ilja doršnerhepworkshop.ijs.si/2016-mini/talks/brda2016_id.pdf · 2019. 7. 11. · ilja doršner...

ONE-LOOP NEUTRINO MASS IN SU(5)*

Ilja Doršner

University of Split

Brda 2016

Selected topics in flavor and collider physics October 21st, 2016

*I. Doršner, S. Fajfer, N. Košnik, work in progress.

• ONE-LOOP NEUTRINO MASS WITH LEPTOQUARKS

• ONE-LOOP NEUTRINO MASS MECHANISM IN SU(5)

• CONCLUSIONS

OUTLINE

ONE-LOOP NEUTRINO MASS MECHANISM

STANDARD MODEL TWO SCALAR LEPTOQUARK MULTIPLETS

+

◎C.-K. Chua, X.-G. He, W.-Y. P. Hwang, Phys. Lett. B479 (2000).

◎

SCALAR LEPTOQUARKS 1

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

LEPTOQUARK (LQ) MULTIPLETS:

◎I. Doršner, S. Fajfer, A. Greljo, J.F. Kamenik, N. Košnik, Phys. Rept. 641 (2016).

◎

1

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

SCALAR LEPTOQUARKS

LQ NOMENCLATURE :

1

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

�mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

u e

s µ

◎W. Büchmuller et al., Phys. Lett. B 191, 442 (1987).

◎

ν MASS LQs:

SCALAR LEPTOQUARKS VS. ν MASS

+ ( ⋁ )

1

yij5i5j10

yij5i5j15

yij10i5j45

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

1

yij5i5j10

yij5i5j15

yij10i5j45

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

1

yij5i5j10

yij5i5j15

yij10i5j45

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

1

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

1

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

�mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

u e

s µ

p DECAY LQs: ( )

SCALAR LEPTOQUARKS VS. p DECAY 1

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

1

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

1

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

�mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

u e

s µ

ν MASS VS. p DECAY 1

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

1

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

�mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

u e

s µ

A(NOTHER) WORD ABOUT NOMENCLATURE 1

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

1

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

≡ Yukawa coupling matrix

i, j (= 1, 2, 3) are flavor indices

a, b (= 1, 2) are SU(2) indices

U ≡ Pontecorvo-Maki-Nakagawa-Sakata unitary mixing matrix

1

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

1

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

1

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

≡ Yukawa coupling matrix

i, j (= 1, 2, 3) are flavor indices

a, b (= 1, 2) are SU(2) indices

A(NOTHER) WORD ABOUT NOMENCLATURE

ONE-LOOP NEUTRINO MASS

⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi

Figure 5: One-loop diagram of neutrino mass generation. Scalar LQ fields that mix due tothe couplings with the SM Higgs boson H are bracketed. Flavor indices are omitted.

in Ref. [95] also addresses the nature of neutrino mass that is of Majorana typethrough an inverse seesaw mechanism.

2.2. Low-energy scenarios of neutrino massLQs have been used to address the question of neutrino masses and associ-

ated mixing parameters within extensions of the SM that do not necessarily aimor lead to unification [98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110].Namely, it has been stipulated that the neutrino masses are of the one-loop ortwo-loop origin, where some of the fields that participate in the loops are scalarLQs. This approach is used to naturally explain or justify observed smallnessof neutrino masses.

Let us outline the main features of this approach. We require the presenceof ˜R2. More specifically, we need a term proportional to yRL

2¯dR⌫L ˜R�1/3

2 , wherewe omit flavor indices. Note that ˜R�1/3

2 couples neutrino to the right-chiraldown-type quark. The other necessary ingredient is the presence of either S1

or S3. Both of these LQs couple the leptonic doublet with the quark doubletrepresentation. They thus couple neutrino to the left-chiral down-type quark.The required couplings are either yLL

1¯dCL⌫LS1 or yLL

3¯dCL⌫LS

1/33 . At this point

it is sufficient to introduce mixing between ˜R2 and either S1 or S3 through theHiggs boson H of the SM to generate neutrino mass(es) at the loop level. Theparticles in the loop are leptoquarks and the down-type quarks. The schematicdepiction of this approach can be written as follows:

yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)

The one-loop diagram of neutrino mass generation that corresponds to the mix-ing between ˜R2 and S3 is given in Fig. 5. The loop is closed through a massinsertion for the down-type quarks. To have a loop with the up-type quarksone would need to start with R2/3

2 leptoquark. It is also possible to generateneutrino masses through the loops that involve leptoquarks of vector nature.This has been done in Ref. [110]. We discuss several explicit realizations of thisapproach in what follows.

