feynrules.irmp.ucl.ac.be · FeynRules Implementation of Sextet Diquarks C. Duhr ∗ IPPP, Durham April 3, 2011 Abstract We describe the implementation of the Sextet Diquarks model

FeynRules Implementation of Sextet Diquarks

C. Duhr ∗

IPPP, Durham

April 3, 2011

Abstract

We describe the implementation of the Sextet Diquarks model using the FeynRules package.

Contents

1 Introduction 2

2 Gauge Symmetries 2

3 Fields 3

3.1 Vector Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.2 Fermion Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.3 Scalar Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.4 Ghost Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4 Lagrangian 6

4.1 L1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.2 L2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.3 L3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.4 L4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.5 L5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

5 Parameters 8

5.1 External Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.2 Internal Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

6 Vertices 15

6.1 V1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

List of Tables

1 Gauge Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Physical Vector Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Unphysical Vector Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Physical Fermion Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Physical Scalar Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Physical Ghost Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Unphysical Ghost Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 External Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 910 External Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1011 External Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1112 Internal Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

∗email: [email protected]

1

13 Internal Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314 Internal Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1 Introduction

We describe the implementation of the Sextet Diquarks model using the FeynRules [1] package.

2 Gauge Symmetries

The gauge group of this model isU1Y × SU2L × SU3C. (1)

Details of these gauge groups can be found in Table 1.

Gauge Coupling Structure SymmetricGroup Abelian

Boson ConstantCharge

Constant TensorReps Defs

U1Y T B g1 Y

SU2L F Wi gw Eps FSU2Lk,k FSU2L[a$ , b$ , c$ ] → -I Eps[a$, b$,

SU3C F G gs f dSUN T 6u,u FSU3C[a$ , b$ , c$ ] → -I f[a$, b$, c$]

Ti,i

FSU3Ca,a

Table 1: Details of gauge groups.

The definitions of the indices can be found in Table 2.

Index Symbol Range

Generation f 1-3

Colour i 1-3

Gluon a 1-8

SU2W k 1-3

Sextet u 1-6

Table 2: Definition of the indices.

2

3 Fields

In this section, we describe the field content of our model implementation.

3.1 Vector Fields

In this subsection, we describe the vector fields of our model. The details of the physical vectors can be found in Table 3.

Class SC I FI QN Mem M W PDG

A T A 0 0 22

Z T Z MZ= 91.1876 WZ= 2.4952 23

W F Q = 1 W MW= Internal WW= 2.085 24

G T a G 0 0 21

Table 3: Details of physical vector fields. The headers are as follows: SC = self conjugate, I = indices, FI = flavor index,QN = quantum numbers, Mem = members, M = mass, W = width, and PDG = particle data group number.

The details of the unphysical vectors can be found in Table 4.

Class SC I FI QN Mem Definitions

Wi T k k Wi Wiµ,1 →Wµ+Wµ

†√

2

Wiµ,2 → −i(−Wµ+Wµ

†)√2

Wiµ,3 → swAµ + cwZµ

B T B Bµ → cwAµ − swZµ

Table 4: Details of unphysical vector fields. The headers are as follows: SC = self conjugate, I = indices, FI = flavor index,QN = quantum numbers, and Mem = members.

3.2 Fermion Fields

In this subsection, we describe the fermion fields of our model. The details of the physical fermions can be found in Table 5.

3.3 Scalar Fields

In this subsection, we describe the scalar fields of our model. The details of the physical scalars can be found in Table 6.

3.4 Ghost Fields

In this subsection, we describe the ghost fields of our model. The details of the physical ghosts can be found in Table 7. Thedetails of the unphysical ghosts can be found in Table 8.

3


vl F f f LeptonNumber = 1

ve 12

vm 14

vt 16

l F f f Q = −1 Ml

LeptonNumber = 1 e Me= 0.000511 11

m MM= 0.10566 13

tt MTA= 1.777 15

uq F f, i f Q = 2/3 Mu

u MU= 0.00255 0 2

c MC= 1.42 0 4

t MT= 172 WT= 1.50834 6

dq F f, i f Q = −1/3 Md

d MD= 0.00504 1

s MS= 0.101 3

b MB= 4.7 5

Table 5: Details of physical fermion fields. The headers are as follows: SC = self conjugate, I = indices, FI = flavor index,QN = quantum numbers, Mem = members, M = mass, W = width, and PDG = particle data group number.


H T H MH= 120 WH= 0.00575309 25

phi T phi MZ= 91.1876 Wphi 250

phi2 F Q = 1 phi2 MW= Internal Wphi2 251

six1 F u Q = 1/3 six1 MSIX1= 500 WSIX1= 4.4108

Y = 1/3

six2 F u Q = −2/3 six2 MSIX2= 500 WSIX2= 4.774

Y = −2/3

six3 F u Q = 4/3 six3 MSIX3= 500 WSIX3= 4.0647

Y = 4/3

Table 6: Details of physical scalar fields. The headers are as follows: SC = self conjugate, I = indices, FI = flavor index, QN= quantum numbers, Mem = members, M = mass, W = width, and PDG = particle data group number.


ghA F GhostNumber = 1 ghA 0

ghZ F GhostNumber = 1 ghZ MZ= 91.1876

ghWp F Q = 1 ghWp MW= Internal

GhostNumber = 1

ghWm F Q = −1 ghWm MW= Internal

GhostNumber = 1

ghG F a GhostNumber = 1 ghG 0

Table 7: Details of physical ghost fields. The headers are as follows: SC = self conjugate, I = indices, FI = flavor index, QN= quantum numbers, Mem = members, M = mass, W = width, and PDG = particle data group number.

