Alignment limit of the NMSSM Higgs sector

The next-to-minimal supersymmetric extension of the Standard Model (NMSSM) with a Higgs boson of mass 125 GeV can be compatible with stop masses of order of the electroweak scale, thereby reducing the degree of fine-tuning necessary to achieve electroweak symmetry breaking. Moreover, in an attractive region of the NMSSM parameter space, corresponding to the “alignment limit” in which one of the neutral Higgs fields lies approximately in the same direction in field space as the doublet Higgs vacuum expectation value, the observed Higgs boson is predicted to have Standard-Model–like properties. We derive analytical expressions for the alignment conditions and show that they point toward a more natural region of parameter space for electroweak symmetry breaking, while allowing for perturbativity of the theory up to the Planck scale. Moreover, the alignment limit in the NMSSM leads to a well-defined spectrum in the Higgs and Higgsino sectors and yields a rich and interesting Higgs boson phenomenology that can be tested at the LHC. We discuss the most promising channels for discovery and present several benchmark points for further study.

Figure 1

In the left panel we show the constraints on the possible singlet and non-SM doublet component of the 125 GeV state derived from precision measurements on its production cross section and branching ratios. In the right panel we show the constraints on the SM and non-SM doublet component of a Higgs state coming from the searches for Higgs bosons decaying into $W$ pairs, away from the SM Higgs mass values.

Figure 2

Left panel: The blue shaded band displays the values of $\lambda$ as a function of $\tan \beta$, necessary for alignment for $m_h=125\pm 3\mathrm{GeV}$. Also shown in the figure as a green band are values of $\lambda$ that lead to a tree-level Higgs mass of $125\pm 3\mathrm{GeV}$. Right panel: Values of $M_S$ necessary to obtain a 125 GeV mass for values of $\lambda$ fixed by the alignment condition and top squark mixing parameter $X_t=0$ and $X_t=M_S$. The dominant two-loop corrections are included.

Figure 3

Left panel: Values of $M_A$ leading to a cancellation of the mixing of the singlet with the SM-like Higgs boson in the Higgs basis, shown in the $|\mu |\text{−}\tan \beta$ plane. The values of $\lambda$ were fixed so that the alignment condition among the doublet components is fulfilled. Values of $\kappa =\frac{1}{2}\lambda$ close to the edge of the perturbativity consistency region were selected. Right panel: Maximum values of $\kappa$ consistent with perturbativity as a function of $\tan \beta$ for $\lambda =0.65$.

Figure 4

Values of the singlet $CP$-even Higgs mass $m_{h_S}$ for $\tan \beta =2$ (left panel) and $\tan \beta =3$ (right panel) in the plane of $m_A$ vs $m_{A_S}$, imposing a SM-like Higgs boson with a mass of 125 GeV (with $\lambda$ and $\mu$ satisfying the alignment conditions and $\kappa =\frac{1}{2}\lambda$).

Figure 5

Values of the mass parameters $M_A$ and $\mu$ consistent with the current LHC constraints on the SM-like Higgs properties, for values of $\kappa ={\kappa }^{\max }$, the maximal value of $\kappa$ leading to perturbative consistency of the theory up to the Planck scale (left panel) and for $\kappa =\frac{1}{4}{\kappa }^{\max }$ (right panel). Solid lines represent the alignment condition, Eq. (57), and the colors blue, red and yellow represent values of $\tan \beta =2$, 2.5 and 3, respectively.

Figure 6

For the points allowed by LHC constraints in the left panel we plot the correlation between the non-SM doublet component of the 125 GeV Higgs state with the product of the non-SM doublet component of the mainly singlet state and the singlet component of the 125 GeV Higgs state. In the right panel we plot the correlation between the SM doublet component of the singlet state with the singlet component of the 125 GeV Higgs state. Blue, red and yellow represent values of $\tan \beta =2$, 2.5 and 3, respectively.

Figure 7

For the points allowed by LHC constraints, in the left panel we show the correlation between the non-SM doublet component and the SM doublet component of the mainly singlet Higgs state. The right panel shows the correlation between the singlet component of the mostly non-SM state and the non-SM doublet component of the mostly singlet Higgs state. Blue, red and yellow represent values of $\tan \beta =2,2.5,\mathrm{a}\mathrm{n}\mathrm{d}3$, respectively.

Figure 8

For the points allowed by LHC constraints, in the left panel we plot the correlation between the non-SM doublet component and the singlet component of the 125 GeV Higgs state. In the right panel we plot the square of the couplings of the 125 GeV Higgs state, normalized to its SM value. Blue, red and yellow represent values of $\tan \beta =2$, 2.5 and 3, respectively.

