Higher-order calculations in the SSM Thomas Biek otter in - - PowerPoint PPT Presentation

SLIDE 1

Higher-order calculations in the µνSSM

Thomas Biek¨

• tter

in collaboration with Sven Heinemeyer and Carlos Mu˜ noz [hep-ph/1712.07475]

Instituto de F´ ısica Te´

• rica (UAM-CSIC)

Universidad Aut´

• noma de Madrid

07/2018 SUSY18 Barcelona

1 / 20

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Introduction The µνSSM 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 Mexp

H

= 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!

2 / 20

SLIDE 3

Introduction The µνSSM 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 Mexp

H

= 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 MH 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

SLIDE 4

Introduction The µνSSM 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 Mexp

H

= 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 MH 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

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Introduction The µνSSM 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

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Introduction The µνSSM 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

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

3 / 20

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Introduction The µνSSM 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

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

Particle content: MSSM + 3 (1) gauge singlets ˆ ⌫c

j

Couplings: Y ν

ij ˆ

Hu ˆ Li ˆ ⌫c

j ) gauge singlet = right-handed neutrino

! EWSB ) Dirac masses for neutrinos (Y ν

ii ⇡ Y e 11)

i ˆ ⌫c

i ˆ

Hu ˆ Hd, 1

3 ijk ˆ

⌫c

i ˆ

⌫c

j ˆ

⌫c

k (NMSSM-like)

! EWSB ) Effective 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

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Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Lagrangian and Symmetries

W = ✏ab ⇣ Y e

ij ˆ

Ha

d ˆ

Lb

i ˆ

ec

j + Y d ij ˆ

Ha

d ˆ

Qb

i ˆ

dc

j + Y u ij ˆ

Hb

u ˆ

Qa

i ˆ

uc

j

⌘ + ✏ab ⇣ Y ν

ij ˆ

Hb

u ˆ

La

i ˆ

⌫c

j − i ˆ

⌫c

i ˆ

Hb

u ˆ

Ha

d

⌘ + 1 3ijk ˆ ⌫c

i ˆ

⌫c

j ˆ

⌫c

k

– Z3 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 B3 to forbid baryon number violation ! no proton decay

4 / 20

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Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Lagrangian and Symmetries

W = ✏ab ⇣ Y e

ij ˆ

Ha

d ˆ

Lb

i ˆ

ec

j + Y d ij ˆ

Ha

d ˆ

Qb

i ˆ

dc

j + Y u ij ˆ

Hb

u ˆ

Qa

i ˆ

uc

j

⌘ + ✏ab ⇣ Y ν

ij ˆ

Hb

u ˆ

La

i ˆ

⌫c

j − i ˆ

⌫c

i ˆ

Hb

u ˆ

Ha

d

⌘ + 1 3ijk ˆ ⌫c

i ˆ

⌫c

j ˆ

⌫c

k

– Z3 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 B3 to forbid baryon number violation ! no proton decay Lsoft = ✏ab ⇣ T e

ij Ha d e

Lb

iL e

e⇤

jR + T d ij Ha d e

Qb

iL e

d⇤

jR + T u ij Hb u e

Qa

iLe

u⇤

jR + h.c.

⌘ + ✏ab ✓ T ν

ij Hb u e

La

iLe

⌫⇤

jR T λ i

e ⌫⇤

iR Ha dHb u + 1

3 T κ

ijk e

⌫⇤

iR e

⌫⇤

jR e

⌫⇤

kR + h.c.

◆ + ⇣ m2

e QL

⌘

ij

e Qa⇤

iL e

Qa

jL +

⇣ m2

e uR

⌘

ij e

u⇤

iR e

ujR + ⇣ m2

e dR

⌘

ij

e d⇤

iR e

djR + ⇣ m2

e LL

⌘

ij

e La⇤

iL e

La

jL

+ ⇣ m2

Hd e LL

⌘

i Ha⇤ d e

La

iL +

⇣ m2

e νR

⌘

ij e

⌫⇤

iR e

⌫jR + ⇣ m2

e eR

⌘

ij e

e⇤

iR e

ejR + m2

Hd Ha d ⇤Ha d + m2 Hu Ha u ⇤Ha u

+ 1 2 ⇣ M3 e g e g + M2 f W f W + M1 e B0 e B0 + 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] 4 / 20

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Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Particle Spectrum and Phenomenology

8 (6) CP-even neutral scalars: 'T = (HR

d , HR u , e

⌫R

iR , e

⌫R

jL )

Left and right sneutrinos can be lighter than 125GeV Mixing of left sneutrinos to H suppressed by Y ν and vL 8 (6) CP-odd neutral scalars: T = (HI

d , HI u , e

⌫I

iR, e

⌫I

jL)

Includes the neutral Goldstone boson Mixing of left sneutrinos to H suppressed by Y ν and vL 8 charged sleptons: C T = (H

d ⇤, H+ u , e

e⇤

iL, e

e⇤

jR)

Includes the charged Goldstone boson Mixing of sleptons to H suppressed by Y ν and vL 5 charginos: ()T = ((eiL)c ⇤, f W , e H

d ) , (+)T = ((ejR)c, f

W +, e H+

u )

Three light states corresponding to e, µ and ⌧ Mixing of leptons to gauginos suppressed by Y ν and vL 10 (8) Majorana fermions: (0)T = ((⌫iL)c ⇤, e B0, f W 0, e H0

d, e

H0

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

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Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Particle Spectrum and Phenomenology

Collider: MSSM-bounds from Atlas/CMS usually do not hold in the µ⌫SSM The LSP1 can be charged or colored ! Opens distinct regions of parameter space ! Different 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] 1Forgetting about the gravitino because it is not relevant for colliders 6 / 20

SLIDE 12

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Particle Spectrum and Phenomenology

Collider: MSSM-bounds from Atlas/CMS usually do not hold in the µ⌫SSM The LSP1 can be charged or colored ! Opens distinct regions of parameter space ! Different 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]