4

Class SC I FI QN Mem Definitions

ghWi F k k ghWi ghWi1 → ghWm+ghWp√2

ghWi2 → − i(ghWm−ghWp)√2

ghWi3 → cwghZ + ghAsw

ghB F ghB ghB → cwghA − ghZsw

Table 8: Details of unphysical ghost fields. The headers are as follows: SC = self conjugate, I = indices, FI = flavor index,QN = quantum numbers, and Mem = members.

5

4 Lagrangian

In this section, we describe the Lagrangian of our model implementation.

4.1 L1

− 14 (−∂ν [Bµ] + ∂µ [Bν ]) 2 −

14 (−∂ν [Gµ,a1] + ∂µ [Gν,a1] + gsfa1,a2,a3Gµ,a2Gν,a3) (−∂ν [Gµ,a1] + ∂µ [Gν,a1] + gsfa1,a4,a5Gµ,a4Gν,a5) −14 (−∂ν [Wiµ,i1] + ∂µ [Wiν,i1] + gwǫi1,i2,i3Wiµ,i2Wiν,i3) (−∂ν [Wiµ,i1] + ∂µ [Wiν,i1] + gwǫi1,i4,i5Wiµ,i4Wiν,i5)

4.2 L2

µ2(

phi2phi2† + 12 (H − iφ + v)(H + iφ + v)

)

−(

phi2phi2† + 12 (H − iφ + v)(H + iφ + v)

)

2λ +

−iephi2Bµ

2cw+ ∂µ[phi2] +

e

„

(H+iφ+v)(Wiµ,1−iWiµ,2)√2

−iphi2Wiµ,3

«

2sw

iephi2†Bµ

2cw+ ∂µ

[

phi2†]

+e

„

(H−iφ+v)(Wiµ,1+iWiµ,2)√2

+iphi2†Wiµ,3

«

2sw

+

(

e(H−iφ+v)Bµ

2√

2cw−

i(∂µ[H]−i∂µ[φ])√2

+e

“

iphi2†(Wiµ,1−iWiµ,2)− (H−iφ+v)Wiµ,3√2

”

2sw

)(

e(H+iφ+v)Bµ

2√

2cw+

i(∂µ[H]+i∂µ [φ])√2

+e

“

−iphi2(Wiµ,1+iWiµ,2)− (H

2sw

4.3 L3

i−dq.γµ.∂µ[dq] + i

−l .γµ.∂µ[l] + i

−uq.γµ.∂µ[uq] + i

−vl.γµ.∂µ[vl] +

eBµ

−dq.γµ.P−.dq

6cw−

eBµ

−dq.γµ.P+.dq

3cw−

eBµ

−l .γµ.P−.l

2cw−

eBµ

−l .γµ.P+.l

cw+

eBµ−uq.γµ.P−.uq

6cw+

2eBµ−uq.γµ.P+.uq

3cw−

eBµ

−vl.γµ.P−.vl

2cw+ gs

(

−dq.T a.γµ.dq +

−uq.T a.γµ.uq

)

Gµ,a +

e

„√2−vl.γµ.P−.lWµ+

√2

−uq.CKM.γµ.P−.dqWµ+

√2−l .γµ.P−.vlWµ

†+√

2−dq.CKM†.γµ.P−.uqWµ

†−−dq.γµ.P−.dqWiµ,3−

−l .γµ.P−.lWiµ,3+

−uq.γµ.P−.uqWiµ,3+

−vl.γ

2sw

4.4 L4

iphi2CKMn$1406,m$1406−uqs$1406,n$1406,i$1406.dqr$1406,m$1406,i$1406P+s$1406,r$1406y

dm$1406 −

iphi2†CKMn$1407,m$1407∗−dqr$1408,m$1407,i$1407.uqr$1409,n$1407,i$1407P−r$1408,r$1409y

dm$1407 −

(H+iφ+v)−dqs$1406,n$1406,i$1406.dqr$1406,n$1406,i$1406P+s$1406,r$1406yd

n$1406√2

−

(H−iφ+v)−dqr$1410,n$1407,i$1407.dqr$1411,n$1407,i$1407P−r$1410,r$1411yd

n$1407√2

−(H+iφ+v)

