Constraints on the alignment limit of the MSSM Higgs - PowerPoint PPT Presentation

Constraints ¡on ¡the ¡alignment ¡ limit ¡of ¡the ¡MSSM ¡Higgs ¡sector ¡ ¡ ¡Howard ¡E. ¡Haber ¡ ¡ ¡February ¡14, ¡2015 ¡ ¡ ¡Toyama, ¡Japan ¡

Outline • The CP-conserving 2HDM—a brief review – The alignment limit with and without decoupling • The MSSM Higgs Sector at tree-level • The radiatively-corrected Higgs sector – The exact alignment limit via an accidental cancellation • Is alignment without decoupling in the MSSM viable? – Recent results from the CMS search for H , A → τ + τ − – Implications of the CMS limits for various MSSM Higgs scenarios – Constraining the m A — tan β plane from the observed Higgs data – Complementarity of the H and A searches and the precision h (125) data • Conclusions This talk is based on M. Carena, H.E. Haber, I. Low, N.R. Shah and C.E.M. Wagner, Phys. Rev. D91 , 035003 (2015) [arXiv:1410.4969 [hep-ph]].

The CP-conserving 2HDM—a brief review � 2 � 2 � � � � V = m 2 11 Φ † 1 Φ 1 + m 2 22 Φ † m 2 12 Φ † Φ † Φ † + 1 + 1 2 Φ 2 − 1 Φ 2 + h . c . 2 λ 1 1 Φ 1 2 λ 2 2 Φ 2 � � 2 � � + λ 3 Φ † 1 Φ 1 Φ † 2 Φ 2 + λ 4 Φ † 1 Φ 2 Φ † Φ † + [ λ 6 Φ † 1 Φ 1 + λ 7 Φ † 2 Φ 2 ]Φ † 1 2 Φ 1 + 2 λ 5 1 Φ 2 1 Φ 2 + h . c . , √ 2 (for i = 1 , 2 ), and v 2 ≡ v 2 such that � Φ 0 1 + v 2 2 = (246 GeV) 2 . For i � = v i / simplicity, we have assumed a CP-conserving Higgs potential where v 1 , v 2 , m 2 12 , λ 5 , λ 6 and λ 7 are real. We parameterize the scalar fields as � � φ + tan β ≡ v 2 i Φ i = , . 1 2 ( v i + φ 0 i + ia 0 v 1 i ) √ The two neutral CP-even Higgs mass eigenstates are then defined via � � � � � � φ 0 H c α s α 1 = , ( m h < m H ) , φ 0 h − s α c α 2 where c α ≡ cos α and s α ≡ sin α , and the mixing angle α is defined mod π .

Implications of SM-like Higgs couplings to V V The tree-level coupling of h to V V (where V V = W + W − or ZZ ), normalized to the corresponding SM coupling, is given by g hV V = g SM hV V s β − α . Thus, if the hV V coupling is SM-like, it follows that | c β − α | ≪ 1 , where c β − α ≡ cos( β − α ) and s β − α ≡ sin( β − α ) . REMARK : If H is the SM-like Higgs, then we use g HV V = g SM hV V c β − α to conclude that | s β − α | ≪ 1 . However, this region of parameter space is highly constrained, and is probably not viable within the MSSM.

Constraints in the cβ − α vs. tan β plane for mh ∼ 125 . 5 GeV. Blue points are those that passed all constraints given the Higgs signal strengths as of Spring 2013, red points are those that remain valid when employing the Summer 2014 updates, and orange points are those newly allowed after Summer 2014 updates. It is assumed that h produced through the decay of heavier Higgs states via “feed down” (FD) does not distort the observed Higgs data. Taken from B. Dumont, J.F. Gunion, Y. Jiang and S. Kraml, arXiv:1409.4088.

