Decoupling and Alignment in Light of the Higgs Data Howard E. Haber Pi Day, 2014 Bay Area ParCcle Physics Seminar San Francisco State Univ.
Outline I. IntroducCon Ø Snapshot of the LHC Higgs data Ø SuggesCons of a SM- like Higgs boson II. Decoupling and alignment limits of the 2HDM Ø Tree- level consideracons Ø Loop correccons III. ApplicaCon to the MSSM Higgs sector Ø Is the alignment limit allowed by the data? IV. The wrong- sign Yukawa coupling regime Ø Can this be ruled out at the LHC?
The Higgs boson discovered on the 4 th of July 2012 Ø Is it the Higgs boson of the Standard Model? Ø Is it the first scalar state of an enlarged Higgs sector? Ø Is it a premonicon for new physics beyond the Standard Model at the TeV scale? Let s look at a snapshop of the current LHC Higgs data.
* ATLAS Preliminary not in combination ** CMS Preliminary not in combination ATLAS -1 s = 7 TeV: Ldt 4.8 fb -1 s = 8 TeV: Ldt 20.7 fb CMS Prel. -1 s = 7 TeV: Ldt 5.1 fb -1 s = 8 TeV: Ldt 19.6 fb m = 125.5 GeV = 125.7 GeV H m H W,Z H bb µ = 0.2 ± 0.7 A3* µ = 1.15 ± 0.62 C1 H µ = 1.4 +0.5-0.4 A2* µ = 1.10 ± µ = 7 ± 0.41 C1 0.29 C6** (*) H WW l l µ = 0.99 +0.31-0.28 A1 µ = 0.68 ± 0.20 C1 (*) H ZZ llll µ = 1.43 +0.40-0.35 A1 µ = 0.92 ± 0.28 C1 H µ = 1.55 +0.33-0.28 A1 µ = 0.77 ± 0.27 C1 Combined µ = 1.33 +0.21-0.18 A1 µ = 0 ± 0.14 C1-1 0 1 2-1 0 1 2 Best fit signal strength (µ)
Even with the limited Higgs data set, it is fair to say that this is a Standard Model like Higgs boson. F 6 4 Tevatron T1 95% C.L. 68% C.L. Loc. Min. ATLAS A1 95% C.L. 68% C.L. Best Fit CMS Prel. C1 95% C.L. 68% C.L. Best Fit Stand. Model g 1.6 1.4 ATLAS A1 95% C.L. 68% C.L. Best Fit CMS Prel. C1 95% C.L. 68% C.L. Best Fit Stand. Model 2 1.2 0 1-2 -4 0.6 0.4 0.6 1 1.2 1.4 1.6 1.8 V 0.4 0.6 1 1.2 1.4 1.6 1.8
Any theory that introduces new physics beyond the Standard Model (SM) must contain a SM- like Higgs boson. This constrains all future model building. In this talk I will exhibit how this constraint impacts the two- Higgs doublet Model (2HDM), which will be a stand- in for a general extended Higgs sector or a supersymmetric extension of the SM, which requires at least two Higgs doublet fields.
The 2HDM with a SM-like Higgs boson Typically, none of the scalar states of the 2HDM will resemble a SM-Higgs boson. However, a SM-like Higgs boson (h SM ) can arise in two different ways: The decoupling limit (Haber and Nir 1990, Gunion and Haber 2003) All but one of the scalar states (h) are very heavy (M m h ). Integrating out the heavy states below the mass scale M yields an effective one-higgs-doublet theory i.e. the Standard Model, and h h SM. The alignment limit (Craig, Galloway and Thomas 2013, Haber 2013) In the Higgs basis {H 1, H 2 }, the vev v = 246 GeV resides completely in the neutral component of one of the Higgs doublets, H 1. In the limit where the mixing between H 1 and H 2 in the mass matrix goes to zero, one of the neutral mass eigenstates aligns with Re(H1 0 v). This state h is nearly indistinguishable from the SM Higgs boson.
