陽子崩壊と大統一理論研究の現状と展望...mental interaction based on the gauge...

陽子崩壊と大統一理論研究の現状と展望永田夏海（東京大学）

日本物理学会第75回年次大会2020年3月18日名古屋大学

Goal of the talk

次世代の陽子崩壊実験で，超対称大統一理論のベンチマーク模型を検証することができる。

様々な崩壊モードを探索することが，大統一理論の構造を探る上で重要となる。

SU(5) Grand Unified Theory (GUT)VOr. UME 32, NUMaER 8 P H Y S I C A I. R E V I E %' I.E T T K R S 25 I'KBRUARY 1974

Unity of All Elementary-Particle Forces

Howard Georgi~ and S. L. GlashowI yman Labo~ato~y of Physics, Harvard University, Cambndge, Massachusetts 02138

(Received 10 January 1974}

Strong, electromagnetic, and weak forces are conjectured to arise from a single funda-mental interaction based on the gauge group SU(5).

We present a series of hypotheses and spec-ulations leading inescapably to the conclusionthat SU(5) is the gauge group of the world~hatall elementary particle forces (strong, weak,and electromagnetic) are different manifestationsof the same fundamental interaction involving asingle coupling strength, the fine-structure con-stant. Our hypotheses may be wrong and ourspeculations idle, but the uniqueness and sim-plicity of our scheme are reasons enough that itbe taken seriously.Our starting point is the assumption that ueaA

and electromagnetic forces are mediated by thevector bosons of a gauge-invariant theory withspontaneous symmetry breaAinI, . A model de-scribing the interactions of leptons using thegauge group SU(2) Cg U(1) was first proposed byGlashow, and was improved by Weinberg andSalam who incorporated spontaneous symmetrybreaking. ' This scheme can also describe had-rons, and is just one example of an infinite classof models compatible with observed weak-inter-action phenomenology. If we assume that thereare as few fermion fields as Possible and, inparticular, that there are no unobserved leptons,the Weinberg model becomes unique up to exten-sions of the gauge group: The observed leptonsmay be described by six left-handed Weyl fields

v,., vL', e, ', p, , ') and their chargeconjugates. If the gauge couplings do not mixleptons with quarks, these six fields must trans-form as a representation of the gauge group: oneof the 23 subgroups of U(6) containing an SU(2)ISU(1) subgroup in which the leptons behave asthey do in the Weinberg model.To include hadrons in the theory, we must use

the Glashow-Iliopoulos-Maiani (GIM) mechanismand introduce a fourth quark p' carrying charm. 'Still, decisions must be made: Should the quarkshave fractional or integer charges? Should therebe one quartet of quarks or several'P Bouchiat,Iliopoulos, and Meyer suggested what seems themost attractive alternative: three quartets offractionally charged quarhs 'This com. bination

of the GIM mechanism with the notion of coloredquarks' keeps the successes of the quark modeland gives an important bonus: Lepton and hadronanomalies cancel so that the theory of weak andelectromagnetic interactions is renormalizable. 'The next step is to include strong interactions.

We assume that strong interactions are nied~ate~by an octet of neHtral vector gauge gluons as-sociated with local color SU(3) symmetry, andthat there are no fundamental strongly interact-ing scalar-meson fields. " This insures thatparity and hypercharge are conserved to orderz, ' and does not lead to any new anomalies, sothat the theory remains renormalizable. Thestrongest binding forces are in color singletstates which may explain why observed hadronslie in qqq and qq configurations. And, it givesanother important bonus: Since the strong inter-actions are associated with a non-Abelian theory,they may be asymptotically free.Thus, we see how attractive it is for strong,

weak, and electromagnetic interactions to springfrom a gauge theory based on the group P = SU(3)Ig SU(2) SU(1). Alas, this theory is defective inone important respect: It does not truly unifyweak and electromagnetic interactions. TheSU(2)@U(1) gauge couplings describe two inter-actions with two independent coupling constants;a true unification would involve only one.Electric charge is observed to be quantized.

