$\Upsilon\to\gamma A_1$ in the NMSSM at large tan beta

We investigate the effects of the radiatively-generated tan beta-enhanced Higgs-singlet Yukawa couplings on the decay $\Upsilon\to \gamma A_1$ in the NMSSM, where $A_1$ is the lightest CP-odd scalar. This radiative coupling is found to dominate in the case of a highly singlet Higgs pseudoscalar. The branching ratio for the production of such a particle is shown to be within a few orders of magnitude of current experimental constraints across a significant region of parameter space. This represents a potentially observable signal for experiments at present B-factories.

The Next to Minimal Supersymmetric extension of the Standard Model (NMSSM) is a well-motivated model of electroweak symmetry breaking which resolves both the hierarchy problem of the Standard Model (SM) and µ problem of the Minimal Supersymmetric extension of the Standard Model (MSSM) in a natural way [1].The µ parameter of the MSSM is replaced with an additional gauge singlet Higgs superfield Ŝ and an effective doublet mixing term µ eff is generated when the singlet field acquires a vacuum expectation value (VEV).It has long been known that the NMSSM suffers from the formation of electroweak scale cosmic domain walls [2], although mechanisms to resolve this problem have been suggested, e.g.[3].In the NMSSM, all parameters are naturally predicted to be of the order the SUSY-breaking scale M SUSY .
The Higgs sector of the NMSSM may be derived from the superpotential of the model, given by where Ĥ1 ( Ĥ2 ) is the doublet Higgs superfield which gives masses to the down-type quarks and leptons (up-type quarks).The corresponding soft SUSY-breaking terms are given by where Φ 1,2 and S are the scalar components of Ĥ1,2 and Ŝ respectively.At tree level only two further parameters are required, the ratio of doublet VEVs tan β = v 2 v 1 and the effective doublet mixing parameter µ eff = λv S √ 2 .Radiative corrections due to the quarks and scalar quarks of the third generation must also be included in order to raise the mass of the SM-like Higgs H 1 above the LEP bound of 114 GeV. 1   The superpotential of the NMSSM exhibits a global U(1) R symmetry which is spontaneously broken when S, the scalar component of Ŝ, acquires a VEV.In addition, it is explicitly broken by the soft trilinear couplings A λ , A κ [4].The CP-odd scalar component of Ŝ is therefore a pseudo-Goldstone boson of this symmetry, and is massless in the limit A λ , A κ → 0. For small values of the trilinear couplings, the lightest pseudoscalar in the NMSSM spectrum can therefore naturally be very light and highly gauge singlet in nature.Typically this requires A λ ∼ 200 GeV, A κ ∼ 5 GeV.Such a scenario can arise within the context of gauge-or gaugino-mediated SUSY breaking, where both couplings are zero at tree level, with non-zero A λ being radiatively generated at one loop and non-zero A κ at two loops [5].
For a sufficiently light A 1 boson, observation in the decay Υ(1s) → γA 1 becomes a 1 It is also possible to evade the LEP bound if H 1 decays into the lightest pseudoscalars, with branching ratio B(H 1 → A 1 A 1 ) > 0.7 [5].This requirement leads to a lower bound on the doublet component of A 1 , O A 11 > 0.04.Since the radiative corrections are subdominant in this region, we do not include these points in our results.
possibility.2Such a signal has previously been considered in [7,8], with the pseudoscalar coupling to b-quarks only through tree level singlet-doublet mixing.It has recently been shown that the singlet Higgs bosons also receive a direct coupling to fermions at one loop [9].Although loop suppressed, this coupling is enhanced by the ratio of Higgs doublet VEVs tan β and can become competitive with tree-level effects when this parameter is large.
In this Letter we consider the effects of such a direct coupling on the decay Υ → γA 1 .Experimental searches [10] for a light Higgs boson in Υ decays place a 90% confidence level upper bound on the branching ratio B(Υ → γA 1 ) < ∼ 1×10 −4 for a light particle m A 1 < 8 GeV decaying visibly within the detector.The upper bound rises to ∼ 10 −3 for heavier particles due to the softness of the recoil photon and cuts placed on energy deposits in the detector tighten the constraints to ∼ 10 −5 for a stable or invisibly decaying A 1 boson [11].