−l s$1406,n$1406.lr$1406,n$1406P+s$1406,r$1406yl

n$1406√2

+

iphi2−vls$1406,n$1406.lr$1406,n$1406P+s$1406,r$1406y

ln$1406 −

(H−iφ+v)−l r$1412,n$1407.lr$1413,n$1407P−r$1412,r$1413yl

n$1407√2

−

iphi2†−l r$1414,n$1407.vlr$1415,n$1407P−r$1414,r$1415y

ln$1407 +

iphi2†CKMm$1406,n$1406∗−dqs$1406,n$1406,i$1406.uqr$1406,m$1406,i$1406P+s$1406,r$1406y

um$1406 −

iphi2CKMm$1407,n$1407−uqr$1416,m$1407,i$1407.dqr$1417,n$1407,i$1407P−r$1416,r$1417y

um$1407 −

(H−iφ+v)−uqs$1406,n$1406,i$1406.uqr$1406,n$1406,i$1406P+s$1406,r$1406yu

n$1406√2

−

(H+iφ+v)−uqr$1418,n$1407,i$1407.uqr$1419,n$1407,i$1407P−r$1418,r$1419yu

n$1407√2

4.5 L5

2√

2

(

−dqs,n,i.uqr,m,j

CK6bar[k, i, j]LUDLm,nP−s,rsix1k +−dqs,n,i.uqr,m,j

CK6bar[k, i, j]LQQRm,nP+s,rsix1k

)

−

MSIX12six1ksix1k† + LHS1

(

phi2phi2† + 12 (H − iφ + v)(H + iφ + v)

)

six1ksix1k† +

2√

2(

LQQRm,n∗ −uqr$1428,m,j

C .dqr$1429,n,iK6[k, i, j]P−r$1428,r$1429six1k† + LUDLm,n

∗ −uqr$1426,m,j

C .dqr$1427,n,iK6[k, i, j]P+r$1426,r$1427

LSS11six1k1six1k2six1k1†six1k2

† + 2√

2−dqs,n,i.dqr,m,j

CK6bar[k, i, j]LDDLm,nP−s,rsix2k +

2√

2LDDLm,n∗−dqr$1430,m,j

C .dqr$1431,n,iK6[k, i, j]P+r$1430,r$1431six2k† − MSIX22six2ksix2k

† +

LHS2(

phi2phi2† + 12 (H − iφ + v)(H + iφ + v)

)

six2ksix2k† + LSS122six1k2six1k1

†six2k1six2k2† +

6

LSS121six1k1six1k1†six2k2six2k2

† +LSS22six2k1six2k2six2k1†six2k2

† +2√

2−uqs,n,i.uqr,m,j

CK6bar[k, i, j]LUULm,nP−s,rsix3k +

2√

2LUULm,n∗ −uqr$1432,m,j

C .uqr$1433,n,iK6[k, i, j]P+r$1432,r$1433six3k† − MSIX22six3ksix3k

† +

LHS3(

phi2phi2† + 12 (H − iφ + v)(H + iφ + v)

)

six3ksix3k† + LSS132six1k2six1k1

†six3k1six3k2† +

LSS232six2k2six2k1†six3k1six3k2

† + LSS131six1k1six1k1†six3k2six3k2

† + LSS231six2k1six2k1†six3k2six3k2

† +LSS33six3k1six3k2six3k1

†six3k2† +

(

∂µ

[

six1k†]+ 1

3 ig1Bµsix1k† + igsGµ,a$1420six1i$1420

†T6i$1420,ka$1420

) (

∂µ [six1k] − 13 ig1Bµsix1k − igsGµ,a$1421six1i$1421T6k,i$1421

a$1421

(

∂µ

[

six2k†]− 2


†T6i$1422,ka$1422

) (

∂µ [six2k] + 23 ig1Bµsix2k − igsGµ,a$1423six2i$1423T6k,i$1423

a$1423

(

∂µ

[

six3k†]+ 4


†T6i$1424,ka$1424

) (

∂µ [six3k] − 43 ig1Bµsix3k − igsGµ,a$1425six3i$1425T6k,i$1425

a$1425

7

5 Parameters

In this section, we describe the parameters of our model implementation.

5.1 External Parameters

In this subsection, we describe the external parameters of our model. The details of the external parameters can be foundin Tables 9, 10, 11.

8

P C I V D PN BN OB IO Description

αEWM1 F 127.9 aEWM1 SMINPUTS QED, -2 Inverse of the electroweak

coupling constant

Gf F 0.0000116637 SMINPUTS QED, 2 Fermi constant

αs F 0.1184 aS SMINPUTS QCD, 2 Strong coupling constant at

the Z pole.

ymdo F 0. YUKAWA 1 Down Yukawa mass

ymup F 0. YUKAWA 2 Up Yukawa mass

yms F 0. YUKAWA 3 Strange Yukawa mass

ymc F 0. YUKAWA 4 Charm Yukawa mass

ymb F 4.7 YUKAWA 5 Bottom Yukawa mass

ymt F 172. YUKAWA 6 Top Yukawa mass

yme F 0. YUKAWA 11 Electron Yukawa mass

ymm F 0. YUKAWA 13 Muon Yukawa mass

ymtau F 1.777 YUKAWA 15 Tau Yukawa mass

θc F 0.227736 CKMBLOCK Cabibbo angle

LQQRR F f, f LQQRR1,1 → 0.1 QCD, 1

LQQRR1,2 → 0.

LQQRR1,3 → 0.

LQQRR2,1 → 0.

LQQRR2,2 → 0.1

LQQRR2,3 → 0.

LQQRR3,1 → 0.

LQQRR3,2 → 0.

LQQRR3,3 → 0.1

LQQRI F f, f LQQRI1,1 → 0. QCD, 1

LQQRI1,2 → 0.

LQQRI1,3 → 0.

LQQRI2,1 → 0.

LQQRI2,2 → 0.

LQQRI2,3 → 0.