Dark Matter: Gravitino (one possiblity) with lifetime longer than age of universe Searches: -ray lines in Fermi-LAT or smooth background

Choi, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/0906.3681] Gomez-Vargas, Fornasa, Zandanel, Cuesta, Munoz, Prada, Yepes [hep-ph/1110.3305] 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] 1Forgetting about the gravitino because it is not relevant for colliders 6 / 20

SLIDE 13

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Particle Spectrum and Phenomenology

Collider: MSSM-bounds from Atlas/CMS usually do not hold in the µ⌫SSM The LSP1 can be charged or colored ! Opens distinct regions of parameter space ! Different 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]

Dark Matter: Gravitino (one possiblity) with lifetime longer than age of universe Searches: -ray lines in Fermi-LAT or smooth background

Choi, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/0906.3681] Gomez-Vargas, Fornasa, Zandanel, Cuesta, Munoz, Prada, Yepes [hep-ph/1110.3305] 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: m2

12, ∆m2 13 and and s2 12, s2 13, s2 23 can be reproduced (NO and IO)

Electroweak seesaw with Y ν

ii ⇠ Y e ⇠ 106 ) viL ⇠ 104 1Forgetting about the gravitino because it is not relevant for colliders 6 / 20

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Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Neutrino physics

At tree-level in basis (viL, e B0, f W 0, e H0

d, e

H0

u, vjR):

mν = B B B B B B B B B B B B B B B B B B B B B @

g1v1L p 2 g2v1L p 2 viR Y ν 1i p 2 vuY ν 11 p 2 vuY ν 12 p 2 vuY ν 13 p 2 g1v2L p 2 g2v2L p 2 viR Y ν 2i p 2 vuY ν 21 p 2 vuY ν 22 p 2 vuY ν 23 p 2 g1v3L p 2 g2v3L p 2 viR Y ν 3i p 2 vuY ν 31 p 2 vuY ν 32 p 2 vuY ν 33 p 2 g1v1L 2 g1v2L 2 g1v3L 2 M1 g1vd 2 g1vu 2 g2v1L 2 g2v2L 2 g2v3L 2 M2 g2vd 2 g2vu 2 g1vd 2 g2vd 2 λi viR p 2 λ1vu p 2 λ2vu p 2 λ3vu p 2 viR Y ν 1i p 2 viR Y ν 2i p 2 viR Y ν 3i p 2 g1vu 2 g2vu 2 λi viR p 2 vd λ1+viLY ν i1 p 2 vd λ2+viLY ν i2 p 2 vd λ3+viLY ν i3 p 2 vuY ν 11 p 2 vuY ν 21 p 2 vuY ν 31 p 2 vuλ1 p 2 vd λ1+viLY ν i1 p 2 p 2κ11i vR p 2κ12i vR p 2κ13i vR vuY ν 12 p 2 vuY ν 22 p 2 vuY ν 32 p 2 vuλ2 p 2 vd λ2+viLY ν i2 p 2 p 2κ12i vR p 2κ22i vR p 2κ23i vR vuY ν 13 p 2 vuY ν 23 p 2 vuY ν 33 p 2 vuλ3 p 2 vd λ3+viLY ν i3 p 2 p 2κ13i vR p 2κ23i vR p 2κ33i vR

1 C C C C C C C C C C C C C C C C C C C C C A

7 / 20

SLIDE 15

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Neutrino physics

At tree-level in basis (viL, e B0, f W 0, e H0

d, e

H0

u, vjR):

mν = B B B B B B B B B B B B B B B B B B B B B @

g1v1L p 2 g2v1L p 2 viR Y ν 1i p 2 vuY ν 11 p 2 vuY ν 12 p 2 vuY ν 13 p 2 g1v2L p 2 g2v2L p 2 viR Y ν 2i p 2 vuY ν 21 p 2 vuY ν 22 p 2 vuY ν 23 p 2 g1v3L p 2 g2v3L p 2 viR Y ν 3i p 2 vuY ν 31 p 2 vuY ν 32 p 2 vuY ν 33 p 2 g1v1L 2 g1v2L 2 g1v3L 2 M1 g1vd 2 g1vu 2 g2v1L 2 g2v2L 2 g2v3L 2 M2 g2vd 2 g2vu 2 g1vd 2 g2vd 2 λi viR p 2 λ1vu p 2 λ2vu p 2 λ3vu p 2 viR Y ν 1i p 2 viR Y ν 2i p 2 viR Y ν 3i p 2 g1vu 2 g2vu 2 λi viR p 2 vd λ1+viLY ν i1 p 2 vd λ2+viLY ν i2 p 2 vd λ3+viLY ν i3 p 2 vuY ν 11 p 2 vuY ν 21 p 2 vuY ν 31 p 2 vuλ1 p 2 vd λ1+viLY ν i1 p 2 p 2κ11i vR p 2κ12i vR p 2κ13i vR vuY ν 12 p 2 vuY ν 22 p 2 vuY ν 32 p 2 vuλ2 p 2 vd λ2+viLY ν i2 p 2 p 2κ12i vR p 2κ22i vR p 2κ23i vR vuY ν 13 p 2 vuY ν 23 p 2 vuY ν 33 p 2 vuλ3 p 2 vd λ3+viLY ν i3 p 2 p 2κ13i vR p 2κ23i vR p 2κ33i vR

1 C C C C C C C C C C C C C C C C C C C C C A

7 / 20

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Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Neutrino physics

