Gomez-Vargas, Lopez-Fogliani, Munoz, Perez, Ruiz de Austri [hep-ph/1608.08640]

Neutrinos: δm²₁₂, ∆m²₁₃and ands₁₂²,s₁₃²,s₂₃² can be reproduced (NO and IO) Electroweak seesaw withY_ii^ν∼Y^e∼10⁻⁶

8 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Particle spectrum

”Higgses”:

CP-even: (H_d^R,H_u^R,νe_iR^R,νe_jL^R)

⇒Includesh^SM CP-odd: (H_d^I,H_u^I,eν_iR^I,eν^I_jL)

⇒Includes one unphysical GB Charged: (H_d^−∗,H_u⁺,ee_iL^∗,ee^∗_jR)

⇒Includes one unphysical GB

”Neutralinos”:

((νiL)^c∗,Be⁰,Wf⁰,He⁰_d,He⁰_u, ν^∗_jR)

⇒3 light neutrinos, MSSM-like neutralinos, 3 heavy sterile neutrinos

”Charginos”:

((e_jR)^c,Wf⁺,He_u⁺)

⇒e,µ,τ, gaugino, Higgsino

Quarks and squarks practically like in MSSM.

Phenomenology

Collider: MSSM-bounds from Atlas/CMS usually do not hold in theµνSSM The LSP can be charged or colored

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,γγ+ 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]

Talk tomorrow, Inaki Lara Perez:µνSSM and stealth bosons at the LHC

Albert, Gomez-Vargas, Grefe, Munoz, Weniger, Bloom, Charles, Mazziotta, Morselli [hep-ph/1406.3430] Gomez-Vargas, Lopez-Fogliani, Munoz, Perez, Ruiz de Austri [hep-ph/1608.08640]

Neutrinos: δm²₁₂, ∆m²₁₃and ands₁₂²,s₁₃²,s₂₃² can be reproduced (NO and IO) Electroweak seesaw withY_ii^ν∼Y^e∼10⁻⁶

8 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Particle spectrum

”Higgses”:

CP-even: (H_d^R,H_u^R,νe_iR^R,νe_jL^R)

⇒Includesh^SM CP-odd: (H_d^I,H_u^I,eν_iR^I,eν^I_jL)

⇒Includes one unphysical GB Charged: (H_d^−∗,H_u⁺,ee_iL^∗,ee^∗_jR)

⇒Includes one unphysical GB

”Neutralinos”:

((νiL)^c∗,Be⁰,Wf⁰,He⁰_d,He⁰_u, ν^∗_jR)

⇒3 light neutrinos, MSSM-like neutralinos, 3 heavy sterile neutrinos

”Charginos”:

((e_jR)^c,Wf⁺,He_u⁺)

⇒e,µ,τ, gaugino, Higgsino

Quarks and squarks practically like in MSSM.

Phenomenology

Collider: MSSM-bounds from Atlas/CMS usually do not hold in theµνSSM The LSP can be charged or colored

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,γγ+ 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]

Talk tomorrow, Inaki Lara Perez:µνSSM and stealth bosons at the LHC Dark Matter: Gravitino (one possiblity) with lifetime longer than age of universe

Albert, Gomez-Vargas, Grefe, Munoz, Weniger, Bloom, Charles, Mazziotta, Morselli [hep-ph/1406.3430]

Gomez-Vargas, Lopez-Fogliani, Munoz, Perez, Ruiz de Austri [hep-ph/1608.08640]

Neutrinos: δm²₁₂, ∆m²₁₃and ands₁₂²,s₁₃²,s₂₃² can be reproduced (NO and IO) Electroweak seesaw withY_ii^ν∼Y^e∼10⁻⁶

8 / 16

Particle spectrum

”Higgses”:

CP-even: (H_d^R,H_u^R,νe_iR^R,νe_jL^R)

⇒Includesh^SM CP-odd: (H_d^I,H_u^I,eν_iR^I,eν^I_jL)

⇒Includes one unphysical GB Charged: (H_d^−∗,H_u⁺,ee_iL^∗,ee^∗_jR)

⇒Includes one unphysical GB

”Neutralinos”:

((νiL)^c∗,Be⁰,Wf⁰,He⁰_d,He⁰_u, ν^∗_jR)

⇒3 light neutrinos, MSSM-like neutralinos, 3 heavy sterile neutrinos

”Charginos”:

((e_jR)^c,Wf⁺,He_u⁺)

⇒e,µ,τ, gaugino, Higgsino

Quarks and squarks practically like in MSSM.