LQQRI3,1 → 0.

LQQRI3,2 → 0.

LQQRI3,3 → 0.

LUDLR F f, f LUDLR1,1 → 0.1 QCD, 1

LUDLR1,2 → 0.

LUDLR1,3 → 0.

LUDLR2,1 → 0.

LUDLR2,2 → 0.1

LUDLR2,3 → 0.

LUDLR3,1 → 0.

LUDLR3,2 → 0.

Table 9: Details of external parameters. The headers are as follows: P = parameter, C = complex, I = indices, V = value,D = definition, PN = parameter name, BN = block name, OB = order block, and IO = interaction order.

9


LUDLR3,3 → 0.1

LUDLI F f, f LUDLI1,1 → 0. QCD, 1

LUDLI1,2 → 0.

LUDLI1,3 → 0.

LUDLI2,1 → 0.

LUDLI2,2 → 0.

LUDLI2,3 → 0.

LUDLI3,1 → 0.

LUDLI3,2 → 0.

LUDLI3,3 → 0.

LUULR F f, f LUULR1,1 → 0.1 QCD, 1

LUULR1,2 → 0.

LUULR1,3 → 0.

LUULR2,1 → 0.

LUULR2,2 → 0.1

LUULR2,3 → 0.

LUULR3,1 → 0.

LUULR3,2 → 0.

LUULR3,3 → 0.1

LUULI F f, f LUULI1,1 → 0. QCD, 1

LUULI1,2 → 0.

LUULI1,3 → 0.

LUULI2,1 → 0.

LUULI2,2 → 0.

LUULI2,3 → 0.

LUULI3,1 → 0.

LUULI3,2 → 0.

LUULI3,3 → 0.

LDDLR F f, f LDDLR1,1 → 0.1 QCD, 1

LDDLR1,2 → 0.

LDDLR1,3 → 0.

LDDLR2,1 → 0.

LDDLR2,2 → 0.1

LDDLR2,3 → 0.

LDDLR3,1 → 0.

LDDLR3,2 → 0.

LDDLR3,3 → 0.1


10


LDDLI F f, f LDDLI1,1 → 0. QCD, 1

LDDLI1,2 → 0.

LDDLI1,3 → 0.

LDDLI2,1 → 0.

LDDLI2,2 → 0.

LDDLI2,3 → 0.

LDDLI3,1 → 0.

LDDLI3,2 → 0.

LDDLI3,3 → 0.

LHS1 F 0.1 QED, 2

LHS2 F 0.1 QED, 2

LHS3 F 0.1 QED, 2

LSS11 F 0.1 QCD, 2

LSS121 F 0.1 QCD, 2

LSS122 F 0.1 QCD, 2

LSS131 F 0.1 QCD, 2

LSS132 F 0.1 QCD, 2

LSS22 F 0.1 QCD, 2

LSS231 F 0.1 QCD, 2

LSS232 F 0.1 QCD, 2

LSS33 F 0.1 QCD, 2


11

5.2 Internal Parameters

In this subsection, we describe the internal parameters of our model. The details of the internal parameters can be found

P C I V NV D PN IO Description

αEW F Eq. 2 0.00781861 aEW QED, 2 Electroweak coupling contant

MW F Eq. 3 79.8244 W mass

sw2 F Eq. 4 0.233699 Squared Sin of the Weinberg

angle

e F Eq. 5 0.313451 QED, 1 Electric coupling constant

cw F Eq. 6 0.875386 Cos of the Weinberg angle

sw F Eq. 7 0.483424 Sin of the Weinberg angle

gw F Eq. 8 0.648397 QED, 1 Weak coupling constant

g1 F Eq. 9 0.358072 QED, 1 U(1)Y coupling constant

gs F Eq. 10 1.21978 G QCD, 1 Strong coupling constant

v F Eq. 11 246.221 QED, -1 Higgs VEV

λ F Eq. 12 0.118764 lam QED, 2 Higgs quartic coupling

µ F Eq. 13 84.8528 Coefficient of the quadratic

piece of the Higgs potential

yl F f Eq. 14 yl1 → 0. yl

1 → ye QED, 1 Lepton Yukawa coupling

yl2 → 0. yl

2 → ym

yl3 → 0.0102065 yl

3 → ytau

yu F f Eq. 15 yu1 → 0. yu

1 → yup QED, 1 U-quark Yukawa coupling

yu2 → 0. yu

2 → yc

yu3 → 0.987914 yu

3 → yt

yd F f Eq. 16 yd1 → 0. yd

1 → ydo QED, 1 D-quark Yukawa coupling

yd2 → 0. yd

2 → ys

yd3 → 0.0269953 yd

3 → yb

CKM F f, f Eq. 17 CKM1,1 → 0.97418 CKM-Matrix

CKM1,2 → 0.225773

CKM1,3 → 0.

CKM2,1 → −0.225773

CKM2,2 → 0.97418

CKM2,3 → 0.

CKM3,1 → 0.

CKM3,2 → 0.

CKM3,3 → 1.

Table 12: Details of internal parameters. The headers are as follows: P = parameter, C = complex, I = Indices, V = value,NV = numerical value, D = definition, PN = parameter name, and IO = interaction order.

in Tables 12, 13, 14. The values and definitions of the internal parameters will be written below.

