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) 1 / 19
Outline Introduction & Motivation Theoretical Constraints Bounds in U (1) B − L model Bounds in Minimal LRSM Conclusions 2 / 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. 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. 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) . 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. 3 / 19
Introduction & Motivation In such cases, there are upper and lower limits on the gauge couplings by requiring perturbativity upto GUT scale. 4 / 19
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. 4 / 19
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. 4 / 19
Theoretical Constraint on Gauge Couplings Consider a SM extension: SU (2) L × U (1) X × U (1) Z such that: Q = I 3 L + I X + Q Z 2 5 / 19
Theoretical Constraint on Gauge Couplings Consider a SM extension: SU (2) L × U (1) X × U (1) Z such that: Q = I 3 L + I X + Q Z 2 Then following relation holds: 1 = 1 + 1 g 2 g 2 g 2 Y X Z 5 / 19
Theoretical Constraint on Gauge Couplings Consider a SM extension: SU (2) L × U (1) X × U (1) Z such that: Q = I 3 L + I X + Q Z 2 Then following relation holds: 1 = 1 + 1 ← This holds even if coupling g X is SU(2) g 2 g 2 g 2 Y X Z 5 / 19
Theoretical Constraint on Gauge Couplings Consider a SM extension: SU (2) L × U (1) X × U (1) Z such that: Q = I 3 L + I X + Q Z 2 Then following relation holds: 1 = 1 + 1 ← This holds even if coupling g X is SU(2) g 2 g 2 g 2 Y X Z Then requiring that coupling g Z is perturbative at breaking scale, � − 1 / 2 � r g ≡ g X 1 − 4 π α EM > tan θ W ⇒ cos 2 θ W g 2 g L Z 5 / 19
U (1) B − L model Particle content of the SU (2) L × U (1) I 3 R × U (1) B − L model: SU (2) L U (1) I 3 R U (1) B − L 1 0 Q 2 3 + 1 1 u R 1 2 3 − 1 1 d R 1 2 3 L 0 − 1 2 + 1 N − 1 1 2 − 1 e R − 1 1 2 − 1 0 H 2 2 ∆ R − 1 2 1 6 / 19
U (1) B − L model Particle content of the SU (2) L × U (1) I 3 R × U (1) B − L model: SU (2) L U (1) I 3 R U (1) B − L 1 0 Q 2 3 + 1 1 u R 1 2 3 − 1 1 d R 1 2 3 L 0 − 1 2 + 1 N − 1 1 2 − 1 e R − 1 1 2 − 1 0 H 2 2 ∆ R − 1 2 1 The RGEs for the gauge couplings of the two U (1) ’s are respectively 16 π 2 β ( g I 3 R ) = 9 2 g 3 16 π 2 β ( g BL ) = 3 g 3 I 3 R , BL . 6 / 19
SU (2) L × U (1) I 3 R × U (1) B − L (Gauge Couplings) 7 / 19
SU (2) L × U (1) I 3 R × U (1) B − L (Gauge Couplings) 1.0 upper bound U ( 1 ) B - L model 0.9 0.8 g BL [ v R ] 0.7 0.6 lower bound upper bound 0.5 0.4 lower bound 0.3 0.4 0.5 0.6 0.7 0.8 g R [ v R ] 7 / 19
SU (2) L × U (1) I 3 R × U (1) B − L (Gauge Couplings) 1.0 upper bound U ( 1 ) B - L model 0.9 0.8 g BL [ v R ] 0.7 0.6 lower bound upper bound 0.5 0.4 lower bound 0.3 0.4 0.5 0.6 0.7 0.8 g R [ v R ] 0 . 398 < g R < 0 . 768; 0 . 416 < g BL < 0 . 931 , with 0 . 631 < r g < 1 . 218 at v R = 5 TeV 8 / 19
SU (2) L × U (1) I 3 R × U (1) B − L ( Z R searches) 100 U ( 1 ) B - L model 50 50 TeV Z R mass [ TeV ] h perturbativelimit F C C h perturbativelimit - 20 TeV 10 10 TeV HL - LHC 5 v R = 5 TeV LHC13 0.6 0.7 0.8 0.9 1.0 1.1 1.2 r g = g R / g L (ATLAS-CONF-2016-045) (CMS-PAS-EXO-16-031) 9 / 19