The branching ratio for Υ decays through the Wilczek mechanism [8,12] is given by Here F ∼ 1/2 includes QCD corrections [13] and The SM-normalised pseudoscalar coupling g P A i bb is given by [9] g with O A the 2 × 2 orthogonal pseudoscalar mixing matrix, such that where a is the would-be CP-odd scalar in the MSSM limit and a S is the CP-odd singlet Higgs boson.In addition, ∆ a 2,S b are the one-loop non-holomorphic Yukawa couplings of the states a 2,S to b quarks.At zero external momentum, they may be calculated by where ∆ b [Φ 1 , Φ 2 , S] is a Coleman-Wienberg type functional [14] of the background Higgs fields which encodes radiative corrections to the b quark self-energy.Here . . .denotes taking the VEV of the enclosed expression.The dominant contributions to ∆ a 2,S b are due to gluino-sbottom quark and chargino-stop quark loops.In the single-Higgs-insertion approximation, neglecting subdominant terms proportional to the weak gauge coupling α w , they may be given by where MQ,t,b are the soft squark masses, A t is the top-squark soft trilinear coupling and M3 is the gluino mass.The one-loop function I(x, y, z) is given by In Fig. 1 we present results from a scan over the parameters whilst fixing tan β = 50 and µ eff = 120 GeV.We require a light Higgs pseudoscalar m A 1 < 9 GeV along with a lightest Higgs scalar m H 1 > 114 GeV, in agreement with constraints from LEP II.The soft-SUSY breaking parameters which enter the calculation of ∆ a 2,S b are taken to be equal at M SUSY = 600 GeV.The branching ratio B(Υ → γA 1 ) is plotted against the non-singlet fraction of A 1 , described by the mixing matrix element O A 11 .The threshold corrections are independent of the tree-level coupling proportional to the pseudoscalar mixing, and enter the expression for g P A 1 bb with opposing sign.For a relatively large non-singlet component above f ew %, the threshold corrections represent a small suppression to the branching ratio of up to ∼ 10%.In the case of a highly singlet A 1 boson, the threshold corrections become the dominant effect, producing a branching ratio of the order ∼ 1 × 10 −6 across a significant region of parameter space.This prediction is found to be generic for electroweak-scale soft SUSY-breaking terms around a TeV.At the intersection of these regimes, the contributions cancel giving a highly suppressed decay rate.
Fig. 2 shows results from a scan over the parameter range of Eq. ( 10) for tan β = 10, keeping µ = 120 GeV and the common soft-SUSY breaking scale M SUSY = 600 GeV.Both the doublet-singlet mixing and threshold correction contributions to g P A 1 bb are tan β enhanced, such that the branching ratio at low tan β is smaller by 1 ∼ 2 orders of magnitude across the full parameter space.Due to their common enhancement, the relative importance  The points in green (light grey) include the one-loop threshold effects ∆ as b , points in red (dark grey) neglect these corrections.Here µ eff = 120 GeV and λ, κ, A λ , A κ are scanned over the range given in Eq. (10).All other soft-SUSY breaking parameters are taken to equal M SUSY = 600 GeV.Experimental bounds are shown in dark blue (black) for a stable or invisibly decaying pseudoscalar and in light blue (grey) for a visibly decaying particle, assuming here m A 1 ∼ 5 GeV.The full limits are strongly dependent on the value of m A 1 and are less restrictive by one to two orders of magnitude for a heavy A 1 boson (m A 1 > 8 GeV).
of the two terms in Eq. ( 4) varies only slowly with tan β, so that for all values of tan β > ∼ 5, minimal branching ratios are observed for singlet-doublet mixing around f ew × 0.1%.The magnitude of the branching ratio is not found to vary strongly with M SUSY or µ, although the available parameter space consistent with out requirements m H 1 > 114 GeV, m A 1 < 9 GeV decreases as µ increases, such that small values of the singlet-doublet mixing O A 11 do not appear.