This has no natural explanation in the frameworkof conventional quantum electrodynamics, but itis necessarily true in any unified theory' ~etanother reason to search for a true unification.We must assume that the gauge group is larger

than F. Suppose it is of the form SU(3) I3% where'vV contains SU(2) @,U(1) but has a unique gaugecoupling constant. W must be simple, or the di-rect product of isomorphic simple factors withdiscrete symmetries which interchange them.This embedding of the Weinberg model implies arelationship between the coupling constants ofthe SU(2) and U(1) subgroups. Because leptonsare singlets under color SU(3), leptons and quarks

クォーク・レプトン場の統一

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標準模型ゲージ群の統一

SU(3)C ⇥ SU(2)L ⇥U(1)Y ! SU(5)

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Supersymmetric GUTs大統一理論は，超対称性 (SUSY) と非常に相性が良い。

0

10

20

30

40

50

60

102 104 106 108 1010 1012 1014 1016

−1

Scale (GeV)

U(1)

SU(2)

SU(3) 実線：標準模型点線：MSSM

ゲージ階層性問題

ゲージ結合定数の統一

S. Dimopoulos and H. Georgi, Nucl. Phys. B193, 150 (1981);N. Sakai, Z. Phys. C11, 153 (1981).

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Current status of SUSY現時点までのLHCの結果，特に

• 超対称粒子への制限• 125 GeV ヒッグス質量

は，超対称標準模型に強い制限を与えている。この現状が

超対称大統一理論に与える示唆

を概観した上で

次世代陽子崩壊実験の展望を議論する。

Future proton decay experiments高い感度を持つ陽子崩壊実験が近い将来に予定されている。

Hyper-Kamiokande

DUNE

JUNO

•単位: 1033 年• 10 (20) 年のデータを仮定

Current limits and future sensitivitiesDecay Mode Current (90% CL) Future (Discovery) Future (90% CL)

p! K+⌫ 6.6 JUNO: 12 (20) JUNO: 19 (40)DUNE: 30 (50) DUNE: 33 (65)Hyper-K: 20 (30) Hyper-K: 32 (50)

p! ⇡+⌫ 0.39

p! e+⇡0 16 DUNE: 15 (25) DUNE: 20 (40)Hyper-K: 63 (100) Hyper-K: 78 (130)

p! µ+⇡0 7.7 Hyper-K: 69 Hyper-K: 77

n! K0S ⌫ 0.26

n! ⇡0⌫ 1.1

n! e+⇡� 5.3 Hyper-K: 13 Hyper-K: 20

n! µ+⇡� 3.5 Hyper-K: 11 Hyper-K: 18

感度が飛躍的に向上することが期待される。

超対称大統一理論では，カラー三重項ヒッグス交換過程によって誘導される � がしばしば支配的。p → K+ν

非超対称大統一理論において，また上の過程が抑制されている場合においては，大統一ゲージ粒子交換過程によって誘導される � がしばしば支配的。p → π0e+

Dominant proton decay modes

ヒッグス多重項

カラー三重項ヒッグス

MSSM ヒッグス

Proton decay in SUSY GUTs

fW

eQL

fW

eLL( eQL)

HC HC

QL

QL

LL(QL)

QL(LL)

HC

etR

HC

e⌧R

eHueHd

sL(dL)

dR(sR)

⌫⌧

uR

H. Murayama and A. Pierce (2002).

超対称スケールが高ければ問題なくなる。

カラー三重項ヒッグス交換過程により陽子崩壊が生じる。

J. Hisano, D. Kobayashi, T. Kuwahara, N. Nagata, JHEP 1307, 038 (2013).

p → K+ν

超対称スケールが電弱スケール程度の場合，陽子崩壊の寿命が短くなりすぎて実験制限に抵触。

Constrained MSSM (CMSSM)

低エネルギーの値はくりこみ群方程式を解くことで得られる。

Constrained MSSM (CMSSM)

• 伝統的なベンチマーク模型• 大統一スケールで，超対称性の破れのパラメーターに対し統一条件を課す

m0, m1/2, A0, tan β, sign(μ)

インプット・パラメーター

Current status in the CMSSM

1 10 1529

30

31

32

33

34

35

5m1/2 (TeV)

Log(τ

p/yrs)

A0/m0 = 3, tan β = 5, μ > 0Min = MGUT

115

120

130

135

125

mh (GeV)

τp (c ≠ 0) τp (c = 0)

mh

現在の制限 (SK)

ヒッグス質量（理論誤差）

� は暗黒物質残存量を説明するように選んだ。m0

J. Ellis, J. L. Evans, N. Nagata, K. A. Olive, L. Velasco-Sevilla, arXiv:1912.04888.

� のとき，陽子崩壊の実験を逃れつつヒッグス質量の観測値を説明できる。m1/2 ∼ 10 TeV

最小SU(5)大統一理論

p → K+ν

W�ge↵ =

c

MPTr [⌃WW ]