Example: the 2HDM with a softly-broken Z 2 symmetry V = m 2 11Φ 1 Φ 1 + m 2 22Φ 2 Φ 2 ( ) m 2 12Φ 1 Φ 2 + h.c. +λ 3 Φ 1 Φ 1Φ 2 Φ 2 + λ 4 Φ 1 Φ 2Φ 2 Φ 1 + + 1 2 λ 1 [ ( 1 2 λ 5 Φ 1 Φ 2 ( 2 ( ) 2 Φ 1 1) Φ + 1 2 λ 2 Φ 2 Φ 2 ) ] 2 + h.c., such that Φ 0 a = v a / 2 (for a = 1, 2), and v 2 v1 2 + v2 2 = (246 GeV) 2. The m 2 12 term of the Higgs potential softly breaks the discrete symmetry Φ 1 +Φ 1, Φ 2 Φ 2. This discrete symmetry can be extended to the Higgs-fermion Yukawa interactions in a number of different ways. Φ 1 Φ 2 U R D R E R U L, D L, N L, E L Type I + + Type II (MSSM like) + + + + Type X (lepton specific) + + + Type Y (flipped) + + + Four possible Z 2 charge assignments that forbid tree-level Higgs-mediated FCNC effects.
The Higgs basis of the CP-conserving softly-broken Z 2 symmetric 2HDM Assume m 2 12, λ 5 real and a CP-conserving vacuum. Define Higgs basis fields, ( ) ( ) H 1 + H 1 = v 1Φ 1 + v 2 Φ 2 H 2 +, H H1 0 2 = v 2Φ 1 + v 1 Φ 2, v H2 0 v so that H 0 1 = v/ 2 and H 0 2 = 0. The Higgs basis is uniquely defined up to H 2 H 2. In the Higgs basis, the scalar potential is given by: V = Y 1 H 1 H 1 + Y 2 H 2 H 2 + [Y 3 H 1 H 2 + h.c.] + 1 2 Z 1(H 1 H 1) 2 + 1 2 Z 2(H 2 H 2) 2 + Z 3 (H 1 H 1)(H 2 H 2) + Z 4 (H 1 H 2)(H 2 H 1) { 1 + 2 Z 5(H 1 H 2) 2 + [ Z 6 (H 1 H 1) + Z 7 (H 2 H 2) ] } H 1 H 2 + h.c.. Scalar potential minimum conditions are: Y 1 = 1 2 Z 1v 2, Y 3 = 1 2 Z 6v 2, leaving Y 2 as the only free squared-mass parameter of the model.
We define tan β = v 2 /v 1, c β cos β, s β sin β, etc. Z 1 λ 1 c 4 β + λ 2s 4 β + 2(λ 3 + λ 4 + λ 5 )s 2 β c2 β, Z 2 λ 1 s 4 β + λ 2c 4 β + 2(λ 3 + λ 4 + λ 5 )s 2 β c2 β, Z i (λ 1 + λ 2 2λ 3 2λ 4 2λ 5 )s 2 β c2 β + λ i, for i = 3, 4, 5, Z 6 s β c β [ λ1 c 2 β λ 2s 2 β (λ 3 + λ 4 + λ 5 )c 2β ], Z 7 s β c β [ λ1 s 2 β λ 2c 2 β + (λ 3 + λ 4 + λ 5 )c 2β ]. Mass eigenstates: CP-even scalars: h and H (with Higgs mixing angle α), CP-odd scalars: A, charged Higgs pair: H ±. Some useful relations: Z 1 v 2 = m 2 h s2 β α + m2 H c2 β α, Z 3 v 2 = 2(m 2 H ± Y 2 ), Z 4 v 2 = m 2 h c2 β α + m2 H s2 β α + m2 A 2m2 H ± Z 5 v 2 = m 2 h c2 β α + m2 H s2 β α m2 A Z 6 v 2 = (m 2 H m2 h )s β αc β α.
