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--- 2019:groups:higgs:gildener [2019/10/30 15:59]
jonathan.butterworth
+++ 2019:groups:higgs:gildener [2019/10/31 12:58] (current)
jonathan.butterworth
@@ Line 6: / Line 6: @@
 KL: The definition of $\sin(\beta-\alpha)$ is inverted in this file compared to usual convention of Branco et al.,
-so the alignment limit is achieved when $\sin(\beta-\alpha) = 0$ (It is $\sin(\beta-\alpha) = 1$ in the standard definition of Branco et al. because they define the $\rho_1,\rho_2 \rightarrow h,H (= h1,h2$ below) mixing angle $\alpha$ as $\pi/2$ in the alignment limit. KL & Will Shepherd defined $\alpha = \beta$ in the alignment limit because it is in line with the Higgs $h1 = H(125)$ being a Goldstone boson of spontaneous scale symmetry breaking. Thus, in the KL-WS convention, $\sin(\beta - \alpha) = \sin\delta$ where $\delta$ is the misalignment angle in their paper, [[https://arxiv.org/abs/1808.07927]] PRD 99, 055015 (2019); $\delta = 0$ in the alignment limit -- which is tree approximation in the GW-2HDM.).
+so the alignment limit is achieved when $\sin(\beta-\alpha) = 0$ (It is $\sin(\beta-\alpha) = 1$ in the standard definition of Branco et al. because they define the $\rho_1,\rho_2 \rightarrow h,H (= h1,h2$ below) mixing angle $\alpha$ as $\pi/2$ in the alignment limit. KL & Will Shepherd defined $\alpha = \beta$ in the alignment limit because it is in line with the Higgs $h1 = H(125)$ being a Goldstone boson of spontaneous scale symmetry breaking. Thus, in the KL-WS convention, $\sin(\beta - \alpha) = \sin\delta$ where $\delta$ is the misalignment angle in their paper, [[https://arxiv.org/abs/1808.07927]]; $\delta = 0$ in the alignment limit -- which is tree approximation in the GW-2HDM.).
-An example of the Higgs branching ratios for these settings is here:{{ :2019:groups:higgs:lhc-s101-runpoint_0100.log.txt |}}
+KL: It can be seen that the branching ratio to $b$ quarks is about 80%,
-KL: These June 30, 2019, BR's are out of date and incorrect.
+so higher than the SM value. This seems to be due the fact that Herwig is LO and does not use a running $b$ mass.
-KL: It can be seen that the branching ratio to $b$ quarks is about 80%, so higher than the SM value. This seems to be
-due the fact that Herwig is LO and does not use a running $b$ mass (Ken).
 Still do not understand why the $H \rightarrow \gamma\gamma$ branching fraction is zero.
-Higgs labelling conventions (left is the UFO name, right the name in the KL-WS paper, [[PRD 99, 055015 (2019)]https://arxiv.org/abs/1808.07927].):
+Higgs labelling conventions (left is the UFO name, right the name in the KL-WS paper, [[https://arxiv.org/abs/1808.07927]].):
    * h1 = SM higgs
@@ Line 23: / Line 20: @@
    * h+, h- = h+, h-
-Is $\tan\beta$ the usual definition?
+KL: $\tan\beta = v_2/v_1$ is the usual definition. However, the Type-1 set up in the KL-WS paper and the KL-E.Pilon paper, [[https://arxiv.org/abs/1909.02111]], takes the $\Phi_1$ doublet as coupled to ALL quarks, up- and down-type and to all leptons. This is different than the Type-1 convention in Branco et al. and in ATLAS and CMS papers, in which it is $\Phi_2$ that couples to all fermions. (Sorry, folks, this choice was made before KL discovered the Branco, et al. paper.) The net effect of this is that ALL the decay AMPLITUDES of the BSM Higgses (namely, $h2 = H', h3 = A, h+,h- = H^\pm$) to fermion pairs are proportional to $\tan\beta$ (NOT $\cot\beta$); the same is true of such all fermion-loop-induced process such as $gg \rightarrow H',A$  and $H, A \rightarrow gg$ and $\gamma \gamma$. Thus, in determining experimental limits on these BSM Higgses from the LHC experiments assuming Type-1 2HDM, put $\tan\beta \rightarrow \cot\beta$ in those papers.
-KL: \tan\beta = v_2/v_1 is the usual definition. However, the Type-1 set up in the KL-WS paper and the KL-E.Pilon paper, arXiv:1909.02111, takes the $\Phi_1$ doublet as coupled to ALL quarks, up- and down-type and to all leptons. This is different than the Type-1 convention in Branco et al. and in ATLAS and CMS papers, in which it is \Phi_2 that couples to all fermions. (Sorry, folks, this choice was made before KL discovered the Branco, et al. paper.) The net effect of this is that ALL the decay AMPLITUDES of the BSM Higgses (namely, h2 = H', h3 = A, h+,h- = H^\pm) to fermion pairs are proportional to \tan\beta (NOT \cot\beta); the same is true of such all fermion-loop-induced process such as gg -> H',A  and H, A -> gg and \gamma \gamma. Thus, in determining experimental limits on these BSM Higgses from the LHC experiments assuming Type-1 2HDM, put \tan\beta -> \cot\beta in those papers.
 === 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|}}
-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
+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|}}
@@ Line 52: / Line 51: @@
 {{: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_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.)

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