<latexit sha1_base64="LO2rqgPZkqwXRlh3bjoaWIlgNB4=">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</latexit>

次元５の演算子

Proton decay in the CMSSM

1033 1034 1035 1036

p ! e+⇡0 (c 6= 0)

p ! K+⌫ (c 6= 0)

p ! K+⌫ (c = 0)

JUNO

DUNE

HK

SK

90% CL (20 yrs)

� の寿命は，将来の陽子崩壊実験で探りうる程度の値に予言される。p → K+ν

� は，Hyper-Kamiokandeでのみ探りうる。p → e+π0


Dominant proton decay modes

�p → K+ν

超対称性大統一理論でしばしば主要なモードになる。

超対称スケールが O(10—100) TeVのとき，将来実験において観測可能。

�p → π0e+

大統一理論において普遍的に生じるモード。

非超対称大統一理論において主要なモード。

ヒッグス質量も同時に説明可能。

Various decay modes他の崩壊モードを探ることもとても重要。というのも，

SU(5) 以外の大統一群

スフェルミオン間にフレーバー混合がある場合

では上記２つ以外の崩壊率も大きくなりうるので，他の崩壊モードを探ることで大統一理論の構造を探りうる。

N. Nagata and S. Shirai, JHEP 1403, 049 (2014).

V. Lucas and S. Raby (1997); K. S. Babu, J. C. Pati ans F. Wilczek (1998);N. Maekawa and Y. Muramatsu (2013); N. Haba, Y. Mimura and T. Yamada (2020);

J. Ellis, M. A. G. Garcia, N. Nagata, D. Nanopoulos, K. A. Olive, arXiv:2003.03285, etc.

Flipped SU(5)最小SU(5)大統一理論

ゲージ群はSU(5)

　

ハイパーチャージがSU(5)の生成子に比例

5 3�U,L

, 10 3

�Q,D,N

, 1 = E

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Flipped SU(5)

ゲージ群はSU(5) x U(1)

　

ハイパーチャージはSU(5)の生成子とU(1)との線形和

S. M. Barr (1982); J. P. Derendinger, J.E. Kim, D. V. Nanopoulos (1984);I. Antoniadis, J. R. Ellis, J. S. Hagelin, D. V. Nanopoulos (1987).

5 3�D,L

, 10 3

�Q,U,E

, 1 = N

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Features of flipped SU(5) GUTs長所

短所

右巻きニュートリノが必然的に導入される。�yd ≠ yl

二重項・三重項分離問題が解決される。Missing partner mechanism

ゲージ群を完全に統一するわけではない。 SU(5) x U(1)

その他の特徴

カラーヒッグス交換による陽子崩壊が生じない。

GUTヒッグス場の表現次元が小さい。 10, 10 vs 24

Flipped vs unflipped SU(5)普通のSU(5)とflipped SU(5)とで陽子崩壊分岐比の予言が異なる。最小SU(5)大統一理論

Flipped SU(5)

�(p ! ⇡0µ+)flipped�(p ! ⇡0e+)flipped

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(NO)

�(p ! ⇡0µ+)flipped�(p ! ⇡0e+)flipped

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(IO)

CKM行列に依存。

PMNS行列に依存。

�(p ! ⇡0µ+)Minimal SU(5)

�(p ! ⇡0e+)Minimal SU(5)' |VudV

⇤us|2

1 + (1 + |Vud|2)2<latexit sha1_base64="+7q7gJdORe7yS+SlOzf1mEUkjQY=">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</latexit><latexit sha1_base64="+7q7gJdORe7yS+SlOzf1mEUkjQY=">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</latexit><latexit sha1_base64="+7q7gJdORe7yS+SlOzf1mEUkjQY=">AAACnHicfVHbihNBEO0ZbzHeoj4K0hiExECYWZTdNwMKCrKwosku7GSGmk7NbrPdPWN3jxh6+2f8K98Ef8TO5cG9YEHB4Zw6VHGqbAQ3Nkl+RfGNm7du3+nc7d67/+Dho97jJzNTt5rhlNWi1kclGBRc4dRyK/Co0QiyFHhYnr1b6YffURteq6922eBcwoniFWdgA1X0fmaVBuayDyAl0EFDM1vTrOF5QjPZ5qNh4TKLP6zb54pLEPTLdPBm6L2/1oL/MXQzwyV+624Wns8K1y587jxdIePzV+f5jnfpaJCOtmIghoErev1knKyLXgXpFvTf/ibrOih6f7JFzVqJyjIBxhynSWPnDrTlTGA4pDXYADuDEzwOUIFEM3frLD19GZgFrWodWlm6Zv91OJDGLGUZJiXYU3NZW5HXaqX09OJqW+3NHVdNa1GxzeaqFTSkufoUXXCNzIplAMA0D8dTdgohPBv+2Q2ppJczuApmO+M04M+v+5PJJh7SIc/ICzIgKdklE/KRHJApYVEnGke70V78PH4ff4r3N6NxtPU8JRcqnv0FNC/LWw==</latexit><latexit sha1_base64="1FJbF5+tFwGUPd5tUV7A5VoNBkU=">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</latexit>

