Perturbativity constraints in U (1) B L and Left-Right Models Garv - - PowerPoint PPT Presentation

Perturbativity constraints in U(1)B−L and Left-Right Models

Garv Chauhan

Washington University in St. Louis

Particle Physics on the Plains University of Kansas Oct 14, 2018 In collaboration with P.S.B Dev, R.N Mohapatra & Y. Zhang (arXiv: 1810.xxxxx)

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Outline

Introduction & Motivation Theoretical Constraints Bounds in U(1)B−L model Bounds in Minimal LRSM Conclusions

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Introduction & Motivation

The Standard Model(SM) has been highly successful but needs extension to include new physics such as tiny neutrino masses, DM and baryon asymmetry.

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Introduction & Motivation

The Standard Model(SM) has been highly successful but needs extension to include new physics such as tiny neutrino masses, DM and baryon asymmetry. From experimental point of view, interesting to look at prospects of new physics at TeV scale, to be probed by current and planned future experiments.

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Introduction & Motivation

The Standard Model(SM) has been highly successful but needs extension to include new physics such as tiny neutrino masses, DM and baryon asymmetry. From experimental point of view, interesting to look at prospects of new physics at TeV scale, to be probed by current and planned future experiments. Many TeV scale extensions introduce extended gauge groups like extra U(1)’s or SU(2) × U(1).

3 / 19

Introduction & Motivation

The Standard Model(SM) has been highly successful but needs extension to include new physics such as tiny neutrino masses, DM and baryon asymmetry. From experimental point of view, interesting to look at prospects of new physics at TeV scale, to be probed by current and planned future experiments. Many TeV scale extensions introduce extended gauge groups like extra U(1)’s or SU(2) × U(1). Our results apply to a subclass of these gauge extensions of SM, where the generators of the extra gauge groups contribute to the electric charge.

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Introduction & Motivation

In such cases, there are upper and lower limits on the gauge couplings by requiring perturbativity upto GUT scale.

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Introduction & Motivation

In such cases, there are upper and lower limits on the gauge couplings by requiring perturbativity upto GUT scale. The motivation is to embed the TeV-scale gauge extension into a larger gauge symmetry at GUT scale.

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Introduction & Motivation

In such cases, there are upper and lower limits on the gauge couplings by requiring perturbativity upto GUT scale. The motivation is to embed the TeV-scale gauge extension into a larger gauge symmetry at GUT scale. We’ll specifically focus on U(1)B−L & minimal LRSM, and discuss the implications for gauge boson searches.

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Theoretical Constraint on Gauge Couplings

Consider a SM extension: SU(2)L × U(1)X × U(1)Z such that: Q = I3L + IX + QZ 2

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Theoretical Constraint on Gauge Couplings

Consider a SM extension: SU(2)L × U(1)X × U(1)Z such that: Q = I3L + IX + QZ 2 Then following relation holds: 1 g2

Y

= 1 g2

X

+ 1 g2

Z

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Theoretical Constraint on Gauge Couplings

Consider a SM extension: SU(2)L × U(1)X × U(1)Z such that: Q = I3L + IX + QZ 2 Then following relation holds: 1 g2

Y

= 1 g2

X

+ 1 g2

Z

← This holds even if coupling gX is SU(2)

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Theoretical Constraint on Gauge Couplings

Consider a SM extension: SU(2)L × U(1)X × U(1)Z such that: Q = I3L + IX + QZ 2 Then following relation holds: 1 g2

Y

= 1 g2

X

+ 1 g2

Z

← This holds even if coupling gX is SU(2)

Then requiring that coupling gZ is perturbative at breaking scale, ⇒ rg ≡ gX gL > tan θW

• 1 − 4π

g2

Z

αEM cos2 θW −1/2

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U(1)B−L model

Particle content of the SU(2)L × U(1)I3R × U(1)B−L model:

SU(2)L U(1)I3R U(1)B−L Q 2

1 3

uR 1 + 1

2 1 3

dR 1 − 1

2 1 3

L 2 −1 N 1 + 1

2

−1 eR 1 − 1

2

−1 H 2 − 1

2

∆R 1 −1 2

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U(1)B−L model

Particle content of the SU(2)L × U(1)I3R × U(1)B−L model:

SU(2)L U(1)I3R U(1)B−L Q 2

1 3

uR 1 + 1

2 1 3

dR 1 − 1

2 1 3

L 2 −1 N 1 + 1

2

−1 eR 1 − 1

2

−1 H 2 − 1

2

∆R 1 −1 2

The RGEs for the gauge couplings of the two U(1)’s are respectively 16π2β(gI3R) = 9 2 g3

I3R ,

16π2β(gBL) = 3 g3

BL .

