K. Cheung 1 Light Pseudoscalar Higgs boson in NMSSM Kingman Cheung NTHU, December 2006 (with Abdesslam Arhrib, Tie-Jiun Hou, Kok-Wee Song, hep-ph/0606114
K. Cheung 2 Outline Motivations for NMSSM The scenario of a very light A 1 in the zero mixing limit Various phenomenology of the light A 1 Associated production with a pair of charginos Predictions at the ILC and LHC
K. Cheung 3 Little hierarchy problem in SUSY Higgs boson mass m H > 115 GeV. From the radiative corrections to m 2 H: ( m 2 H m 2 Z + 3 m 2 t 4π 2 y2 t m 2 t ln we require m t > 1000GeV. RGE effect from M GUT to M weak : We need to obtain m 2 t m 2 H u 3 4π 2 y2 t m 2 t ln ( MGUT M weak m 2 t O(100 2 GeV 2 = (1000 GeV 2 (990 GeV 2 a fine tuning of O(10 2.
K. Cheung 4 Various approaches to the Little hierarchy problem Little Higgs models (Arkani et al., with T parity (Cheng, Low Twin Higgs models (Chacko et al. Reducing the h b b branching ratio, or the ZZh couplings, such that the LEPII production rate is reduced. To evade the LEP II bound. Add singlets to MSSM NMSSM or other variants. By reducing the RGE effects on m 2 H, µ, B terms (e.g., mixed modulus-anomaly mediation, K. Choi et al.
K. Cheung 5 Motivations for NMSSM 1. Relieve the fine tuning in the little hierarchy problem (Dermisek and Gunion 2005. 2. Additional decay modes available to the Higgs boson such that the LEP bound could be evaded. 3. A natural solution to the µ problem. 4. More particle contents in the Higgs sector and in the neutralino sector. Here we are interested in a decouple scenario the extra pseudoscalar boson entirely decouples from the MSSM pseudoscalar.
K. Cheung 6 Fine Tuning of NMSSM (Dermisek,Gunion 2005 + : dominance of h 1 A 1 A 1, : m h1 > 114 GeV (evade the LEP constraint F = Max a d log m Z d log a, a = µ, B µ,...
K. Cheung 7 The NMSSM Superpotential Superpotential: W = h u ˆQ Ĥ u Û c h d ˆQ Ĥ d ˆDc h e ˆL Ĥ d Ê c + λŝ Ĥu Ĥd + 1 3 κ Ŝ3. When the scalar field S develops a VEV S = v s / 2, the µ term is generated µ eff = λ v s 2 Note that the W has a discrete Z 3 symmetry, which is used to avoid the Ŝ and Ŝ2 terms. The Z 3 symmetry may cause domain-wall problem, which can be solved by introducing nonrenormalizable operators at the Planck scale to break the Z 3 symmetry through the harmless tadpoles that they generate.
K. Cheung 8 Higgs Sector Higgs fields: ( ( H u = H + u, H d = H 0 d, S. H 0 u H d Tree-level Higgs potential: V = V F + V D + V soft : V F = λs 2 ( H u 2 + H d 2 + λh u H d + κs 2 2 V D = 1 8 (g2 + g 2 ( H d 2 H u 2 2 + 1 2 g2 H u H d 2 V soft = m 2 Hu H u 2 + m 2 H H d 2 + m 2 d S S 2 + [λa λ SH u H d + 1 3 κa κs 3 + h.c.] Minimization of the Higgs potential links M 2 Hu, M 2 H, M 2 d S H u, H d, S. with VEV s of
K. Cheung 9 In the electroweak symmetry, the Higgs fields take on VEV: H d = 1 2 ( vd 0, H u = 1 2 ( 0 v u, S = 1 2 v s Then the mass terms for the Higgs fields are: V = + 1 2 + 1 2 ( H + d H+ u M 2 charged ( (ImH 0 d ImH0 u ImS (ReH 0 d ReH0 u ReS H d H u M 2 pseudo M 2 scalar ImH0 d ImH 0 u ImS ReH0 d ReH 0 u ReS