SU (2) L × U (1) I 3 R × U (1) B − L ( Z R searches) U ( 1 ) B - L model 100 U ( 1 ) B - L model 50 50 TeV 50 FCC - hh 50 TeV perturbative limit perturbative limit Z R mass [ TeV ] h perturbativelimit F C C h perturbativelimit - 20 TeV 20 v R [ TeV ] 20 TeV 10 TeV 10 10 10 TeV HL - LHC HL - LHC 5 M Z R = 5 TeV 5 v R = 5 TeV LHC13 LHC13 2 0.6 0.7 0.8 0.9 1.0 1.1 1.2 0.6 0.7 0.8 0.9 1.0 1.1 1.2 r g = g R / g L r g = g R / g L (ATLAS-CONF-2016-045) (CMS-PAS-EXO-16-031) 9 / 19
SU (2) L × U (1) I 3 R × U (1) B − L ( Z R searches) U ( 1 ) B - L model 100 U ( 1 ) B - L model 50 50 TeV 50 FCC - hh 50 TeV perturbative limit perturbative limit Z R mass [ TeV ] h perturbativelimit F C C h perturbativelimit - 20 TeV 20 v R [ TeV ] 20 TeV 10 TeV 10 10 10 TeV HL - LHC HL - LHC 5 M Z R = 5 TeV 5 v R = 5 TeV LHC13 LHC13 2 0.6 0.7 0.8 0.9 1.0 1.1 1.2 0.6 0.7 0.8 0.9 1.0 1.1 1.2 r g = g R / g L r g = g R / g L 10 / 19
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 � u L � 1 Q L ≡ 2 1 d L 3 � � u R 1 Q R ≡ 1 2 d R 3 � � ν L − 1 ψ L ≡ 2 1 e L � � N − 1 ψ R ≡ 1 2 e R φ + � φ 0 � 1 2 Φ = 0 2 2 φ 0 φ − 1 2 � 1 � 2 ∆ + ∆ ++ √ R R ∆ R = 2 1 3 ∆ 0 − 1 2 ∆ + √ R R 11 / 19
Minimal LRSM The RGEs for the gauge couplings in the minimal LRSM are 1 16 π 2 β ( g L ) = − 3 g 3 L , 16 π 2 β ( g R ) = − 7 3 g 3 R , 16 π 2 β ( g BL ) = 11 3 g 3 BL 1 I. Z. Rothstein, Nucl. Phys. B358, 181 (1991) 12 / 19
SU (2) L × SU (2) R × U (1) B − L (Gauge Couplings) 13 / 19
SU (2) L × SU (2) R × U (1) B − L (Gauge Couplings) 1.0 0.9 upper bound 0.8 perturbative limit lower bound 0.7 g BL [ v R ] 0.6 0.5 0.4 lower bound 0.3 0.5 1 2 5 g R [ v R ] 13 / 19
SU (2) L × SU (2) R × U (1) B − L (Gauge Couplings) 1.0 0.9 upper bound 0.8 perturbative limit lower bound 0.7 g BL [ v R ] 0.6 0.5 0.4 lower bound 0.3 0.5 1 2 5 g R [ v R ] √ 0 . 406 < g R < 4 π ; 0 . 369 < g BL < 0 . 857 , with 0 . 648 < r g < 5 . 65 at v R = 10 TeV 14 / 19
λ λ λ λ μ α ρ α α ρ μ SU (2) L × SU (2) R × U (1) B − L (Scalar sector) 100 perturbativelimit 10 r g = 1.1, v R = 6 TeV λ 1 quartic couplings 1 λ 3 0.1 λ 4 10 - 2 λ 2 10 - 3 10 - 4 10 4 10 5 10 6 10 7 μ [ GeV ] 15 perturbativelimit r g = 1.1, v R = 6 TeV quartic couplings 10 α 3 5 α 1 ρ 1 α 2 0 ρ 2 - 5 10 4 10 5 10 6 10 7 μ [ GeV ] 15 / 19
SU (2) L × SU (2) R × U (1) B − L (Scalar sector) 100 1 perturbativelimit r g = 1.1, v R = 12 TeV 10 λ 1 r g = 1.1, v R = 6 TeV λ 1 0.1 quartic couplings quartic couplings λ 3 1 λ 3 λ 4 10 - 2 0.1 λ 4 λ 2 10 - 2 10 - 3 λ 2 10 - 3 10 - 4 10 - 4 10 4 10 5 10 6 10 7 10 5 10 7 10 9 10 11 10 13 10 15 μ [ GeV ] μ [ GeV ] 15 perturbativelimit 0.8 r g = 1.1, v R = 12 TeV r g = 1.1, v R = 6 TeV quartic couplings 0.6 quartic couplings 10 α 3 α 3 0.4 ρ 1 5 α 1 α 1 ρ 1 0.2 α 2 α 2 0 0.0 ρ 2 ρ 2 - 0.2 - 5 10 4 10 5 10 6 10 7 10 5 10 7 10 9 10 11 10 13 10 15 μ [ GeV ] μ [ GeV ] 15 / 19
SU (2) L × SU (2) R × U (1) B − L ( Z R and W R searches) 50 perturbative limit ( gauge ) FCC - hh 50 TeV W R mass [ TeV ] 20 20 TeV r a ) a l c s t 10 m i ( l i e v i HL - LHC a t b u r t e r 10 TeV p 5 LHC13 v R = 5 TeV 2 0.5 1.0 1.5 2.0 r g = g R / g L (ATLAS-CONF-2016-045) (CMS-PAS-EXO-16-031) (arXiv: 1809.11105) (arXiv: 1803.11116) 16 / 19
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