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2019:groups:higgs:gildener [2019/10/30 16:06] jonathan.butterworth |
2019:groups:higgs:gildener [2019/10/31 12:58] (current) jonathan.butterworth |
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It would be interesting to investigate how much this mass equality can be relaxed and remain consistent with the T-parameter constraint. | It would be interesting to investigate how much this mass equality can be relaxed and remain consistent with the T-parameter constraint. | ||
- | KL: The sum rule constraint for this model, ($M^4_{h_2} + M^4_{h_3} + 2M^4_{h^+})^{1/4} = 540$ GeV, follows from the Higgs-mass (M_{h1}) formula derived by E. Gildener and S. Weinberg in PRD 13, 3333 (1976). It is determined by minimizing the one-loop approximation to the S. Coleman--E. Weinberg potential for this model. Because of this sum rule constraint, when M_{h+} = M_{h3} \simge 400 GeV, the mass M_{h2} and various branching ratios of h+/- and h3 are very sensitive to small changes in M_{h+} = M_h3}. Especially the BR's for h+/- -> W+/- h2 and h3 -> Z h2 grow rapidly and become more important than t bbar and t tbar, respectively. | + | KL: The sum rule constraint for this model, ($M^4_{h_2} + M^4_{h_3} + 2M^4_{h^+})^{1/4} = 540$ GeV, follows from the Higgs-mass ($M({h_1}$) formula derived by E. Gildener and S. Weinberg in PRD 13, 3333 (1976). It is determined by minimizing the one-loop approximation to the S. Coleman--E. Weinberg potential for this model. Because of this sum rule constraint, when $M(h^+) = M(h_3) \simge 400$ GeV, the mass $M(h_2)$ and various branching ratios of $h^\pm$ and $h_3$ are very sensitive to small changes in $M(h^+) = M(h_3)$. Especially the BR's for $h^\pm \rightarrow W^\pm h_2$ and $h_3 \rightarrow Z h_2$ grow rapidly and become more important than $t \bar{b}$ and $t \bar{b}$, respectively. |
Therefore, it is interesting and important to see how much the sum rule is affected by, e.g., the two-loop correction to the effective potential. That is, how seriously we should take the 540 GeV RHS of the sum rule? | Therefore, it is interesting and important to see how much the sum rule is affected by, e.g., the two-loop correction to the effective potential. That is, how seriously we should take the 540 GeV RHS of the sum rule? | ||
{{:2019:groups:higgs:combinedhybrid2hdm_lh2.png?500|}} | {{:2019:groups:higgs:combinedhybrid2hdm_lh2.png?500|}} | ||
- | As you can see, the measurements disfavour $\tan\beta > 1$ regardless of $M = M_A$. There is some increase in sensitivity at high $M_A$. We can also plot the same data as a function of $M_{H^\prime}$: | + | Explanation of the legend: |
+ | On the left, yellow means excluded at 95% c.l. or more, green at 68%-95% (ie 2 and 1 sigma). | ||
+ | On the right, the same exclusions are shown but on a continuous scale (indicated by the bar on the right) with | ||
+ | 1 being fully excluded, 0 being zero sensitivity. | ||
- | KL: The sensitivity plots BELOW are new (received from JB on 23 October 2019). | + | |
+ | As you can see, the measurements disfavour $\tan\beta > 1$ regardless of $M = M_A$. There is some increase in sensitivity at high $M_A$. We can also plot the same data as a function of $M_{H^\prime}$: | ||
{{:2019:groups:higgs:combinedhybrid2hdm_lh2_mh2.png?500|}} | {{:2019:groups:higgs:combinedhybrid2hdm_lh2_mh2.png?500|}} | ||
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{{:2019:groups:higgs:atlas_8_lljetmesh_lh2_mh3.png?200|}} | {{:2019:groups:higgs:atlas_8_lljetmesh_lh2_mh3.png?200|}} | ||
- | Lepton+MET+X measurements (mostly $W$+jet or top) also have their best sensitivity at quite $M$, but a bit lower than the dileptons, so at intermediate $M_{H^\prime}$, see below the same scan plotted against the two different masses. | + | Looking into the processes which might be cause this, for the point $M_A = M(h_3) = 410$ GeV and $\tan\beta=0.35$, |
+ | we get about $2\sigma$ exclusion coming from the ATLAS and CMS $Z+$jet measurements. For these parameters, | ||
+ | $H$ and $H^\prime$ decay mainly to $b\bar{b}$, but $A$ decays 90% to $H^\prime Z$, which seems to be the likely source of this sensitivity. | ||
+ | |||
+ | Lepton+MET+X measurements (mostly $W$+jet or top) also have their best sensitivity at quite high $M$, but a bit lower than the dileptons, so at intermediate $M_{H^\prime}$, see below the same scan plotted against the two different masses. | ||
{{:2019:groups:higgs:cms_13_lmetjetmesh_lh2_mh2.png?200|}} | {{:2019:groups:higgs:cms_13_lmetjetmesh_lh2_mh2.png?200|}} | ||
{{:2019:groups:higgs:cms_13_lmetjetmesh_lh2_mh3.png?200|}} | {{:2019:groups:higgs:cms_13_lmetjetmesh_lh2_mh3.png?200|}} | ||
+ | |||
+ | This seems to likely come from the $h^\pm \rightarrow W H^\prime$ decay (88% BF). | ||
The inclusive $\gamma$ measurements also have some sensitivity, which shows a sharp cutoff once $M_A > 350$ GeV. (See below.) | The inclusive $\gamma$ measurements also have some sensitivity, which shows a sharp cutoff once $M_A > 350$ GeV. (See below.) |