αEW =1

αEWM1(2)

MW =

√

√

√

√

MZ2

2+

√

MZ4

4−

MZ2παEW√

2Gf

(3)

sw2 = 1 −MW

2

MZ2(4)

12


LQQR T f, f Eq. 18 LQQR1,1 → 0.1 + 0.I QCD, 1

LQQR1,2 → 0.

LQQR1,3 → 0.

LQQR1,2 → 0.

LQQR2,2 → 0.1 + 0.I

LQQR2,3 → 0.

LQQR1,3 → 0.

LQQR2,3 → 0.

LQQR3,3 → 0.1 + 0.I

LUDL T f, f Eq. 19 LUDL1,1 → 0.1 + 0.I QCD, 1

LUDL1,2 → 0.

LUDL1,3 → 0.

LUDL1,2 → 0.

LUDL2,2 → 0.1 + 0.I

LUDL2,3 → 0.

LUDL1,3 → 0.

LUDL2,3 → 0.

LUDL3,3 → 0.1 + 0.I

LUUL T f, f Eq. 20 LUUL1,1 → 0.1 + 0.I QCD, 1

LUUL1,2 → 0.

LUUL1,3 → 0.

LUUL1,2 → 0.

LUUL2,2 → 0.1 + 0.I

LUUL2,3 → 0.

LUUL1,3 → 0.

LUUL2,3 → 0.

LUUL3,3 → 0.1 + 0.I

LDDL T f, f Eq. 21 LDDL1,1 → 0.1 + 0.I QCD, 1

LDDL1,2 → 0.

LDDL1,3 → 0.

LDDL1,2 → 0.

LDDL2,2 → 0.1 + 0.I

LDDL2,3 → 0.



LDDL1,3 → 0.

LDDL2,3 → 0.

LDDL3,3 → 0.1 + 0.I


13

e = 2√

π√

αEW (5)

cw =√

1 − sw2 (6)

sw =√

sw2 (7)

gw =e

sw

(8)

g1 =e

cw

(9)

gs = 2√

π√

αs (10)

v =2MWsw

e(11)

λ =MH2

2v2(12)

µ =√

v2λ (13)

yl1 =

√2ymev

yl2 =

√2ymm

v

yl3 =

√2ymtau

v

(14)

yu1 =

√2ymup

v

yu2 =

√2ymcv

yu3 =

√2ymtv

(15)

yd1 =

√2ymdo

v

yd2 =

√2ymsv

yd3 =

√2ymbv

(16)

CKM1,1 = Cos [θc]

CKM1,2 = Sin [θc]

CKM1,3 = 0

CKM2,1 = −Sin [θc]

CKM2,2 = Cos [θc]

CKM2,3 = 0

CKM3,1 = 0

CKM3,2 = 0

CKM3,3 = 1

(17)

LQQRi,j = iLQQRIi,j + LQQRRi,j (18)

LUDLi,j = iLUDLIi,j + LUDLRi,j (19)

LUULi,j = iLUULIi,j + LUULRi,j (20)

LDDLi,j = iLDDLIi,j + LDDLRi,j (21)

14

6 Vertices

In this section, we describe the vertices of our model implementation.