Phenomenology

Collider: MSSM-bounds from Atlas/CMS usually do not hold in theµνSSM The LSP can be charged or colored

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,γγ+ 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]

Talk tomorrow, Inaki Lara Perez:µνSSM and stealth bosons at the LHC Dark Matter: Gravitino (one possiblity) with lifetime longer than age of universe

Albert, Gomez-Vargas, Grefe, Munoz, Weniger, Bloom, Charles, Mazziotta, Morselli [hep-ph/1406.3430]

Gomez-Vargas, Lopez-Fogliani, Munoz, Perez, Ruiz de Austri [hep-ph/1608.08640]

Neutrinos: δm²₁₂, ∆m²₁₃and ands₁₂²,s₁₃²,s₂₃² can be reproduced (NO and IO) Electroweak seesaw withY_ii^ν∼Y^e∼10⁻⁶

8 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Higgs potential

Parts ofLcontributing:

WHiggs=ab

Yν ijHˆb

uLˆa iνˆc

j −λiνˆc i Hˆb

uHˆa d

+1 3

κijkνˆc iνˆc

jνˆc k LHiggs

soft =ab

Tν ijHb

ueLa iLνe∗

jR−Tλ

i νe∗ iR Ha

d Hb u+1

3Tκ ijkνe∗

iRνe∗ jRνe∗

kR + h.c.

+

m2 eLL

ij eLa∗

iLeLa jL+

m2

HdLLe

i Ha∗

d Lea iL+

m2

νeR

ijeν∗ ReνR+m2

HdHa d∗Ha

d+m2 HuHa

u∗Ha u

↓

– Absent in tree-level Lagrangian because it spoils the EW seesaw mechanism

⇒viL→0 whenYν ii →0

– Justified if one assumes diagonal K¨ahler metric in certain supergravity models Brignole, Ibanez, Munoz [hep-ph/9707209] Ghosh, Lara, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/1707.02471] – Included here because needed for renormalization already at one-loop (however =0 at tree-level)

AssumingCP-conservation:

H0 d= 1

√2

HR d +vd+ iHI

d

, H0 u= 1

√2

HR u +vu+ iHI

u

eνiR= 1

√2

νeR

iR+viR+ iνeI iR

, νeiL= 1

√2

νeR iL +viL+ iνeI

iL

vu,d,R

Replacements:

– m2 Hd,m2

Hu, m2 eLL

!

ii ,

m2

νeR

ii Tadpole eq.

−−−−−−−→T HR

d ,T

HR u

,T νeR

iL ,T

eνR iR

whereTϕ∼∂VHiggs

∂ϕ – vd,vu→tanβ,vwith tanβ=vu

vd,v2 =v2 u+v2

d+viLviL – g1 ,g2→M2

W,M2 ZwithM2

W = 14g2 2v2 ,M2

Z= 14(g2 1+g2

2)v2

9 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Higgs potential

Parts ofLcontributing:

WHiggs=ab

Yν ijHˆb

uLˆa iνˆc

j −λiνˆc i Hˆb

uHˆa d

+1 3

κijkνˆc iνˆc

jνˆc k LHiggs

soft =ab

Tν ijHb

ueLa iLνe∗

jR−Tλ

i νe∗ iR Ha

d Hb u+1

3Tκ ijkνe∗

iRνe∗ jRνe∗

kR + h.c.

+

m2 eLL

ij eLa∗

iLeLa jL+

m2

HdLLe

i Ha∗

d Lea iL+

m2

νeR

ijeν∗ ReνR+m2

HdHa d∗Ha

d+m2 HuHa

u∗Ha u

↓

– Absent in tree-level Lagrangian because it spoils the EW seesaw mechanism

⇒viL→0 whenYν ii →0

– Justified if one assumes diagonal K¨ahler metric in certain supergravity models Brignole, Ibanez, Munoz [hep-ph/9707209]

Ghosh, Lara, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/1707.02471]

– Included here because needed for renormalization already at one-loop (however =0 at tree-level)

H0 d= 1

√2

HR d +vd+ iHI

d

, H0 u= 1

√2

HR u +vu+ iHI

u

eνiR= 1

√2

νeR

iR+viR+ iνeI iR

, νeiL= 1

√2

νeR iL +viL+ iνeI

iL

vu,d,R

Replacements:

– m2 Hd,m2

Hu, m2 eLL

!

ii ,

m2

νeR

ii Tadpole eq.

−−−−−−−→T HR

d ,T

HR u

,T νeR

iL ,T

eνR iR

whereTϕ∼∂VHiggs

∂ϕ – vd,vu→tanβ,vwith tanβ=vu

vd,v2 =v2 u+v2

d+viLviL – g1 ,g2→M2

W,M2 ZwithM2

W = 14g2 2v2 ,M2

Z= 14(g2 1+g2

2)v2

9 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Higgs potential

Parts ofLcontributing:

WHiggs=ab

Yν ijHˆb

uLˆa iνˆc

j −λiνˆc i Hˆb

uHˆa d

+1 3

κijkνˆc iνˆc

jνˆc k LHiggs

soft =ab

Tν ijHb

ueLa iLνe∗

jR−Tλ

i νe∗ iR Ha

d Hb u+1

3Tκ ijkνe∗

iRνe∗ jRνe∗

kR + h.c.

