Higgs boson studies at the Tevatron

We combine searches by the CDF and D0 Collaborations for the standard model Higgs boson with mass in the range $90–200\mathrm{GeV}/c^2$ produced in the gluon-gluon fusion, $WH$, $ZH$, $t\overline{t}H$, and vector boson fusion processes, and decaying in the $H\to b\overline{b}$, $H\to W^{+}{W}^{-}$, $H\to ZZ$, $H\to {\tau }^{+}{\tau }^{-}$, and $H\to \gamma \gamma$ modes. The data correspond to integrated luminosities of up to $10{\mathrm{fb}}^{-1}$ and were collected at the Fermilab Tevatron in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$. The searches are also interpreted in the context of fermiophobic and fourth generation models. We observe a significant excess of events in the mass range between 115 and $140\mathrm{GeV}/c^2$. The local significance corresponds to 3.0 standard deviations at $m_H=125\mathrm{GeV}/c^2$, consistent with the mass of the Higgs boson observed at the LHC, and we expect a local significance of 1.9 standard deviations. We separately combine searches for $H\to b\overline{b}$, $H\to W^{+}{W}^{-}$, $H\to {\tau }^{+}{\tau }^{-}$, and $H\to \gamma \gamma$. The observed signal strengths in all channels are consistent with the presence of a standard model Higgs boson with a mass of $125\mathrm{GeV}/c^2$.

Figure 1

Distribution of ${log}_{10}(s/b)$, for the data from all contributing Higgs boson search channels from CDF and D0, for $m_H=125\mathrm{GeV}/c^2$. The data are shown with points, and the expected signal is shown stacked on top of the backgrounds, which are fit to the data within their systematic uncertainties. The error bars shown on the data correspond in each bin to the square root of the observed data count. Underflows and overflows are collected into the leftmost and rightmost bins, respectively.

Figure 2

Background-subtracted distribution of the reconstructed dijet mass, summed over CDF’s and D0’s channels contributing to the $VZ$ analysis. The $VZ$ signal and the background contributions are fit to the data, and the fitted background is subtracted. The fitted $VZ$ and expected SM Higgs ($m_H=125\mathrm{GeV}/c^2$) contributions are shown with filled histograms. The error bars shown on the data points correspond in each bin to the square root of the sum of the expected signal and background yields.

Figure 3

Background-subtracted distribution of the discriminant histograms, summed for bins with similar signal-to-background ratio ($s/b$) over all contributing Higgs boson search channels from CDF and D0, for $m_H=125\mathrm{GeV}/c^2$. The background is fit to the data, and the uncertainty on the background, shown with the unfilled histogram, is after the fit. The signal model, scaled to the SM expectation, is shown with a filled histogram. The error bars shown on the data points correspond in each bin to the square root of the sum of the expected signal and background yields.

Figure 4

LLR as a function of Higgs boson mass for all of CDF’s and D0’s SM Higgs boson searches in all decay modes combined. The solid line shows the observed LLR values, the dark long-dashed line shows the median expectation assuming no Higgs boson signal is present, and the dark- and light-shaded bands correspond, respectively, to the regions encompassing 1 and 2 s.d. fluctuations around the background-only expectation. The red long-dashed line shows the median expectation assuming a SM Higgs boson signal is present at each value of $m_H$ in turn. The blue short-dashed line shows the median expected LLR assuming the SM Higgs boson is present at $m_H=125\mathrm{GeV}/c^2$.

Figure 5

Observed and median expected (for the background-only hypothesis) 95% C.L. Bayesian upper production limits expressed as multiples of the SM cross section as a function of Higgs boson mass for the combined CDF and D0 searches in all decay modes. The dark- and light-shaded bands indicate, respectively, the 1 and 2 s.d probability regions in which the limits are expected to fluctuate in the absence of signal. The blue short-dashed line shows median expected limits assuming the SM Higgs boson is present at $m_H=125\mathrm{GeV}/c^2$.

