Sensitivity to the supersymmetric scalar states $\phi$ at the future linear
$e^+e^-$ and photon colliders is discussed. In particular it is illustrated a
search strategy for massive sgoldstinos, the supersymmetric partners of the
goldstino

Checchia, Paolo

Piotto, Enrico

English

arXiv

Sensitivity to the supersymmetric scalar states $\phi$ at the future linear $e^+e^-$ and photon colliders is discussed. In particular it is illustrated a search strategy for massive sgoldstinos, the supersymmetric partners of the goldstino.Sensitivity to the supersymmetric scalar states $\phi$ at the future linear $e^+e^-$ and photon colliders is discussed. In particular it is illustrated a search strategy for massive sgoldstinos, the supersymmetric partners of the goldstino.Sensitivity to the supersymmetric scalar states $\phi$ at the future linear $e^+e^-$ and photon colliders is discussed. In particular it is illustrated a search strategy for massive sgoldstinos, the supersymmetric partners of the goldstino.Sensitivity to the supersymmetric scalar states $\phi$ at the future linear $e^+e^-$ and photon colliders is discussed. In particular it is illustrated a search strategy for massive sgoldstinos, the supersymmetric partners of the goldstino

CERN Document Server

arXiv:hep-ph/0102208v1  16 Feb 2001LC-TH-2001-015.November 29, 2013Sensitivity to sgoldstino states at thefuture linear e+e− and photoncollidersPaolo ChecchiaI.N.F.N sezione di Padova and Dipartimento di Fisica G.Galilei,Padova, ItalyandEnrico PiottoCERN, European Organization for Nuclear Research, Geneva,Switzerland.AbstractSensitivity to the supersymmetric scalar states φ at the future linear e+e− andphoton colliders is discussed. In particular it is illustrated a search strategy formassive sgoldstinos, the supersymmetric partners of the goldstino.11 IntroductionIn the Supersymmetric extension of the Standard Model, once Supersymmetry is sponta-neously broken the gravitino G˜ can acquire a mass absorbing the degrees of freedom ofthe goldstino. The mechanism is analogous to the spontaneous breaking of the electro-weak symmetry in the Standard Model, when Z and W bosons acquire mass absorbingthe goldstone bosons.A very light gravitino G˜ as predicted by supersymmetric models [1] has been searchedfor at LEP and Tevatron experiments [2, 3] and the sensitivity to its signatures of anexperiment at a future linear collider has been studied [4]. Limits on the G˜ mass arerelated to the supersymmetry-breaking scale√F .It has been pointed out [5] that in such supersymmetric extensions of the StandardModel with a light gravitino, the effective theory at the weak scale must contain alsothe supersymmetric partner of the goldstino, called sgoldstino. The production of thisparticle, which could be massive, may be relevant at the LEP and Tevatron energies [6] ifthe supersymmetry-breaking scale and the sgoldstino mass are not too large. Two statesare considered in [5, 6], S CP-even and P CP-odd. Assuming R-parity conservation, it hasto be noticed that, while the goldstino is R-odd, the sgoldstino is R-even and therefore itcan be produced together with Standard Model particles.At LEP 2 sgoldstino signatures have been searched for by the DELPHI experiment[7] and preliminary results from CDF [8] show the higher sensitivity of hadron colliders.None of the two searches found an evidence for such states.At an e+e− collider one of the most interesting channels for the production of suchscalars (from now on the symbol φ will be used to indicate a generic state) is the processe+e− → φγ which depends on the φ mass mφ and on√F :dσdcosθ(e+e− → φγ) = |Σ|2 s64piF 2(1− m2φs)3(1 + cos2θ) (1)where θ is the scattering angle in the centre-of-mass and|Σ|2 = e2M2γγ2s+g2Z(v2e + a2e)M2γZs2(s−m2Z)2+egZveMγγMγZs−m2Z(2)with ve = sin2θW − 1/4, ae = 1/4 and gZ = e/(sinθW cosθW ). The parameters Mγγ andMγZ are related to the diagonal mass term for the U(1)Y and SU(2)L gauginos M1 andM2:Mγγ = M1cos2θW +M2sin2θW , MγZ = (M2 −M1)sinθW cosθW . (3)Other interesting processes are due to γγ- or gg-fusion occurring, respectively, at e+e−and hadron colliders. In both cases the production cross sections are proportional to thecorresponding widths:σ(e+e− → e+e−φ) ∝ σγγ0 =4pi2m3φΓ(φ→ γγ), σ(pp¯→ φ) ∝ σgg0 =pi28m3φΓ(φ→ gg) (4)and they can be obtained, respectively, from the photon and gluon distribution functions.2The decay modes φ→ γγ and φ→ gg widths areΓ(φ→ γγ) = m3φM2γγ32piF 2(5)andΓ(φ→ gg) = m3φM234piF 2(6)where M3 is the