Plank-Valencia-2016 R.Frezzotti M.Garofalo G.C.Rossi Theuniﬁcationofelectro-weakandstronginteractionsinanon-supersymmetricmodel

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The unification of electro-weak and strong interactions in a non-supersymmetric model

based on Phys. Rev. D 93 (2016) 105030

R. Frezzotti a) M. Garofalo b) G.C. Rossi a)c)

a)

Dipartimento di Fisica - Università di Roma Tor Vergata, INFN - Sezione di Roma Tor Vergata

b)

Higgs Centre for Theoretical Physics, The University of Edinburgh

c)

Centro Fermi - Museo Storico della Fisica, Piazza del Viminale 1 - 00184 Roma, Italy

Plank-Valencia-2016

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Unification fails in the Standard Model (SM)

It can be achieved including supersimmetry as in the Minimal Supersimmetryc Standard Model (MSSM)

[S. Dimopoulos, S. Raby and F. Wilczek,Phys. Rev. D 24 (1981) 1681]

[S. P. Martin, Adv. Ser. Direct. High Energy Phys. 21 (2010) 1]

Figure: The running of electro-weak and strong couplings in the SM (black dotted lines) and in the MSSM

R. Frezzotti M. Garofalo G.C. Rossi

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Non-supersymmetric extension of the Standard Model (BSMM) → unification to a similar accuracy of the MSSM.

Inspired from the work [R. Frezzotti and G. C. Rossi, Phys. Rev. D 92 (2015) 5, 054505.] → conjecture of a non-perturbative mechanism for the mass generation m ∼ αΛ (R. Frezzotti talk, “ Mass hierarchy and naturalness from TeV scale strong dynamics”)

m top requires the inclusion of a new superstrong interaction SU(N T ) with Λ T ∼ O(few TeV) and Λ T > Λ QCD

Set of superstrong interacting particles Q T and L T subject

to SU(N T )

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The lagrangian of the BSMM is

L

^{BSM M}

= L

gauge

+ L

^SMF

+ L

scalar

+ L

^SS

,

L

gauge

= 1 4

F

^B

F

^B

+ F

^W

F

^W

+ F

^A

F

^A

+ F

^G

F

^G

, L

^SM_F

=

ng

X

f=1

h

¯

q

_L^f

6D

^{BW A}

q

_L^f

+ ¯ q

^{f u}_R

6D

^BA

q

^{f u}_R

+ ¯ q

_R^{f d}

6D

^BA

q

_R^{f d}

+

+¯ `

^f_L

6D

^BW

`

^f_L

+ ¯ `

^{f u}_R

6D

^B

`

^{f u}_R

+ ¯ `

^{f d}_R

6D

^B

`

^{f d}_R

i

, L

scalar

= 1

2 Tr h

D

^BW_µ

Φ

^†

D

^BW_µ

Φ i + µ

²0

2 Tr h

Φ

^†

Φ i + λ

0

4

Tr h

Φ

^†

Φ i

2

,

L

^SS

=

ν_Q

X

s=1

h Q ¯

^s_L

6D

^{BW AG}

Q

^s_L

+ ¯ Q

^{s u}_R

6D

^BAG

Q

^{s u}_R

+ ¯ Q

^{s d}_R

6D

^BAG

Q

^{s d}_R

i +

+

ν_L

X

t=1

h L ¯

^tL

6D

^{BW G}

L

^tL

+ ¯ L

^{t u}R

6D

^BG

L

^{t u}R

+ ¯ L

^{t d}R

6D

^BG

L

^{t d}R

i ,

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Magnitude of the masses

SM particles have their phenomenological masses Superstrong interacting particles Q and L

m SS ∼ Λ T Λ QCD

The scalar mass m Φ ∼ Λ GU T → decoupled from the

dynamics

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Hypercharge of Q and L

Non standard hypercharge assignment obtained requiring:

