Models as existence proofs, speculations or... peaces of physical reality Riccardo Barbieri Zuoz II, July 16/21, 2006 An example of what could happen, based on: An ultra-bottom-up hypothesis 2 concrete realizations (why not a single one?)
The idea RB, Hall Seek simple Higgs sector that: 1. Agrees with all data (EWPT) 2. Is fully natural up to 1.5 TeV ( + maybe something else) A modest ultra-bottom-up approach, with crucial consequences for LHC
A Heavy SM Higgs and the EWPT T IDM = T SM +!T S IDM = S SM +!S A heavy Higgs m h = 400 600 GeV + a positive ΔT Origin of ΔT?? (Peskin, Wells and many others) prefer models that populate the 1-2σ ellipse in most of parameter space. Are there any?
2 HDM in an alternative phase RB, Hall, Rychkov IDM controlled by approximate SU(2) V
The IDM is natural and perturbative up to ~1.5 TeV (instead of the SM only up to ~ 400 GeV) H NL L with and m h = 400 600 GeV ] m H m NL ]!m mh mnl 140 120 100 80 60 and an average mass m av (m L,m NL,m H ) 100 GeV 1 TeV 40 20 0 0 50 100 150 200 250 300 350 m
A Dark Matter candidate Unbroken H 2 H 2 Inert scalars always in pair (for natural flavour conservation) Stable lightest inert scalar To get the observed! m need co-annihilation of S, A into light fermions as dominant process m GeV 12 11 10 9 8 60 62 64 66 68 70 72 74 m L GeV Shouldn t one have seen S and A at LEP2 via e + e A + S (Z + S) + S What about direct DM detection! h (Lp Lp) 2 10 9 pb ( "L 0.5? ) 2 ( ) 2 ( 70GeV 500GeV m L? m h ) 4
Can one do better than! nat 1.5 TeV? 2H doublets Supersymmetry ( UV completion )... but without a light Higgs boson! How?? In the most straightforward way: Add a coupling λ through! f = "SH 1 H 2 with λ only constrained by perturbativity up to 10-12 TeV λsusy NMSSM with! low energy 2 dominating over all other couplings RB, Hall, Nomura, Rychkov Not consistent with gauge unification? An open question, depending on the physics above 10-12 TeV See, e.g., Harnik et al, Gripaios and West
ElectroWeak Precision Tests in λsusy S and T from Higgs s M( S)! = 2 S and T from Higgsinos tan! 2.5 m( H ± ) For and s-particles in their natural range, most of parameter space inside the 1-2σ ellipse tan! = 1 an exact custodial symmetry point
Particle spectrum (naturalness bounds) in λsusy! = 2 with up to 20% tuning (m max! "/5) and no significant bound on other s-fermions and SU(2)xU(1) gauginos! mess = 100 TeV
Dark Matter in λsusy blue:!h 2 = 0.09 0.13 white:!h 2 < 0.09 red:!h 2 > 0.13 grey: m LSP < 45 GeV black lines: m LSP = m W,m Z LSP =! S + " H 1 + # H 2 with no special relation among parameters (MSSM)
Provisional conclusions Doubling the Higgs multiplet the simplest solution (?) of the l.h.p., realized in several possible ways 1 TeV H ±,A,H 500 GeV h + possibly something else Relevant to supersymmetry itself? LHC will explore for the first time the relevant energy range, well above the Fermi scale
An example: The Inert Doublet Model Consider the most general 2H doublet model invariant under H 2 H 2 to get natural flavour conservation (i.e., only couples to matter) +! 4 H 1 H 2 2 +! 5 2 [(H 1 H 2) 2 + h.c.] H 1 RB, Hall, Rychkov V = µ 2 1 H 1 2 + µ 2 2 H 2 2 +! 1 H 1 4 +! 2 H 2 4 +! 3 H 1 2 H 2 2! 4,! 5 custodial symmetry! 5 PQ symmetry Take µ 2 1 < 0, µ 2 2 > 0 so that H 1 = ( φ + v + (h + iχ)/ 2 ), H 2 = ( H + (S + ia)/ 2 )
The Inert Doublet Model (continued) Parameter space: µ 2 1,! 1 v(m Z ), m h! 2 (in the usual way) (not relevant to the spectrum) µ 2 2,! 3,4,5 m L,m NL,m H ;! L m 2 H = µ 2 2 +! 3 v 2 m 2 S = µ 2 2 + (! 3 +! 4 +! 5 )v 2 m 2 A = µ 2 2 + (! 3 +! 4! 5 )v 2! L! 3 +! 4! 5 custodial symm. limit: PQ symmetry limit: m H = m S = m A m S = m A absolute minimum:! 1,2 > 0! 3,! L! 3 +! 4! 5 > 2(! 1! 2 ) 1/2
Naturalness, perturbativity, EWPT in the IDM!m 2 h = " t # t 2 + " g # 2 g + " 11 # 2 H 1 + " 12 # 2 H 2!µ 2 2 = 1 ( "g # 2 g + " 22 # 2 H 2 2 + " 21 # 2 ) H 1 16! 2 d" i d log# = $ i(")! nat = min(! i ) 1.5 TeV
T IDM = T SM +!T SIDM = S SM +!S!S!T negligible 1 24" 2 #v 2(m H m A )(m H m S ) In the Standard Model: m h = 91 +45 32 GeV In the IDM: m h = 400 600 GeV (m H m S )(m H m A ) = M 2, M = 120 +20 30 GeV
Collider Signals 1. m h = 400 600 GeV A standard Higgs boson? h SS,AA,H + H at! h = 68 GeV m h = 500 GeV 2. pp W HA or HS H AW or SW A SZ ( ) for the DM parameters, looking for 3 charged leptons! signal 3.5 fb! bg 20 fb