gluino mass.As noticed in [6] the production formulae are similar in form to those for a light SMHiggs production in Born approximation where Γ(H → γγ) and Γ(H → gg) substitutethe φ widths. It is straightforward to apply the same correspondence between thesetwo different physical cases to the φ production on photon colliders. With a reversesubstitution, an effective production cross section in the narrow-width approximation canbe deduced from the studies of Higgs Physics at a γγ collider [9]:σeff =dLγγdWγγmφLγγ× 4pi2Γ(φ→ γγ)m3φ(7)where dLγγ/dWγγ is the luminosity spectrum in the two photon center-of-mass Wγγ andLγγ is defined as the luminosity at the high γγ energy peak.All the above formulae depend on model dependent mass parameters. In [5] two setsfor these parameters are considered to give numerical examples. They are reported inTable. 1.M1 M2 M31) 200 300 4002) 350 350 350Table 1: Two choices for the gaugino mass parameters (in GeV) relevant for the sgoldstinoproduction and decay.The total width for a large interval of the parameter space is dominated by Γ(φ→ gg)and it is narrow (below the few GeV order) except for the region with small√F wherethe production cross section is expected to be very large.In this note the sensitivity to these states of an experiment at a e+e− linear colliderwith a center-of mass energy of 500 GeV and the sensitivity of an experiment at a photoncollider obtained from the same energy primary e+e− beams are evaluated. An integratedluminosity of 500 fb−1 for the e+e− collisions is considered with a reduction factor for theγγ interactions.2 e+e− colliderThe search for these scalars at a future linear collider can be an upgrade of the analysisdone at LEP where the two decay channels φ→ γγ and φ→ gg were considered [7]. Forthe present sensitivity evaluation only the dominant channel is considered. The φ → gg3decay gives rise to events with one photon and two jets. An irreducible background frome+e− → qq¯γ events is associated to this topology and therefore the signal must be searchedfor as an excess of events over the background expectations for every mass hypothesis.To select ggγ candidate events the following selection criteria can be defined:• an electromagnetic energy cluster identified as photon with a polar angle θ > 20◦;the angle between the photon and the nearest jet must be greater than 10◦;• no electromagnetic cluster with θ < 5◦;• to remove γγ fusion events: the total multiplicity > 10; the charged multiplicity> 5; the energy in transverse plane > 0.12 · √s; the sum of absolute values of trackmomentum along thrust axis > 0.20 · √s;• to remove Bhabha background: reject the events with electromagnetic cluster withE > 0.45 · √s and low track multiplicity;• to reduce qq¯γ events: |cos(θp)| < .995 where θp is the polar angle of missing mo-mentum; the visible energy greater than 0.60 · √s; reject events with c or b tag;• to remove WW background the events are reconstructed forcing into 2 jets topologybut removing from jetization the tracks associated to the photon cluster. Eventsare removed if ycut > 0.02.The polar angle acceptance for a φγ signal produced as in (1) is about 80%. It hasbeen evaluated by generating 4-vectors corresponding to the prompt photon and to theφ decay products. Considering the DELPHI results [7], the selection efficiency inside theacceptance region is assumed to be of the order of 50 %.The associated photon is monochromatic (except for the region with small√F wherethe production cross-section is expected to be very large) for a given center-of-mass en-ergy. Therefore the signal can be detected as a peak in the photon energy distributionof the selected events. In addition, the photon energy could be determined very preciselyby means of kinematic constraints if a final state three body topology is assumed. How-ever, the presence of the beamstrahlung (2.8% of mean beam-energy loss [10]) induces asmearing on the photon energy which is comparable with or larger than the experimentalresolution. On the other hand, the signal can be searched for directly in the jet-jet invari-ant mass distribution. Clearly the detector performance plays a crucial role in the optimalsearch strategy. Here a jet energy resolution following the σjetE /E = 40%/√E ⊕ 2% de-pendence and an error of about one degree in the jet angle reconstruction is assumed.With these assumptions the direct mass search is convenient or comparable w.r.t. therecoil photon search. The mass resolution is given in Fig. 