Left fermions SU(2)doublet Right fermions SU(2)singlet Q = τ

₃

+ Y

Anomalies are cancelled within quark and lepton sectors separately

ν Q and ν L generations of Q and L

[S. Weinberg, “ The Quantum Theory of Fields”, Vol. II]

q w ` w Q w L w

y u

L

= 1 6 y ν

L

= − 1 2 y U

_L

= 0 y N

_L

= 0 y u

R

= 2 3 y ν

R

= 0 y U

R

= 1 2 y N

R

= + 1 2 y d

_L

= 1 6 y el

_L

= − 1 2 y D

L

= 0 y L

L

= 0 y d

R

= − 1 3 y el

R

= −1 y D

R

= − 1 2 y L

R

= − 1 2 P y q 2 = 22 36 P

y 2 ` = 3 2 P

y Q 2 = 1 2 P y L 2 = 1 2

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1-loop β-functions With the standard definitions

β x (g x ) = µ dg x

dµ , x = T, s, w, Y

and g T , g s , g w , g Y the coupling of SU(N T ), SU(N c ), SU(2 L ), U(1) respectively, we get

β T BSM M = − 11

3 N T − 4

3 (N c ν Q + ν L ) g T 3

(4π) 2 , ν Q = #Q generations β s BSM M = −

11

3 N c − 4

3 (N T ν Q + n g ) g 3 s

(4π) 2 , ν L = #L generations β w BSM M = −

2 11

3 − 1

3 n g (N c + 1) − 1

3 N T (N c ν Q + ν L ) g w 3

(4π) 2 , β Y BSM M =

2 3

22

36 N c + 3 2

n g + 1

2 N T (N c ν Q + ν L ) g Y 3

(4π) 2 ,

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GUT normalization Tr

(g Y Y ) 2

= Tr

( 1 2 g w τ 3 ) 2

= Tr

( 1 2 g s λ 3 ) 2

= Tr

( 1 2 g T λ 3 T ) 2 setting N c = N T = n g = 3 and ν Q = ν L = 1 we get

g 1 2 := 4

3 g Y 2 , g 2 2 := g w 2 , g 3 2 := g 2 s , g 2 4 := 2 3 g T 2 PDG input m Z ∼ 91GeV α −1 1 (m Z ) = 4π/g 1 2 = 73.76 ± 0.02 While in the SM

g 1 2 := 5

3 g Y 2 , g 2 2 := g w 2 , g 2 3 := g s 2 .

PDG input m Z ∼ 91GeV α −1 1 (m Z ) = 4π/g 1 2 = 59.01 ± 0.02

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GUT normalization Tr

(g Y Y ) 2

= Tr

( 1 2 g w τ 3 ) 2

= Tr

( 1 2 g s λ 3 ) 2

= Tr

( 1 2 g T λ 3 T ) 2 setting N c = N T = n g = 3 and ν Q = ν L = 1 we get

g 1 2 := 4

3 g Y 2 , g 2 2 := g w 2 , g 3 2 := g 2 s , g 2 4 := 2 3 g T 2 PDG input m Z ∼ 91GeV α −1 1 (m Z ) = 4π/g 1 2 = 73.76 ± 0.02 While in the SM

g 1 2 := 5

3 g Y 2 , g 2 2 := g w 2 , g 2 3 := g s 2 .