Figure 6

The best-fit signal cross section expressed as a ratio to the SM cross section as a function of Higgs boson mass for all of CDF’s and D0’s SM Higgs boson searches in all decay modes combined. The dark- and light-shaded bands show the 1 and 2 s.d. uncertainty ranges on the fitted signal, respectively. Also shown with blue lines are the median fitted cross sections expected for a SM Higgs boson with $m_H=125\mathrm{GeV}/c^2$ at signal strengths of 1.0 times (short-dashed) and 1.5 times (long-dashed) the SM prediction.

Figure 7

The solid black line shows the background $p$-value as a function of $m_H$ for all of CDF’s and D0’s SM Higgs boson searches in all decay modes combined. The dotted black line shows the median expected values assuming a SM signal is present, evaluated separately at each $m_H$. The associated dark- and light-shaded bands indicate the 1 and 2 s.d. fluctuations of possible experimental outcomes under this scenario. The blue lines show the median expected $p$-values assuming the SM Higgs boson is present with $m_H=125\mathrm{GeV}/c^2$ at signal strengths of 1.0 times (short-dashed) and 1.5 times (long-dashed) the SM prediction.

Figure 8

The solid black line shows the signal-plus-background $p$-value as a function of $m_H$ for all of CDF’s and D0’s SM Higgs boson searches in all decay modes combined. The dotted black line shows the median expected values assuming no SM signal is present, evaluated separately at each $m_H$. The associated dark- and light-shaded bands indicate the 1 and 2 s.d. fluctuations of possible experimental outcomes under this scenario. The blue lines show the median expected $p$-values assuming the SM Higgs boson is present with $m_H=125\mathrm{GeV}/c^2$ at signal strengths of 1.0 times (short-dashed) and 1.5 times (long-dashed) the SM prediction.

Figure 9

LLR as a function of Higgs boson mass from the combination of CDF’s and D0’s SM Higgs boson searches focusing on the $H\to b\overline{b}$ decay mode. The solid line shows the observed LLR values, the dark short-dashed line shows the median expectation assuming no Higgs boson signal is present, and the dark- and light-shaded bands correspond, respectively, to the regions encompassing 1 and 2 s.d. fluctuations around the background-only expectation. The red long-dashed line shows the median expectation assuming a SM Higgs boson signal is present at each value of $m_H$ in turn. The blue lines show the median expected LLR assuming the SM Higgs boson is present at $m_H=125\mathrm{GeV}/c^2$ with signal strengths of 1.0 times (short-dashed) and 1.5 times (long-dashed) the SM prediction.

Figure 10

The best-fit signal cross section times branching ratio $({\sigma }_{WH}+{\sigma }_{ZH})\times \mathcal{B}(H\to b\overline{b})$ as a function of Higgs boson mass from the combination of CDF’s and D0’s SM Higgs boson searches focusing on the $H\to b\overline{b}$ decay mode. The dark- and light-shaded bands show the 1 and 2 s.d. uncertainty ranges on the fitted signal, respectively. Also shown with blue lines are the median fitted cross sections expected for a SM Higgs boson with $m_H=125\mathrm{GeV}/c^2$ at signal strengths of 1.0 times (short-dashed) and 1.5 times (long-dashed) the SM prediction. The SM prediction is shown as the smooth, falling curve where the narrow band indicates the theoretical uncertainty.

Figure 11

LLR as a function of Higgs boson mass from the combination of CDF’s and D0’s SM Higgs boson searches focusing on the $H\to W^{+}{W}^{-}$ decay mode. The solid line shows the observed LLR values, the dark short-dashed line shows the median expectation assuming no Higgs boson signal is present, and the dark- and light-shaded bands correspond, respectively, to the regions encompassing 1 and 2 s.d. fluctuations around the background-only expectation. The red long-dashed line shows the median expectation assuming a SM Higgs boson signal is present at each value of $m_H$ in turn. The blue lines show the median expected LLR assuming the SM Higgs boson is present at $m_H=125\mathrm{GeV}/c^2$ with signal strengths of 1.0 times (short-dashed) and 1.5 times (long-dashed) the SM prediction.