Under what conditions is | c β − α | ≪ 1 ? It is convenient to define the so-called Higgs basis of scalar doublet fields, � � � � H + H + ≡ v 1 Φ 1 + v 2 Φ 2 ≡ − v 2 Φ 1 + v 1 Φ 2 1 2 H 1 = , H 2 = , H 0 v H 0 v 1 2 √ so that � H 0 2 and � H 0 1 � = v/ 2 � = 0 . The scalar doublet H 1 has SM tree-level couplings to all the SM particles. If one of the CP-even neutral Higgs mass eigenstates is SM-like, then it must be approximately aligned with the real part of the neutral field H 0 1 . This is the alignment limit . In terms of the Higgs basis fields, the scalar potential contains: � 1 � 1 H 1 ) 2 + . . . + 1 H 2 ) 2 + Z 6 ( H † 2 Z 1 ( H † 2 Z 5 ( H † 1 H 1 ) H † V ∋ . . . + 1 1 H 2 + h . c . + . . . , � � Z 1 ≡ λ 1 c 4 β + λ 2 s 4 β + 1 2 ( λ 3 + λ 4 + λ 5 ) s 2 c 2 β λ 6 + s 2 2 β + 2 s 2 β β λ 7 , � � Z 5 ≡ 1 4 s 2 λ 1 + λ 2 − 2( λ 3 + λ 4 + λ 5 ) + λ 5 − s 2 β c 2 β ( λ 6 − λ 7 ) , 2 β � � Z 6 ≡ − 1 λ 1 c 2 β − λ 2 s 2 2 s 2 β β − ( λ 3 + λ 4 + λ 5 ) c 2 β + c β c 3 β λ 6 + s β s 3 β λ 7 .

In the Higgs basis, the CP-even neutral Higgs squared-mass matrix is � � Z 1 v 2 Z 6 v 2 M 2 = , Z 6 v 2 m 2 A + Z 5 v 2 where m A is the mass of the CP-odd neutral Higgs boson A , and α − β is the corresponding mixing angle. It follows that m 2 h ≤ Z 1 v 2 , whereas the off-diagonal element, Z 6 v 2 , governs the H 0 1 — H 0 2 mixing. If Z 6 = 0 and Z 1 < Z 5 + m 2 A /v 2 , then c β − α = 0 and √ m 2 h = Z 1 v 2 . In this case h = 2 H 0 1 − v is identical to the SM Higgs boson. ∗ This is the exact alignment limit of the 2HDM. Approximate alignment can occur if either | Z 6 | ≪ 1 and/or m 2 A ≫ Z i v 2 . In h ≃ Z 1 v 2 and | c β − α | ≪ 1 , i.e., h is SM-like. either case, m 2 The case of A ≫ Z i v 2 is the well-known decoupling limit of the 2HDM. m 2 A /v 2 then Z 6 = 0 implies that s β − α = 0 in which case m 2 H = Z 1 v 2 and we identify ∗ If Z 1 > Z 5 + m 2 √ 2 H 0 H = 1 − v as the SM-like Higgs boson. This is an alignment limit without decoupling, but this case is much harder to achieve in light of the Higgs data.

Thus, if h is SM-like then it follows that | c β − α | ≪ 1 , which implies that the 2HDM is close to the alignment limit. These features can be seen in the following explicit tree-level formulae (no approximations have been made here): Z 2 6 v 4 cos 2 ( β − α ) = H − Z 1 v 2 ) , ( m 2 H − m 2 h )( m 2 Z 2 6 v 4 Z 1 v 2 − m 2 h = H − Z 1 v 2 . m 2 In both the decoupling limit ( m H ≫ m h ) and the alignment limit without H − Z 1 v 2 ∼ O ( v 2 ) ], we see that c β − α → 0 and decoupling [ | Z 6 | ≪ 1 and m 2 m 2 h → Z 1 v 2 . REMARK : Note the upper bound on the mass of h , h ≤ Z 1 v 2 . m 2

The MSSM Higgs Sector at tree-level The dimension-four terms of the MSSM Higgs Lagrangian are constrained by supersymmetry. At tree level, 4 ( g 2 + g ′ 2 ) = m 2 Z /v 2 , λ 1 = λ 2 = − ( λ 3 + λ 4 ) = 1 2 g 2 = − 2 m 2 W /v 2 , λ 4 = − 1 λ 5 = λ 6 = λ 7 = 0 . This yields Z 1 v 2 = m 2 Z 5 v 2 = m 2 Z 6 v 2 = − m 2 Z c 2 Z s 2 2 β , 2 β , Z s 2 β c 2 β . It follows that, m 4 Z s 2 2 β c 2 2 β cos 2 ( β − α ) = 2 β ) . ( m 2 H − m 2 h )( m 2 H − m 2 Z c 2 The decoupling limit is achieved when m H ≫ m h as expected.