K. Cheung 10 We rotate the charged fields and the scalar fields by the angle β to project out the Goldstone modes. We are left with V mass = m 2 H ± H + H + 1 2 (P 1 where M 2 P 11 = M 2 A, P 2 M 2 P M 2 P 12 = M 2 P 21 = 1 2 cot β s ( P 1 + 1 P 2 2 (S 1 S 2 S 3 M 2 S ( M 2 A sin 2β 3λκv2 s M 2 P 22 = 1 4 sin 2β cot2 β s (M 2 A sin 2β + 3λκv2 s, 3 2 κa κ v s, S 1 S 2 S 3 with M 2 A = λv s sin 2β ( 2Aλ + κv s The charged Higgs mass: M 2 H ± = M 2 A + M 2 W 1 2 λ2 v 2
K. Cheung 11 Pseudoscalar Higgs bosons The pseudoscalar fields, P i (i = 1, 2, is further rotated to mass basis A 1 and A 2, through a mixing angle: ( A 2 A 1 = ( ( cos θ A sin θ A P 1 P 2 with tan θ A = M 2 P 12 M 2 P 11 m2 A 1 = 1 2 cot β s M 2 A sin 2β 3λκv2 s M 2 A m2 A 1 In large tan β and large M A, the tree-level pseudoscalar masses become m 2 A 2 M 2 A (1 + 1 4 cot2 β s sin 2 2β, m 2 A 1 3 2 κv s A κ
K. Cheung 12 Small m A1 and tiny mixing θ A A very light m A1 is possible if κ 0 and/or A κ 0 while keeping v s large enough. It is made possible by a PQ-type symmetry. Also, tan θ A in the limit of small m A1 becomes θ A tan θ A 1 2 cot β s sin 2β v v s tan β For a sufficiently large tan β and v s we can achieve θ A < 10 3.
K. Cheung 13 Parameters of NMSSM Parameters in addition to MSSM: We trade We also trade λ, κ (in the superpotential A λ, A κ (in V soft v s λ, v s λ, µ eff because λv s / 2 = µ κ, A λ, A κ M 2 A, M 2 A 1, θ A Therefore, we use the following inputs: µ, M 2 A 1, θ A, M 2 A µ determines the chargino sector, M 2 A 1 and θ A directly determines the decay and production of A 1.
K. Cheung 14 Pseudoscalar couplings with fermions The coupling of the pseudoscalars A i to fermions L Aq q = i gm d 2m W tan β ( cos θ A A 2 + sin θ A A 1 dγ 5 d, i gm u 2m W 1 tan β ( cos θ AA 2 + sin θ A A 1 ūγ 5 u The coupling of A i to charginos comes from the usual Higgs-Higgsino-gaugino source and, specific to NMSSM, from the term λŝĥ u Ĥ d in the superpotential: where L Aχ + χ + = i χ + i ( C ij P L C ji R P + χ j A 2 + i χ + i ( D ij P L D ji P R χ + j A 1, C ij = D ij = g (cos β cos θ A U i1 V j2 + sin β cos θ A V j1 U i2 λ sin θ A U i2 V j2, 2 2 g 2 ( cos β sin θ A U i1 V j2 sin β sin θ A V j1 U i2 λ 2 cos θ A U i2 V j2
K. Cheung 15 Phenomenology of a light pseudoscalar boson g 2 Production via B decays Decay of A 1 H A 1 A 1 Associated production of A 1
K. Cheung 16 g 2 Light pseudoscalar boson contributes largely at 1-loop and 2-loop levels: A 1 µ µ γ We can have t, b, τ, χ + i in the upper loop.
K. Cheung 17 One-loop contribution: a A i µ,1 = α em 8π sin 2 θ w 2 mµ M 2 W m 2 ( µ M 2 A i λ A i µ ( 2 m 2 µ FA M 2 A i where F A (z = 1 The two-loop contributions: a A i µ,2 (f = 0 f=t,b,τ dx x 3 zx 2 x + 1, λa 1 µ = tan β sin θ A N f c α2 2 m em µ λa i µ 8π 2 sin 2 θ w M 2 W Q 2 f λa i f ( m 2 f m 2 f m 2 G A m 2 A i A i, where G A (z = 1 0 dx a A i µ,2 ( χ+ j = α 2 2 m em 4π 2 sin 2 θ w 1 x(1 x z µ λa i µ m W G A i jj ln x(1 x z m χ j m 2 A i G A ( m 2 χj m 2 A i where G A 1 jj = D jj/g, G A 2 jj = C jj/g.
