Precise determination of the Higgs mass in supersymmetric models with vectorlike tops and the impact on naturalness in minimal GMSB

Journal of High Energy Physics, Jul 2015

Abstract We present a precise analysis of the Higgs mass corrections stemming from vectorlike top partners in supersymmetric models. We reduce the theoretical uncertainty compared to previous studies in the following aspects: (i) including the one-loop threshold corrections to SM gauge and Yukawa couplings due to the presence of the new states to obtain the \( \overline{\mathrm{DR}} \) parameters entering all loop calculations, (ii) including the full momentum dependence at one-loop, and (iii) including all two-loop corrections but the ones involving g1 and g2. We find that the additional threshold corrections are very important and can give the largest effect on the Higgs mass. However, we identify also parameter regions where the new two-loop effects can be more important than the ones of the MSSM and change the Higgs mass prediction by up to 10 GeV. This is for instance the case in the low tan β, small MA regime. We use these results to calculate the electroweak fine-tuning of an UV complete variant of this model. For this purpose, we add a complete 10 and \( \overline{10} \) of SU(5) to the MSSM particle content. We embed this model in minimal Gauge Mediated Supersymmetry Breaking and calculate the electroweak fine-tuning with respect to all important parameters. It turns out that the limit on the gluino mass becomes more important for the fine-tuning than the Higgs mass measurements which is easy to satisfy in this setup.

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Precise determination of the Higgs mass in supersymmetric models with vectorlike tops and the impact on naturalness in minimal GMSB