The exact alignment limit ( Z 6 = 0 ) is achieved only when β = 0 , 1 4 π or 1 2 π . None of these choices are realistic. Of course, the tree-level MSSM Higgs h ) max = Z 1 v 2 = m 2 sector also predicts ( m 2 Z c 2 2 β in conflict with the Higgs data. Radiative corrections can be sufficiently large to yield the observed Higgs mass, and can also modify the behavior of the alignment limit. We complete our review of the tree-level MSSM Higgs sector by displaying the Higgs couplings to quarks and squarks. The MSSM employs the Type–II Higgs– fermion Yukawa couplings. Employing the more common MSSM notation, D ≡ ǫ ij Φ j ∗ H i H i U = Φ i 1 , 2 , the tree-level Yukawa couplings are: � � D Q j L H j h b b R H i L + h t t R Q i − L Yuk = ǫ ij + h . c . , U which yields √ √ m b = h b vc β / 2 , m t = h t vs β / 2 .

The leading terms in the coupling of the Higgs bosons to third generation squarks are proportional to the Higgs–top quark Yukawa coupling, h t , � � � Q † H U | 2 � Q j � Q † � U ∗ � µ ∗ ( H † D � Q ) � U � H † U H U ( � Q + � U ) −| � U + A t ǫ ij H i − h 2 L int ∋ h t U +h . c . , t � � � t L with an implicit sum over the weak SU(2) indices i, j = 1 , 2 , where � Q = � b L and � U ≡ � t ∗ R . In terms of the Higgs basis fields H 1 and H 2 , � � Q j � 2 ) � ( s β X t H i 1 + c β Y t H i L int ∋ h t ǫ ij U + h . c . �� � β | H 1 | 2 + c 2 β | H 2 | 2 + s β c β ( H † Q † � U ∗ � ( � Q + � − h 2 s 2 1 H 2 + h . c . ) U ) t �� � Q † H 1 | 2 − c 2 Q † H 2 | 2 − s β c β β | � β | � ( � Q † H 1 )( H † 2 � − s 2 Q ) + h . c . , where X t ≡ A t − µ ∗ cot β , Y t ≡ A t + µ ∗ tan β . Assuming CP-conservation for simplicity, we shall henceforth take µ , A t real.

The radiatively corrected MSSM Higgs Sector We are most interested in the limit where m h , m A ≪ m Q , where m Q characterizes the scale of the squark masses. In this case, we can formally integrate out the squarks and generate a low-energy effective 2HDM Lagrangian. This Lagrangian will no longer be of the tree-level MSSM form but rather a completely general 2HDM Lagrangian. If we neglect CP-violating phases that could appear in the MSSM parameters such as µ and A t , then the resulting 2HDM Lagrangian contains all possible CP-conserving terms of dimension-four or less. At one-loop, leading log corrections are generated for λ 1 , . . . λ 4 . In addition, threshold corrections proportional to A t , A b and µ can contribute significant corrections to all the scalar potential parameters λ 1 . . . , λ 7 . † † Explicit formulae can be found in H.E. Haber and R. Hempfling, “The Renormalization group improved Higgs sector of the minimal supersymmetric model,” Phys. Rev. D48 , 4280 (1993).

� H 1 H 1 H 1 � H 1 Q U ∝ s 3 β c β X 3 � � t Y t � � Q Q U U � H 1 H 2 H 1 � H 2 Q U H 1 H 1 � H 1 � H 1 Q U ∝ s 3 β c β X 2 � � Q U t � H 2 � H 2 Q U H 1 H 1 H 1 H 1 � H 1 � H 1 Q U ∝ s 3 � β c β X t Y t � Q U � H 1 � H 1 Q U H 2 H 2 Threshold Corrections to Z 6