GUT SCALE THRESHOLD EFFECTS ON PROTON DECAY 1 Takumi KUWAHARA - PowerPoint PPT Presentation

GUT SCALE THRESHOLD EFFECTS ON PROTON DECAY 1 Takumi KUWAHARA Nagoya University SUSY 2016 Based on arXiv:1503.08561 NPB 898 (2015) with J.Hisano and Y.Omura (Nagoya U.) arXiv:1603.03568 NPB 910 (2016) with B.Bajc (J.Stefan inst.), J.Hisano and Y.Omura (Nagoya U.)

Introduction 2 Discovery of the 126GeV Higgs boson (in 2012) Success of the Standard Model (SM) Approach to Beyond SM (BSM) more realistically, 
 treat all SM parameters as known values We can prepare theoretical predictions of BSM more precisely. Intensity Frontier Flavor Physics CP violation etc.. => Indirect measurement, 
 but accessible to high-energy

Supersymmetric Grand Unified Theories (SUSY GUTs) => Predicting Baryon-Number Violating Processes (Proton Decay etc..) The promising extension of the SM … Precise prediction towards discovery strong and electro-weak interactions quarks and leptons Unified description of * B# is accidentally preserved in SM 
 * Signature of BSM if we find

4 Introduction SUSY SU(5) GUTs Proton Decay Procedure & Results Summary

SUSY SU(5) GUTs 5 MSSM Higgs doublets are embedded in fields in (anti-)fundamental reps. + GUT breaking Higgs, and etc.. Higgs Sector Matter and Gauge sectors are almost universal in the SUSY SU(5) GUTs Matter Sector: completely embedded in 5 * (Φ) and 10 (Ψ) N. Sakai (1981) S.Dimopoulos H.Georgi (1981) So, Higgs sector depends on models SUSY SU(5) GUTs Gauge Sector U C , Q , E C ∈ Ψ D C , L ∈ Φ , X † ✓ ◆ ✓ ◆ 1 G 2 V ( 24 ) = B √ − X W − 3 2 15 ✓ ◆ ✓ ◆ H C H C H ( 5 ) = H ( 5 ) = H d H u ,

6 Higgs Sector (besides 5+5 * Higgs containing MSSM Higgses) Adjoint (24-dimensional) Higgs Minimal SU(5) Blue Higgses: GUT breaking one Missing Partner Model 50+50 * 75-dimensional Higgs Models for Yukawa Realization additional 45+45 * etc.. Masiero, Nanopoulos, Tamvakis, Yanagida (1982) Grinstein (1982) Georgi, Jarlskog (1979) et al.

7 Higgs Sector (besides 5+5 * Higgs containing MSSM Higgses) Minimal SU(5) Missing Partner Model In this talk, I focus on * Simple * Still valid in high-scale SUSY Scenario (D=5 decay) * with fine-tuning in doublet-triplet splitting * Solving doublet-triplet splitting without fine-tuning * Models requiring huge number of fields 
 => prospect for large quantum correction to proton decay prediction * Free from D=5 proton decay (if imposing Peccei-Quinn symmetry)

Proton Decay 8 Proton Decay induced by gauge-interaction: 10-years exposure Hyper-K Prospect 2016 Moriond Super-K Result X e + π 0 p X bosons give rise to baryon-number violating process! in general, model (= Higgs sector) independent decay 1.0×10 35 yrs Current lower bound (future sensitivity) on proton decay. CURRENT FUTURE p->π 0 +e + 1.67×10 34 yrs ✓ 2 ✓ X † ◆ ◆ 1 G V ( 24 ) = B − √ X W − 3 2 15 Main decay mode: p → π 0 + e +

9 Theoretical progress (Higher-order corrections to Wilson coeff. of D=6 operators) QCD correction (2-loop) 
 RGE in SM (2-loop) 
 RGE in SUSY SM (2-loop) 
 Threshold Corrections Arafune, Nihei (1994) Hisano, Kobayashi, Nagata, Muramatsu (2013) Daniel, Penarrocha (1984) RGE effects are computed @ 2-loop order (Gauge interaction) 
 1-loop threshold corrections are also expected as the same order In addition, Hadron Matrix Elements @ 2GeV are calculated by lattice simulation with 30% errors Aoki, Shintani, Soni (2013)