Received: June Precise determination of the Higgs mass in supersymmetric models with vectorlike tops and the Spin 0 1 0 Open Access , c The Authors 1 1211 Geneva 23 , Switzerland 2 Bethe Center for Theoretical Physics & Physikalisches Institut der Universit ̈at Bonn We present a precise analysis of the Higgs mass corrections stemming from vectorlike top partners in supersymmetric models. We reduce the theoretical uncertainty compared to previous studies in the following aspects: (i) including the one-loop threshold corrections to SM gauge and Yukawa couplings due to the presence of the new states to obtain the DR parameters entering all loop calculations, (ii) including the full momentum dependence at one-loop, and (iii) including all two-loop corrections but the ones involving g1 and g2. We find that the additional threshold corrections are very important and can give the largest effect on the Higgs mass. However, we identify also parameter regions where the new two-loop effects can be more important than the ones of the MSSM and change the Higgs mass prediction by up to 10 GeV. This is for instance the case in the low tan β, small MA regime. We use these results to calculate the electroweak fine-tuning of an UV complete variant of this model. For this purpose, we add a complete 10 and Mediated Supersymmetry Breaking and calculate the electroweak fine-tuning with respect to all important parameters. It turns out that the limit on the gluino mass becomes more important for the fine-tuning than the Higgs mass measurements which is easy to satisfy in this setup. Higgs; supersymmetric; bTheory Division; CERN - impact on naturalness in minimal GMSB Contents 1 Introduction The MSSM with vectorlike tops The minimal model UV completion and fine-tuning Conclusion A Vertices The mass spectrum of the minimal model Tree-level properties Calculation of the Higgs masses at one- and two-loop Threshold corrections One-loop corrections Two-loop corrections Results — Part I: the Higgs mass Gauge coupling unification Gauge mediated SUSY breaking and boundary conditions A.1 Vector boson vertices with vectorlike (s)tops A.2 Quark vertices involving vectorlike (s)tops A.3 Higgs vertices with vectorlike (s)tops B Renormalization Group Equations Gauge couplings Gaugino mass parameters B.3 Trilinear superpotential parameters B.4 Bilinear superpotential parameters B.5 Trilinear soft-breaking parameters B.6 Bilinear soft-breaking parameters B.7 Soft-breaking scalar masses B.8 Vacuum expectation values Introduction d∗ d∗ u∗ e∗ t0∗ Spin 0 − 21 , 2, 1 − 21 , 2, 1 − 32 , 1, 3 (1, 1, 1) − 32 , 1, 3 superfields Tˆ0, T¯ˆ0. on the results of refs. [66–70]. in section 6. The MSSM with vectorlike tops The minimal model for the model reads: notation, we define therefore Yt30 ≡ Yt0 . When we speak about the top-Yukawa coupling Yt, we refer to Yu33. symmetry breaking (EWSB). The soft-SUSY breaking terms for the model are + mt2˜0 |t˜0|2 +mt2˜¯0 | t¯˜0|2 +(m2ut˜0 u˜∗t˜0 +h.c.)+(M1λBλB +M2λW λW +M3λGλG + h.c.) . i UV completion and fine-tuning Gauge coupling unification extension of the superpotential is needed: Q (GeV) the UV complete version: βg(12) = (1 + 3δUV ) g23 βg(13) = (−2 + 2δUV ) g33, βgi ≡ 16π2 βg(1i) + +Yt0,i2 YdYt∗0 i1 βY(1u) = 3Yt0,i2 YuYt∗0 i1 the following: e¯˜0|2 + mq2˜0 |q˜0|2 + mq2˜¯0 | (GMSB) which we introduce now briefly. hSi = M + Θ2F . g(x) ' 1 + + O(x8) , It is convenient to define f (x) ' 1 + For F the scalar soft masses 36 − 450 − 11760 + O(x8) . (2.19) mass M , while the scalars get masses ˜ ˜ φM ± φ¯M m+,− = pM 2 approximations for the soft breaking masses are ml2,jj = m2Hu = m2Hd = mq2,jj = mq2˜0 = mq˜¯0 = m2u,jj = mt2˜0 = mt˜¯0 = me2,jj = me2˜0 = me˜¯0 = m2d,jj = gaugino mass terms, we have the MSSM results Tx = 0 BX = 0 x = d, u, e, t0 X = Q0, E0, T 0 m2ut˜0 = mq2q˜0 = me2e˜0 = Bt = 0 . messenger scale MT 0 = MQ0 = ME0 ≡ MV 0 . for it [97–103]. Thus, our full set of input parameters in this setup is Fine-tuning refs. [104, 105] while all other soft-terms vanish up to two-loop ΔF T ≡ max Abs Δα , ∂ ln MZ2 = respect to is derived. α = {Λ, MV 0 , Yt0 , Yt, g3, μ, Bμ}. mh = (125 ± 3) GeV . Tree-level properties and split in their CP even and odd components: Hd0 → √ (φd + iσd + vd) , Hu0 → √ (φu + iσu + vu) . We have tan β = vvud and v = qvd2 + vu2 ' 246 GeV. Using these conventions, the tree-level −14 g12 +g22 vdvu −< Bμ −14 g12 +g22 vdvu −< Bμ −18 g12 +g22 −3vu2 +vd2 +m2Hu +|μ|2  . (3.3) This matrix is diagonalized by ZH : = − 2 vu Bμ + Bμ∗ + ZH m2hZH,† = m2d,iha g12 + g22 vd − vu2 + vd2 = 0 (3.5) g12 + g22 vu − vd2 + vu2 − vd< Bμ = 0 . m2u˜ =  mu˜Lu˜∗L 2 vuTu − vdYuμ∗ 2 vuTt0 − vdμ∗Yt0  √12 vu MT∗0 Yt0 + YuT mt∗0 with the diagonal entries mu˜Lu˜∗L = − 24 mu˜Ru˜∗R = mt˜0t˜0∗ = mt˜¯0∗t¯˜0 = 12 2 MT 0 mt∗0 + m2u˜t˜0 + vu2Yu∗Yt0 mu˜Ru˜∗R Bt∗0 − 3g22 + g12 1 − vu2 + vd2 2mq2 + vu2 Yt∗0Yt0 + Yu†Yu 2 mt∗0 mt0 + m2u − vu2 + vd2 6 g1 − vu2 + vd2 6 g1 − vd2 + vu2 . the physical pseudo (...truncated)


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Kilian Nickel, Florian Staub. Precise determination of the Higgs mass in supersymmetric models with vectorlike tops and the impact on naturalness in minimal GMSB, Journal of High Energy Physics, 2015, pp. 139, Volume 2015, Issue 7, DOI: 10.1007/JHEP07(2015)139