Decoupling and alignment limits of the 2HDM Adopt a convention where 0 β 1 2π and 0 β α π. Since g hv V g hsm V V = s β α, where V = W ± or Z, it follows that h is SM-like in the limit of c β α 0. In light of: c 2 β α = Z 1v 2 m 2 h m 2 H m2 h s β α c β α = Z 6v 2 m 2 H m2 h where Z 1 /(4π), Z 6 /(4π) < 1 (tree-level unitarity limit), we see that decoupling limit: m H m h (i.e., Y 2 v) = m H m A m H ± v,. alignment limit: Z 6 1. m 2 h Z 1v 2 ) Then, H, A, H ± need not be heavy (and
Since g HV V g hsm V V = c β α, where V = W ± or Z, it follows that H is SM-like in the limit of s β α 0. This is not compatible with the decoupling limit, but is an allowed possibility in the alignment limit. This case is not completely ruled out by Higgs data. But, henceforth, we focus on the case of c β α 1, in which case h h SM. In the decoupling or alignment limits, all tree-level couplings of h approach their SM values. Consider the Type-II Yukawa coupling to up-type and down-type fermions, relative to their SM values: hdd : huu : sin α cos β = s β α c β α tan β, cos α sin β = s β α + c β α cot β. delayed decoupling: if c β α 1 but c β α tan β O(1), then it is possible to see deviations of the hdd coupling from its SM value while all other h couplings to SM particles show no deviations.
Finally, the hhh and hhhh couplings also approach their SM values in the decoupling or alignment limits. For example, in the softly broken Z 2 symmetric 2HDM, g hhh = 3v [ ] s 2 s β c β (c β c 3 β c2 α s β s 3 α)m 2 h c 2 β αc β+α m 2 12, β and it is easy to check that for s β α = 1, we have c α = s β and s α = c β. Hence, in the decoupling and alignment limits, g hhh g SM hhh = 3vm 2 h. In a more general (CP-conserving) 2HDM, g hhh = 3v [ Z 1 s 3 β α + 3Z 6 c β α s 2 β α + (Z 3 + Z 4 + Z 5 )s β α c 2 β α + Z 7 c 3 β α], = g SM hhh[ 1 + 3(Z6 /Z 1 )c β α + O(c 2 β α) ]. Since c β α Z 6 v 2 /(m 2 H m2 h ), we see that the approach to the alignment limit is faster than to the decoupling limit (and similarly for the hhhh coupling).
The decoupling and alignment limits beyond tree level decoupling limit: The corrections to the exchange of H, A, and H ± is suppressed by terms of O(v 2 /M 2 ), where M m H m A m H ±, relative to the SM radiative corrections. alignment limit: Since the masses of H, A, and H ± need not be heavy, loops mediated by these particles can compete with the SM radiative corrections. Thus, we have found two instances where the decoupling and alignment limits can be distinguished in principle. Of course, the primary technique for distinguishing between these two limiting cases is to discover the some of the non-minimal Higgs states (H, A, and H ± ), whose masses may not be significantly larger than m h.