24

1

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

u e

s µ

1

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

u e

s µ


⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24

1

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

u e

s µ

1

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

u e

s µ

1

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)


1

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

u e

s µ

⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24

⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24

⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24


⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24

IMPORTANT ISSUES

WHAT HAPPENED WITH THE LQ DIQUARK COUPLINGS?

LQ MASSES ARE FREE PARAMETERS… 1

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

ARE ALL A PRIORI UNKNOWN MATRICES…

RECENT DEVELOPMENTS

◎K. Cheung, T. Nomura, H. Okada, arXiv:1610.02322.

◎

“A testable radiative neutrino mass model without additional symmetries and explanation for the b → sℓ+ℓ− anomaly”

ONE-LOOP ν MASSES IN SU(5)

2

SCALAR LQs SU(5)

S3 ⌘ (3,3, 1/3) 45

R2 ⌘ (3,2, 7/6) 45˜R2 ⌘ (3,2, 1/6) 10,15˜S1 ⌘ (3,1, 4/3) 45

S1 ⌘ (3,1, 1/3) 5,45¯S1 ⌘ (3,1,�2/3) 10

d e

u ⌫

u e

s µ

c µ

Q = �1

3

Q = +2

3

Q = +5

3

li = e, µ

qi = (u, d), (c, s)

yi

yue yde ycµ ysµ

yd⌫

yu⌫

|yde| 0.34⇣ mLQ

1TeV

⌘

|yue| 0.36⇣ mLQ

1TeV

⌘


1

10

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

1

10

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

1

10

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

UNIFICATION OF GAUGE

COUPLINGS

UNIFICATION

TYPE II SEE-SAW ν MASSES

THE STANDARD MODEL SYMMETRY

BREAKING

CHARGED LEPTON &

DOWN-TYPE QUARK MASSES

◎ ⦿ ◆

SCALAR REPRESENTATIONS IN SU(5):

THE STANDARD

MODEL SYMMETRY BREAKING

◉

1

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

◉H. Georgi, S. L. Glashow, Phys. Rev. Lett. 32 (1974). ◎H. Murayama, T. Yanagida, Mod. Phys. Lett. A7 (1992). ⦿I. Doršner, P. Fileviez Perez, Nucl. Phys. B723 (2005). ◆H. Georgi, C. Jarlskog., Phys. Lett. B86 (1979).

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

CHARGED FERMION MASSES

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘


1

10

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

1

10

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

SCALAR REPRESENTATIONS IN SU(5):

1

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33

2�1/2yij uCL ieL jS

1/33

2�1/2yij dCL i⌫L jS

1/33

yij dCL ieL jS

+4/33

(S3)

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

�51045

COMPRISE THE STANDARD MODEL FERMIONS


1

10

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

1

10

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

1

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

A POSSIBLE SU(5) SET-UP:

1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

+4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1, S1

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

�51045

1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

+4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

�51045


1

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

u e

s µ

⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24

⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24

⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24

1

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

d ⌫

d e

u ⌫

u e

s µ

⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24

⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24

⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

10i5j5 & 10i5j45

5i5j15

�51545

�

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

10i5j5 & 10i5j45

5i5j15

�51545

�

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

10i5j5 & 10i5j45

5i5j15

�51545

�

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

≡ dimensionful parameter


1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

�51045

�

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

+4/33

(S3)

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

�51045

p DECAY

1

(S3)

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

�51045

�

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

⌫ ⌫

(S1/33 , ˜R�1/3⇤

2 )

b b

(S1/3⇤3 , ˜R�1/3

2 )

hHi






2¯dR⌫L ˜R�1/3




1¯dCL⌫LS1 or yLL

3¯dCL⌫LS



yRL2

¯dR⌫L ˜R�1/32

% ˜R2HS1 ! yLL1

¯dCL⌫LS1

& ˜R2HS3 ! yLL3

¯dCL⌫LS1/33

(23)



24

p DECAY

◎

◎I. Doršner, S. Fajfer, N. Košnik, Phys. Rev. D 86, 015013 (2012).

