#
Connecting Electroweak Symmetry Breaking and Flavor: A Light Dilaton
D
and a Sequential Heavy Quark Doublet Q

## Abstract

**:**

## 1. Higgs, Anderson, and All That

## 2. On Observing VBF

## 3. The Yukawa Coupling Enigma

## 4. Ultrastrong Yukawa-Induced EWSB and the Dilaton

## 5. LHC Run 2 Results

- ${\mathit{ZZ}}^{\ast}$: Both experiments have made the analyses up to 2017 data available at 79.8 fb${}^{-1}$ and 77.4 fb${}^{-1}$, respectively, for ATLAS and CMS.For ATLAS [40], while ${\mu}_{\mathrm{ggF}}\simeq 1$ is measured, the ${\mu}_{\mathrm{VBF}}\simeq 2.8$ value is rather large.For CMS [41], ${\mu}_{\mathrm{ggF},\mathrm{b}\overline{\mathrm{b}}\mathrm{H}}={1.15}_{-0.16}^{+0.18}$ is measured and ${\mu}_{\mathrm{VBF}}={0.69}_{-0.57}^{+0.75}$ is barely 1$\sigma $, reflecting, in part, the absence of events in the 2016 data (36.9 fb${}^{-1}$).Could these “fluctuations” reflect a much larger ggF production rate but with an analysis strategy centered around SM expectation?
- $\mathit{\gamma}\mathit{\gamma}$: The results are for 36.1 fb${}^{-1}$ and 35.9 fb${}^{-1}$, respectively, (i.e., 2016 data) for ATLAS and CMS.For ATLAS [42], ${\mu}_{\mathrm{ggF}}={0.81}_{-0.18}^{+0.19}$ is mildly less than 1, but ${\mu}_{\mathrm{VBF}}={2.0}_{-0.5}^{+0.6}$ is, again, rather large.For CMS [43], ${\mu}_{\mathrm{ggF}}={1.10}_{-0.18}^{+0.20}$ looks reasonable, but ${\mu}_{\mathrm{VBF}}={0.8}_{-0.5}^{+0.6}$ is not inconsistent with zero.The trends for ATLAS and CMS are again opposite. In addition to the possibility that ggF production could be much stronger than assumed, this may reflect differences in analysis choice(s).
- ${\mathit{WW}}^{\ast}$: Both experiments are only for 2016 data.For ATLAS [44], the measured ${\sigma \xb7\mathcal{B}|}_{\mathrm{ggF}}$ at 6.3$\sigma $ is ≃$20\%$ larger than the SM expectation, while ${\sigma \xb7\mathcal{B}|}_{\mathrm{VBF}}$ is found at 1.9$\sigma $, w.r.t. SM expectation at 2.7$\sigma $.For CMS [45], ${\mu}_{\mathrm{ggF}}={1.38}_{-0.24}^{+0.21}$ is 1.6$\sigma $ above SM, while $\mathrm{VBF}={0.29}_{-0.29}^{+0.66}$ is consistent with zero, reflecting, in part, the null result in 2016 data.
- $\mathit{\tau}\mathit{\tau}$: Based on 2016 data, ATLAS has recently joined CMS in claiming observation. Given the large backgrounds for $gg\to H\to {\tau}^{+}{\tau}^{-}$, the observation was made with “jet assistance”.For CMS [46], $\mu ={1.09}_{-0.26}^{+0.27}$ is at 4.9$\sigma $ (combining with Run 1 to become 5.9$\sigma $) which combines the 0-jet, Boosted, and VBF measurements. Not surprisingly, 0-jet is barely 1$\sigma $, so the measurement comes from the latter two. However, our question of jet-tagged ggF vs. VBF remains.For ATLAS [47], combining Boosted and VBF categories gives 4.4$\sigma $ (4.1$\sigma $), improving to 6.4$\sigma $ (5.4$\sigma $) when combined further with Run 1. The expected SM significance is given in parenthesis.
- $\mathit{b}\overline{\mathit{b}}$: Both ATLAS and CMS find evidence for this. The large $b\overline{b}$ cross section from QCD implies jet-tag-assistance would not work, and measurements are based on $VH$ associated production, where both experiments use $VZ$ production for validation. By combining the 2016 data with Run 1, ATLAS [48] and CMS [49] experiments find evidence at 3.6$\sigma $ (4.0$\sigma $) and 3.8$\sigma $ (3.8$\sigma $), respectively. Both experiments find excess events in ${m}_{b\overline{b}}$ above the Z pole.
- Combinations: CMS has put out a combination of analyses based on 2016 data, while ATLAS has combination of only $Z{Z}^{\ast}$ and $\gamma \gamma $ modes.For CMS [50], ${\mu}_{\mathrm{ggF}}\simeq 1.23$ is about 1$\sigma $ above SM, while ${\mu}_{\mathrm{VBF}}\simeq 0.73$ is about 1$\sigma $ below. $WH$ is found to be large, about twice the SM expectation, while $ZH$ is consistent with SM and 2$\sigma $ away from zero.For ATLAS [51], ${\mu}_{\mathrm{ggF}}$ is consistent with 1, but ${\mu}_{\mathrm{VBF}}$ is greater than 2 and is rather large. $VH$ is found to be consistent with zero.
- $\mathit{t}\overline{\mathit{t}}\mathit{H}$: By adding the 2017 data for the $H\to Z{Z}^{\ast}$ and $\gamma \gamma $ modes, ATLAS has recently joined CMS in observation of $t\overline{t}H$ production at the LHC.For CMS [52], based on H decay to the five modes of $W{W}^{\ast}$, $Z{Z}^{\ast}$, $\gamma \gamma $, ${\tau}^{+}{\tau}^{-}$ and $b\overline{b}$, and combining 2016 data with Run 1, the measurement of ${\mu}_{t\overline{t}H}={1.26}_{-0.26}^{+0.31}$ makes a 5.2$\sigma $ observation.ATLAS [53] was a bit unlucky with a similar data set. Adding data from 2017 to $H\to Z{Z}^{\ast}$ and $\gamma \gamma $ and combining this with 2016 data for the other three modes gives ${\mu}_{t\overline{t}H}={1.32}_{-0.26}^{+0.28}$, achieving an observation of 5.8$\sigma $ (4.9$\sigma $) with 13 TeV data alone. Combined with Run 1, the significance becomes 6.3$\sigma $ (5.1$\sigma $).

## 6. Discussion and Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Gluon–gluon fusion production and $Z{Z}^{\ast}$, $\gamma \gamma $ decay of 125 GeV boson (dashed line).

**Figure 3.**(

**left**) $Q\overline{Q}\to Q\overline{Q}$ scattering by the exchange of Nambu–Goldstone (NG) boson (G, or longitudinal ${V}_{L}$); (

**center**) connecting Q to $\overline{Q}$ across the exchanged G; (

**right**) self-energy of Q by G loop, with the mass generation illustrated by cross (×).

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Hou, W.-S.
Connecting Electroweak Symmetry Breaking and Flavor: A Light Dilaton *Q*. *Symmetry* **2018**, *10*, 312.
https://doi.org/10.3390/sym10080312

**AMA Style**

Hou W-S.
Connecting Electroweak Symmetry Breaking and Flavor: A Light Dilaton *Q*. *Symmetry*. 2018; 10(8):312.
https://doi.org/10.3390/sym10080312

**Chicago/Turabian Style**

Hou, Wei-Shu.
2018. "Connecting Electroweak Symmetry Breaking and Flavor: A Light Dilaton *Q*" *Symmetry* 10, no. 8: 312.
https://doi.org/10.3390/sym10080312