6.1 V1

H 1

H 2

H 3

H 4

−6iλ

H 1

H 2

φ 3

φ 4

−2iλ

φ 1

φ 2

φ 3

φ 4

−6iλ

H 1

H 2

phi2 3

phi2† 4

−2iλ

φ 1

φ 2

phi2 3

phi2† 4

−2iλ

phi2 1

phi2 2

phi2† 3

phi2† 4

−4iλ

H 1

H 2

H 3

−6ivλ

H 1

φ 2

φ 3

−2ivλ

H 1

phi2 2

phi2† 3

−2ivλ

A 1

A 2

phi2 3

phi2† 4

2ie2ηµ1,µ2

A 1

phi2 2

phi2† 3

iep2µ1 − iep3

µ1

15

ghA† 1

ghWm 2

W 3

iep2µ3 + iep3

µ3

ghA† 1

ghWp 2

W † 3

−iep2µ3 − iep3

µ3

ghWm† 1

ghA 2

phi2† 3

eMW

ghWm† 1

ghA 2

W † 3

iep2µ3 + iep3

µ3

ghWm† 1

ghWm 2

H 3

− ieMW

2sw

ghWm† 1

ghWm 2

φ 3

− eMW

2sw

A 1

ghWm† 2

ghWm 3

−iep1µ1 − iep3

µ1

ghWm† 1

ghWm 2

Z 3

−icwep2

µ3

sw−

icwep3µ3

sw

ghWm† 1

ghZ 2

phi2† 3

cweMW

2sw− eMW sw

2cw

ghWm† 1

ghZ 2

W † 3

icwep2µ3

sw+ icwep3

µ3

sw

ghWp† 1

ghA 2

phi2 3

−eMW

ghWp† 1

ghA 2

W 3

−iep2µ3 − iep3

µ3

16

ghWp† 1

ghWp 2

H 3

− ieMW

2sw

ghWp† 1

ghWp 2

φ 3

eMW

2sw

A 1

ghWp† 2

ghWp 3

iep1µ1 + iep3

µ1

ghWp† 1

ghWp 2

Z 3

icwep2µ3

sw+

icwep3µ3

sw

ghWp† 1

ghZ 2

phi2 3

− cweMW

2sw+ eMW sw

2cw

ghWp† 1

ghZ 2

W 3

−icwep2

µ3

sw−

icwep3µ3

sw

ghZ† 1

ghWm 2

phi2 3

eMZ2sw

ghZ† 1

ghWm 2

W 3

icwep2µ3

sw+

icwep3µ3

sw

ghZ† 1

ghWp 2

phi2† 3

− eMZ2sw

ghZ† 1

ghWp 2

W † 3

−icwep2

µ3

sw−

icwep3µ3

sw

ghZ† 1

ghZ 2

H 3

− ieMZ2cwsw

G 1

ghG† 2

ghG 3

gsfa1,a2,a3p1µ1 + gsfa1,a2,a3p3

µ1

G 1

G 2

G 3

gsfa1,a2,a3p1µ3ηµ1,µ2 − gsfa1,a2,a3p2

µ3ηµ1,µ2 − gsfa1,a2,a3p1µ2ηµ1,µ3 + gsfa1,a2,a3p3

µ2ηµ1,µ3 +gsfa1,a2,a3p2

µ1ηµ2,µ3 − gsfa1,a2,a3p3µ1ηµ2,µ3

17

G 1

G 2

G 3

G 4

igs2fa1,a3,a1fa2,a4,a1ηµ1,µ4ηµ2,µ3 +igs

2fa1,a2,a1fa3,a4,a1ηµ1,µ4ηµ2,µ3 +igs2fa1,a4,a1fa2,a3,a1ηµ1,µ3ηµ2,µ4−

igs2fa1,a2,a1fa3,a4,a1ηµ1,µ3ηµ2,µ4 − igs

2fa1,a4,a1fa2,a3,a1ηµ1,µ2ηµ3,µ4 − igs2fa1,a3,a1fa2,a4,a1ηµ1,µ2ηµ3,µ4

A 1

six1 2

six1† 3

13 icwg1p2

µ1δu2,u3 −13 icwg1p3

µ1δu2,u3

−dq 1

six1 2−uq 3

2i√

2K6bar [u2, i1, i3] LUDLf1,f3P−s1,s3 + 2i√

2K6bar [u2, i1, i3] LQQRf1,f3P+s1,s3

dq 1

six1† 2

uq 3

2i√

2LQQRf1,f3∗K6 [u2, i1, i3] P−s1,s3 + 2i

√2LUDLf1,f3

∗K6 [u2, i1, i3] P+s1,s3

H 1

H 2

six1 3

six1† 4

iLHS1δu3,u4

φ 1

φ 2

six1 3

six1† 4

iLHS1δu3,u4

phi2 1

phi2† 2

six1 3

six1† 4

iLHS1δu3,u4

H 1

six1 2

six1† 3

iLHS1vδu2,u3

A 1

A 2

six1 3

six1† 4

29 icw

2g12δu3,u4ηµ1,µ2

six1 1

six1 2

six1† 3

six1† 4

2iLSS11δu1,u4δu2,u3 + 2iLSS11δu1,u3δu2,u4

A 1

six2 2

six2† 3

− 23 icwg1p2

µ1δu2,u3 + 23 icwg1p3

µ1δu2,u3

−dq 1−dq 2

six2 3

4i√

2K6bar [u3, i1, i2] LDDLf1,f2P−s1,s2

dq 1

dq 2

six2† 3

4i√

2LDDLf1,f2∗K6 [u3, i1, i2] P+s1,s2

18

H 1

H 2

six2 3

six2† 4

iLHS2δu3,u4

φ 1

φ 2

six2 3

six2† 4

iLHS2δu3,u4

phi2 1

phi2† 2

six2 3

six2† 4

iLHS2δu3,u4

H 1

six2 2

six2† 3

iLHS2vδu2,u3

A 1

A 2