Flipped vs unflipped SU(5)

10�2 10�1 100 101 102

�(p ! ⇡0µ+)/�(p ! ⇡0e+)

0

100

200

300

400

500

Num

ber

Unflip

ped

SU

(5)

NO

IO

J. Ellis, M. A. G. Garcia, D. Nanopoulos, N. Nagata, K. A. Olive, arXiv:2003.03285.

NOとIOとで異なる値を予言する。

普通のSU(5)よりもミューオンへの分岐比が大きくなる。

Flipped vs unflipped SU(5)

10�3 10�2 10�1 100 101 102 103

�(p ! K0µ+)/�(p ! ⇡0µ+)

�(p ! K0e+)/�(p ! ⇡0e+)

Pi �(p ! ⇡+⌫i)/�(p ! ⇡0e+)

�(p ! ⇡0µ+)/�(p ! ⇡0e+)

�!

Unflipped

Flipped (NO/IO)

Flipped (NO)

Flipped (IO)

J. Ellis, M. A. G. Garcia, D. Nanopoulos, N. Nagata, K. A. Olive, arXiv:2003.03285.

これに加えて，flipped SU(5)では � となる。Γ(p → K+ν) = 0

いくつかの崩壊率の比を測定することで，大統一群の可能性を選別しうる。

CKM行列のユニタリ性より従う。

Summary

次世代の陽子崩壊実験で，超対称大統一理論＋CMSSM を検証することができる。

様々な崩壊モードを探索することが，大統一理論の模型選別の上で重要となる。

Flipped vs Unflipped SU(5)

Backup

Current status in the CMSSM


5.0×10 1.0×10 1.5×105.0×10

1.0×10

2.0×104

m1/2 (GeV)

m 0(G

eV)

A0/m0 = 3, tan β = 5, μ > 0Min = MGUT

129

121

4

24 42

Stop LSP

Stau LSP

ヒッグス質量 [GeV]陽子崩壊からの制限 �c = 0陽子崩壊からの制限 �c ≠ 0

W�ge↵ =

c

MPTr [⌃WW ]

<latexit sha1_base64="LO2rqgPZkqwXRlh3bjoaWIlgNB4=">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</latexit>

次元５の演算子

ΩDM h2 = 0.12

� のとき，陽子崩壊の実験を逃れつつヒッグス質量の観測値を説明できる。m1/2 ∼ 10 TeV

Gauge coupling unification

10

20

30

40

50

10 6 10 8 10 10 10 12 10 14 10 16

α−1

Scale (GeV)

25

26

27

28

10 16

α−1

Scale (GeV)

拡大

高スケール低スケールゲージ結合の統一は保たれる。

� in CMSSMp → e+π0

10�4 10�3 10�2 10�1 100

�0

1034

1035

1036

1037

1038

1039

1040

⌧(p

!e+

⇡0 )

[yrs

]

SK (90% CL)

HK (90% CL)

DUNE (90% CL)

J. Ellis, J. L. Evans, N. Nagata, K. A. Olive, L. Velasco-Sevilla, arXiv: 1912.04888.

Flipped SU(5) S. M. Barr (1982); J. P. Derendinger, J.E. Kim, D. V. Nanopoulos (1984);I. Antoniadis, J. R. Ellis, J. S. Hagelin, D. V. Nanopoulos (1987).

Superpotential

W = �ij1 FiFjh+ �

ij2 Fifj h+ �

ij3 fi`

cjh+ �4HHh+ �5HHh

+ �ia6 FiH�a + �

a7hh�a + �

abc8 �a�b�c + µ

ab�a�b .