1.The background rate depends on the considered φ mass hypothesis as it can be seenin Fig. 2 where the reconstructed jet-jet invariant mass of qq¯γ events generated withPYTHIA [11] in the acceptance region is shown. The events are scaled in order to re-produce the number of expected events with an integrated Le+e− luminosity of 500 fb−1.However the statistical fluctuations are not reproduced.Given the background event distribution as function ofmφ and the detection efficiencyfor any φ mass hypothesis it is possible to estimate a 95% Confidence Level cross sectionlimit for the φ production cross section. Only statistical fluctuations are considered here.4Figure 1: Mass resolution as function of the considered φ mass hypothesis. The full linecorresponds to a linear fit.Figure 2: Jet-jet invariant mass spectrum for the qq¯γ events.5The bin to bin fluctuations on the number of background events due to the reduced MonteCarlo statistics are removed by a spline function.By comparing the experimental limits with the production cross section computed from(1) it is possible to determine a 95% Confidence Level excluded region on the parameterspace and a 5 σ discovery region. The beamstrahlung effects which are more relevant thanthe Initial State Radiation one’s are taken into account. The limit and the 5 σ regionsare shown in Fig. 3. The φ width for all the considered mφ values is smaller than theexperimental resolution in all the points corresponding to the limit curves. Therefore thelimit has been computed integrating the signal only over the experimental resolution. Theregion where the expected width is larger than the experimental resolution is indicated inFig. 3. For mφ < 420 it is possible to cover this region of parameter space given the highcross section. This is no more true for mφ > 420 GeV where the decreasing cross sectionand the increasing width result in a drop of experimental sensitivity.Figure 3: Exclusion region at the 95% Confidence Level and > 5 σ signal discoveryregion in mφ√F space for the two sets of parameters of Tab. 1. The thick lines indicatethe region where the decay width Γ is larger than the experimental resolution.In the near future the Fermilab Tevatron Collider is expected to increase the luminosityby a factor ∼ 20 [12] and consequently an increase of about 1.5 in their √F limits canbe envisaged. The limits shown in Fig. 3 are then competitive with the future improvedTevatron results.At e+e− colliders, additional information can be obtained by searching for the as-sociated φZ0 production as described in [5]. As far as the production cross section isconsidered, competitive results are expected in the mφ <√s−mZ region. However, sincethis channel has a different final state topology requiring a more sophisticated analysis,it is not considered here.63 γγ colliderThe effective cross section given in eq. (7) depends on the luminosity factor fL =dLγγdWγγmφLγγ.In the photon collider projects [13] there are several possible scenarios concerning thephoton energy spectra. It may be desirable a photon energy distribution peaked as muchas possible toward the primary electron/positron energy. In [9] fL = 7 is assumed andLγγ is taken as the integral luminosity for z > zmin = 0.65 where z = Wγγ/2Ee and Ee isthe primary electron beam energy. The luminosity high energy peak is expected to have aFWHM of ∼ 10− 15% with a sharp edge at z ∼ 0.8. Therefore the unexcluded mφ−√Fparameter space achievable at these machines with 2Ee = 500 GeV ensures that the φwidth is negligible.The effective cross section obtained with fL = 7 is much higher (several orders of mag-nitude, depending on mφ) than the e+e− → φγ cross section with the same parameters.Considering the photon and gluon decay channels, the signal would appear as a peak oftwo high energy photons or jets with no transversal missing energy. The two jets finalstate has to compete with large Standard Model background which can be suppressedusing polarized photon beams with polarizations λ1, λ2: σ(γγ → qq¯) ∝ 1 − λ1λ2 whileσ(γγ → φ) ∝ 1 + λ1λ2. However, taking into account QCD corrections [14, 15], the qq¯gfinal state with unresolved gluon jet gives rise to a sizeable background which may be hardto reject. Therefore, despite of the smaller decay branching ratio, only the two photonsfinal state which has a very little Standard Model background is considered here.The selection of events with two collinear high energetic photons is rather simple andthe LEP experience can be used [16]. An efficient way to select photons and to rejectelectrons is to require two energy clusters in the electromagnetic calorimeter not associatedto hits in the vertex detector. Events with tracks detected in the other tracking devicesonly in one hemisphere can be accepted to recover photon conversions. Other requirementsare:• acollinearity between the e.m. clusters smaller than 30◦;• acoplanarity smaller than 5◦;• polar angle θ > 30◦;• Eγ > 0.9 · zmin · Ee.The detection efficiency is very high (> 90%) in the region Wγγ/2Ee > zmin and theacceptance for the decay of a scalar particle is 86%.The irreducible Standard Model background of γγ → γγ events has been discussedin [17, 18]. In the Wγγ region above 200-250 GeV the cross section is in the range8-14 fb for θ > 30◦ and then, assuming Lγγ ∼ 0.15 · Le+e−, the number of expectedevents is of the order of 600-1000. As a consequence any New Physics signal has toexceed the corresponding statistical error ( which is of the order of 3 to 4 %) and thesystematic uncertitude including the precision on the background calculation. For thepresent sensitivity study an overall background uncertitude of 5 % is assumed, leavingmore detailed analysis of the signal and background including the comparison of theirangular distributions to a later stage. With these assumptions, the sensitivity to a scalarstate decaying in two photons is given by the expected 95 % Confidence Level limit on7the cross section times branching ratio and it isσ(γγ → φ)× B.R.(φ→ γγ) < 1 fbat the 95 % Confidence Level for mφ ∼ 400 GeV.This value is obtained following the hypothesis that the whole luminosity is collectedat the maximal energy spectrum available with 250 GeV electron beams. The actualsensitivity for several φ mass hypothesis depends on the machine run strategy, on theavailable energy spectrum and on the photon beam polarization. Nevertheless, takingthe given limit just as an evaluation of the order of magnitude for the sensitivity, it isworth investigating the effect on the supersymmetry breaking scale from (5) and (7).In particular, defining as a reference cross-section-branching-ratio-product the value σBobtained withMγγ = 350 GeV and a 10% branching ratio to two photons, the limit on√Fand the 5 σ signal can be expressed in terms of the ratio R = σeff ×B.R.(φ→ γγ)/σB.They are then proportional to R14 as shown in Fig. 4. The sensitivity is clearly muchlarger than the one expected at the e+e− machines.Figure 4: Limit at 95 % Confidence Level on the supersymmetry breaking scale and 5 σsignal (thick line) for the production of a ∼ 400 GeV φ scalar state as function of theratio R.4 ConclusionsThe sensitivity to the supersymmetric scalar φ at the future linear e+e− and photoncolliders is such that unexplored parameter space regions can be investigated. The e+e−machines with center of mass energy of 500 GeV can set limits for the production of8sgoldstino scalars up to about 420 GeV. These limits are competitive w.r.t. the expectedfuture results from the Tevatron RUN II. The sensitivity at the photon colliders obtainedfrom the same electron-positron beam energy is expected to be much higher for mφ ∼ 400GeV.AcknowledgementsWe want to thank F. Zwirner for useful explanations on the theoretical framework andfor suggestions on the experimental possibilities, A. Castro for discussions concerning thefuture CDF results and M. Mazzucato for comments and for reading the manuscript.9References[1] P.Fayet, Phys. Lett. B86 (1979) 272;J.Ellis, K.Enqvist and D.Nanopoulos, Phys. Lett. B151 (1985) 357;D.Dicus, S.Nandi, and J.Woodside, Phys. Rev. D 43(1991) 2951A. Brignole, F. Feruglio and F. Zwirner Nucl. Phys. B 516 (1998) 13and references therein.[2] L3 collab., O. Adriani et al., Phys. Lett. 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Sensitivity to sgoldstino states at the future linear $e^+e^-$ and photon colliders

Sensitivity to the supersymmetric scalar states $\phi$ at the future linear $e^+e^-$ and photon colliders is discussed. In particular it is illustrated a search strategy for massive sgoldstinos, the supersymmetric partners of the goldstino

Sensitivity to sgoldstino states at the future linear $e^+e^-$ and photon colliders

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Sensitivity to sgoldstino states at the future linear e+e−e^+e^-e+e− and photon colliders

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Sensitivity to sgoldstino states at the future linear $e^+e^-$ and photon colliders