example: the H ± loop contribution to h γγ In a general CP-conserving 2HDM, g hh + H = v[ Z 3 s β α +Z 7 c β α ] O(v). Specializing to the softly-broken Z 2 symmetric 2HDM, g hh + H = 1 v [ (2m 2 A 2m 2 H ± m 2 h λ 5 v 2) s β α + ( m 2 A m 2 h + λ 5 v 2) ] (cot β tan β)c β α. Since m 2 A m2 H ± = 1 2 v2 (λ 5 λ 4 ), and m 2 A c β α O(v 2 ) in the decoupling limit, we see that the above expression is consistent with g hh + H O(v). But, there exists a regime where Z 3 and Z 7 are approaching their unitarity bounds such that g hh + H O(m2 H ± /v). In this case, the H ± loop contribution to the h γγ decay amplitude is approximately constant. This is analogous to the non-decoupling contribution of the top-quark in a regime where m t > m h unitarity bound. but the Higgs top Yukawa coupling lies below its
The alignment limit of the MSSM Higgs sector The Higgs sector of the SM is a softly-broken Z 2 symmetric 2HDM with additional relations imposed by SUSY on the quartic Higgs potential parameters. In terms of the Z i, we have: Z 1 = Z 2 = 1 4 (g2 + g 2 ) cos 2 2β, Z 3 = Z 5 + 1 4 (g2 g 2 ), Z 4 = Z 5 1 2 g2, Z 5 = 1 4 (g2 + g 2 ) sin 2 2β, Z 7 = Z 6 = 1 4 (g2 + g 2 ) sin 2β cos 2β, There is no phenomenologically relevant alignment limit at tree-level since Z 6 v 2 = 1 2 m2 Z sin 4β is not that much smaller than m2 h for sensible values of tan β. But at one-loop order, each of the Z i receive radiative corrections, Z i. Non-decoupling contributions exist (with tan β enhancements), since below M SUSY the low-energy effective theory is a general 2HDM. Is it possible to have for a suitably chosen tan β? 1 4 (g2 + g 2 ) sin 2β cos 2β + Z 6 0,
The following approximate expressions were obtained by M. Carena, I. Low, N.R. Shah and C.E.M. Wagner, arxiv:1310.2248, where L 12 1 32π 2 L 12 + L 11 tan β m2 h + m2 Z v2 ( L 11 + L 12 ) v 2 L 12, [ h 4 t 3 µ 2 16π 2 M 2 SUSY µa t M 2 SUSY [ h 4 t ( A 2 t M 2 SUSY ) 6 ( 1 A2 t 2M 2 SUSY ) + h 4 b + h 4 b µ 3 A b M 4 SUSY ], ( 1 A2 b 2M 2 SUSY )], and the τ contributions have been omitted. Can the MSSM alignment region be ruled out by LHC Higgs data? Using recent data from the CMS collaboration, and working in collaboration with M. Carena, I. Low, N.R. Shah and C.E.M. Wagner, we have examined various MSSM Higgs scenarios and checked whether they survive the CMS limits.
-1-1 CMS Preliminary, H ττ, 4.9 fb at 7 TeV, 19.7 fb at 8 TeV tanβ max h M SUSY MSSM m scenario = 1 TeV 10 95% CL Excluded: observed SM H injected expected ± 1σ expected ± 2σ expected LEP 1 100 200 300 400 1000 m A [GeV]
shbbhêa+gghêal BRHHêA Æ t tl H8 TeVL 50 shbbhêa+gghêal BRHHêA Æ t tl H8 TeVL 50 40 40 tan b 30 m max h, m = 400 GeV m max h, m = 800 GeV m max h, m = 2 TeV tan b 30 m h max, m = 400 GeV m h max, m=200 GeV 20 m h max, m=200 GeV 20 10 10 200 300 400 500 600 700 800 m A HGeVL 200 300 400 500 600 700 800 m A HGeVL shbbhêa+gghêal BRHHêA Æ t tl H8 TeVL 50 shbbhêa+gghêal BRHHêA Æ t tl H8 TeVL 50 40 40 tan b 30 20 m h max, m = 800 GeV m h max, m=200 GeV tan b 30 20 m h max, m = 2 TeV m h max, m=200 GeV 10 10 200 300 400 500 600 700 800 m A HGeVL 200 300 400 500 600 700 800 m A HGeVL
shbbhêa+gghêal BRHHêA Æ t tl H8 TeVL 50 shbbhêa+gghêal BRHHêA Æ t tl H8 TeVL 50 40 40 tan b 30 m h max, m=200 GeV m h alt, m=200 GeV tan b 30 m h max, m = 400 GeV m h alt, m=400 GeV 20 20 10 10 200 300 400 500 600 700 800 m A HGeVL 200 300 400 500 600 700 800 m A HGeVL shbbhêa+gghêal BRHHêA Æ t tl H8 TeVL 50 shbbhêa+gghêal BRHHêA Æ t tl H8 TeVL 50 40 1.2 40 1.2 tan b 30 m h max, m = 800 GeV m h alt, m=800 GeV tan b 30 m h max, m = 2 TeV m h alt, m=2 TeV 20 20 10 10 200 300 400 500 600 700 800 m A HGeVL 200 300 400 500 600 700 800 m A HGeVL
Wrong-sign Yukawa couplings Returning to the (non-susy) softly-broken Z 2 symmetric 2HDM with Type-II Higgs-fermion Yukawa couplings, we had hdd : huu : sin α cos β = s β α c β α tan β, cos α sin β = s β α + c β α cot β. We noted the phenomenon of delayed decoupling where c β α tan β O(1). Suppose nature were devious and chose (recall that 0 β α π) s β α c β α tan β = 1 + ɛ. where we allow for a small error ɛ (the precision of the experimental measurement). For ɛ = 0, the partial widths of h b b and h τ + τ would be the same as in the SM. Could we experimentally distinguish the case of the wrong-sign hdd coupling from the SM Higgs boson?