Results Hisano, TK, Omura (2015) Analytic formula for Threshold Corrections Vertex + Box Vacuum polarization For each threshold corrections, we obtain; Threshold corrections to Wilson coeff. λ (I) In the Effective theory (~ MSSM), 10 Vacuum polarization strongly depends on GUT mass spectrum = − g 2 C ( 0 ) = C ( 0 ) 5 1 2 M 2 X O ( 0 ) = e abg e rs U C † a D C † b Q r g L s 1 O ( 0 ) = e abg e rs E C † U C † a Q b r Q s g 2 Z ( 1 − l ( I ) ) C ( 0 ) I O ( 0 ) d 4 q ∑ = + h.c. L dim.6 I I = 1,2 ! g 2 1 − ln M 2 Σ ( 0 ) 16 λ ( 1 ) = 5 X X + Σ ( 0 ) + , M 2 16 π 2 µ 2 5 ! g 2 1 − ln M 2 Σ ( 0 ) 18 λ ( 2 ) = 5 X X + Σ ( 0 ) + . M 2 16 π 2 µ 2 5

11 2.23×10 36 yrs scale due to many fields <= Large unified coupling @GUT Short lifetime <= thanks to threshold effects Suppressed rate * M X2 M ∑ * Color-triplet Mass 
 Constraining on Numerical Results: among the GUT models (M X = 2×10 16 GeV) Determination of GUT Mass Spectrum Depends on GUT Scale Masses MSSM couplings Unified coupling 7.09×10 35 yrs τ(p→e + π 0 ) SU(5) Comparing with the previous study Ratio of decay rate 
 with and without threshold correction s Minimal SU(5) 0.394 Missing-Partner Ratio 0.994 Bajc, Hisano, TK, Omura (2015) Γ ( p → π 0 + e + ) � � w ( Ratio ) ≡ Γ ( p → π 0 + e + ) | w/o α − 1 ( µ ) = α − 1 G ( µ ) + λ i ( µ ) i

Summary 12 We have derived 1-loop threshold correction to Wilson coefficients of Dim.-6 operators at GUT scale. Proton lifetime becomes longer about a few % due to threshold corrections in the minimal SUSY SU(5). Large suppression of decay rate in the missing-partner SU(5) model (due to many fields and mass splitting)

13 Backups

SUSY SU(5) GUTs and Its Spectrum Minimal SUSY SU(5) GUT 14 Higgs Sector Gauge Sector Matter Sector e abc U C Q as D C ✓ ◆ ✓ ◆ Ψ AB ( 10 ) = c a Φ A ( 5 ) = e rs L s − Q br e rs E C , X † ✓ ◆ ✓ ◆ 1 G 2 V ( 24 ) = B √ − X W − 3 2 15 ✓ ◆ ✓ ◆ H C H C H ( 5 ) = H ( 5 ) = H d H u , ✓ ◆ ✓ ◆ Σ 8 Σ ( 3,2 ) 1 2 0 Σ 24 = + Σ S √ Σ ( 3 ∗ ,2 ) Σ 3 0 − 3 2 15

15 Minimal SUSY SU(5) GUT D E ( Σ 24 ) α = 2 v 24 δ α h ( Σ 24 ) r s i = � 3 v 24 δ r s , β β K 24 = ( Σ † 24 ) A B ( e 2 g 5 V ) B C ( e − 2 g 5 V ) D A ( Σ 24 ) C M X = 5 g 5 v 24 D , → W = λ H ( Σ 24 + 3 v 24 ) H , M H C = 5 λ v 24 → W = f 3 Tr ( Σ 24 ) 3 + m 24 2 Tr ( Σ 24 ) 2 → W = m 8 8 + m 3 3 + m S 2 Σ A 8 Σ A 2 Σ A 3 Σ A 2 Σ S Σ S + · · · m 8 : m 3 : m S = 5 m 24 /2 : 5 m 24 /2 : m 24 /2 = 5 : 5 : 1

