Unification without supersymmetry - Agenda (Indico) · 2016. 5. 25. · Frezzotti, RossiPhys. Rev. D 92 (2015) 5, 054505 Frezzotti, Garofalo, Rossi[arXiv:1602.03684] to be published

Unification without supersymmetry

R. Frezzottia)b), M. Garofaloc), G.C. Rossia)b)d)

a)Dipartimento di Fisica - Università di Roma Tor Vergatab)INFN - Sezione di Roma Tor Vergata

c)University of Edinburghd)Centro Fermi

Frezzotti, Rossi Phys. Rev. D 92 (2015) 5, 054505Frezzotti, Garofalo, Rossi [arXiv:1602.03684] to be published in PRD

May 24, 2016

Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 1 / 18

Outline of the talk1 Motivation & Introduction

expose a non-Susy model with a level of unification as in MSSM2 The model

SM matter + superstrongly interacting extra matter→a kind of BSMM with

NP generation of all elementary particle massesnatural mass hierarchy

3 Unificationstrong & electro-weak coupling unification owing to

new matter (superstrongly interacting quarks and leptons)with unusual hypercharge assignment (half-integer charges)

superstrong, strong & electro-weak coupling unification owing tofurther extra fermions endowed with only superstrong interactionsand masses around the unification scale ΛGUT

4 Conclusions & Outlooklattice checks of the NP mass generation mechanismlook for a GUT group


Motivation

Figure : Running of electro-weak and strong couplings in SM (black dottedlines) and MSSM. Displacement of blue and red curves at small scales isassociated to the opening of the SUSY threshold, either 0.5 TeV (bluecurve) or 1.5 TeV (red curve) with initial conditions αs(mZ ) = 0.117 andαs(mZ ) = 0.121, respectively.


A non-supersymmetric model

LBSMM =14(F BF B + F W F W + F AF A)+

+

ng∑f=1

[q̄f

L /DBWAqf

L + q̄f uR /DBAqf u

R + q̄f dR /DBAqf d

R +

+¯̀fL /D

BW `fL + ¯̀f u

R /DB`f uR + ¯̀f d

R /DB`f dR

]+ SM masses +

+14

F GF G+

νQ∑s=1

[Q̄s

L /DBWAGQs

L + Q̄s uR /DBAGQs u

R + Q̄s dR /DBAGQs d

R

]+

+

νL∑t=1

[L̄t

L /DBWGLt

L + L̄t uR /DBGLt u

R + L̄t dR /DBGLt d

R

]+ O(TeV) masses

DBWAGµ = ∂µ − iYgY Bµ − igwτ

r W rµ − igs

λa

2Aaµ − igT

λαT2

Gαµ


A non-supersymmetric BSM model

LBSMM =14(F BF B + F W F W + F AF A)+

+

ng∑f=1

[q̄f

L /DBWAqf

L + q̄f uR /DBAqf u

R + q̄f dR /DBAqf d

R +

+¯̀fL /D

BW `fL + ¯̀f u

R /DB`f uR + ¯̀f d

R /DB`f dR

]+

+14

F GF G+

νQ∑s=1

[Q̄s

L /DBWAGQs

L + Q̄s uR /DBAGQs u

R + Q̄s dR /DBAGQs d

R

]+

+

νL∑t=1

[L̄t

L /DBWGLt

L + L̄t uR /DBGLt u

R + L̄t dR /DBGLt d

R

]+

+ . . .

—————————————————————————————-

mQ = O(αTαT )ΛT mtop = O(αsαT )ΛT mτ = O(αYαT )ΛT

MW = O(√αW )ΛT

ΛT ∼ O(TeV )


SM hypercharge assignments

q `

yuL = 23 − 1

2 = 16 yνL = 0− 1

2 = −12

yuR = 23 − 0 = 2

3 yνR = 0

ydL = −13 + 1

2 = 16 yelL = −1 + 1

2 = −12

ydR = −13 − 0 = −1

3 yelR = −1− 0 = −1∑y2

q = 2236

∑y2` = 3

2

Table : Hypercharges of SM fermions

Q = T 3 + YAnomaly cancellation occurs between quarks and leptons


Non-standard hypercharge assignments→ unique

Q L

yUL = 12 − 1

2 = 0 yNL = 12 − 1

2 = 0

yUR = 12 − 0 = 1

2 yNR = 12 − 0 = 1

2

yDL = −12 + 1

2 = 0 yLL = −12 + 1

2 = 0

yDR = −12 − 0 = −1

2 yLR = −12 − 0 = −1

2∑y2

Q = 12

∑y2

L = 12

Table : Non-standard hypercharge assignments

Anomalies separately zero for quarks and leptons→ YL = 0L-handed doublets→ QL = T 3

L = ±1/2R-handed singlets→ QR = YR

QR = QL = ±1/2The above is the only possible choice


BSMM β-functionsTable 2 assignment for SIP hypercharges→ above TeV scale we get

βBSMMT = −

[113

NT −43

(NcνQ + νL)

]g3

T(4π)2

βBSMMs = −

[113

Nc −43

(NTνQ + ng)

]g3

s

(4π)2

βBSMMw = −

[2

113− 1

3ng(Nc + 1)− 1

3NT (NcνQ + νL)