At tree-level in basis (viL, e B0, f W 0, e H0

d, e

H0

u, vjR):

mν = B B B B B B B B B B B B B B B B B B B B B @

g1v1L p 2 g2v1L p 2 viR Y ν 1i p 2 vuY ν 11 p 2 vuY ν 12 p 2 vuY ν 13 p 2 g1v2L p 2 g2v2L p 2 viR Y ν 2i p 2 vuY ν 21 p 2 vuY ν 22 p 2 vuY ν 23 p 2 g1v3L p 2 g2v3L p 2 viR Y ν 3i p 2 vuY ν 31 p 2 vuY ν 32 p 2 vuY ν 33 p 2 g1v1L 2 g1v2L 2 g1v3L 2 M1 g1vd 2 g1vu 2 g2v1L 2 g2v2L 2 g2v3L 2 M2 g2vd 2 g2vu 2 g1vd 2 g2vd 2 λi viR p 2 λ1vu p 2 λ2vu p 2 λ3vu p 2 viR Y ν 1i p 2 viR Y ν 2i p 2 viR Y ν 3i p 2 g1vu 2 g2vu 2 λi viR p 2 vd λ1+viLY ν i1 p 2 vd λ2+viLY ν i2 p 2 vd λ3+viLY ν i3 p 2 vuY ν 11 p 2 vuY ν 21 p 2 vuY ν 31 p 2 vuλ1 p 2 vd λ1+viLY ν i1 p 2 p 2κ11i vR p 2κ12i vR p 2κ13i vR vuY ν 12 p 2 vuY ν 22 p 2 vuY ν 32 p 2 vuλ2 p 2 vd λ2+viLY ν i2 p 2 p 2κ12i vR p 2κ22i vR p 2κ23i vR vuY ν 13 p 2 vuY ν 23 p 2 vuY ν 33 p 2 vuλ3 p 2 vd λ3+viLY ν i3 p 2 p 2κ13i vR p 2κ23i vR p 2κ33i vR

1 C C C C C C C C C C C C C C C C C C C C C A

7 / 20

SLIDE 17

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Neutrino physics

At tree-level in basis (viL, e B0, f W 0, e H0

d, e

H0

u, vjR):

mν = B B B B B B B B B B B B B B B B B B B B B @

g1v1L p 2 g2v1L p 2 viR Y ν 1i p 2 vuY ν 11 p 2 vuY ν 12 p 2 vuY ν 13 p 2 g1v2L p 2 g2v2L p 2 viR Y ν 2i p 2 vuY ν 21 p 2 vuY ν 22 p 2 vuY ν 23 p 2 g1v3L p 2 g2v3L p 2 viR Y ν 3i p 2 vuY ν 31 p 2 vuY ν 32 p 2 vuY ν 33 p 2 g1v1L 2 g1v2L 2 g1v3L 2 M1 g1vd 2 g1vu 2 g2v1L 2 g2v2L 2 g2v3L 2 M2 g2vd 2 g2vu 2 g1vd 2 g2vd 2 λi viR p 2 λ1vu p 2 λ2vu p 2 λ3vu p 2 viR Y ν 1i p 2 viR Y ν 2i p 2 viR Y ν 3i p 2 g1vu 2 g2vu 2 λi viR p 2 vd λ1+viLY ν i1 p 2 vd λ2+viLY ν i2 p 2 vd λ3+viLY ν i3 p 2 vuY ν 11 p 2 vuY ν 21 p 2 vuY ν 31 p 2 vuλ1 p 2 vd λ1+viLY ν i1 p 2 p 2κ11i vR p 2κ12i vR p 2κ13i vR vuY ν 12 p 2 vuY ν 22 p 2 vuY ν 32 p 2 vuλ2 p 2 vd λ2+viLY ν i2 p 2 p 2κ12i vR p 2κ22i vR p 2κ23i vR vuY ν 13 p 2 vuY ν 23 p 2 vuY ν 33 p 2 vuλ3 p 2 vd λ3+viLY ν i3 p 2 p 2κ13i vR p 2κ23i vR p 2κ33i vR

1 C C C C C C C C C C C C C C C C C C C C C A

7 / 20

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Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Neutrino physics

At tree-level in basis (viL, e B0, f W 0, e H0

d, e

H0

u, vjR):

mν = B B B B B B B B B B B B B B B B B B B B B @

g1v1L p 2 g2v1L p 2 viR Y ν 1i p 2 vuY ν 11 p 2 vuY ν 12 p 2 vuY ν 13 p 2 g1v2L p 2 g2v2L p 2 viR Y ν 2i p 2 vuY ν 21 p 2 vuY ν 22 p 2 vuY ν 23 p 2 g1v3L p 2 g2v3L p 2 viR Y ν 3i p 2 vuY ν 31 p 2 vuY ν 32 p 2 vuY ν 33 p 2 g1v1L 2 g1v2L 2 g1v3L 2 M1 g1vd 2 g1vu 2 g2v1L 2 g2v2L 2 g2v3L 2 M2 g2vd 2 g2vu 2 g1vd 2 g2vd 2 λi viR p 2 λ1vu p 2 λ2vu p 2 λ3vu p 2 viR Y ν 1i p 2 viR Y ν 2i p 2 viR Y ν 3i p 2 g1vu 2 g2vu 2 λi viR p 2 vd λ1+viLY ν i1 p 2 vd λ2+viLY ν i2 p 2 vd λ3+viLY ν i3 p 2 vuY ν 11 p 2 vuY ν 21 p 2 vuY ν 31 p 2 vuλ1 p 2 vd λ1+viLY ν i1 p 2 p 2κ11i vR p 2κ12i vR p 2κ13i vR vuY ν 12 p 2 vuY ν 22 p 2 vuY ν 32 p 2 vuλ2 p 2 vd λ2+viLY ν i2 p 2 p 2κ12i vR p 2κ22i vR p 2κ23i vR vuY ν 13 p 2 vuY ν 23 p 2 vuY ν 33 p 2 vuλ3 p 2 vd λ3+viLY ν i3 p 2 p 2κ13i vR p 2κ23i vR p 2κ33i vR

1 C C C C C C C C C C C C C C C C C C C C C A Simplified formula for the effective neutrino mixing matrix: (Y ν diagonal) (meff

ν )ij '