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SU(2)L × U(1)I3R × U(1)B−L (Gauge Couplings)

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SU(2)L × U(1)I3R × U(1)B−L (Gauge Couplings)

0.4 0.5 0.6 0.7 0.8 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

gR[vR] gBL[vR] U(1)B-L model

lower bound upper bound lower bound upper bound

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SU(2)L × U(1)I3R × U(1)B−L (Gauge Couplings)

0.4 0.5 0.6 0.7 0.8 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

gR[vR] gBL[vR] U(1)B-L model

lower bound upper bound lower bound upper bound

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0.398 < gR < 0.768; 0.416 < gBL < 0.931, with 0.631 < rg < 1.218 at vR = 5 TeV

SU(2)L × U(1)I3R × U(1)B−L (ZR searches)

0.6 0.7 0.8 0.9 1.0 1.1 1.2 5 10 50 100

rg = gR/gL ZR mass [TeV] U(1)B-L model perturbativelimit perturbativelimit vR = 5 TeV 10 TeV 20 TeV 50 TeV

LHC13 HL-LHC F C C

• h

h 9 / 19

(ATLAS-CONF-2016-045) (CMS-PAS-EXO-16-031)

SU(2)L × U(1)I3R × U(1)B−L (ZR searches)

0.6 0.7 0.8 0.9 1.0 1.1 1.2 5 10 50 100

rg = gR/gL ZR mass [TeV] U(1)B-L model perturbativelimit perturbativelimit vR = 5 TeV 10 TeV 20 TeV 50 TeV

LHC13 HL-LHC F C C

• h

h 0.6 0.7 0.8 0.9 1.0 1.1 1.2 2 5 10 20 50

rg = gR/gL vR [TeV] U(1)B-L model perturbative limit perturbative limit

LHC13 HL-LHC FCC-hh

MZR = 5 TeV 10 TeV 20 TeV 50 TeV

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(ATLAS-CONF-2016-045) (CMS-PAS-EXO-16-031)

SU(2)L × U(1)I3R × U(1)B−L (ZR searches)

0.6 0.7 0.8 0.9 1.0 1.1 1.2 5 10 50 100

rg = gR/gL ZR mass [TeV] U(1)B-L model perturbativelimit perturbativelimit vR = 5 TeV 10 TeV 20 TeV 50 TeV

LHC13 HL-LHC F C C

• h

h 0.6 0.7 0.8 0.9 1.0 1.1 1.2 2 5 10 20 50

rg = gR/gL vR [TeV] U(1)B-L model perturbative limit perturbative limit

LHC13 HL-LHC FCC-hh

MZR = 5 TeV 10 TeV 20 TeV 50 TeV

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Minimal LRSM

Particle content of the minimal LRSM based on the gauge group SU(2)L × SU(2)R × U(1)B−L:

SU(2)L SU(2)R U(1)B−L QL ≡ uL dL

• 2

1

1 3

QR ≡

• uR

dR

• 1

2

1 3

ψL ≡

• νL

eL

• 2

1 −1 ψR ≡

• N

eR

• 1

2 −1 Φ = φ0

1

φ+

2

φ−

1

φ0

2

• 2

2 ∆R = 1

√ 2∆+ R

∆++

R

∆0

R

− 1

√ 2∆+ R

• 1

3 2

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Minimal LRSM

The RGEs for the gauge couplings in the minimal LRSM are 1 16π2β(gL) = −3 g3

L ,

16π2β(gR) = −7 3 g3

R ,

16π2β(gBL) = 11 3 g3

BL

• 1I. Z. Rothstein, Nucl. Phys. B358, 181 (1991)

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SU(2)L × SU(2)R × U(1)B−L (Gauge Couplings)

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SU(2)L × SU(2)R × U(1)B−L (Gauge Couplings)

0.5 1 2 5 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

gR[vR] gBL[vR]

perturbative limit lower bound lower bound upper bound 13 / 19

SU(2)L × SU(2)R × U(1)B−L (Gauge Couplings)

0.5 1 2 5 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

gR[vR] gBL[vR]

perturbative limit lower bound lower bound upper bound 14 / 19

0.406 < gR < √ 4π; 0.369 < gBL < 0.857, with 0.648 < rg < 5.65 at vR = 10 TeV

SU(2)L × SU(2)R × U(1)B−L (Scalar sector)

104 105 106 107 10-4 10-3 10-2 0.1 1 10 100

μ [GeV] quartic couplings λ1 λ2 λ3 λ4 perturbativelimit rg = 1.1, vR = 6 TeV

104 105 106 107

• 5

5 10 15

μ [GeV] quartic couplings ρ1 ρ2 α1 α2 α3 perturbativelimit rg = 1.1, vR = 6 TeV μ λ λ λ λ μ ρ ρ α α α

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SU(2)L × SU(2)R × U(1)B−L (Scalar sector)

104 105 106 107 10-4 10-3 10-2 0.1 1 10 100

μ [GeV] quartic couplings λ1 λ2 λ3 λ4 perturbativelimit rg = 1.1, vR = 6 TeV

104 105 106 107

• 5

5 10 15

μ [GeV] quartic couplings ρ1 ρ2 α1 α2 α3 perturbativelimit rg = 1.1, vR = 6 TeV

105 107 109 1011 1013 1015 10-4 10-3 10-2 0.1 1

μ [GeV] quartic couplings λ1 λ2 λ3 λ4 rg = 1.1, vR = 12 TeV

105 107 109 1011 1013 1015

• 0.2

0.0 0.2 0.4 0.6 0.8

μ [GeV] quartic couplings ρ1 ρ2 α1 α2 α3 rg = 1.1, vR = 12 TeV

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SU(2)L × SU(2)R × U(1)B−L (ZR and WR searches)