K. Cheung 18 In the limit of very small mixing: M 2 P = M 2 A ( 1 ɛ ɛ δ, where ɛ, δ 1. In this case, the mass of A 1 and A 2, and the mixing angle θ A are given by m 2 A M 2 2 A (1 + ɛ2, m 2 A M 2 1 A δ, θ A ɛ The A 1 couplings simplify to A 1 χ + i χ + i λ 2 U i2 V i2 γ5, A 1 ūu gm u 2m W ɛ cot βγ 5, A 1 dd gm d 2m W ɛ tan βγ 5 (a A 1 (b γ A 1 χ ± i γ The leading contribution in ɛ is with χ + 1 in the upper loop.
K. Cheung 19 The Barr-Zee chargino loop contribution becomes a A 1 µ,2 ( χ+ 1,2 = λɛ tan βm2 µ 2πs W m 2 W ( α 2π 3 2 2 i=1 m W m χ + i U i2v i2 [ 1 + log ] + m χ i m A1 With the known SM values and the chargino mass at the electroweak scale M EW, λ and U, V are O(1, a A 1 µ,2 2.5 10 11 ( ɛ tan β log M EW m A1 sign(ɛλ a A 1 µ,2 < 10 11 for ɛ < 10 3 The g 2 constraint can be safely satisfied if sin θ A is small enough.
K. Cheung 20 Production via B meson decays b sa 1 : (Hiller 2004 She studied b sγ, b sa 1, and b sll, A 1 masses down to 2m e cannot be excluded from these constraints. In Upsilon and J/ψ decays: (Gunion, Hooper, McElrath 2005 Γ(V γa 1 Γ(V µ + µ = G F m 2 b 2απ (1 M 2 A 1 M 2 V where X = tan β(cot β for Υ (ψ. X 2 sin 2 θ A
K. Cheung 21 Decays of a light A 1 q A 1 q A 1 q g γ γ, g A 1 χ ± i A 1 q A 1 decays through mixing with the MSSM-like A 2 into q q, l + l, gg A 1 χ + χ and χ 0 χ 0 if kinematically allowed. In zero-mixing and very light, via chargino loop, A 1 γγ
K. Cheung 22 Partial Decay widths The partial widths of A 1 into f f, γγ and gg are given by Γ(A 1 f f = N c G µ m 2 f 4 2π (λa 1 f 2 M A1 (1 4m 2 f /M 2 A 1 1/2 Γ(A 1 γγ = G µα 2 M 3 A 1 128 2π 3 Γ(A 1 gg = G µα 2 s M 3 A 1 64 2π 3 f q N c Q 2 f λa 1 f f(τ f + 2 λ A 1 f f(τ q 2 2 i=1 M W m χ ± i λ A 1 χ f(τ ± i χ i 2 where λ A 1 d,l = sin θ A tan β, λ A 1 u λ A 1 χ i = D ii /g. = sin θ A cot β, and the chargino-a 1 coupling
K. Cheung 23 Br(A 1 -->xx 1 0.1 0.01 0.001 1e-04 1e-05 1e-06 1e-07 1e-08 ee γγ M A1 =0.1 GeV, tan β=10 1e-05 1e-04 0.001 0.01 0.1 1 sinθ A Br(A 1 -->xx 1 0.1 0.01 0.001 0.0001 1e-05 1e-06 1e-07 1e-08 1e-09 ee γγ M A1 =0.1 GeV, tan β=30 1e-05 0.0001 0.001 0.01 0.1 1 ε Br(A 1 -->xx 1 0.1 0.01 0.001 1e-04 1e-05 ττ cc γγ gg M A1 =5 GeV, tan β=10 1e-06 1e-05 1e-04 0.001 0.01 0.1 1 sinθ A Br(A 1 -->xx 1 0.1 0.01 0.001 0.0001 1e-05 1e-06 1e-07 1e-08 M A1 =15 GeV, tan β=30 1e-05 0.0001 0.001 0.01 0.1 1 ε bb cc γγ gg
K. Cheung 24 1 0.1 ε=10-4, tan β=3 Br(A 1 -->xx 0.01 0.001 0.0001 ττ cc γγ gg 1e-05 0.001 0.01 0.1 1 λ Br(A 1 -->xx 1 0.1 0.01 0.001 0.0001 1e-05 1e-06 1e-07 bb µµ ττ γγ gg ε=10-4 1 10 100 M A1 (GeV Br(A 1 -->xx 1 0.1 0.01 0.001 0.0001 1e-05 bb µµ ττ γγ gg ε=10-3 1 10 100 M A1 (GeV
K. Cheung 25 Production: H A 1 A 1 Even in the zero-mixing limit, the A 1 can still couple to the Higgs boson via λa λ SH u H d term. So A 1 can be produced in the decay of the Higgs boson (Dermisek,Gunion 2005; Dobrescu, Landsberg, Matchev 2001 h A 1 A 1 4γ, 4τ Since A 1 is very light and so energetic that the two photons are very collimated. It may be difficult to resolve them. Effectively, like h γγ. If the mixing angle is larger than 10 3 and A 1 is heavier than a few GeV, it can decay into τ + τ. Thus, 4τs in the final state (Graham, Pierce, Wacker 2006.