Y ν

i Y ν j v 2 u

6 p 2vR (1 3ij) viLvjL 4Meff 1 4Meff 2 4 vd ⇣ Y ν

i vjL + Y ν j viL

⌘ 3 + Y ν

i Y ν j v 2 d

92 3 5

Fidalgo, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/0904.3112]

with Meff ⌘ M v 2 2 p 2

• v 2

R + vuvd

• 3vR

2v 2

R

vuvd v 2 + v 2 2 ! , M = M1M2 g 02M2 + g 2M1

7 / 20

SLIDE 19

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Neutrino physics

At tree-level in basis (viL, e B0, f W 0, e H0

d, e

H0

u, vjR):

mν = B B B B B B B B B B B B B B B B B B B B B @

g1v1L p 2 g2v1L p 2 viR Y ν 1i p 2 vuY ν 11 p 2 vuY ν 12 p 2 vuY ν 13 p 2 g1v2L p 2 g2v2L p 2 viR Y ν 2i p 2 vuY ν 21 p 2 vuY ν 22 p 2 vuY ν 23 p 2 g1v3L p 2 g2v3L p 2 viR Y ν 3i p 2 vuY ν 31 p 2 vuY ν 32 p 2 vuY ν 33 p 2 g1v1L 2 g1v2L 2 g1v3L 2 M1 g1vd 2 g1vu 2 g2v1L 2 g2v2L 2 g2v3L 2 M2 g2vd 2 g2vu 2 g1vd 2 g2vd 2 λi viR p 2 λ1vu p 2 λ2vu p 2 λ3vu p 2 viR Y ν 1i p 2 viR Y ν 2i p 2 viR Y ν 3i p 2 g1vu 2 g2vu 2 λi viR p 2 vd λ1+viLY ν i1 p 2 vd λ2+viLY ν i2 p 2 vd λ3+viLY ν i3 p 2 vuY ν 11 p 2 vuY ν 21 p 2 vuY ν 31 p 2 vuλ1 p 2 vd λ1+viLY ν i1 p 2 p 2κ11i vR p 2κ12i vR p 2κ13i vR vuY ν 12 p 2 vuY ν 22 p 2 vuY ν 32 p 2 vuλ2 p 2 vd λ2+viLY ν i2 p 2 p 2κ12i vR p 2κ22i vR p 2κ23i vR vuY ν 13 p 2 vuY ν 23 p 2 vuY ν 33 p 2 vuλ3 p 2 vd λ3+viLY ν i3 p 2 p 2κ13i vR p 2κ23i vR p 2κ33i vR

1 C C C C C C C C C C C C C C C C C C C C C A Simplified formula for the effective neutrino mixing matrix: (Y ν diagonal) (meff

ν )ij '

Y ν

i Y ν j v 2 u

6 p 2vR (1 3ij) viLvjL 4Meff 1 4Meff 2 4 vd ⇣ Y ν

i vjL + Y ν j viL

⌘ 3 + Y ν

i Y ν j v 2 d

92 3 5

Fidalgo, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/0904.3112]

with Meff ⌘ M v 2 2 p 2

• v 2

R + vuvd

• 3vR

2v 2

R

vuvd v 2 + v 2 2 ! , M = M1M2 g 02M2 + g 2M1

7 / 20

SLIDE 20

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Higgs potential

Parts of L contributing:

W Higgs = ✏ab ⇣ Y ν

ij ˆ

Hb

u ˆ

La

i ˆ

⌫c

j i ˆ

⌫c

i ˆ

Hb

u ˆ

Ha

d

⌘ + 1 3 ijk ˆ ⌫c

i ˆ

⌫c

j ˆ

⌫c

k

LHiggs

soft

= ✏ab ✓ T ν

ij Hb u e

La

iLe

⌫⇤

jR T λ i

e ⌫⇤

iR Ha dHb u + 1

3 T κ

ijk e

⌫⇤

iR e

⌫⇤

jR e

⌫⇤

kR + h.c.

◆ + ⇣ m2

e LL

⌘

ij

e La⇤

iL e

La

jL +

⇣ m2

Hd e LL

⌘

i Ha⇤ d e

La

iL +

⇣ m2

e νR

⌘

ij e

⌫⇤

R e

⌫R + m2

Hd Ha d ⇤Ha d + m2 Hu Ha u ⇤Ha u 8 / 20

SLIDE 21

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Higgs potential

Parts of L contributing:

W Higgs = ✏ab ⇣ Y ν

ij ˆ

Hb

u ˆ

La

i ˆ

⌫c

j i ˆ

⌫c

i ˆ

Hb

u ˆ

Ha

d

⌘ + 1 3 ijk ˆ ⌫c

i ˆ

⌫c

j ˆ

⌫c

k

LHiggs

soft

= ✏ab ✓ T ν

ij Hb u e

La

iLe

⌫⇤

jR T λ i

e ⌫⇤

iR Ha dHb u + 1

3 T κ

ijk e

⌫⇤

iR e

⌫⇤

jR e

⌫⇤

kR + h.c.

◆ + ⇣ m2

e LL

⌘

ij

e La⇤

iL e

La

jL +

⇣ m2

Hd e LL

⌘

i Ha⇤ d e

La

iL +

⇣ m2

e νR

⌘

ij e

⌫⇤

R e

⌫R + m2

Hd Ha d ⇤Ha d + m2 Hu Ha u ⇤Ha u

↓

– Absent in tree-level Lagrangian because it spoils the EW seesaw mechanism ) viL ! 0 when Y ν

ij ! 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

8 / 20

SLIDE 22

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Higgs potential

Parts of L contributing:

W Higgs = ✏ab ⇣ Y ν

ij ˆ

Hb

u ˆ

La

i ˆ

⌫c

j i ˆ

⌫c

i ˆ

Hb

u ˆ

Ha

d

⌘ + 1 3 ijk ˆ ⌫c

i ˆ

⌫c

j ˆ

⌫c

k

LHiggs

soft

= ✏ab ✓ T ν

ij Hb u e

La

iLe

⌫⇤

jR T λ i

e ⌫⇤

iR Ha dHb u + 1

3 T κ

ijk e

⌫⇤

iR e

⌫⇤

jR e

⌫⇤

kR + h.c.