Figure 9

Correlation between $m_H\simeq m_A$ and the lightest non-SM-like $CP$-even Higgs boson mass (left panel) and anticorrelation between the masses of the lightest non-SM-like $CP$-even Higgs boson and the lightest, mostly singlet $CP$-odd Higgs boson (right panel), for values of $\kappa ={\kappa }^{\max }$. Blue, red and yellow represent values of $\tan \beta =2$, 2.5 and 3, respectively.

Figure 10

Branching ratio of the decay of the heaviest $CP$-even Higgs boson into pairs of identical $CP$-even Higgs bosons. The left panel shows the decay into pairs of $h$ and the right panel shows the decay into pairs of $h_S$. Blue, red and yellow represent values of $\tan \beta =2$, 2.5 and 3, respectively.

Figure 11

Branching ratios of the decay of the heavy $CP$-even Higgs boson into a pair of nonidentical lighter $CP$-even Higgs bosons $H\to h{h}_S$ (left panel) and into the lightest $CP$-odd Higgs boson and a $Z$ boson (right panel). Blue, red and yellow represent values of $\tan \beta =2$, 2.5 and 3, respectively.

Figure 12

Branching ratio of the decay of the heaviest CP-odd Higgs boson into a pair of nonidentical Higgs bosons consisting of the lightest CP-odd Higgs boson and one of the two lighter CP-even Higgs bosons, $h_S$ (shown in the left panel) or $h$ (shown in the right panel). Blue, red and yellow represent values of $\tan \beta =2$, 2.5 and 3, respectively.

Figure 13

Branching ratio of the decay of the heaviest $CP$-odd Higgs boson into a $Z$ and the lightest $CP$-even Higgs bosons $h$ (left panel) and $h_S$ (right panel). Blue, red and yellow represent values of $\tan \beta =2$, 2.5 and 3, respectively.

Figure 14

Branching ratio of the decay of the heaviest $CP$-even (left panel) and $CP$-odd (right panel) Higgs bosons into charginos and neutralinos. Blue, red and yellow represent values of $\tan \beta =2$, 2.5 and 3, respectively.

Figure 15

Branching ratio of the decay of the heaviest $CP$-even Higgs boson (left panel) and the heaviest $CP$-odd Higgs boson (right panel) into pairs of top quarks. Blue, red and yellow represent values of $\tan \beta =2$, 2.5 and 3, respectively.

Figure 16

Branching ratio of the lightest non-SM-like $CP$-even Higgs boson into bottom quarks (left panel) and pair of $W$ gauge bosons (right panel). Blue, red and yellow represent values of $\tan \beta =2$, 2.5 and 3, respectively.

Figure 17

The production cross section times branching ratio (left panel), and the ratio of the observed limit to the production cross section times branching ratio (right panel) of the decay of the heaviest $CP$-odd Higgs boson into a $Z$ and a $CP$-even Higgs boson as a function of the heaviest $CP$-odd and the singletlike $CP$-even Higgs boson masses. The cross sections are computed for LHC processes with $\sqrt{s}=8\mathrm{TeV}$, and the branching ratio includes the subsequent decay of the $Z$ boson into dileptons and $h_S$ into a bottom-quark pair.

Figure 18

The production cross section times branching ratio of the decay of the second heaviest $CP$-even Higgs into pairs of $W$, showing the ratio of the observed limit for the heaviest $CP$-odd Higgs boson into a $Z$ and a $CP$-even Higgs bosons.

Figure 19

Ratio of the observed limit to the production cross section times branching ratio of the decay of the heaviest $CP$-even Higgs boson into a $Z$ and the lightest $CP$-odd Higgs bosons.

Figure 20

The left panel shows the ratio of the two channels, $A\to Z{h}_S$ and $H\to Z{A}_S$, vs the ratio of the observed limit to the model limit. The right panel shows the correlation between the two channels for the ratio of the observed limit to the production cross sections.

Figure 21

Production cross section times branching ratio of the decay of the heaviest $CP$-even Higgs boson into $h$ and $h_S$, with $h$ decaying into $b\overline{b}$ and $h_S$ decaying into $WW$.

Figure 22

Production cross section times branching ratio of the decay of the heaviest $CP$-even Higgs boson into $h$ and $h_S$, with both $h$ and $h_S$ decaying into $b\overline{b}$.