Alternatives to an elementary Higgs

Strongly coupled and extra-dimensional models of electroweak symmetry breaking are reviewed. Models examined include warped extra dimensions, bulk Higgs, “little” Higgs, dilaton Higgs, composite Higgs, twin Higgs, quantum critical Higgs, and “fat” SUSY Higgs. Also discussed are current bounds and future LHC searches for this class of models.

Figure 1

Parameter space of alternative Higgs models, the vertical axis is the scaling dimension $\mathrm{\Delta }$ of the operator that condenses and breaks the electroweak gauge symmetry, the horizontal axis is the fraction of the $W$ and $Z$ masses that arise from mixing. Precision electroweak measurements rule out models that lie too far to the right. The location of the SM, at the origin, is marked by a star. The dash-dotted lines denote the approximate range of composite Higgs models, while the thin blue dashes denote the approximate range of quantum critical Higgs models. The thick green dashed lines enclosing a wedge-shaped area denote the approximate region for dilaton models, with $\mathrm{\Delta }$ denoting the dimension of the scale breaking condensate.

Figure 2

Light radion decay fractions: the decay to gluons is enhanced while the decays to $b\overline{b}$ and $\gamma \gamma$ are suppressed. From [221].

Figure 3

Realistic RS models: the gauged $SU(2{)}_L\times SU(2{)}_R$ symmetry in the bulk corresponds to a custodial global symmetry in the hypothetical dual CFT. The gauge symmetry is broken to the SM gauge group on the Planck (UV) brane and is broken by the Higgs VEV down to the diagonal subgroup on the TeV (IR) brane.

Figure 4

KK gluons decay mainly to $t\overline{t}$ pairs. From [9].

Figure 5

KK gluons production cross section at the 14 TeV LHC. From [9].

Figure 6

KK gluons typically have a large width. From [9].

Figure 7

CMS bound on KK gluon production. From [280].

Figure 8

Decay branching fractions for the first KK photon. From [15].

Figure 9

Decay branching fractions for the first KK $Z$ mode. From [15].

Figure 10

Decay branching fractions for the KK $Z_x$ mode. From [15].

Figure 11

Bound on the KK graviton from the dilepton channel in the RS model for different coupling strengths $k/{\overline{M}}_{\text{Pl}}$. From [284].

Figure 12

Bound on the KK graviton from the dijet channel in the RS model. From [283].

Figure 13

Bound on the KK graviton from the diphoton channel in the RS model for different coupling strengths $k/{\overline{M}}_{\text{Pl}}$. From [4].

Figure 14

Bound on the KK graviton from the $\ell \ell q\overline{q}\ell \nu q{\overline{q}}^{\prime }$ and channel in the “bulk RS” model for different coupling strengths $k/{\overline{M}}_{\text{Pl}}$. From [96], and [5].

Figure 15

Ratio of discovery significance for the radion in the realistic RS model (solid), and RS1 model (dashed) to that of a Higgs with the same mass. From [141].

Figure 16

Bound on the mass of the RS radion ($m_{\varphi }$) as a function of its coupling (${\mathrm{\Lambda }}_{\mathrm{\Phi }}$), where the coupling is given by ${(\mathrm{\Phi }/{\mathrm{\Lambda }}_{\mathrm{\Phi }})T}_{\mu }^{\mu }$. From [110].

Figure 17

Cross sections times branching ratios for various Higgs production and decay channels for the SM (solid lines) and bulk Higgs (dashed lines) for $\beta =2$ with $V=300$ (top) and $V=500$ (bottom). From [71].

Figure 18

$WZ$ scattering in $pp$ collisions.

Figure 19

CMS bound on the $W^{\prime }$ mass. From [282].

Figure 20

Model-independent bounds on neutral spin-1 resonances in the mass-coupling plane for different $Z^{\prime }$ widths. From [229].

Figure 21

Approximate contribution to $pp\to WH$ from an intermediate $W^{\prime }$. From [202].

Figure 22

Higgs and unitarity bounds combined to put an upper bound on the spin-1 resonance $\rho$ for different cutoffs $\mathrm{\Lambda }=3\mathrm{TeV}$, 5 TeV, $2m_{\rho }$, and $3m_{\rho }$. Here $a$ is the strength of the Higgs coupling to $WW$ relative to the SM. From [54].

Figure 23

Cancellation of the quadratic divergences in the top loop for little Higgs models. From [336].

Figure 24

Cancellation of the quadratic divergences in gauge loops for little Higgs models. From [336].

Figure 25

Lower bound on the littlest Higgs scale $f$. From [139].

Figure 26

Coset space for global symmetry group $G$ spontaneously broken to $H$. If $G$ has a weakly gauged subgroup $F$ then $I$ will be the unbroken gauge group. From [100].

Figure 27

The amount of tuning required to suppress $v/f$ in pseudo-Goldstone boson Higgs models. Generically a tuning at the percent level is required to be in the acceptable shaded (blue) region, as shown on the left. By carefully choosing other input parameters the apparent fine-tuning in $c_u$ is reduced, shown on the right, at the price of fine-tuning other parameters. From [132].

Figure 28

Lower bound on the little Higgs scale $f$. From [338].

Figure 29

CMS bound on the $T$-even top-partner production cross section for branching fractions into $bW$, $tH$, and $tZ$ of 50%, 25%, and 25%, respectively. From [97].

Figure 30

CMS mass bound on the $T$-even top partner as a function of branching fractions into $bW$, $tH$, and $tZ$. From [97].

Figure 31

Examples of deviations from the SM predictions of the Higgs couplings in the minimal composite models. The red bars denote the sensitivity of these couplings at the ILC. From [200].

Figure 32

Double Higgs production in composite pseudo-Goldstone boson Higgs models have contributions that grow with the square of the center-of-mass energy.

Figure 33

Difficult $4W$ search channel for a pseudo-Goldstone boson Higgs from strong double Higgs production by vector boson fusion. From [122].

Figure 34

Displaced decay of the SM Higgs due to decays to long-lived mirror glueballs which eventually decay to SM particles via mixing with the SM Higgs. From [143].

Figure 35

Expected sensitivity of run II displaced searches for displaced Higgs decays. The vertical axis is the branching fraction of the Higgs into the displaced decays, while the horizontal is the lifetime of the metastable decay products, for three different values of the mass of these intermediate states. From [143].

Figure 36

The four gauge boson two (quantum critical) Higgs contribution to $WW$ scattering. From [375].

Figure 37

The effects of a quantum critical Higgs two-point function in the production of on-shell $Z$-boson pairs, with different values of the threshold $\mu$. From [53].