◆ + ⇣ m2

e LL

⌘

ij

e La⇤

iL e

La

jL +

⇣ m2

Hd e LL

⌘

i Ha⇤ d e

La

iL +

⇣ m2

e νR

⌘

ij e

⌫⇤

R e

⌫R + m2

Hd Ha d ⇤Ha d + m2 Hu Ha u ⇤Ha u

↓

– Absent in tree-level Lagrangian because it spoils the EW seesaw mechanism ) viL ! 0 when Y ν

ij ! 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

Assuming CP-conservation:

H0

d =

1 p 2 ⇣ HR

d

+ vd + i HI

d

⌘ , H0

u =

1 p 2 ⇣ HR

u

+ vu + i HI

u

⌘ e ⌫iR = 1 p 2 ⇣ e ⌫R

iR + viR + i e

⌫I

iR

⌘ , e ⌫iL = 1 p 2 ⇣ e ⌫R

iL + viL + i e

⌫I

iL

⌘ ⌧ vu,d,R

8 / 20

SLIDE 23

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Higgs potential

Parts of L contributing:

W Higgs = ✏ab ⇣ Y ν

ij ˆ

Hb

u ˆ

La

i ˆ

⌫c

j i ˆ

⌫c

i ˆ

Hb

u ˆ

Ha

d

⌘ + 1 3 ijk ˆ ⌫c

i ˆ

⌫c

j ˆ

⌫c

k

LHiggs

soft

= ✏ab ✓ T ν

ij Hb u e

La

iLe

⌫⇤

jR T λ i

e ⌫⇤

iR Ha dHb u + 1

3 T κ

ijk e

⌫⇤

iR e

⌫⇤

jR e

⌫⇤

kR + h.c.

◆ + ⇣ m2

e LL

⌘

ij

e La⇤

iL e

La

jL +

⇣ m2

Hd e LL

⌘

i Ha⇤ d e

La

iL +

⇣ m2

e νR

⌘

ij e

⌫⇤

R e

⌫R + m2

Hd Ha d ⇤Ha d + m2 Hu Ha u ⇤Ha u

↓

– Absent in tree-level Lagrangian because it spoils the EW seesaw mechanism ) viL ! 0 when Y ν

ij ! 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

Assuming CP-conservation:

H0

d =

1 p 2 ⇣ HR

d

+ vd + i HI

d

⌘ , H0

u =

1 p 2 ⇣ HR

u

+ vu + i HI

u

⌘ e ⌫iR = 1 p 2 ⇣ e ⌫R

iR + viR + i e

⌫I

iR

⌘ , e ⌫iL = 1 p 2 ⇣ e ⌫R

iL + viL + i e

⌫I

iL

⌘ ⌧ vu,d,R

Parameter counting:

Total: 69 needed for renormalization In practice: 26 needed for phenomenology (avoiding large flavour-mixing)

8 / 20

SLIDE 24

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Higgs potential

Replacements: – m2

Hd , m2 Hu,

⇣ m2

e LL

⌘

ii,

• m2

e νR

• ii

Tadpole eq.

− − − − − − → THR

d , THR u , Te

νR

iL , Te

νR

iR

– vd, vu → tan , v with tan = vu

vd , v 2 = v 2 u + v 2 d + viLviL

– g1, g2 → M2

W , M2 Z with M2 W = 1 4g 2 2 v 2, M2 Z = 1 4(g 2 1 + g 2 2 )v 2

9 / 20

SLIDE 25

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Higgs potential

Replacements: – m2

Hd , m2 Hu,

⇣ m2

e LL

⌘

ii,

• m2

e νR

• ii

Tadpole eq.

− − − − − − → THR

d , THR u , Te

νR

iL , Te

νR

iR

– vd, vu → tan , v with tan = vu

vd , v 2 = v 2 u + v 2 d + viLviL

– g1, g2 → M2

W , M2 Z with M2 W = 1 4g 2 2 v 2, M2 Z = 1 4(g 2 1 + g 2 2 )v 2

The effective µ-term gets three contributions: µ = iviR √ 2

9 / 20

SLIDE 26

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Higgs potential

Replacements: – m2

Hd , m2 Hu,

⇣ m2

e LL

⌘

ii,

• m2

e νR

• ii

Tadpole eq.

− − − − − − → THR

d , THR u , Te

νR

iL , Te

νR

iR

– vd, vu → tan , v with tan = vu

vd , v 2 = v 2 u + v 2 d + viLviL

– g1, g2 → M2

W , M2 Z with M2 W = 1 4g 2 2 v 2, M2 Z = 1 4(g 2 1 + g 2 2 )v 2

The effective µ-term gets three contributions: µ = iviR √ 2 Tree-level upper bound on the lightest Higgs mass: m2

h ≤ M2 Z

✓ cos2 2 + 2ii cos2 ΘW g 2

2

sin2 2 ◆

GUT

∼ M2

Z

⇣ cos2 2 + 1.77 sin2 2 ⌘

9 / 20

SLIDE 27

Introduction The µνSSM Scalar potential 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

(N)MSSM-pieces treated as in (N)MSSM (FeynHiggs)

10 / 20

SLIDE 28

Introduction The µνSSM Scalar potential 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

(N)MSSM-pieces treated as in (N)MSSM (FeynHiggs)

On-shell parameters:

THR

d

! THR

d

+ THR

d

, THR

u

! THR

u

+ THR

u

, Te

νR iR ! Te νR iR + Te νR iR ,

Te

νR iL ! Te νR iL + Te νR iL ,

M2

W ! M2 W + M2 W ,

M2

Z ! M2 Z + M2 Z . δM2 V = Re ΣT ⇣ M2 V ⌘ 10 / 20

SLIDE 29

Introduction The µνSSM Scalar potential 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

(N)MSSM-pieces treated as in (N)MSSM (FeynHiggs)