Note that the wrong-sign hdd Yukawa coupling arises when tan β = 1 + s β α ɛ c β α 1, under the assumption that the hv V coupling is SM-like. It is convenient to rewrite: hdd : huu : sin α cos β = s β+α + c β+α tan β, cos α sin β = s β+α + c β+α cot β. Thus, the wrong-sign hdd Yukawa coupling actually corresponds to s β+α = 1. Indeed, one can check that s β+α s β α = 2(1 ɛ) cos 2 β, which shows that the regime of the wrong-sign hdd Yukawa is consistent with a SM-like h for tan β 1.
In collaboration with P. Ferreira, J.F. Gunion and R. Santos, we have scanned the 2HDM parameter space, imposing theoretical constraints, direct LHC experimental constraints, and indirect constraints (from precision electroweak fits, B physics observables, and R b ). The latter requires that m H ± > 340 GeV in the Type-II 2HDM. Given a final state f resulting from Higgs decay, we define µ h f(lhc) = σ2hdm (pp h) BR 2HDM (h f) σ SM (pp h SM ) BR(h SM f). Our baseline will be to require that the µ h f (LHC) for final states f = W W, ZZ, b b, γγ and τ + τ are each consistent with unity within 20% (blue), which is a rough approximation to the precision of current data. We will then examine the consequences of requiring that all the µ h f (LHC) be within 10% (green) or 5% (red) of the SM prediction.
The main effects of the wrong-sign hdd coupling is to modify the hgg and hγγ loop amplitudes due to the interference of the b-quark loop with the t-quark loop (and the W loop in the case of h γγ). In addition, the possibility of a contributing non-decoupling charged Higgs contribution can reduce the partial width of h γγ by as much as 10%. The absence of a red region for sin α > 0 (the wrong-sign hdd Yukawa regime) demonstrates that a precision in the Higgs data at the 5% level is sufficient to rule out this possibility.
The Yukawa coupling ratio κ D = h 2HDM D /h SM D with all µh f (LHC) within 20% (blue) and 10% (green) of their SM values. If one demands consistency at the 5% level, no points survive. As the Higgs data requires h to be more SM-like (and s β α is pushed closer to 1), the value of tan β required to achieve the wrong-sign hdd coupling becomes larger and larger, and κ D is forced to be closer to 1.
Γ(h gg) 2HDM /Γ(h SM gg) as a function of κ D = h 2HDM D /h SM D with all µh f (LHC) within 20% (blue), 10% (green) and 5% (red) of their SM values. Left panel: sin α < 0. Right panel: sin α > 0. Remarkably, despite the large deviation in the h gg partial width in the wrong-sign hdd coupling regime, the impact on σ(gg h) is significantly less due to NLO and NNLO effects. Indeed, M. Spria finds σ(gg h) NNLO /σ(gg h SM ) NNLO 1.06 while the ratio of partial widths, Γ(h gg)/γ(h SM gg) does not suffer any significant change going from leading order to NNLO.