six2 3

six2† 4

89 icw


six1 1

six1† 2

six2 3

six2† 4

iLSS122δu1,u4δu2,u3 + iLSS121δu1,u2δu3,u4

six2 1

six2 2

six2† 3

six2† 4


A 1

six3 2

six3† 3

43 icwg1p2

µ1δu2,u3 −43 icwg1p3

µ1δu2,u3

six3 1−uq 2−uq 3

4i√

2K6bar [u1, i2, i3] LUULf2,f3P−s2,s3

six3† 1

uq 2

uq 3

4i√

2LUULf2,f3∗K6 [u1, i2, i3] P+s2,s3

H 1

H 2

six3 3

six3† 4

iLHS3δu3,u4

φ 1

φ 2

six3 3

six3† 4

iLHS3δu3,u4

19

phi2 1

phi2† 2

six3 3

six3† 4

iLHS3δu3,u4

H 1

six3 2

six3† 3

iLHS3vδu2,u3

A 1

A 2

six3 3

six3† 4

329 icw


six1 1

six1† 2

six3 3

six3† 4


six2 1

six2† 2

six3 3

six3† 4


six3 1

six3 2

six3† 3

six3† 4


dq 1−dq 2

G 3

igsγs2,s1µ3δf1,f2Ti2,i1

a3

G 1

uq 2−uq 3

igsγs3,s2µ1δf2,f3Ti3,i2

a1

G 1

six1 2

six1† 3

igsp2µ1T6u3,u2

a1 − igsp3µ1T6u3,u2

a1

A 1

G 2

six1 3

six1† 4

23 icwg1gsηµ1,µ2T6u4,u3

a2

G 1

G 2

six1 3

six1† 4

igs2ηµ1,µ2T6a1,u3

a1T6u4,a1a2 + igs

2ηµ1,µ2T6u4,a1a1T6a1,u3

a2

G 1

six2 2

six2† 3

igsp2µ1T6u3,u2


a1

A 1

G 2

six2 3

six2† 4

− 43 icwg1gsηµ1,µ2T6u4,u3

a2

20

G 1

G 2

six2 3

six2† 4


a1T6u4,a1a2 + igs


a2

G 1

six3 2

six3† 3

igsp2µ1T6u3,u2


a1

A 1

G 2

six3 3

six3† 4

83 icwg1gsηµ1,µ2T6u4,u3

a2

G 1

G 2

six3 3

six3† 4


a1T6u4,a1a2 + igs


a2

A 1

H 2

phi2† 3

W 4

−e2ηµ1,µ4

2sw

A 1

φ 2

phi2† 3

W 4

−ie2ηµ1,µ4

2sw

A 1

phi2† 2

W 3

−e2vηµ1,µ3

2sw

H 1

phi2† 2

W 3

−

ep1µ3

2sw+

ep2µ3

2sw

φ 1

phi2† 2

W 3

−

iep1µ3

2sw+ iep2

µ3

2sw

A 1

W 2

W † 3

−igwswp1µ3ηµ1,µ2 + igwswp2

µ3ηµ1,µ2 + igwswp1µ2ηµ1,µ3 − igwswp3

µ2ηµ1,µ3 − igwswp2µ1ηµ2,µ3 +

igwswp3µ1ηµ2,µ3

A 1

H 2

phi2 3

W † 4

e2ηµ1,µ4

2sw

A 1

φ 2

phi2 3

W † 4

−ie2ηµ1,µ4

2sw

A 1

phi2 2

W † 3

e2vηµ1,µ3

2sw

21

H 1

phi2 2

W † 3

−

ep1µ3

2sw+ ep2

µ3

2sw

φ 1

phi2 2

W † 3

iep1µ3

2sw−

iep2µ3

2sw

H 1

H 2

W 3

W † 4

ie2ηµ3,µ4

2sw2

φ 1

φ 2

W 3

W † 4

ie2ηµ3,µ4

2sw2

phi2 1

phi2† 2

W 3

W † 4

ie2ηµ3,µ4

2sw2

H 1

W 2

W † 3

ie2vηµ2,µ3

2sw2

A 1

A 2

W 3

W † 4

igw2sw

2ηµ1,µ4ηµ2,µ3 + igw2sw

2ηµ1,µ3ηµ2,µ4 − 2igw2sw

2ηµ1,µ2ηµ3,µ4

W 1

W † 2

Z 3

−icwgwp1µ3ηµ1,µ2 + icwgwp2

µ3ηµ1,µ2 + icwgwp1µ2ηµ1,µ3 − icwgwp3

µ2ηµ1,µ3 − icwgwp2µ1ηµ2,µ3 +

icwgwp3µ1ηµ2,µ3

W 1

W 2

W † 3

W † 4

−igw2ηµ1,µ4ηµ2,µ3 − igw

2ηµ1,µ3ηµ2,µ4 + 2igw2ηµ1,µ2ηµ3,µ4

dq 1

phi2 2−uq 3

−CKMf3,f1δi1,i3P+s3,s1y

df1 + CKMf3,f1δi1,i3P−s3,s1y

uf3

−dq 1

phi2† 2

uq 3

CKMf3,f1∗δi1,i3P−s1,s3y

df1 − CKMf3,f1

∗δi1,i3P+s1,s3yuf3

dq 1−dq 2

H 3

−iδi1,i2δf1,f2

δs2,s1ydf1√

2

dq 1−dq 2

φ 3

γs2,s15δi1,i2δf1,f2

ydf1√

2

22

H 1

l 2−l 3

−iδf2,f3

δs3,s2ylf2√

2

l 1−l 2

φ 3

γs2,s15δf1,f2

ylf1√

2

l 1

phi2 2−vl 3

−δf1,f3P+s3,s1ylf1

−l 1

phi2† 2

vl 3

δf1,f3P−s1,s3ylf1

H 1

uq 2−uq 3

−