1

(S3)

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

�51045

�

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

2

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

LEPTOQUARK MULTIPLET COULD BE LIGHT IF NEEDED…

1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

�51045

p DECAY

1

10

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

1

10

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

1

S3, R2, S1, S1, S1

yij5i5j10

yij5i5j15

yij10i5j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

Q

1/3

−2/3

4/3

3

SCALAR LQs SU(5)

S3 ⌘ (3,3, 1/3) 45

R2 ⌘ (3,2, 7/6) 45

R2 ⌘ (3,2, 1/6) 10,15

S1 ⌘ (3,1, 4/3) 45

S1 ⌘ (3,1, 1/3) 5,45

S1 ⌘ (3,1,�2/3) 10

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

1

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

1

R�1/3 ⇤2

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

3

SCALAR LQs SU(5)

S3 ⌘ (3,3, 1/3) 45

R2 ⌘ (3,2, 7/6) 45

R2 ⌘ (3,2, 1/6) 10,15

S1 ⌘ (3,1, 4/3) 45

S1 ⌘ (3,1, 1/3) 5,45

S1 ⌘ (3,1,�2/3) 10

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

1

R2/3 ⇤2

R�1/3 ⇤2

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

1

R2/3 ⇤2

R�1/3 ⇤2

S�2/33

S1/33

S4/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

1

R2/3 ⇤2

R�1/3 ⇤2

S�2/33

S1/33

S4/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

1

R2/3 ⇤2

R�1/3 ⇤2

S�2/33

S1/33

S4/33

S1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

1

R2/3 ⇤2

R5/32

R2/3 ⇤2

R�1/3 ⇤2

S�2/33

S1/33

S4/33

S1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

1

R2/3 ⇤2

R5/32

R2/3 ⇤2

R�1/3 ⇤2

S�2/33

S1/33

S4/33

S1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

5/3

p DECAY

3

SCALAR LQs SU(5)

S3 ⌘ (3,3, 1/3) 45

R2 ⌘ (3,2, 7/6) 45

R2 ⌘ (3,2, 1/6) 10,15

S1 ⌘ (3,1, 4/3) 45

S1 ⌘ (3,1, 1/3) 5,45

S1 ⌘ (3,1,�2/3) 10

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

1

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

1

R�1/3 ⇤2

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

3

SCALAR LQs SU(5)

S3 ⌘ (3,3, 1/3) 45

R2 ⌘ (3,2, 7/6) 45

R2 ⌘ (3,2, 1/6) 10,15

S1 ⌘ (3,1, 4/3) 45

S1 ⌘ (3,1, 1/3) 5,45

S1 ⌘ (3,1,�2/3) 10

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

[ ]

3

SCALAR LQs SU(5)

S3 ⌘ (3,3, 1/3) 45

R2 ⌘ (3,2, 7/6) 45

R2 ⌘ (3,2, 1/6) 10,15

S1 ⌘ (3,1, 4/3) 45

S1 ⌘ (3,1, 1/3) 5,45

S1 ⌘ (3,1,�2/3) 10

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

1

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

1

R�1/3 ⇤2

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

3

SCALAR LQs SU(5)

S3 ⌘ (3,3, 1/3) 45

R2 ⌘ (3,2, 7/6) 45

R2 ⌘ (3,2, 1/6) 10,15

S1 ⌘ (3,1, 4/3) 45

S1 ⌘ (3,1, 1/3) 5,45

S1 ⌘ (3,1,�2/3) 10

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

*

0 0 0 0

0 0 0 0

4 × 4

p DECAY

3

SCALAR LQs SU(5)

S3 ⌘ (3,3, 1/3) 45

R2 ⌘ (3,2, 7/6) 45

R2 ⌘ (3,2, 1/6) 10,15

S1 ⌘ (3,1, 4/3) 45

S1 ⌘ (3,1, 1/3) 5,45

S1 ⌘ (3,1,�2/3) 10

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

1

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

1

R�1/3 ⇤2

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

3

SCALAR LQs SU(5)

