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--- 2019:groups:higgs:gildener [2019/10/30 16:03]
jonathan.butterworth
+++ 2019:groups:higgs:gildener [2019/10/30 17:06]
jonathan.butterworth
@@ Line 24: / Line 24: @@
 === Scanning the parameter space ===
-Fix the m(h+/-) and A masses to be equal to $M$ and related to the $H^\prime$ mass via $(540 GeV)^4 = M_{H^\prime}^4 + 3M^4$, and scan over $0.1 < \tan\beta < 10$ and $150 < M < 410$GeV.
+Fix the $h^\pm$ and $A$ masses to be equal to $M$ and related to the $H^\prime$ mass via $(540 GeV)^4 = M_{H^\prime}^4 + 3M^4$, and scan over $0.1 < \tan\beta < 10$ and $150 < M < 410$GeV.
-KL: The reason for M(h+/-) = M(h3) is that this makes the BSM Higgses' contribution to the T-parameter vanish through one-loop order. (See Lee & Pilaftsis, PRD 86, 035004 (2012) and the KL-WS PRD cited above.)
+KL: The reason for $M(h^\pm) = M(h_3)$ is that this makes the BSM Higgses' contribution to the T-parameter vanish to one-loop order. (See Lee & Pilaftsis, PRD 86, 035004 (2012) and the KL-WS PRD cited above.)
 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_{h2} + M^4_{h3} + 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?
 {{:2019:groups:higgs:combinedhybrid2hdm_lh2.png?500|}}
+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
+being fully excluded, 0 being zero sensitivity.
 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 $M_{H^\prime}$:

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