]g3

w

(4π)2

βBSMMY =

{23

[(2236

Nc +32

)ng +

12

NT (NcνQ + νL)

]}g3

Y(4π)2

Alternatively with the standard assignment one would have

βBSMMY st =

{23

[(2236

Nc +32

)ng +

12

NT

(2218

NcνQ + 3νL

)]}g3

Y(4π)2

with ng , νQ , νL = # of generations of (q, `), Q and L


SM β-functions

βSMs = −

(113

Nc −43

ng

)g3

s(4π)2 ,

βSMw = −

[2

113− 1

3ng(Nc + 1)− 1

6

]g3

w(4π)2 ,

βSMY =

[23

(2236

Nc +32

)ng +

16

]g3

Y(4π)2 .


GUT normalization conditions - BSSM

If all the fermions must belong to an irreducible GGUT representation,one must have

Tr[(gY Y )2

]= Tr

[(12

gwτ3)2]

= Tr[

(12

gsλ3)2]

= Tr[

(12

gTλ3T )2]

An explicit computation reveals that the unifying couplings arenon-standard hypercharge assignments

g21 :=

43

g2Y , g2

2 := g2w , g2

3 := g2s , g2

4 :=23

g2T

standard hypercharge assignments

g21 :=

53

g2Y , g2

2 := g2w , g2

3 := g2s , g2

4 :=23

g2T

We took for concreteness NT = Nc = ng = 3 & νQ = νL = 1


GUT normalization conditions - SM

Tr[(gY Y )2

]= Tr

[(12

gwτ3)2]

= Tr[

(12

gsλ3)2]

g21 :=

53

g2Y , g2

2 := g2w , g2

3 := g2s


Evolution equations

dgi

d logµ= βgi , i = 1,2,3,4

BSMM 1-loop β-functions with GUT normalization

βg1 = 8g3

1(4π)2 , βg2 =

46

g32

(4π)2 ,

βg3 = −3g3

3

(4π)2 , βg4 = −172

g34

(4π)2

Standard and non-standard Y assignments yield the same βg1

SM 1-loop β-functions with GUT normalization

βg1 =4110

g31

(4π)2 , βg2 = −196

g32

(4π)2 , βg3 = −7g3

3(4π)2

Note - βg2 is positive in the BSMM and negative in the SM.


BSMM vs. SM

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 electro-weak and strong couplings in theBSMM (red curves) and in the SM (black curves). The visible change ofslope of red curves at “low” scales is associated with the opening of thesuperstrong threshold that we take at ΛT = 5 TeV

SM

α−11 (mZ ) = 59.01 ± 0.02

α−12 (mZ ) = 29.57 ± 0.02

α−13 (mZ ) = 8.45 ± 0.05

BSSM

α−11 (mZ ) = 73.76 ± 0.02

α−12 (mZ ) = 29.57 ± 0.02

α−13 (mZ ) = 8.45 ± 0.05


BSMM vs. 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 electro-weak and strong couplings in theBSMM (red curves) and in the MSSM (blue curves). The superstrong andsupersymmetry thresholds have been set at ΛT = 5 and ΛMSSM = 1 TeV,respectively

MSSM

α−11 (mZ ) = 59.01 ± 0.02

α−12 (mZ ) = 29.57 ± 0.02

α−13 (mZ ) = 8.45 ± 0.05

BSSM

α−11 (mZ ) = 73.76 ± 0.02

α−12 (mZ ) = 29.57 ± 0.02

α−13 (mZ ) = 8.45 ± 0.05


Changing hypercharge assignment to SIPs

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 electro-weak and strong couplings in theBSMM with the hyperchage assignment of Table 2 (red curves) and the“standard” hyperchage assignment of Table 1 (green curve)


A full unification in BSMM?

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 electro-weak strong and superstrongcouplings in the BSMM with NS extra particles having purely superstrongvector interactions and masses O(ΛGUT ). NS = 4 (blue line) NS = 5 (blackline), NS = 6 (green line)


Conclusions

A non-SUSY BSMM model with unification at the level of MSSMThe salient features of the BSMM outlined in slide 5 are

elementary particle masses generated by a NP mechanismtriggered by irrelevant d = 6 chiral breaking op’s in L → no Higgsa neat solution of “naturalness” & “hierarchy” problems

at the price of giving up a bit of universalitycorrect order of magnitude of the NP-ly generated top mass =⇒

SIPs with an RGI scale ΛT � ΛQCD , ΛT ∼ O(TeV)SIPs (must) have unusual hypercharge assignments

electric charge quantized in units of e/2.neutral SIP bound states with non-zero fermion number→ CDM?

125 resonance is a WW/ZZ state bound by superstrong forces

TM

QT

+ . . . =⇒ + . . . =⇒ h

(a) (b) (c)

Existence of NP effects needs a numerical confirmation


Thank you for your attention


Documents

Unification without supersymmetry - Agenda (Indico) · 2016. 5. 25. · Frezzotti, RossiPhys. Rev. D 92 (2015) 5, 054505 Frezzotti, Garofalo, Rossi[arXiv:1602.03684] to be published