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

SLIDE 1

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.)

SLIDE 2

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

SLIDE 3

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

SLIDE 4

4

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

SLIDE 5

SUSY SU(5) GUTs

5 SUSY SU(5) GUTs Gauge Sector

V(24) = ✓ G X† X W ◆

−

1 2

√

15 ✓ 2

−3

◆ B

DC, L ∈ Φ, UC, Q, EC ∈ Ψ

N. Sakai (1981) S.Dimopoulos H.Georgi (1981)

Matter Sector: completely embedded in 5* (Φ) and 10 (Ψ) Matter and Gauge sectors are almost universal in the SUSY SU(5) GUTs Higgs Sector

H(5) = ✓ HC Hd ◆ , H(5) = ✓ HC Hu ◆

+ GUT breaking Higgs, and etc.. MSSM Higgs doublets are embedded in fields in (anti-)fundamental reps. So, Higgs sector depends on models

SLIDE 6

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.

SLIDE 7

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)

SLIDE 8

Proton Decay

8 CURRENT FUTURE p->π0+e+ 1.67×1034yrs 1.0×1035yrs

Current lower bound (future sensitivity) on proton decay. V(24) = ✓ G X† X W ◆

−

1 2

√

15 ✓ 2

−3

◆ B Main decay mode: p → π0 + e+ X bosons give rise to baryon-number violating process! p π0 e+ X Super-K Result 2016 Moriond Hyper-K Prospect 10-years exposure Proton Decay induced by gauge-interaction: in general, model (= Higgs sector) independent decay

SLIDE 9

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)

SLIDE 10

Results

10 C(0)

1

= C(0)

2

= − g2

5

M2

X

O(0)

1

= eabgersUC†aDC†bQr gLs O(0)

2

= eabgersEC†UC † aQbrQsg

In the Effective theory (~ MSSM),

Threshold corrections to Wilson coeff. λ(I) For each threshold corrections, we obtain; Vacuum polarization Vertex + Box

Analytic formula for Threshold Corrections

Vacuum polarization strongly depends on GUT mass spectrum Hisano, TK, Omura (2015)

λ(1) = Σ(0) M2

X + Σ(0) +

g2

5

16π2 16 5 1 − ln M2

X

µ2 ! , λ(2) = Σ(0) M2

X + Σ(0) +

g2

5

16π2 18 5 1 − ln M2

X

µ2 ! .

Ldim.6 =

Z

d4q ∑

I=1,2

(1 − l(I))C(0)

I O(0) I

+ h.c.

SLIDE 11

11

(Ratio) ≡

Γ(p → π0 + e+)

w

Γ(p → π0 + e+)|w/o

Comparing with the previous study

Ratio of decay rate   with and without threshold corrections

Minimal SU(5) Missing-Partner SU(5) Ratio 0.994 0.394 τ(p→e+π0) 2.23×1036yrs 7.09×1035yrs

α−1

i

(µ) = α−1

G (µ) + λi(µ)

Unified coupling MSSM couplings Depends on GUT Scale Masses

Determination of GUT Mass Spectrum

Numerical Results: among the GUT models (MX = 2×1016GeV)

Constraining on * Color-triplet Mass  * MX2M∑ Suppressed rate <= thanks to threshold effects Short lifetime <= Large unified coupling @GUT scale due to many fields Bajc, Hisano, TK, Omura (2015)

SLIDE 12

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)

SLIDE 13

13 Backups

SLIDE 14

SUSY SU(5) GUTs and Its Spectrum

14 Minimal SUSY SU(5) GUT

ΦA(5) = ✓ DC

a

ersLs ◆ , ΨAB(10) = ✓ eabcUC

c

Qas

−Qbr

ersEC ◆

Matter Sector Gauge Sector Higgs Sector

V(24) = ✓ G X† X W ◆

−

1 2

√

15 ✓ 2

−3

◆ B

H(5) = ✓ HC Hd ◆ , H(5) = ✓ HC Hu ◆

Σ24 = ✓ Σ8 Σ(3,2) Σ(3∗,2) Σ3 ◆

+

1 2

√

15 ✓ 2

−3

◆ ΣS

SLIDE 15

15 Minimal SUSY SU(5) GUT

K24 = (Σ†

24)A B (e2g5V)B C(e−2g5V)D A(Σ24)C D,

→

MX = 5g5v24 h(Σ24)r

si = 3v24δr s,

D

(Σ24)α

β

E

= 2v24δα

β

W = λH(Σ24 + 3v24)H,

→

MHC = 5λv24

W = f 3 Tr(Σ24)3 + m24 2 Tr(Σ24)2

→ W = m8

2 ΣA

8 ΣA 8 + m3

2 ΣA

3 ΣA 3 + mS

2 ΣSΣS + · · ·

m8 : m3 : mS = 5m24/2 : 5m24/2 : m24/2

= 5 : 5 : 1

SLIDE 16

16 Missing-Partner SU(5) D

(Σ75)[rs]