<latexit sha1_base64="7moX8P4hJb1yxAMIk/qYKup3RDQ=">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</latexit>

Matter chiral superfields

Fi 3nQi, Vije

�i'jdcj , (U⌫c)ij ⌫cj

o,

fi 3nuci , Lj (Ul)ji

o,

`ci = (Ulc)ij ecj

<latexit sha1_base64="DezUItkyYn0SMyiinMFGMFts32U=">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</latexit>

Neutrino sector in Flipped SU(5)Lagrangian

Lmass = �1

2

�⌫i ⌫c

j�a

�0

@0 �ij

2 hh0i 0�ij

2 hh0i 0 �ja

6 h⌫cHi

0 �ja

6 h⌫cHi µa

1

A

0

@⌫i⌫cj

�a

1

A+ h.c.

<latexit sha1_base64="MGXSS3or6tAUNWME7m1pZ+xATic=">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</latexit>

Right-handed neutrino mass matrix

(m⌫c)ij =X

a=0,1,2

�ia

6 �ja

6

µah⌫c

Hi2

<latexit sha1_base64="KiJNYWMqPJnVYtp65ORNGZXCXco=">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</latexit>

mD⌫c = UT

⌫cm⌫cU⌫c

<latexit sha1_base64="ybPcsZ7LJs4JybPYHLWC5fxSTAs=">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</latexit>

Light neutrino mass matrix

(m⌫)ij =X

k

�i2�

j2(U⌫c)ik(U⌫c)jkhh0i2

(mD⌫c)k

<latexit sha1_base64="b/b1+xGa1DugkJ3I0+XOHRZSNT8=">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</latexit>

mD⌫ = U⇤

⌫m⌫U†⌫

<latexit sha1_base64="pmX1s9+EVFbOrena9O1+PQDX0qw=">AAACjHicbVHdahQxFM5O/WlHrdt62ZvgVhHB7UzZoiDFBUW8kopuW9iMSyaTmQnNz5Bk1CXkDfo0vdUX8S18BLOze+G2Hkj48p3zcXK+kzecGZskv3vRxq3bd+5ubsX37j/Yftjf2T01qtWETojiSp/n2FDOJJ1YZjk9bzTFIuf0LL94u8iffaPaMCW/2HlDM4EryUpGsA3UrP9UzJBsv76Lj+GkQ89hx8DVExW4qqie9QfJMOkC3gTpCgze/AFdnMx2eh9RoUgrqLSEY2OmadLYzGFtGeHUx6g1tMHkAld0GqDEgprMdQN5+CQwBSyVDkda2LH/KhwWxsxFHioFtrW5nluQ/8tNW1u+yhyTTWupJMtGZcuhVXDhDiyYpsTyeQCYaBb+CkmNNSY2eLjWJRc+jpGk34kSAsvCoc9hzNpP08w5pBTmrJIO1SXjB92NiCZ6f5Due+/Xhal3SOTqh0s9qk1oQN2LZHh4RIVf8jwowgbS637fBKeHw3Q0PPo0GozHy1WATbAHHoNnIAUvwRh8ACdgAgi4BFfgJ/gVbUej6HV0vCyNeivNI7AW0fu/QvHIvQ==</latexit>

UPMNS = U⇤l U

T⌫

<latexit sha1_base64="xSwNPQPXzaYQmVcGb7YGaG7BGb0=">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</latexit>

Sfermion flavor and proton decayスフェルミオン間にフレーバー混合がある場合，

様々な崩壊過程が可能になる。グルイーノ交換過程が重要になる。

u d

s νµ, ντ

˜b˜t

u ˜d

δQL∗

13δQL∗

13

g

HC HC

Qi

Qj

Qk

Ll

U i

Ej

Uk

Dl

HC HC

陽子崩壊の予言が変更される。

Sfermion flavor and proton decay

1027

1028

1029

1030

1031

1032

1033

1034

1035

1036

1037

0.01 0.1

1/Γ(p

→K

+ν)

[yea

r]

δ

δQL

13

δQL

12

δuR

13

δQL

23

SK Limit1030

1032

1034

1036

1038

0.01 0.1

1/Γ(p

→π0µ+)

[yea

r]