16 Missing-Partner SU(5) after integrating out 50+50* with typically, ~10 15 GeV = 3 = 1 D ( Σ 75 ) [ rs ] E D ( Σ 75 ) [ αβ ] E γ δ β δ δ β 2 v 75 ( δ α δ − δ α 2 v 75 ( δ r t δ s u − δ r u δ s t ) , γ ) , [ tu ] [ γδ ] = − 1 D ( Σ 75 ) [ α r ] E 2 v 75 δ α β δ r s , [ β s ] 75 ) [ AB ] B ( Σ 75 ) [ EF ] K 75 = ( Σ † [ CD ] ( e 2 g 5 V ) C E ( e 2 g 5 V ) D F ( e − 2 g 5 V ) G A ( e − 2 g 5 V ) H [ GH ] . √ M X = 2 6 g 5 v 75 → W = M H C H C H 0 C H 0 C + M H 0 C H C , M H C ⌘ 48 v 2 M H C ⌘ 48 v 2 75 75 g H g 0 g 0 H , H g H . M Pl M Pl

17 Missing-Partner SU(5) with = 2 : 4 : (NG Mode) : 2 : 1 : 5 = 3 = 1 D ( Σ 75 ) [ rs ] E D ( Σ 75 ) [ αβ ] E γ δ β δ δ β 2 v 75 ( δ α δ − δ α 2 v 75 ( δ r t δ s u − δ r u δ s t ) , γ ) , [ tu ] [ γδ ] = − 1 D ( Σ 75 ) [ α r ] E 2 v 75 δ α β δ r s , [ β s ] [ CD ] − 1 W = m 75 ( Σ 75 ) [ CD ] [ AB ] ( Σ 75 ) [ AB ] 3 λ 75 ( Σ 75 ) [ AB ] [ EF ] ( Σ 75 ) [ CD ] [ AB ] ( Σ 75 ) [ EF ] [ CD ] 75 = ( 1 , 1 ) 0 ⊕ ( 3 , 1 ) − 5 3 ⊕ ( 3 , 1 ) 5 3 ⊕ ( 3 , 2 ) 5 6 ⊕ ( 3 , 2 ) − 5 6 ⊕ ( 6 , 2 ) 5 6 ⊕ ( 6 , 2 ) − 5 6 ⊕ ( 8 , 1 ) 0 ⊕ ( 8 , 3 ) 0 M ( 8 , 3 ) 0 = 5 m 75

Constrained Mass Spectra 18 Minimal SU(5) MP SU(5) By using central values for couplings (& sparticles around 1 TeV) 5 ln M H C 3 2 1 1 12 M H C = 6.4 × 10 15 GeV 1 ( µ ) = , 2 ( µ ) − 3 ( µ ) − g 2 g 2 g 2 8 π 2 µ X M Σ 24 ) 1/3 = 1.5 × 10 16 GeV ( M 2 8 π 2 12 ln M 2 X M Σ 24 5 3 2 1 3 ( µ ) = . 1 ( µ ) − 2 ( µ ) − g 2 g 2 g 2 µ 3 ! M H C M H C + 6 ln 2 6 3 2 1 1 12 1 ( µ ) = 5 ln , 2 ( µ ) � 3 ( µ ) � g 2 g 2 g 2 8 π 2 5 5 M H 0 f µ ! 12 ln M 2 X M Σ 75 5 3 2 1 + 54 ln 5 3 ( µ ) = . 1 ( µ ) � 2 ( µ ) � g 2 g 2 g 2 8 π 2 µ 3 4 M H C M H C = 1.1 ⇥ 10 20 GeV M H 0 f X M Σ 75 ) 1/3 = 5.4 × 10 15 GeV ( M 2