S3 ⌘ (3,3, 1/3) 45

R2 ⌘ (3,2, 7/6) 45

R2 ⌘ (3,2, 1/6) 10,15

S1 ⌘ (3,1, 4/3) 45

S1 ⌘ (3,1, 1/3) 5,45

S1 ⌘ (3,1,�2/3) 10

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

[ ]

3

SCALAR LQs SU(5)

S3 ⌘ (3,3, 1/3) 45

R2 ⌘ (3,2, 7/6) 45

R2 ⌘ (3,2, 1/6) 10,15

S1 ⌘ (3,1, 4/3) 45

S1 ⌘ (3,1, 1/3) 5,45

S1 ⌘ (3,1,�2/3) 10

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

1

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

1

R�1/3 ⇤2

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

3

SCALAR LQs SU(5)

S3 ⌘ (3,3, 1/3) 45

R2 ⌘ (3,2, 7/6) 45

R2 ⌘ (3,2, 1/6) 10,15

S1 ⌘ (3,1, 4/3) 45

S1 ⌘ (3,1, 1/3) 5,45

S1 ⌘ (3,1,�2/3) 10

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

(3,1, 1/3)

(3,1, 4/3)

(3,1,�2/3)

SU(3)⇥ SU(2)⇥ U(1)

*

0 0 0 0

0 0 0 0

ONE-LOOP ν MASSES

1

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

1

R�1/3 ⇤2

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

[ ] 1

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

1

R�1/3 ⇤2

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

* m11 m12

m12 m22

1

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

1

R�1/3 ⇤2

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

cθ sθ

−sθ cθ

1

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

5i5j10

1

R�1/3 ⇤2

S1/33

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

(S1)

(R2)

(S3, S1)

(S3)

(R2, S1, S1)

10i5j5 & 10i5j45

5i5j15

�51545

→

m1 0

0 m2

→

2 2

2 2

m11 m12

m12 m22

2 2

2 2

2

2

ONE-LOOP ν MASSES 1

(m⌫)ij =3s✓c✓16⇡2

X

k=d,s,b

mk[B0(0,m2k,m

21)�B0(0,m

2k,m

22)]{yiky0jk + yjky

0ik}

B0(0,m2k,m

21)�B0(0,m

2k,m

22) =

m22[lnm

22 � lnm2

k]

m22 �m2

k

� m21[lnm

21 � lnm2

k]

m21 �m2

k

R2/3 ⇤2

R5/32

R2/3 ⇤2

R�1/3 ⇤2

S�2/33

S1/33

S4/33

S1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

1

(m⌫)ij =3s✓c✓16⇡2

X

k=d,s,b

mk[B0(0,m2k,m

21)�B0(0,m

2k,m

22)]{yiky0jk + yjky

0ik}

B0(0,m2k,m

21)�B0(0,m

2k,m

22) =

m22[lnm

22 � lnm2

k]

m22 �m2

k

� m21[lnm

21 � lnm2

k]

m21 �m2

k

R2/3 ⇤2

R5/32

R2/3 ⇤2

R�1/3 ⇤2

S�2/33

S1/33

S4/33

S1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

B0 – Passarino-Veltman function

ONE-LOOP ν MASSES

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

1

y0ij10i5j45

(m⌫)ij =3s✓c✓16⇡2

X

k=d,s,b

mk[B0(0,m2k,m

21)�B0(0,m

2k,m

22)]{yiky0jk + yjky

0ik}

B0(0,m2k,m

21)�B0(0,m

2k,m

22) =

m22[lnm

22 � lnm2

k]

m22 �m2

k

� m21[lnm

21 � lnm2

k]

m21 �m2

k

R2/3 ⇤2

R5/32

R2/3 ⇤2

R�1/3 ⇤2

S�2/33

S1/33

S4/33

S1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

1

(m⌫)ij =3s✓c✓16⇡2

X

k=d,s,b

mk[B0(0,m2k,m

21)�B0(0,m

2k,m

22)]{yiky0jk + yjky

0ik}

B0(0,m2k,m

21)�B0(0,m

2k,m

22) =

m22[lnm

22 � lnm2

k]

m22 �m2

k

� m21[lnm

21 � lnm2

k]