δ

δQL

13

δQL

12

δuR

13

SK Limit

p → K+ν p → π0μ+

<latexit sha1_base64="SrBmanQK+i4vbvB2myhormXRgoM=">AAACl3icbVHbbhMxEHWWWwm3FJ4QLxYpUhEiXUcgeEFEQkJ9Qq0gbaU4RF7vbNaqLyvbC0SWv4Ov4RW+gb/BuTw0LSPZPjpzjsYzUzRSOJ/nfzvZtes3bt7aud29c/fe/Qe93YcnzrSWw5gbaexZwRxIoWHshZdw1lhgqpBwWpx/WOZPv4F1wugvftHAVLG5FpXgzCdq1iNqFqgXsoRQxfh1iN9hNcvTu08JfoFpCdKzi5Lns14/H+SrwFcB2YA+2sTRbLfziZaGtwq055I5NyF546eBWS+4hNilrYOG8XM2h0mCmilw07DqLeJniSlxZWw62uMVe9ERmHJuoYqkVMzX7nJuSf4vN2l99XYahG5aD5qvC1WtxN7g5aBwKSxwLxcJMG5F+ivmNbOM+zTOrSqFit0u1fCdG6WYLgP9nNqs44RMQ6DGMCnmOtC6EvJgdVNuud3rk70Y47aRxEBVYX4EEmntUgEIL/PB8DWouOZlcqQNkMvzvgpOhgOS8PGr/mi02cUOeoKeon1E0Bs0QofoCI0RRz/RL/Qb/ckeZ++zj9nhWpp1Np5HaCuy439518v+</latexit>

線の幅は大統一湯川結合定数中の位相因子からくる不定性を表す。


様々な崩壊過程が有意に起きる。グルーオン交換過程の寄与により陽子崩壊率が上昇する。

スフェルミオン質量混合があると

m0 = 100 TeVMHC= 1016 GeV tan β = 5

Sfermion flavor and proton decay<latexit sha1_base64="SrBmanQK+i4vbvB2myhormXRgoM=">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</latexit>

m0 = 100 TeVMHC= 1016 GeV tan β = 5

1030

1032

1034

1036

1038

1040

0.01 0.1

1/Γ(p

→π0e+

)[y

ear]

δ

δQL

13

δQL

12

δuR

13

SK Limit1030

1032

1034

1036

1038

0.01 0.1

1/Γ(p

→K

0µ+)

[yea

r]δ

δQL

13

δQL

12

δuR

13

SK Limit


線の幅は大統一湯川結合定数中の位相因子からくる不定性を表す。

μ = m0 MB = 600 GeV MW = 300 GeV Mg = − 2 TeV


1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(a) Minimal FV

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(b) δQL

13= 0.1

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(c) δQL

23= 0.5

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(d) δQL

12= 0.5

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(e) δuR

13= 0.5

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(f) δuR

12= 0.5

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(g) δeR13

= 0.5

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(h) δLL

13= 0.5


赤: 軽いゲージーノ質量緑: 重いゲージーノ質量


1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(a) Minimal FV

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(b) δQL

13= 0.1

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(c) δQL

23= 0.5

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(d) δQL

12= 0.5

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(e) δuR

13= 0.5

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(f) δuR

12= 0.5

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(g) δeR13

= 0.5

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

(h) δLL

13= 0.5


Sfermion flavor and proton decayフレーバー混合が

• スクォーク• スレプトン

のどちらで起こるか，また，どの成分が混合するか，によって各陽子崩壊モードの分岐比が大きく異なってくる。

フレーバー実験やニュートリノ振動実験の結果と合わせてフレーバー模型の検証に有用。

Dimension-six proton decay


U i Dj

Qk

X

U k

Ll Qi Qj

E l

X

1030 1032 1034 1036 1038 1040

Γ−1 [year]

π0e+

π0µ+

π+ν

K0e+

K0µ+

K+ν

ηe+

ηµ+

Dimension-five operators

HC HC

Qi

Qj

Qk

Ll

U i

Ej

Uk

Dl

HC HC

有効ラグランジアン

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Wilson係数

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演算子

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Proton decay and flavor演算子

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カラー添字の反対称性により，全てのクォーク場が同世代にはなれない。

終状態に異なる世代のクォークを含む過程が支配的。例） p → K+νWilson係数

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3世代の湯川結合定数が大きいことから，フレーバーの変化を伴って３世代の湯川結合定数を拾う寄与が重要となる。

Proton decay and flavorスフェルミオン質量混合がない場合，グルイーノ，ビーノ交換過程は効かない。理由

これらの交換過程で � に寄与する演算子はp → K+ν

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結果得られる４フェルミ演算子はフレーバー・一重項。

３つのスピン1/2フェルミオンを添字の交換に対して完全対称に組まねばならないが，そのような演算子はかけない。

よって，このような寄与はゼロになる。

陽子崩壊と大統一理論研究の 現状と展望...mental interaction based on the gauge...

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陽子崩壊と大統一理論研究の現状と展望...mental interaction based on the gauge...