iδi2,i3δf2,f3δs3,s2yu

f2√2

φ 1

uq 2−uq 3

−

γs3,s25δi2,i3δf2,f3

yuf2√

2

A 1

phi2 2

phi2† 3

Z 4

icwe2ηµ1,µ4

sw−

ie2swηµ1,µ4

cw

H 1

φ 2

Z 3

−

cwep1µ3

2sw−

eswp1µ3

2cw+ cwep2

µ3

2sw+ eswp2

µ3

2cw

phi2 1

phi2† 2

Z 3

icwep1µ3

2sw−

ieswp1µ3

2cw−

icwep2µ3

2sw+ ieswp2

µ3

2cw

six1 1

six1† 2

Z 3

− 13 ig1swp1

µ3δu1,u2 + 13 ig1swp2

µ3δu1,u2

A 1

six1 2

six1† 3

Z 4

− 29 icwg1

2swδu2,u3ηµ1,µ4

six2 1

six2† 2

Z 3

23 ig1swp1

µ3δu1,u2 −23 ig1swp2

µ3δu1,u2

A 1

six2 2

six2† 3

Z 4

− 89 icwg1

2swδu2,u3ηµ1,µ4

six3 1

six3† 2

Z 3

− 43 ig1swp1

µ3δu1,u2 + 43 ig1swp2

µ3δu1,u2

23

A 1

six3 2

six3† 3

Z 4

− 329 icwg1

2swδu2,u3ηµ1,µ4

G 1

six1 2

six1† 3

Z 4

− 23 ig1gsswηµ1,µ4T6u3,u2

a1

G 1

six2 2

six2† 3

Z 4

43 ig1gsswηµ1,µ4T6u3,u2

a1

G 1

six3 2

six3† 3

Z 4

− 83 ig1gsswηµ1,µ4T6u3,u2

a1

H 1

phi2† 2

W 3

Z 4

e2ηµ3,µ4

2cw

φ 1

phi2† 2

W 3

Z 4

ie2ηµ3,µ4

2cw

phi2† 1

W 2

Z 3

e2vηµ2,µ3

2cw

H 1

phi2 2

W † 3

Z 4

−e2ηµ3,µ4

2cw

φ 1

phi2 2

W † 3

Z 4

ie2ηµ3,µ4

2cw

phi2 1

W † 2

Z 3

−e2vηµ2,µ3

2cw

A 1

W 2

W † 3

Z 4

−2icwgw2swηµ1,µ4ηµ2,µ3 + icwgw

2swηµ1,µ3ηµ2,µ4 + icwgw2swηµ1,µ2ηµ3,µ4

H 1

H 2

Z 3

Z 4

ie2ηµ3,µ4 +icw

2e2ηµ3,µ4

2sw2 +

ie2sw2ηµ3,µ4

2cw2

24

φ 1

φ 2

Z 3

Z 4

ie2ηµ3,µ4 +icw

2e2ηµ3,µ4

2sw2 +

ie2sw2ηµ3,µ4

2cw2

phi2 1

phi2† 2

Z 3

Z 4

−ie2ηµ3,µ4 +icw

2e2ηµ3,µ4

2sw2 +

ie2sw2ηµ3,µ4

2cw2

H 1

Z 2

Z 3

ie2vηµ2,µ3 +icw

2e2vηµ2,µ3

2sw2 +

ie2sw2vηµ2,µ3

2cw2

six1 1

six1† 2

Z 3

Z 4

29 ig1

2sw2δu1,u2ηµ3,µ4

six2 1

six2† 2

Z 3

Z 4

89 ig1


six3 1

six3† 2

Z 3

Z 4

329 ig1


W 1

W † 2

Z 3

Z 4

icw2gw

2ηµ1,µ4ηµ2,µ3 + icw2gw

2ηµ1,µ3ηµ2,µ4 − 2icw2gw

2ηµ1,µ2ηµ3,µ4

A 1

dq 2−dq 3

− 13 ieγs3,s2

µ1δi2,i3δf2,f3

A 1

l 2−l 3

−ieγs3,s2µ1δf2,f3

A 1

uq 2−uq 3

23 ieγs3,s2

µ1δi2,i3δf2,f3

l 1−vl 2

W 3

ieδf1,f2γµ3 .P−s2,s1√2sw

dq 1−uq 2

W 3

ieCKMf2,f1δi1,i2γµ3 .P−s2,s1√

2sw

−l 1

vl 2

W † 3

ieδf1,f2γµ3 .P−s1,s2√2sw

25

−dq 1

uq 2

W † 3

ieCKMf2,f1∗δi1,i2γµ3 .P−s1,s2√

2sw

dq 1−dq 2

Z 3

−icweδi1,i2δf1,f2

γµ3 .P−s2,s1

2sw−

ieswδi1,i2δf1,f2γµ3 .P−s2,s1

6cw+

ieswδi1,i2δf1,f2γµ3 .P+s2,s1

3cw

l 1−l 2

Z 3

−icweδf1,f2

γµ3 .P−s2,s1

2sw+

ieswδf1,f2γµ3 .P−s2,s1

2cw+

ieswδf1,f2γµ3 .P+s2,s1

cw

uq 1−uq 2

Z 3

icweδi1,i2δf1,f2γµ3 .P−s2,s1

2sw−

ieswδi1,i2δf1,f2γµ3 .P−s2,s1

6cw−

2ieswδi1,i2δf1,f2γµ3 .P+s2,s1

3cw

vl 1−vl 2

Z 3

icweδf1,f2γµ3 .P−s2,s1

2sw+

ieswδf1,f2γµ3 .P−s2,s1

2cw

26

References

[1] N. D. Christensen and C. Duhr, arXiv:0806.4194 [hep-ph].

27

Documents

feynrules.irmp.ucl.ac.be · FeynRules Implementation of Sextet Diquarks C. Duhr ∗ IPPP, Durham April 3, 2011 Abstract We describe the implementation of the Sextet Diquarks model