On-shell parameters:

THR

d

! THR

d

+ THR

d

, THR

u

! THR

u

+ THR

u

, Te

νR iR ! Te νR iR + Te νR iR ,

Te

νR iL ! Te νR iL + Te νR iL ,

M2

W ! M2 W + M2 W ,

M2

Z ! M2 Z + M2 Z . δM2 V = Re ΣT ⇣ M2 V ⌘

DR parameters:

m2

e LL i6=j ! m2 e LL i6=j + m2 e LL i6=j ,

m2

Hd e LL i ! m2 Hd e LL i + m2 Hd e LL i ,

m2

e νR i6=j ! m2 e νR i6=j + m2 e νR i6=j ,

tan ! tan + tan , v 2 ! v 2 + v 2 , v 2

iR ! v 2 iR + v 2 iR ,

v 2

iL ! v 2 iL + v 2 iL ,

i ! i + i , ijk ! ijk + ijk , Y ν

ij ! Y ν ij + Y ν ij ,

T λ

i

! T λ

i

+ T λ

i

, T κ

ijk ! T κ ijk + T κ ijk ,

T ν

ij ! T ν ij + T ν ij .

bla

Details in: TB, Heinemeyer, Munoz [hep-ph/1712.07475] 10 / 20

SLIDE 30

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Loop-correction to scalar masses

ˆ Γh = i h p2

• ⇣

m2

h ˆ

Σh ⇣ p2⌘⌘i , ˆ Σh: Renormalized self-energies det ⇣ ˆ Γh(p2) ⌘

• p2=p2

i

= 0 then m2

hi = Re(p2 i ) 11 / 20

SLIDE 31

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Loop-correction to scalar masses

ˆ Γh = i h p2

• ⇣

m2

h ˆ

Σh ⇣ p2⌘⌘i , ˆ Σh: Renormalized self-energies det ⇣ ˆ Γh(p2) ⌘

• p2=p2

i

= 0 then m2

hi = Re(p2 i )

Fixed-order Feynman-diagrammatic calculation:

Advantages: All contribution of the order included Full control of scalar self-energies (momentum-dependence) Many scales included Disadvantages: Large logs of higher orders missing Cannot be extended to very large scales

11 / 20

SLIDE 32

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Loop-correction to scalar masses

ˆ Γh = i h p2

• ⇣

m2

h ˆ

Σh ⇣ p2⌘⌘i , ˆ Σh: Renormalized self-energies det ⇣ ˆ Γh(p2) ⌘

• p2=p2

i

= 0 then m2

hi = Re(p2 i )

Fixed-order Feynman-diagrammatic calculation:

Advantages: All contribution of the order included Full control of scalar self-energies (momentum-dependence) Many scales included Disadvantages: Large logs of higher orders missing Cannot be extended to very large scales

⇒ Full one-loop corrections supplemented by partial (MSSM-like) two-loop corrections and resummed large logs ˆ Σh ⇣ p2⌘ = ˆ Σ(1)

h

⇣ p2⌘ + ˆ Σ(20)

h

+ ˆ Σresum

h

ˆ Σ(1)

h : Full µ⌫SSM one-loop

ˆ Σ(20)

h

: Partial two-loop O(↵s↵t, ↵s↵b, ↵2

t , ↵t↵b) from FeynHiggs v. 2.13

ˆ Σresum

h

: Resummation of large logs from FeynHiggs v. 2.13

11 / 20

SLIDE 33

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

µνSSM with 1 right-handed sneutrino

viL/ p 2 = 104 GeV Y ν

i

= 106 Aν

i = 1000 GeV

tan = 8 µ = 125 GeV  = 0.2 Aκ = 300 GeV At = 2000 GeV Ab = 1500 GeV

50 100 125 200 400 800 1600 0.04 0.08 0.12 0.16 0.2 0.24 0.28

λ GeV

h-like H-like e νR-like e νiL-like Tree-level Two-loop

80 90 100 110 120 125 130 140 0.04 0.08 0.12 0.16 0.2 0.24 0.28

λ GeV

Tree-level One-loop Two-loop

⇒ MSSM-like 2-loop corrections are crucial for reproducing the correct value of the SM-like Higgs boson mass

12 / 20

SLIDE 34

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

µνSSM with 1 right-handed sneutrino

m2

e νR iL e νR iL

⇡ Y ν

i vRvu

2viL

• p

2Aν

i vR +

p 2µ tan ! ) v1,2L/ p 2 = 105 GeV v3L/ p 2 = 4 · 104 GeV Y ν

i

= 5 · 107 Aν

i = 400 GeV

tan = 10 µ = 270 GeV  = 0.3 Aκ = 1000 GeV

Benchmark point studied in: Ghosh, Lara, Lopez-Fogliani, Munoz, Ruiz de Austri [hep-ph/1707.02471]

50 100 125 200 400 800 1600 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3

λ GeV

Tree-level Two-loop

h e νR e ν3L e ν1,2L H

m2 fin

e νR

iL e

νR

iL = −T fin

e νiL

viL + · · · ⇒ Light left-handed sneutrinos get huge loop corrections

13 / 20

SLIDE 35

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

µνSSM with 1 right-handed sneutrino

Can we explain an excess at ∼ 96 GeV of LEP and CMS?

from [CMS PAS HIG-17-013] µCMS (gg ! h ! γγ) = 0.6 ± 0.2 from [hep-ex/0306033] µLEP ⇣ e+e ! Zh ! Zb¯ b ⌘ = 0.117 ± 0.057 Value from [arXiv:1612.08522]

• 300
• 301
• 302
• 303
• 304
• 305
• 306
• 307
• 308
• 309
• 310
• 311
• 312
• 313
• 314
• 315
• 316
• 317
• 318
• 300
• 301
• 302
• 303
• 304
• 305
• 306
• 307
• 308
• 309
• 310
• 311
• 312
• 313
• 314
• 315
• 316
• 317
• 318

