Relation Between Neutrino Sector and Proton Decay in Flipped SU(5

Relation between neutrino sector and proton decay in ﬂipped SU(5) uniﬁcation

Helena Koleˇsov´a

Faculty of Nuclear Sciences and Physical Engineering, CTU in Prague Institute of Particle and Nuclear Physics, FMP CU

Joint work with Michal Malinsk´y(IPNP) and Carolina Arbel´aez Rodriguez (University of Valencia)

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 1/9 Outline

1 Witten’s mechanism (=loop generation of RH neutrino masses) in SO(10) uniﬁcation

2 Witten’s mechanism in non-SUSY ﬂipped SU(5) uniﬁcation 3 Interplay between neutrino sector and proton decay predictions 4 Witten’s mechanism in SUSY: Qualitatively the same conclusions are valid if split SUSY considered!

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 2/9 Precise measurements of sin θW ⇒ gauge coupling unification for non-SUSY 13 models only if M ∼ 10 GeV (intermediate scale) ⇒ mνL too big.

Witten’s mechanism

Edward Witten: Neutrino Masses in the Minimal O(10) Theory, Phys. Lett. B91, 81 (1980)

<ϕ> = M

2 g ...

m g Y≈ q MW

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 3/9 Witten’s mechanism

Edward Witten: Neutrino Masses in the Minimal O(10) Theory, Phys. Lett. B91, 81 (1980)

<ϕ> = M

2 g ...

m g Y≈ q MW

Precise measurements of sin θW ⇒ gauge coupling uniﬁcation for non-SUSY 13 models only if M ∼ 10 GeV (intermediate scale) ⇒ mνL too big.

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 3/9 Witten’s mechanism in the flipped SU(5) unification

ﬂipped SU(5) [De R´ujula,Georgi, Glashow (1980)], [Barr (1982)], [Derendinger, Kim, Nanopoulos (1984)]

based on gauge group SU(5) × U(1)X ⇒ no constraints from gauge uniﬁcation 1 SM hypercharge Y = 5 (X − T24) ⇒  c   c c  u1 0 d3 −d2 u1 d1 c c c  u2   −d3 0 d1 u2 d2  X =+5 c ¯X =−3  c  X =+1  c c  1F = e , 5F = u3 , 10F = d2 −d1 0 u3 d3    c   e   −u1 −u2 −u3 0 ν  c −ν −d1 −d2 −d3 −ν 0

h10X =+1i∼1016 GeV H X =−2 SU(5) × U(1)X −−−−−−−−−−−→ SM, SM Higgs ∈ 5H

∗ D T L 3 Y1010F 10F 5H + Y510F 5F 5H + Y15F 1F 5H + h.c. ⇒ Mν = Mu

2 gG

g 2 μ G 1 2 4 h10H i MνR = 2 gG Y10 µ 2 × O(1) 16π MG Y10

F F F F Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 4/9 Seesaw mechanism:

D −1 D T † −1 ∗ MνL = −Mν (MνR ) (Mν ) ⇒ MνR = −DuUν Dν Uν Du

(Du/ν – diagonal mass matrices for up-type quarks/light neutrinos T Uν – unitary matrix such that MνL = Uν Dν Uν )

⇒ constraint on Uν (dependent on light neutrino masses!)

Witten’s mechanism in the ﬂipped SU(5) uniﬁcation

2 gG

g 2 μ G 1 2 4 h10H i MνR = 2 gG Y10 µ 2 × O(1) 16π MG Y10

F F F F

MG ≈ gG h10H i (VB mass), µ ≤ λh10H i (non-tachyonic spectrum).

αG Perturbativity of couplings ⇒ max |(MνR )ij | ≤ MG × O(1) i,j∈{1,2,3} 16π2

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 5/9 ⇒ constraint on Uν (dependent on light neutrino masses!)

Witten’s mechanism in the ﬂipped SU(5) uniﬁcation

2 gG

g 2 μ G 1 2 4 h10H i MνR = 2 gG Y10 µ 2 × O(1) 16π MG Y10

F F F F

MG ≈ gG h10H i (VB mass), µ ≤ λh10H i (non-tachyonic spectrum).

αG Perturbativity of couplings ⇒ max |(MνR )ij | ≤ MG × O(1) i,j∈{1,2,3} 16π2

Seesaw mechanism:

D −1 D T † −1 ∗ MνL = −Mν (MνR ) (Mν ) ⇒ MνR = −DuUν Dν Uν Du

(Du/ν – diagonal mass matrices for up-type quarks/light neutrinos T Uν – unitary matrix such that MνL = Uν Dν Uν )

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 5/9 Witten’s mechanism in the flipped SU(5) unification

2 gG

g 2 μ G 1 2 4 h10H i MνR = 2 gG Y10 µ 2 × O(1) 16π MG Y10

F F F F

MG ≈ gG h10H i (VB mass), µ ≤ λh10H i (non-tachyonic spectrum).