Figure 12

The best-fit signal cross section expressed as a ratio to the SM cross section as a function of Higgs boson mass from the combination of CDF’s and D0’s SM Higgs boson searches focusing on the $H\to W^{+}{W}^{-}$ decay mode. The dark- and light-shaded bands show the 1 and 2 s.d. uncertainty ranges on the fitted signal, respectively. Also shown with blue lines are the median fitted cross sections expected for a SM Higgs boson with $m_H=125\mathrm{GeV}/c^2$ at signal strengths of 1.0 times (short-dashed) and 1.5 times (long-dashed) the SM prediction.

Figure 13

Observed and median expected (for the background-only hypothesis) 95% C.L. Bayesian upper production limits expressed as multiples of the SM cross section as a function of Higgs boson mass from the combination of CDF’s and D0’s SM Higgs boson searches focusing on the $H\to \gamma \gamma$ decay mode. The dark- and light-shaded bands indicate, respectively, the 1 and 2 s.d. probability regions in which the limits are expected to fluctuate in the absence of signal.

Figure 14

Observed and median expected (for the background-only hypothesis) 95% C.L. Bayesian upper production limits expressed as multiples of the SM cross section as a function of Higgs boson mass from the combination of CDF’s and D0’s SM Higgs boson searches focusing on the $H\to {\tau }^{+}{\tau }^{-}$ decay mode. The dark- and light-shaded bands indicate, respectively, the 1 and 2 s.d. probability regions in which the limits are expected to fluctuate in the absence of signal.

Figure 15

Best-fit values of $R=(\sigma \times \mathcal{B})/\mathrm{SM}$ using the Bayesian method for the combinations of CDF’s and D0’s Higgs boson search channels focusing on the $H\to W^{+}{W}^{-}$, $H\to b\overline{b}$, $H\to \gamma \gamma$, and $H\to {\tau }^{+}{\tau }^{-}$ decay modes for a Higgs boson mass of $125\mathrm{GeV}/c^2$. The shaded band corresponds to the 1 s.d. uncertainty on the best-fit value of $R$ for all SM Higgs boson decay modes combined.

Figure 16

(a) Posterior probability densities for $R=(\sigma \times \mathcal{B})/\mathrm{SM}$ using the Bayesian method from the combinations of CDF’s and D0’s Higgs boson search channels focusing on the $H\to W^{+}{W}^{-}$, $H\to b\overline{b}$, $H\to \gamma \gamma$, and $H\to {\tau }^{+}{\tau }^{-}$ decay modes and for all SM Higgs boson decay modes combined. The same curves are shown on an expanded scale in (b).

Figure 17

Posterior probability density for ${\kappa }_W$ from the combination of Tevatron searches for a SM-like Higgs boson with $m_H=125\mathrm{GeV}/c^2$. The couplings of the Higgs boson to fermions and to the $Z$ boson are assumed to be as predicted by the SM. The values that maximize the local posterior probability densities are shown with dashed lines, and the 68% and 95% C.L. intervals are indicated with the dark- and light-shaded regions, respectively. The predicted SM value of ${\kappa }_W$ is indicated by the solid vertical line.

Figure 18

Posterior probability density for ${\kappa }_Z$ from the combination of Tevatron searches for a SM-like Higgs boson with $m_H=125\mathrm{GeV}/c^2$. The couplings of the Higgs boson to fermions and to the $W^{\pm }$ boson are assumed to be as predicted by the SM. The values that maximize the local posterior probability densities are shown with dashed lines, and the 68% and 95% C.L. intervals are indicated with the dark- and light-shaded regions, respectively. The predicted SM value of ${\kappa }_Z$ is indicated by the solid vertical line.