413 413.5 414 414.5 415 415.5 416 416.5 417 417.5 413 413.5 414 414.5 415 415.5 416 416.5 417 417.5

µ µ Aκ Aκ

0.27 0.29 0.31 0.33 0.35 0.37

µCMS

0.12 0.14 0.16 0.18 0.20

µLEP

Details in: TB, Heinemeyer, Munoz [hep-ph/1712.07475]

⇒ Simultaneously explained at 1 by a right-handed sneutrino with me

νR ∼ 96 GeV

14 / 20

SLIDE 36

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

µνSSM with 1 right-handed sneutrino

Can we explain an excess at ∼ 96 GeV of LEP and CMS?

from [CMS PAS HIG-17-013] µCMS (gg ! h ! γγ) = 0.6 ± 0.2 from [hep-ex/0306033] µLEP ⇣ e+e ! Zh ! Zb¯ b ⌘ = 0.117 ± 0.057 Value from [arXiv:1612.08522]

• 300
• 301
• 302
• 303
• 304
• 305
• 306
• 307
• 308
• 309
• 310
• 311
• 312
• 313
• 314
• 315
• 316
• 317
• 318
• 300
• 301
• 302
• 303
• 304
• 305
• 306
• 307
• 308
• 309
• 310
• 311
• 312
• 313
• 314
• 315
• 316
• 317
• 318

413 413.5 414 414.5 415 415.5 416 416.5 417 417.5 413 413.5 414 414.5 415 415.5 416 416.5 417 417.5

µ µ Aκ Aκ

0.27 0.29 0.31 0.33 0.35 0.37

µCMS

0.12 0.14 0.16 0.18 0.20

µLEP

Details in: TB, Heinemeyer, Munoz [hep-ph/1712.07475]

⇒ Simultaneously explained at 1 by a right-handed sneutrino with me

νR ∼ 96 GeV

However: Atlas update from ICHEP ) no excess in diphoton channel

• Int. Conf. on HEP, 5. July 2018

[ATLAS-CONF-2018-025] 14 / 20

SLIDE 37

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

µνSSM with 3 right-handed sneutrinos

Fitting the SM-like Higgs mass and the neutrino properties:

1200 1225 1250 1275 1300 1325 1350 1375 1400 vR (GeV) 101 102 103 GeV e νµL e ντL e νeL e νiR H h Tree-level One-loop Two-loop 1200 1220 1240 1260 1280 1300 1320 vR (GeV) 20 40 60 80 100 120 140 160 GeV e νiR h Tree-level One-loop Two-loop

viR = vR tan = 11 i = 0.08 iii = 0.3 Aλ

i = 1000 GeV

Aν

ii = −1000 GeV

Aκ

iii = −1000 GeV

At = −2000 GeV Ab = −1500 GeV Aτ = −1000 GeV

15 / 20

SLIDE 38

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

µνSSM with 3 right-handed sneutrinos

Fitting the SM-like Higgs mass and the neutrino properties:

10−2 mν (eV) Tree-level 10×10 Semi-analytical appr. 0.020 0.021 0.022 0.023 0.024 0.025 sin Θ13

2

3σ 6.0 6.5 7.0 7.5 8.0 δm2

12 (eV2 · 10−5)

3σ 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 sin Θ12

2

3σ 1200 1225 1250 1275 1300 1325 1350 1375 1400 vR (GeV) 2.400 2.425 2.450 2.475 2.500 2.525 2.550 2.575 2.600 ∆m2

13 (eV2 · 10−3)

3σ 1200 1225 1250 1275 1300 1325 1350 1375 1400 vR (GeV) 0.425 0.450 0.475 0.500 0.525 0.550 0.575 0.600 sin Θ23

2

3σ

m2

12 = (7.41 ± 0.61) · 105 eV2

∆m2

13 = (2.4655 ± 0.0965) · 103 eV2

sin2 Θ13 = 0.022085 ± 0.002275 sin2 Θ12 = 0.309 ± 0.037 sin2 Θ23 = 0.5155 ± 0.0975

from NuFIT ’18 results

v1L = 2.45 · 10−4 GeV v2L = 9.73 · 10−4 GeV v3L = 7.71 · 10−4 GeV Y ν

11 = 3.52 · 10−7

Y ν

22 = 1.93 · 10−7

Y ν

33 = 5.06 · 10−7

M1 = 3011 GeV M2 = 6000 GeV

16 / 20

SLIDE 39

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

How restrictive are neutrino limits?

Best-fit point: vR ∼ 1210 GeV

• 1. Vary v2L ) How much does mass of e

⌫µL change?

1200 1225 1250 1275 1300 1325 1350 1375 1400 vR (GeV) 101 102 103 GeV e νµL e ντL e νeL e νiR H h Tree-level One-loop Two-loop

10−2 mν (eV) Tree-level 10×10 Semi-analytical appr. 0.020 0.021 0.022 0.023 0.024 0.025 sin Θ13

2

3σ 6.0 6.5 7.0 7.5 8.0 δm2

12 (eV2 · 10−5)

3σ 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 sin Θ12

2

3σ 1200 1225 1250 1275 1300 1325 1350 1375 1400 vR (GeV) 2.400 2.425 2.450 2.475 2.500 2.525 2.550 2.575 2.600 ∆m2

13 (eV2 · 10−3)

3σ 1200 1225 1250 1275 1300 1325 1350 1375 1400 vR (GeV) 0.425 0.450 0.475 0.500 0.525 0.550 0.575 0.600 sin Θ23

2

3σ

17 / 20

SLIDE 40

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

How restrictive are neutrino limits?

Best-fit point: vR ∼ 1210 GeV

• 1. Vary v2L ) How much does mass of e

⌫µL change?