αG Perturbativity of couplings ⇒ max |(MνR )ij | ≤ MG × O(1) i,j∈{1,2,3} 16π2

Seesaw mechanism:

D −1 D T † −1 ∗ MνL = −Mν (MνR ) (Mν ) ⇒ MνR = −DuUν Dν Uν Du

(Du/ν – diagonal mass matrices for up-type quarks/light neutrinos T Uν – unitary matrix such that MνL = Uν Dν Uν )

⇒ constraint on Uν (dependent on light neutrino masses!)

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 5/9 GUT = Theories of Proton Decay

In the simplest ﬂipped SU(5) scenarios (with down quark mass matrix symmetric):

Ci - calculable factors, Uν constrained in our model! Lower bound on proton lifetime determined experimentally: e.g. τ(p → π0 + e+) > 8.2 × 1033 y [Super-Kamiokande Collaboration (2012)]

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 6/9 Results 2 |(VPMNS Uν )α1| computed if constraints on Uν applied and the mass of the −4 lightest neutrino m1 varied from 10 eV to 0.08 eV.

⇒ Global upper/lower limits on

Γ(p → π0µ+) Xµ ≡ 1 + 2 2 Γ(p → π ν)|(VCKM )11| Γ(p → π0e+) + Γ(p → π0µ+) Xe+µ ≡ 1 + 2 2 Γ(p → π ν)|(VCKM )11| Brown dots = points consistent with constraints on Uν , full lines = analytically computed bounds of the regions with consistent points The model parameterized by the multiplicative constant in the expression for the loop-generated RH neutrino mass ⇒ diﬀerent curves. Absolute scale: Γ−1(p → π+ν) ∼ 1039y

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 7/9 Qualitatively no change if our model considered in the split SUSY context!

Witten’s mechanism in SUSY SO(10) Gauge uniﬁcation works for SUSY SO(10) without intermediate scale ⇒ VEV 16 entering the Witten’s loop of order MG ∼ 10 GeV ⇒ realistic neutrino masses , Soft SUSY breaking @TeV ⇒ Witten’s loop compensated by superpartner contributions (non-renormalization theorem) / B. Bajc and G. Senjanovi´c,Phys. Lett. B 610 (2005) 80 Implementation of Witten’s mechanism in maximally split SUSY SO(10) model Gauginos and higgsinos @ TeV ⇒ remains Sfermions @ GUT scale ⇒ solved, Loop contributions to charged/ fermion masses ⇒ possible cure for wrong mass relations like Md = Ml for down-type quark and charged lepton mass matrices

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 8/9 Witten’s mechanism in SUSY SO(10) Gauge unification works for SUSY SO(10) without intermediate scale ⇒ VEV 16 entering the Witten’s loop of order MG ∼ 10 GeV ⇒ realistic neutrino masses , Soft SUSY breaking @TeV ⇒ Witten’s loop compensated by superpartner contributions (non-renormalization theorem) / B. Bajc and G. Senjanović,Phys. Lett. B 610 (2005) 80 Implementation of Witten’s mechanism in maximally split SUSY SO(10) model Gauginos and higgsinos @ TeV ⇒ remains Sfermions @ GUT scale ⇒ solved, Loop contributions to charged/ fermion masses ⇒ possible cure for wrong mass relations like Md = Ml for down-type quark and charged lepton mass matrices

Qualitatively no change if our model considered in the split SUSY context! Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 8/9 Thank you for your attention!

Conclusion

Viable model based on SU(5) × U(1) gauge group (“flipped SU(5)”) constructed To generate Majorana masses of RH neutrinos no new fields added – generated via Witten’s mechanism ⇒ “minimal” setting Predictions on potentially measurable quantities (all proton decay partial widths) calculable N.B.: Alternative option for generating RH neutrino masses in flipped SU(5) model: adding 50H scalar representation. No correlation between neutrino sector and proton decay in this case! Our results are valid qualitatively in the split SUSY context as well For further details see C. A. Rodr´ıguez,H. Koleˇsová,and M. Malinský,Phys.Rev. D89 (2014) 055003, arXiv:1309.6743 [hep-ph]

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 9/9 Conclusion

Thank you for your attention!

Helena Koleˇsová: Witten’s mechanism in the flipped SU(5) unification 9/9