Left-Right Models Radiatively Broken by a Doublet Nathan Papapietro University of Alabama Pheno 2015, May 4-6 In collaboration with Nobuchika Okada (University of Alabama) Nathan Papapietro Left-Right Models Radiatively Broken by a Doublet
Breaking Path The existing gauge symmetries at low energies, SU (3) c × U (1) em , are vector-like. At higher energies ( µ ∼ Λ SM ) there is a parity violation in nature due to the axial nature of SU (2) L . Gauge parity can be restored at even higher energies using Left-Right Models, first proposed by Pati and Salam 1 SU (4) c × SU (2) L × SU (2) R We choose to start at: SU (3) c × SU (2) L × SU (2) R × U (1) B − L → SU (3) c × SU (2) L × U (1) Y Which is broken down into the Standard Model. 1 Pati, J. C. and Salam, A., Phys. Rev. D 10, 275 (1974) Nathan Papapietro Left-Right Models Radiatively Broken by a Doublet
Particle Contents To achieve realistic fermion masses, a 2nd higgs bidoublet is added. SU (3) c SU (2) L SU (2) R U (1) B − L 3 2 1 1 / 3 Q ¯ Q c 3 1 2 − 1 / 3 1 2 1 − 1 (1) L L c 1 1 2 1 h 1 2 2 0 h ′ 1 2 2 0 The superpotential is W = Y q QhQ c + Y ′ q Qh ′ Q c + Y e LhL c + Y ′ e Lh ′ L c + α Tr hh + α ′ Tr h ′ h ′ + β Tr hh ′ + h . c . The soft mass terms are L c | ˜ L | ˜ Q c | ˜ Q | ˜ V soft = m 2 L c | 2 + m 2 L | 2 + m 2 Q c | 2 + m 2 Q | 2 + m 2 h | h | 2 + m 2 h ′ | h ′ | 2 + O ( hh ′ ) (2) In order to achieve radiative breaking, there needs to be a soft mass splitting at some higher energy, meaning this model does not have matter parity symmetry, only gauge parity symmetry. Nathan Papapietro Left-Right Models Radiatively Broken by a Doublet
Breaking Mechanism Doublets were initially proposed 2 , but after the seesaw was introduced 3 triplet models were introduced to achieve a seesaw mechanism without R-Parity breaking. However to achieve LRM breaking without Q em violation, R-Parity has to be broken as well 4 leading to nonzero VEV of � ˜ L c � = v R 2 . √ m 2 ˜ ˜ N c N c † g 2 BL Figure: Soft mass insertions in D-term corrections must be larger than F-term and Gaugino corrections 2 Mohapatra, R. N. and Pati, J. C., Phys. Rev. D 11, 2558 (1975). ,Senjanovic, G. and Mohapatra, R. N., Phys. Rev. D 12, 1502 (1975) 3 Minkowski, P., Physics Letters B 67, 421 (1977) 4 Kuchimanchi, R. and Mohapatra, R. N., Phys. Rev. D 48, 4352 (1993) Nathan Papapietro Left-Right Models Radiatively Broken by a Doublet
Lepton RGEs 8 π 2 dm 2 ˜ L | 2 � � L i � | Y ijh m 2 L i + m 2 j + m 2 − g 2 BL Tr [ Q BL m 2 ] d ln µ = ˜ ˜ h L c j , k − 4 g 2 BL M 2 BL − 3 g 2 L M 2 L (3) 8 π 2 dm 2 ˜ L c L | 2 � � � | Y ijh m 2 L i + m 2 j + m 2 + g 2 BL Tr [ Q BL m 2 ] d ln µ = i ˜ ˜ L c h j , k − 4 g 2 BL M 2 BL − 3 g 2 R M 2 R The soft slepton mass runnings at one-loop can easily be derived. The U (1) B − L charge dictates sign of the trace: 3 � � � g 2 � Q BL m 2 � 2 g 2 m 2 Q i − m 2 i − m 2 L i + m 2 = . (4) BL Tr BL ˜ ˜ ˜ ˜ Q c L c i i We only need a single large left handed scalar quark doublet to be large which would dominate over even the gaugino masses. Nathan Papapietro Left-Right Models Radiatively Broken by a Doublet
Inputs M 2 2 M Lc1 1.5 � 10 8 2 M Lc2 2 M Lc3 2 M L 1.0 � 10 8 2 M Qc 2 M Q 2 M h1 5.0 � 10 7 2 M h2 Ln � Μ � 6 8 10 12 14 16 µ GUT = 10 16 GeV and the breaking is around 7 TeV Yukawas and g y , for one heavy generation, were ran from low energy with θ R ≈ 50 ◦ 2 = 2TeV, m 2 Q = 13 TeV, m 2 At the GUT scale M 1 1 = 2 TeV, and all ˜ ˜ L c else is 8 TeV Nathan Papapietro Left-Right Models Radiatively Broken by a Doublet
Breaking Relations 2 M L � 1 4 � 10 6 2 � 10 6 Ln � Μ � 6 8 10 12 14 16 � 2 � 10 6 � 4 � 10 6 g Y = g R sin θ R M W R = 1 2 g R v R tan θ R = 2 g BL M Z R = 1 � (5) g R 4 g 2 BL + g 2 2 v R R Y W = Y BL − ( T 3 ) R M A Y = 0 2 Nathan Papapietro Left-Right Models Radiatively Broken by a Doublet
Masses � − 8 m 2 Lc We define the VEV to be v R = BL ) ∼ 13 TeV ( g 2 R + g 2 M W R ∼ 3 TeV and M Z R ∼ 5 TeV The mass matrix after the LRM breaking is M R 0 g R v R M ν c , ˜ R = 0 M BL g BL v R (6) λ BL , ˜ λ 3 g R v R g BL v R 0 We still get a heavy neutrino but after EW breaking we can still induce a light neutrino spectrum via see-saw. m ν ∼ | ˜ Y L | 2 ˜ v 2 u (7) (2 M ν c ) Nathan Papapietro Left-Right Models Radiatively Broken by a Doublet
Conclusions The Left-Right Models offer great parity restoring phenomnology at higher energies Minimal LRMs without triplets can be broken via right-handed sneutrino radiatively. Radiative breaking can happen with just one order difference in squarks masses and all other sparticles. Small neutrino masses can still be produced via gaugino mixings Future parameter scans will be done to tune the inputs based on experimental constraints Nathan Papapietro Left-Right Models Radiatively Broken by a Doublet
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