Radiative EWSB in a Little Higgs Model Carl Schmidt Michigan State - PowerPoint PPT Presentation

Radiative EWSB in a Little Higgs Model Carl Schmidt Michigan State University arXiv:1001.0584, R. Foadi, J. T. Laverty, CS, and J.-H. Yu May 11, 2010 PHENO 2010

Motivation Little Hierarchy: v 2 << f 2 << Λ 2 (0.25 TeV) 2 (~1 TeV) 2 (~10 TeV) 2 Little Higgs (LH): Collective Symmetry Breaking: If g 1 = 0 or g 2 = 0, H is a Goldstone Boson. => Quadratic divergences ~ Λ 2 vanish at one loop Higgs Potential: V = m 2 | H | 2 + λ | H | 4 If potential is purely radiative, expect m 2 ~ g 4 f 2 , λ ~ g 4 => v 2 ~ - m 2 / λ 2 ~ f 2 => Too big! Typically, LH models introduce new operators to make λ larger. Plaquettes, mass terms, quartic terms

Motivation (cont’d) Fermions: Collective Symmetry Breaking also Generic contribution to m 2 from heavy top partner T : 2 2 ln � 2 � m 2 = � 3 � t 8 � 2 M T 2 M T Good: Gives negative contribution to m 2 . Necessary for symmetry breaking. Bad: Since m H 2 ~ -2 m 2 , it gives contribution to Higgs mass of more than 1 TeV. Still must have cancellation to get light Higgs. => Reconsider pure radiative EWSB

The Model Global Symmetry: SO( 5 ) 0 x SO( 5 ) 1 → SO(5) Gauge Symmetry: [ SU( 2 ) x U( 1 ) ] 0 x [ SU( 2 ) x SU( 2 ) ] 1 → SU(2) L x U( 1 ) Y Collective Symmetry Breaking: If (g 0 L = g 0 R = 0) or (g 1 L = g 1 R = 0), H is a Goldstone Boson. => Quadratic divergences vanish at one loop Related Models: 5-dimensional Gauge-Higgs Model (Medina, Shah, Wagner) Custodial Minimal Moose (Chang, Wacker) Gauge Sector (Barbieri, Bellazzini, Rychkov, Varagnolo)

Heavy Gauge Bosons Z L 2 = g 1 R 2 = 6 g 1 L W L Z R f = 1 TeV W R 2 � 1 2 + g 1 L ( ) f 2 2 � 1 2 + g 1 R 2 M Z L 2 g 0 L ( ) f 2 2 M Z R 2 g 0 R (Also SM W and Z ) 2 + g 1 L 2 f 2 ( ) f 2 2 2 M W L � 1 2 g 0 L 2 � 1 M W R 2 g 1 R Higgs boson is only light scalar. All other GB’s from Σ are eaten.

Fermions Q L and t R are in 5’s of SO( 5 ) : A A B B � � � � � � � � Q 0 Q Q � � � � � � � � � � A = A = B = B = � L � � R � � L � � R � � � � � � � � � � � � � � � � � t � t � 0 t � � � � � � � � L R L R • Dirac Fermions with missing SM partners • Transform under SU(2) 0 L x U(1) 0 R • χ is SU(2) doublet with charge +5/3, +2/3 fermions • b R can be included in a 10 of SO(5) , with more heavy fermions � � 0 � � 0 � � SO(5) 1 -breaking spurion E = � 0 � Fermion mass terms: � � 0 � � � � 1 A � � B f � B � � 1 f � B + h.c. � � L mass = � � A f � A � EE � � � � R A � R B � R L L L Breaks SO(5) 0 Collective Preserves SO(5) 0 => Preserves SO(5) 1 Symmetry Breaking Breaks SO(5) 1

Heavy Fermions T A 2 � t � A = � 1 = � B = 0.981 � t T B f = 1 TeV 1 2 = 1 2 + 1 t 2 � t � 1 � A 2 � � A 2 + � 1 ( ) f 2 2 M T A Three fermion masses 2 f 2 2 � � B M T B depend on Higgs field 2 v 2 /2 2 � � t M t

Effective Potential Possible to obtain EW scale v, because fermions give 2 ) ln � 2 � m 2 � 3 � 1 2 � � A ( 2 8 � 2 2 � B 2 M T A 2 f 2 2 3 � A 2 + 2 � B 2 � A �� 2 � 1 ( ) f 2 2 � 1 2 � 1

Higgs Boson Mass 2 = g 1 R 2 = 0.5, 2 � , 4 � g 1 L f = 10 TeV � 1 sin � t = 2 + � A 2 � 1 f = 1 TeV • Higgs boson is typically light. • Mass insensitive to gauge couplings.

Sensitivity to UV Physics Possible to have separate fermion cutoffs, Λ A and Λ B Then: � � 2 2 2 � m 2 � 3 � 1 2 ln � B 2 ln � A 8 � 2 2 � B � 2 � � A � � � 2 M T A M T A � � In fact, can make this precise: � B � A • Make and complete Dirac multiplets (5s of SO(5) ) B A • Add new SU(2) doublet and singlet t � � Q � � R L • Add new mass term: A � � B t B � B + h.c. � L mass = � � A A Q R Q t � � � L L R Gives above fermion contribution --- finite at one loop!

Sensitivity to UV Physics 2 = g 1 R 2 = 2 � g 1 L f = 1 TeV � 1 sin � t = 2 + � A 2 � 1 � � 4 � f , � B � A � � 4 � f � � Why is Higgs mass solution typically light? � 2 � 4 4 ln M T A � � 3 � t 1 2 � 2 � v 2 ( ) 2 2 with F sin � t , M T A M T B � + � M H 4 � 2 2 M t � � Compare to SUSY

Electroweak Constraints g 1 = g 1 L = g 1 R ˆ ˆ Bounds using universal electroweak parameters, S , T , Y , W Heavy fermion contributions still to be done

Conclusions • Presented a Little Higgs model with Higgs Potential fully radiatively-generated • Cancellation in m 2 occurs between two heavy fermion contributions • Higgs boson mass is generically light ( < 200 GeV ) • Higgs is the only light scalar • Electroweak constraints considered, but more phenomenology to be done