PDG input m Z ∼ 91GeV α −1 1 (m Z ) = 4π/g 1 2 = 59.01 ± 0.02

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• m Z < µ < Λ T SM

β g

1

= 41 10

g 1 3 (4π) 2 β g

2

= − 19

6 g 2 3 (4π) 2 β g

3

= −7 g 3 3

(4π) 2 BSSM

β g

₁

= 5 g 3 1 (4π) 2 β g

₂

= −3 g 2 3

(4π) 2 β g

₃

= −7 g 3 3

(4π) 2

• µ > Λ T SM

β g

1

= 41 10

g 1 3 (4π) 2 β g

2

= − 19

6 g 2 3 (4π) 2 β g

3

= −7 g 3 3

(4π) 2 BSSM

β g

₁

= 8 g 3 1 (4π) 2 β g

₂

= 4

6 g 2 3 (4π) 2 β g

₃

= −3 g 3 3 (4π) 2

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• m Z < µ < Λ T SM

β g

1

= 41 10

g 1 3 (4π) 2 β g

2

= − 19

6 g 2 3 (4π) 2 β g

3

= −7 g 3 3

(4π) 2 BSSM

β g

₁

= 5 g 3 1 (4π) 2 β g

₂

= −3 g 2 3

(4π) 2 β g

₃

= −7 g 3 3

(4π) 2

• µ > Λ T SM

β g

1

= 41 10

g 1 3 (4π) 2 β g

2

= − 19

6 g 2 3 (4π) 2 β g

3

= −7 g 3 3

(4π) 2 BSSM g 2 loses asymptotic freedom

β g

₁

= 8 g 3 1 (4π) 2 β g

₂

= 4

6

g 2 3

(4π) 2

β g

₃

= −3 g 3 3

(4π) 2

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0 10 20 30 40 50 60 70 80

1e+02 1e+04 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20

α-1

µ(GeV)

Figure: 1-loop running of α

i

= g

_i²

/4π in the SM and in the BSSM.

The superstrong threshold is set to Λ

T

= 1TeV

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If we compare it with the MSSM

0 10 20 30 40 50 60 70 80

1e+02 1e+04 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20

α-1

µ(GeV)

Figure: The 1-loop running of α

i

= g

_i²

/4π in the BSMM and in the

MSSM. The superstrong and supersymmetry thresholds have been set

at Λ

T

= Λ

M SSM

= 1 TeV.

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input Λ T Λ T 2-loop GUT Total value value threshold effect threshold

error ∆ A ∆ B ∆ C ∆ D ∆ E ∆ tot

α −1 1 0.02 0.15 0.02 0.6 0.42 0.75 α −2 2 0.02 0.2 0.03 0.8 0.42 0.93 α −3 3 0.05 0.25 0.06 0.75 0.42 0.90

α −4 4 1 0.5 3 3.2

∆ A : Phenomenological error at m z ∼ 91GeV

∆ B : Value of Λ T = 1 ÷ 2TeV

∆ C : Spread of LO to NLO matching function; with M L = 1 TeV M Q = 1.5 TeV and µ T = 1.25 TeV

∆ D : α −1 2loop (Λ GU T ) − α −1 1loop (Λ GU T )

∆ E : Taken from a supersymmetric SU(5) grand unified model (PDG), as a GUT candidate for our BSSM not yet identified

∆ tot = q

∆ 2 A + ∆ 2 B + ∆ 2 C + ∆ 2 D + ∆ 2 E

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Figure: running of α

i

= g

²_i

/4π in the SM and in the BSSM.

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Unification of the SU(N T ) coupling requires adding N S purely superstrong interacting particles

N

S

X

f =1

ψ ¯ f 6D G ψ f + m h ψ ¯ f ψ f m f ∼ Λ GU T

β g

₄

= − 17 3

12 8 + N S

g 4 3 (4π) 2 reasonable values of N S = 4, 6, 8

⁰

10 20 30 40 50 60 70 80

1e+02 1e+04 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20

α-1

µ(GeV)

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Summary of BSMM

Inspired from NP mechanism of elementary particle mass generation (R. Frezzotti talk)

SU(N T ) interaction with Q and L

Non standard hypercharge assignment of Q and L, necessary for the unification (not for the NP mechanism) Scalar mass m Φ ∼ Λ GU T ,

natural choice in the framework of the NP mechanism

however not crucial for gauge coupling unification

Including Ψ to unify the SU(N T ) coupling

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Conclusions

Unification at the same accuracy as in MSSM Alternative hypercharge assignment

crucial for the unification

superstrongly confined “hadrons” with charge quantized in units of e/2

Superstrongly bound glueball state lighter than mesons (may be compatible with possible LHC resonance at ∼ 750 GeV)

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m Φ = m higgs or m Φ ∼ Λ GU T

20 22 24 26 28 30 32 34

1e+16 1e+17 1e+18 1e+19 1e+20

α-1

µ(GeV)

without scalar with scalar

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Standard hypercharge assignment Q and L g 1 2 := 5 3 g Y 2 like SM vs Non standard g 2 1 := 4 3 g Y 2

0 10 20 30 40 50 60 70 80

1e+02 1e+04 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20

α-1

µ(GeV)