Figure 19

Posterior probability density for ${\kappa }_f$ from the combination of Tevatron searches for a SM-like Higgs boson with $m_H=125\mathrm{GeV}/c^2$. The couplings of the Higgs boson to the $W^{\pm }$ and $Z$ bosons are assumed to be as predicted by the SM. The values that maximize the local posterior probability densities are shown with dashed lines, and the 68% and 95% C.L. intervals are indicated with the dark- and light-shaded regions, respectively. The predicted SM value of ${\kappa }_f$ is indicated by the solid vertical line.

Figure 20

Two-dimensional constraints in the $({\kappa }_W,{\kappa }_Z)$ plane, for the combined Tevatron searches for a SM-like Higgs boson with mass $125\mathrm{GeV}/c^2$ allowing ${\kappa }_f$ to float. The points that maximize the local posterior probability densities are marked with dots, and the 68% and 95% C.L. intervals are indicated with the dark- and light-shaded regions, respectively. The SM prediction for $({\kappa }_W,{\kappa }_Z)$ is marked with a triangle.

Figure 21

Posterior probability density for ${\theta }_{WZ}={tan}^{-1}({\kappa }_Z/{\kappa }_W)$, from the combination of Tevatron searches for a SM-like Higgs boson with $m_H=125\mathrm{GeV}/c^2$ allowing ${\kappa }_f$ to float. The value that maximizes the posterior probability density is shown with a dashed vertical line, and the 68% and 95% C.L. intervals are indicated with the dark- and light-shaded regions, respectively. The predicted SM value of ${\theta }_{WZ}$ is indicated by the solid vertical line.

Figure 22

Two-dimensional constraints in the $({\kappa }_V,{\kappa }_f)$ plane, for the combined Tevatron searches for a SM-like Higgs boson with mass $125\mathrm{GeV}/c^2$ assuming custodial symmetry (${\lambda }_{WZ}=1$). The points that maximize the local posterior probability densities are marked with dots, and the 68% and 95% C.L. intervals are indicated with the dark- and light-shaded regions, respectively. The SM prediction for $({\kappa }_V,{\kappa }_f)$ is marked with a triangle.

Figure 23

Observed and median expected (for the background-only hypothesis) 95% C.L. Bayesian upper limits on the cross section times branching ratio $\sigma (gg\to H)\times \mathcal{B}(H\to W^{+}{W}^{-})$ from the combination of CDF’s and D0’s Higgs boson search channels focusing on this production and decay mode. The dark and light-shaded bands indicate, respectively, the 1 and 2 s.d. probability regions in which the limits are expected to fluctuate in the absence of signal. Theoretical predictions for SM4 in the low- and high-mass scenarios are shown with blue and red lines, respectively. The hatched band indicates the theoretical uncertainty associated with the SM4 low-mass scenario.

Figure 24

Observed and median expected (for the background-only hypothesis) 95% C.L. Bayesian upper production limits expressed as multiples of the SM4 (low-mass scenario) cross section as a function of Higgs boson mass from the combination of CDF’s and D0’s Higgs boson searches focusing on the $gg\to H$ production and $H\to W^{+}{W}^{-}$ decay modes. Uncertainties associated with theoretical cross section and branching ratio predictions are incorporated in the limit. The dark- and light-shaded bands indicate, respectively, the 1 and 2 s.d. probability regions in which the limits are expected to fluctuate in the absence of signal. The red line shows the prediction for the signal rate in the high-mass scenario, divided by that of the low-mass scenario.

Figure 25

Observed and median expected (for the background-only hypothesis) 95% C.L. Bayesian upper production limits expressed as multiples of the FHM cross section as a function of Higgs boson mass for the combined CDF and D0 searches. The dark- and light-shaded bands indicate, respectively, the 1 and 2 s.d. probability regions in which the limits are expected to fluctuate in the absence of signal.