The inclusion of threshold corrections can clearly alter the phenomenology of highly singlet light pseudoscalars in a dramatic way, allowing for the possibility of detectable Υ → A 1 γ decays in a new corner of parameter space.In the limit of vanishing singletdoublet mixing the tree level coupling of the A 1 boson to τ leptons also vanishes, however an analogous threshold correction also contributes to the A 1 τ + τ − coupling g P A 1 τ + τ − , through a wino-stau loop.The pseudoscalar is therefore predicted to decay into τ + τ − pairs with branching ratio of order one, for 2m τ < m A 1 < m Υ , independently of the singlet-doublet  Here µ eff = 120 GeV and M SUSY = 600 GeV, with λ, κ, A λ , A κ scanned over the range given in Eq. (10).Points in green (light grey) include the one-loop threshold effects ∆ a S b , points in red (dark grey) neglect these corrections.Experimental bounds are shown as for Fig. 1.
mixing.An order-of-magnitude estimate suggests that current B-factories should be sensitive to branching ratios of the order B(Υ → γA 1 ) < ∼ 10 −6 , for observing such a final state.
At masses above ∼ 9 GeV, the A 1 boson can mix with the η b meson.This can lead to significant enhancement or suppression of B(Υ → γA 1 ) [15].In addition, there is a broadening of the A 1 width, and the resonance in the energy spectrum of the recoil photon is less sharply peaked.There has been a suggestion to search for such a light Higgs boson through precision tests of lepton universality in the decays of the Υ [16].Such searches would also be sensitive to decays in the zero-mixing limit.If the A 1 boson is below the τ + τ − threshold, the dominant decay channels are ss, gg (and hence light mesons) or photon pairs, since the coupling to cc is tan β suppressed. 3This remains a favourable situation for the clean environment of an e + e − collider, where these final states can be reliably measured.
Unfortunately, despite the tremendous production rates for b-mesons at the LHC, a discovery of the A 1 boson through this mechanism appears difficult.The final state consists of low-energy τ jets and a photon, neither of which presents a clean signal above background activity.An alternative production mechanism has been suggested in [17], which considers instead the process pp → χ+ 1 χ− 1 A 1 in the limit of vanishing doublet-singlet mixing.The possibility for observing such a signal is strongly dependent on the masses and decay channels of both the lightest chargino and the A 1 boson.
If both terms contributing to g P A 1 b b are of similar magnitude, typically for around ∼ 0.5% mixing, detection of the A 1 boson may be extremely challenging.In this case, the branching fraction of Υ → A 1 γ becomes extremely suppressed.An alternative experimental strategy is to look for A 1 pair production from Higgs boson decays [18].In the small singletdoublet mixing scenario at large tan β, the lightest CP-even Higgs boson H 1 is highly SMlike, and the branching fraction B(H 1 → A 1 A 1 ) is conservatively bounded from above at around ∼ 10 −3 .Associated production of the A 1 boson with a chargino pair would remain a possibility.
In conclusion, we have shown that the branching ratio for production of a light Higgs pseudoscalar in Υ(1s) decays does not vanish in the absence of doublet-singlet mixing.We found that the decay Υ → γA 1 is predicted to be observable at existing experimental facilities if supersymmetry is broken at the TeV scale with large tan β.In the event of a cancellation between the threshold corrections and tree-level mixing contributions to the A 1 b b coupling the branching ratio may be highly suppressed even though the doublet-singlet mixing is still significant, and further phenomenological considerations would be needed.We hope to return to this issue in a future communication.

Figure 1 :
Figure 1: The branching ratio B(Υ → γA 1 ) vs. the non-singlet fraction O A11 at tan β = 50.The points in green (light grey) include the one-loop threshold effects ∆ as b , points in red (dark grey) neglect these corrections.Here µ eff = 120 GeV and λ, κ, A λ , A κ are scanned over the range given in Eq.(10).All other soft-SUSY breaking parameters are taken to equal M SUSY = 600 GeV.Experimental bounds are shown in dark blue (black) for a stable or invisibly decaying pseudoscalar and in light blue (grey) for a visibly decaying particle, assuming here m A 1 ∼ 5 GeV.The full limits are strongly dependent on the value of m A 1 and are less restrictive by one to two orders of magnitude for a heavy A 1 boson (m A 1 > 8 GeV).

Figure 2 :
Figure 2: The branching ratio B(Υ → γA 1 ) vs. the non-singlet fraction O A 11 at tan β = 10.Here µ eff = 120 GeV and M SUSY = 600 GeV, with λ, κ, A λ , A κ scanned over the range given in Eq.(10).Points in green (light grey) include the one-loop threshold effects ∆ a S b , points in red (dark grey) neglect these corrections.Experimental bounds are shown as for Fig.1.