+

m2 eLL

ij eLa∗

iLeLa jL+

m2

HdLLe

i Ha∗

d Lea iL+

m2

νeR

ijeν∗ ReνR+m2

HdHa d∗Ha

d+m2 HuHa

u∗Ha u

↓

– Absent in tree-level Lagrangian because it spoils the EW seesaw mechanism

⇒viL→0 whenYν ii →0

– Justified if one assumes diagonal K¨ahler metric in certain supergravity models Brignole, Ibanez, Munoz [hep-ph/9707209]

Ghosh, Lara, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/1707.02471]

– Included here because needed for renormalization already at one-loop (however =0 at tree-level)

AssumingCP-conservation:

H0 d= 1

√ 2

HR

d +vd+ iHI d

, H0

u= 1

√ 2

HR

u +vu+ iHI u

eνiR= 1

√2

νeR

iR+viR+ iνeI iR

, eνiL= 1

√2

νeR iL +viL+ iνeI

iL

vu,d,R

Replacements:

– m2 Hd,m2

Hu, m2 eLL

!

ii ,

m2

νeR

ii Tadpole eq.

−−−−−−−→T HR

d ,T

HR u

,T νeR

iL ,T

eνR iR

whereTϕ∼∂VHiggs

∂ϕ – vd,vu→tanβ,vwith tanβ=vu

vd,v2 =v2 u+v2

d+viLviL – g1 ,g2→M2

W,M2 ZwithM2

W = 14g2 2v2 ,M2

Z= 14(g2 1+g2

2)v2

9 / 16

Higgs potential

Parts ofLcontributing:

WHiggs=ab

Yν ijHˆb

uLˆa iνˆc

j −λiνˆc i Hˆb

uHˆa d

+1 3

κijkνˆc iνˆc

jνˆc k LHiggs

soft =ab

Tν ijHb

ueLa iLνe∗

jR−Tλ

i νe∗ iR Ha

d Hb u+1

3Tκ ijkνe∗

iRνe∗ jRνe∗

kR + h.c.

+

m2 eLL

ij eLa∗

iLeLa jL+

m2

HdLLe

i Ha∗

d Lea iL+

m2

νeR

ijeν∗ ReνR+m2

HdHa d∗Ha

d+m2 HuHa

u∗Ha u

↓

– Absent in tree-level Lagrangian because it spoils the EW seesaw mechanism

⇒viL→0 whenYν ii →0

– Justified if one assumes diagonal K¨ahler metric in certain supergravity models Brignole, Ibanez, Munoz [hep-ph/9707209]

Ghosh, Lara, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/1707.02471]

– Included here because needed for renormalization already at one-loop (however =0 at tree-level)

AssumingCP-conservation:

H0 d= 1

√ 2

HR

d +vd+ iHI d

, H0

u= 1

√ 2

HR

u +vu+ iHI u

eνiR= 1

√2

νeR

iR+viR+ iνeI iR

, eνiL= 1

√2

νeR iL +viL+ iνeI

iL

vu,d,R

Replacements:

– m2 Hd,m2

Hu, m2 eLL

!

ii ,

m2

νeR

ii Tadpole eq.

−−−−−−−→T HR

d ,T

HR u

,T νeR

iL ,T

eνR iR

whereTϕ∼∂VHiggs

∂ϕ – vd,vu→tanβ,vwith tanβ=vu

vd,v2 =v2 u+v2

d+viLviL – g1 ,g2→M2

W,M2 ZwithM2

W = 14g2 2v2 ,M2

Z= 14(g2 1+g2

2)v2

9 / 16

Introduction TheµνSSM Renormalization Results Conclusion

Renormalization scheme

Calculations in DR schemes have the disadvantage that parameters cannot directly be related to physical observables.

⇒ Mixed On-Shell/DR scheme

On-shell parameters:

T_HR d →T_HR

d

+δT_HR d

,

T_HR u →T_HR

u +δT_HR u , T

νeR

iR →T

νeR iR

+δT

eνR

iR ,

T

νeR iL →T

νeR iL

+δT

νeR iL

,

M_W² →M_W² +δM_W² ,

M_Z²→M_Z²+δM_Z². _δM2 V= Re ΣT

M2 V

DR parameters:

m²

eLL i6=j→m²

eLL i6=j+δm²

eLL i6=j, m²

HdeLL i→m²

HdeLL i+δm²_Hde

LL i, m²

νeRi6=j→m²

eνRi6=j+δm²

νeRi6=j, tanβ→tanβ+δtanβ ,

v²→v²+δv², v_iR² →v_iR² +δv_iR² ,

v_iL²→v_iL²+δv_iL², λi→λi+δλi, κijk→κijk+δκijk,

Y_ij^ν→Y_ij^ν+δY_ij^ν, T_i^λ→T_i^λ+δT_i^λ, T_ijk^κ→T_ijk^κ+δT_ijk^κ, T_ij^ν→T_ij