[tu]

E

= 3

2v75(δr

tδs u − δr uδs t),

D

(Σ75)[αβ]

[γδ]

E

= 1

2v75(δα

γδβ δ − δα δ δβ γ),

D

(Σ75)[αr]

[βs]

E

= −1

2v75δα

βδr s,

K75 = (Σ†

75)[AB]

[CD](e2g5V)C

E(e2g5V)D F (e−2g5V)G A(e−2g5V)H B (Σ75)[EF]

[GH].

→

MX = 2

√

6g5v75

W = MHC HCH0

C + MH0

C H0

CHC, MHC ⌘ 48v2

75

MPl gHg0

H,

MHC ⌘ 48v2

75

MPl g0

HgH.

with after integrating out 50+50* typically, ~1015 GeV

SLIDE 17

17 Missing-Partner SU(5) D

(Σ75)[rs]

[tu]

E

= 3

2v75(δr

tδs u − δr uδs t),

D

(Σ75)[αβ]

[γδ]

E

= 1

2v75(δα

γδβ δ − δα δ δβ γ),

D

(Σ75)[αr]

[βs]

E

= −1

2v75δα

βδr s,

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

= 2 : 4 : (NG Mode) : 2 : 1 : 5

M(8,3)0 = 5m75

with

W = m75(Σ75)[CD]

[AB](Σ75)[AB] [CD] − 1

3λ75(Σ75)[AB]

[EF] (Σ75)[CD] [AB](Σ75)[EF] [CD]

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

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

SUSY SU(5) GUTs Gauge Sector

V(24) = ✓ G X† X W ◆

−

1 2

√

15 ✓ 2

−3

◆ B

DC, L ∈ Φ, UC, Q, EC ∈ Ψ

Matter Sector: completely embedded in 5* (Φ) and 10 (Ψ) Matter and Gauge sectors are almost universal in the SUSY SU(5) GUTs Higgs Sector

H(5) = ✓ HC Hd ◆ , H(5) = ✓ HC Hu ◆

+ GUT breaking Higgs, and etc.. MSSM Higgs doublets are embedded in fields in (anti-)fundamental reps. So, Higgs sector depends on models

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..

7

Proton Decay

8

CURRENT FUTURE p->π0+e+ 1.67×1034yrs 1.0×1035yrs

Current lower bound (future sensitivity) on proton decay. V(24) = ✓ G X† X W ◆

−

1 2

√

15 ✓ 2

−3

◆ B Main decay mode: p → π0 + e+ X bosons give rise to baryon-number violating process! p π0 e+ X Super-K Result 2016 Moriond Hyper-K Prospect 10-years exposure Proton Decay induced by gauge-interaction: in general, model (= Higgs sector) independent decay

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

10

C(0)

= C(0)

= − g2

M2

O(0)

= eabgersUC†aDC†bQr gLs O(0)

= eabgersEC†UC † aQbrQsg

In the Effective theory (~ MSSM),

Threshold corrections to Wilson coeff. λ(I) For each threshold corrections, we obtain; Vacuum polarization Vertex + Box

Analytic formula for Threshold Corrections

Vacuum polarization strongly depends on GUT mass spectrum Hisano, TK, Omura (2015)

λ(1) = Σ(0) M2

X + Σ(0) +

g2

5

16π2 16 5 1 − ln M2

X

µ2 ! , λ(2) = Σ(0) M2

X + Σ(0) +

g2

5

16π2 18 5 1 − ln M2

X

µ2 ! .

Ldim.6 =

Z

d4q ∑

I=1,2

(1 − l(I))C(0)

I O(0) I

+ h.c.

11

(Ratio) ≡

Γ(p → π0 + e+)

strong and electro-weak interactions quarks and leptons Unified description of * B# is accidentally preserved in SM  * Signature of BSM if we find

QCD correction (2-loop)  RGE in SM (2-loop)  RGE in SUSY SM (2-loop)  Threshold Corrections

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

Ratio of decay rate   with and without threshold corrections

Constraining on * Color-triplet Mass  * MX2M∑ Suppressed rate <= thanks to threshold effects Short lifetime <= Large unified coupling @GUT scale due to many fields Bajc, Hisano, TK, Omura (2015)