10−2 mν (eV) Tree-level 10×10 Semi-analytical appr. 0.020 0.021 0.022 0.023 0.024 sin Θ13

2

3σ 6.8 7.0 7.2 7.4 7.6 7.8 8.0 δm2

12 (eV2 · 10−5)

3σ 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 sin Θ12

2

3σ 0.95 0.96 0.97 0.98 0.99 1.00 v2L (GeV ·10−3) 2.40 2.45 2.50 2.55 2.60 2.65 ∆m2

13 (eV2 · 10−3)

3σ 0.95 0.96 0.97 0.98 0.99 1.00 v2L (GeV ·10−3) 0.425 0.450 0.475 0.500 0.525 0.550 0.575 0.600 sin Θ23

2

3σ

0.95 0.96 0.97 0.98 0.99 1.00 v2L (GeV ·10−3) 160.0 162.5 165.0 167.5 170.0 172.5 175.0 177.5 180.0 GeV Tree-level One-loop

1.: 160 GeV < me

νµL < 165 GeV

18 / 20

SLIDE 41

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

How restrictive are neutrino limits?

Best-fit point: vR ∼ 1210 GeV

• 2. Vary Y ν

22 ) How much does mass of e

⌫µL change?

10−2 mν (eV) Tree-level 10×10 Semi-analytical appr. 0.020 0.021 0.022 0.023 0.024 sin Θ13

2

3σ 6.8 7.0 7.2 7.4 7.6 7.8 8.0 δm2

12 (eV2 · 10−5)

3σ 0.28 0.30 0.32 0.34 sin Θ12

2

3σ 0.17 0.18 0.19 0.20 0.21 Y ν

22 (10−6)

2.400 2.425 2.450 2.475 2.500 2.525 2.550 2.575 2.600 ∆m2

13 (eV2 · 10−3)

3σ 0.17 0.18 0.19 0.20 0.21 Y ν

22 (10−6)

0.425 0.450 0.475 0.500 0.525 0.550 0.575 0.600 sin Θ23

2

3σ

0.17 0.18 0.19 0.20 0.21 Y ν

22 (10−6)

150 155 160 165 170 175 180 185 GeV Tree-level One-loop

1.: 160 GeV < me

νµL < 165 GeV

2.: 150 GeV < me

νµL < 170 GeV

19 / 20

SLIDE 42

Introduction The µνSSM Scalar potential Renormalization Results Conclusion

Conclusions

– Neutral scalar potential is renormalized at 1-loop – SM-like Higgs mass is reproduced when MSSM-like 2-loop corrections are taken into account (crucial) – In the µ⌫SSM the 96 GeV LEP+CMS excess could be explained by a right-handed sneuntrino – Simultaneously, neutrino physics and SM-like Higgs can be reproduced – Neutrino measurements can (in principle) be used to constrain mass range

• f sneutrinos

– Interesting collider signals when sneutrinos are light (when loop corrections are important)

THANKS

20 / 20

SLIDE 43

Tadpole equations

THR d = m2 Hd vd ✓ m2 Hd e LL ◆ i viL 1 8 ⇣ g2 1 + g2 2 ⌘ vd ⇣ v2 d + viLviL v2 u ⌘

• 1

2 vd v2 u λi λi + 1 p 2 vuviR Tλ i + 1 2 v2 u Y ν ji λi vjL 1 2 vd viR λi vjR λj + 1 2 vuκikj λi vjR vkR + 1 2 viR λi vjLY ν jk vkR , (1) THR u = m2 Hu vu + 1 8 ⇣ g2 1 + g2 2 ⌘ vu ⇣ v2 d + viLviL v2 u ⌘

• 1

2 v2 d vuλi λi + 1 p 2 vd viR Tλ i + vd vuY ν ji λi vjL 1 p 2 viLTν ij vjR 1 2 vuviR λi vjR λj

• 1

2 vuY ν ji Y ν ki vjLvkL 1 2 vuY ν ij Y ν ik vjR vkR + 1 2 vd κijk λi vjR vkR 1 2 Y ν li κikj vjR vkR vlL , (2) Te νR iR = ✓ m2 e νR ◆ ij vjR 1 p 2 vuvjLTν ji

• 1

2 v2 u Y ν ji Y ν jk vkR + vd vuκijk λj vkR 1 p 2 Tκ ijk vjR vkR + 1 2 vd vjLY ν ji vkR λk vuY ν lj κijk vkR vlL 1 2 vjLY ν ji vkLY ν kl vlR κijmκjlk vkR vlR vmR

• 1

2 ⇣ v2 d + v2 u ⌘ λi λj vjR + 1 2 vd vjLY ν jk vkR λi + 1 p 2 vd vuTλ i , (3) Te νR iL = ✓ m2 e LL ◆ ij vjL ✓ m2 Hd e LL ◆ i vd 1 8 ⇣ g2 1 + g2 2 ⌘ viL ⇣ v2 d + vjLvjL v2 u ⌘ + 1 2 vd v2 u Y ν ij λj 1 p 2 vuvjR Tν ij

• 1

2 v2 u Y ν ij Y ν kjvkL + 1 2 vd vjR Y ν ij vkR λk

• 1

2 vuY ν ij κjkl vkR vlR 1 2 vjR Y ν ij vkLY ν kl vlR . (4) 1 / 2

SLIDE 44

Renormalization scheme

DR field renormalization:

B @ Hd Hu e ⌫iR e ⌫jL 1 C A ! p Z B @ Hd Hu e ⌫iR e ⌫jL 1 C A = ✓ + 1 2 Z ◆ B @ Hd Hu e ⌫iR e ⌫jL 1 C A p Z: 8 (6) ⇥ 8 (6) matrix, equal sign valid in 1L DR conditions: Zij =

d dp2 Σϕi ϕj

• div

Not diagonal in gauge eigenstate basis (/ L, LFV) Z1,5+a = ∆ 16⇡2 iY ν

ai

Z2+a,2+b = ∆ 16⇡2

• aijbij + ab + Y ν

ia Y ν ib

• Z5+a,5+b =

∆ 16⇡2

• Y e

iaY e ib + Y ν ai Y ν bi

• 2 / 2