0.5 1.0 1.5 2.0 2 5 10 20 50

rg = gR/gL WR mass [TeV] perturbative limit (gauge) vR = 5 TeV 10 TeV 20 TeV 50 TeV p e r t u r b a t i v e l i m i t ( s c a l a r )

LHC13 HL-LHC FCC-hh 16 / 19

(ATLAS-CONF-2016-045) (CMS-PAS-EXO-16-031) (arXiv: 1809.11105) (arXiv: 1803.11116)

SU(2)L × SU(2)R × U(1)B−L (ZR and WR searches)

0.5 1.0 1.5 2.0 2 5 10 20 50

rg = gR/gL WR mass [TeV] perturbative limit (gauge) vR = 5 TeV 10 TeV 20 TeV 50 TeV p e r t u r b a t i v e l i m i t ( s c a l a r )

LHC13 HL-LHC FCC-hh 0.5 1.0 1.5 2.0 5 10 50 100

rg = gR/gL ZR mass [TeV] perturbative limit (gauge) v

R

= 5 T e V 1 T e V 2 T e V 5 T e V p e r t u r b a t i v e l i m i t ( s c a l a r )

LHC13 HL-LHC FCC-hh 16 / 19

(ATLAS-CONF-2016-045) (CMS-PAS-EXO-16-031) (arXiv: 1809.11105) (arXiv: 1803.11116)

SU(2)L × SU(2)R × U(1)B−L (ZR and WR searches)

0.5 1.0 1.5 2.0 2 5 10 20 50

rg = gR/gL WR mass [TeV] perturbative limit (gauge) vR = 5 TeV 10 TeV 20 TeV 50 TeV p e r t u r b a t i v e l i m i t ( s c a l a r )

LHC13 HL-LHC FCC-hh 0.5 1.0 1.5 2.0 5 10 50 100

rg = gR/gL ZR mass [TeV] perturbative limit (gauge) v

R

= 5 T e V 1 T e V 2 T e V 5 T e V p e r t u r b a t i v e l i m i t ( s c a l a r )

LHC13 HL-LHC FCC-hh 17 / 19

SU(2)L × SU(2)R × U(1)B−L (vR bound)

0.5 1.0 1.5 2.0 5 10 50 100

rg = gR/gL vR [TeV] WR searches perturbative limit (gauge)

L H C 1 3 H L

• L

H C F C C

• h

h

p e r t u r b a t i v e l i m i t ( s c a l a r ) MW

R

= 5 T e V 1 T e V 2 T e V 5 T e V

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SU(2)L × SU(2)R × U(1)B−L (vR bound)

0.5 1.0 1.5 2.0 5 10 50 100

rg = gR/gL vR [TeV] WR searches perturbative limit (gauge)

L H C 1 3 H L

• L

H C F C C

• h

h

p e r t u r b a t i v e l i m i t ( s c a l a r ) MW

R

= 5 T e V 1 T e V 2 T e V 5 T e V

0.5 1.0 1.5 2.0 2 5 10 20 50

rg = gR/gL vR [TeV] ZR searches perturbative limit (gauge)

LHC13 HL-LHC F C C

• h

h

perturbative limit (scalar) MZR = 5 TeV 10 TeV 20 TeV 50 TeV

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Conclusions

There are strong limits on the gauge couplings from the requirement to be perturbative till the GUT scale.

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Conclusions

There are strong limits on the gauge couplings from the requirement to be perturbative till the GUT scale. For U(1)B−L model, we found that it can be probed(almost) at HL-LHC for vR at 5 TeV .

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Conclusions

There are strong limits on the gauge couplings from the requirement to be perturbative till the GUT scale. For U(1)B−L model, we found that it can be probed(almost) at HL-LHC for vR at 5 TeV . For minimal LRSM, we found WR and ZR couldn’t have been seen at LHC13.

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Conclusions

There are strong limits on the gauge couplings from the requirement to be perturbative till the GUT scale. For U(1)B−L model, we found that it can be probed(almost) at HL-LHC for vR at 5 TeV . For minimal LRSM, we found WR and ZR couldn’t have been seen at LHC13. In case, ZR is found in HL-LHC run then couldn’t be from minimal LRSM.

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Conclusions

There are strong limits on the gauge couplings from the requirement to be perturbative till the GUT scale. For U(1)B−L model, we found that it can be probed(almost) at HL-LHC for vR at 5 TeV . For minimal LRSM, we found WR and ZR couldn’t have been seen at LHC13. In case, ZR is found in HL-LHC run then couldn’t be from minimal LRSM. The results can be generalized to other gauge group extensions.

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