K. Cheung 26 Associated production with a pair of charginos χ + 1 χ + 1 γ, Z A 1 γ, Z A 1 χ 1 χ 1 We consider the associated production of A 1 with a chargino pair. The A 1 radiates off the chargino leg and so will be less energetic. The two photons from A 1 decay is easier to be resolved. The charginos can decay into a charged lepton or a pair of jets plus missing energy. Therefore, the final state can be 2 charged leptons + a pair of photons + E T A charged lepton + 2 jets + a pair of photons + E T 4 jets + a pair of photons The leptonic branching ratio can be large if ν or l is light.
K. Cheung 27 Rate dependence In the zero-mixing limit, the size of χ + 1 -A 1 coupling: λ 2 cos θ A U 12 V 12 It implies a larger higgsino component of χ + 1 section. We choose can enhance the cross µ = 150 GeV M 2 = 500 GeV The other parameters are λ = 1, sin θ A = 10 4, tan β = 10 Little dependence on tan β and sin θ A as long as it is small.
K. Cheung 28 Cross Section at e + e colliders 1 Cross Section (fb 0.9 0.8 0.7 0.6 0.5 E CM = 0.5 TeV 1 TeV 1.5 TeV e - e + -> χ + 1 χ- 1 A 1 µ=150 GeV, M 2 =500 GeV λ=1, sin θ A = 10-4 0.4 0.3 0 5 10 15 20 25 30 35 40 45 50 (GeV M A1 µ = 150 GeV, M 2 = 500 GeV, tan β = 10, λ = 1, sin θ A = 10 4
K. Cheung 29 Cross Section at the LHC Cross Section (fb 0.9 0.8 0.7 0.6 0.5 LHC χ + 1 χ- 1 A 1 Production µ = 150 GeV, M 2 = 500 GeV λ = 1, sin θ A = 10-4 0.4 0.3 0 5 10 15 20 25 30 35 40 45 50 (GeV M A1 µ = 150 GeV, M 2 = 500 GeV, tan β = 10, λ = 1, sin θ A = 10 4.
K. Cheung 30 Resolving the two photons The crucial part is to resolve the γγ pair from A 1 decay, otherwise it would look a single photon. We impose p Tγ > 10 GeV η γ < 2.6 which are in accord with the ECAL of the CMS detector The preshower detector of the ECAL has a strong resolution to resolve the γγ pair. It is intended to separate the background π 0 γγ decay from the H γγ. It has a resolution as good as 6.9 mrad Then we look at the angular separation of the two photons
K. Cheung 31 Opening angle distribution 10-1 LHC p Tγ > 10 GeV, y γ < 2.6 dσ/d sin θ γγ (pb 10-2 10-3 M A1 = 5 GeV M A1 = 1 GeV M A1 = 0.1 GeV 10-4 0 0.02 0.04 0.06 0.08 0.1 sin θ γγ
K. Cheung 32 Cross sections in fb for associated production of χ + 1 χ 1 A 1 followed by A 1 γγ. The cuts applied to the two photons are: p T γ > 10 GeV, y γ < 2.6, and θ γγ > 10 mrad. M A1 ( GeV Cross Section (fb 0.1 0.0 0.2 0.011 0.3 0.0405 0.4 0.078 0.5 0.12 1 0.26 2 0.38 3 0.42 4 0.44 5 0.44
K. Cheung 33 Conclusions 1. NMSSM can have a very light pseudoscalar Higgs boson, which has very small mixing with the MSSM pseudoscalar. 2. Such a light A 1 may be hidden in the Higgs decay h A 1 A 1 such that the LEP bound on the Higgs is evaded. 3. It can survive the constraints from K and B decays, such as b sa 1, B s µ + µ, B B mixing, Υ A 1 γ by taking the mixing angle θ A 0. 4. Associated production of A 1 with a chargino or a neutralino pair can reveal the A 1 even in the zero mixing. 5. The signature can be: 2l + 2γ+ E T. The event rates are sizable for detectability.