m21 �m2

k

R2/3 ⇤2

R5/32

R2/3 ⇤2

R�1/3 ⇤2

S�2/33

S1/33

S4/33

S1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

ONE-LOOP ν MASSES 1

(m⌫)ij =3s✓c✓16⇡2

X

k=d,s,b

mk[B0(0,m2k,m

21)�B0(0,m

2k,m

22)]{yiky0jk + yjky

0ik}

B0(0,m2k,m

21)�B0(0,m

2k,m

22) =

m22[lnm

22 � lnm2

k]

m22 �m2

k

� m21[lnm

21 � lnm2

k]

m21 �m2

k

R2/3 ⇤2

R5/32

R2/3 ⇤2

R�1/3 ⇤2

S�2/33

S1/33

S4/33

S1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

yij dCL ieL jS

4/33

(S3)

1

y0 ⇠ (MTe �Md)/v45

y0ij10i5j45

(m⌫)ij =3s✓c✓16⇡2

X

k=d,s,b

mk[B0(0,m2k,m

21)�B0(0,m

2k,m

22)]{yiky0jk + yjky

0ik}

B0(0,m2k,m

21)�B0(0,m

2k,m

22) =

m22[lnm

22 � lnm2

k]

m22 �m2

k

� m21[lnm

21 � lnm2

k]

m21 �m2

k

R2/3 ⇤2

R5/32

R2/3 ⇤2

R�1/3 ⇤2

S�2/33

S1/33

S4/33

S1

10i & 5i (i = 1, 2, 3)

126 � (5, 10, 15, ,45 )

yij16i16j126

�yij uCL i⌫L jS

�2/33


1/33


1/33

1

(S1)

(R2)

(S3, S1)

S3, R2, S1, S1, S1

yij10i5j5

yij10i10j5

yij5i5j10

yij5i5j15

yij10i5j45

yij10i10j45

5

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

Me – charged lepton mass matrix Md – down-type quark mass matrix

A LIST OF BENEFITS

p DECAY CONSTRAINTS CAN BE ACCOMMODATED

LQ MASSES COULD BE CONSTRAINED THROUGH THE GAUGE COUPLING UNIFICATION…

RELEVANT YUKAWA COUPLING MATRICES ARE RELATED TO FERMION MASSES AND/OR POSSESS ADDITIONAL SYMMETRY. THIS NOT ONLY REDUCES THE TOTAL NUMBER OF PARAMETERS BUT HELPS RELATE LEPTOQUARK DECAY PATTERNS TO NEUTRINO MASSES…

◎

◎P. Fileviez Perez, T. Han, Gui-Yu Huang, T. Li, K. Wang, Phys. Rev. D 78, 071301, (2008).

CONCLUSIONS

SU(5) CAN ACCOMMODATE WITH EASE THE ONE-LOOP NEUTRINO MASS MECHANISM THAT IS BASED ON THE LEPTOQUARK MULTIPLET MIXING. THE USE OF SU(5) CAN INCREASE PREDICTIVITY OF THE SET-UP. THIS COULD ESPECIALLY BE REFLECTED IN THE DECAY PATTERNS OF THE RELEVANT LEPTOQUARK MULTIPLETS.

THANK YOU

[email protected]

100 105 108 1011 1014 101710

20

30

40

50

60

ΜGeV

Α i#

Α1#1

Α2#1

Α3#1

(GeV)

1

m = 10 GeVLQ2

1

10

15

45

H ⌘ (1,2,�1/2)

yRL2 , yLL

1 , yLL3

yRL2

L � �yRL2 ij d

iRR

a2✏

abLj,bL

L � �yRL2 ij d

iRe

jLR

2/32 + (yRL

2 U)ij diR⌫

jLR

�1/32

S3 ⌘

R2 ⌘

R2 ⌘

S1 ⌘

S1 ⌘

S1 ⌘

mDdLdR

SU(3)⇥ SU(2)⇥ U(1)

(3,3, 1/3)

(3,2, 7/6)

(3,2, 1/6)

◎

◎H. Murayama, T. Yanagida, Mod. Phys. Lett. A7 (1992).

STANDARD MODEL + ( 2 × )

ilja doršnerhepworkshop.ijs.si/2016-mini/talks/brda2016_id.pdf · 2019. 7. 11. · ilja doršner...

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