Monojets and mono-photons from light higgsino pair production at LHC14

Naturalness arguments imply the existence of higgsinos lighter than 200-300 GeV. However, because these higgsinos are nearly mass degenerate, they release very little visible energy in their decays, and signals from electroweak higgsino pair production typically remain buried under Standard Model backgrounds. Moreover, gluinos, squarks and winos may plausibly lie beyond the reach of the LHC14, so that signals from naturalness-inspired supersymmetric models may well remain hidden via conventional searches. We examine instead prospects for detecting higgsino pair production via monojets or mono-photons from initial state radiation. We find typical signal-to-background rates at best at the 1 % level, leading to rather pessimistic conclusions regarding detectability via these channels.


Introduction
The minimization of the (renormalization group improved one-loop) electroweak scalar potential of the Minimal Supersymmetric Standard Model (MSSM) leads to the well-known relation [1], where the running potential parameters are evaluated at the scale M SUSY = √ mt 1 mt 2 and where Σ u u and Σ d d are radiative corrections that arise from the derivatives of ∆V evaluated at the potential minimum. The sensitivity of M 2 Z to the input parameters has been used to construct the necessary (though not sufficient) condition for naturalness defined by the electroweak fine-tuning measure [2,3], where C H d = m 2 H d /(tan 2 β − 1), C Hu = −m 2 Hu tan 2 β/(tan 2 β − 1) and C µ = −µ 2 . Also, C Σ u u (k) = −Σ u u (k) tan 2 β/(tan 2 β − 1) and C Σ d d (k) = Σ d d (k)/(tan 2 β − 1), where k labels the various loop contributions included in Eq. (1). Expressions for the Σ u u and Σ d d are given in the Appendix of the second paper of Ref. [3].
Note that ∆ EW is essentially determined by the SUSY spectrum. It is independent of both the underlying mechanism by which the super-partners acquire their masses and of the messenger scale -Λ -at which this mechanism is operative. This is in sharp contrast to conventional measures of fine-tuning such as ∆ BG [4,5] or ∆ HS [6,7,3] where corrections such as ∼ m 2 Hu (Λ) ln Λ 2 m 2 SUSY lead to very high values of these fine-tuning measures especially in models -such as mSUGRA -where the parameters defined at a very high energy scale. There is, of course, no contradiction since small ∆ EW is, as we have mentioned, just a necessary condition for fine-tuning [3,8].
An immediate consequence of Eq. (1) is that models with values of µ 2 ≫ M 2 Z are necessarily fine-tuned. We emphasize that although we have used the electroweak scale minimization conditions to argue this, the same conclusion follows even with the use of popular fine-tuning measures. This is because µ 2 runs very little between M GUT and M SUSY so that the sensitivity of M 2 Z to µ 0 , the GUT scale value of µ, is changed by just ∼ 10%. 1 We thus conclude that a small value of µ 2 /(M 2 Z /2) is a robust and necessary condition for naturalness irrespective of the fine-tuning measure that is used. Stated differently, models with higgsinos heavier than 200 GeV (300 GeV) necessarily have a fine-tuning worse than 10% (3%). Experimental probes of light higgsinos pair production can thus decisively probe naturalness of SUSY models. 2 Motivated by these considerations, we have examined the spectra and aspects of the phenomenology that result in models where ∆ EW ∼ 10 − 30. Typically, the dominant radiative corrections to Eq. (1) come from the top-squark contributions Σ u u (t 1,2 ). For negative values of 1 This simple fact often remains obscured because the values of both ∆ HS and ∆ BG are defined by the input parameter that M 2 Z is most sensitive to, and this is almost never µ 2 0 . 2 Note that the link between fine-tuning and the higgsino mass breaks down if the dominant contribution to the higgsino mass is non-supersymmetric [9]. If there are no singlets that couple to higgsinos, such a contribution would be soft. However, in all high scale models that we know, the higgsino mass has a supersymmetric origin. the trilinear soft term A t somewhat larger than the GUT scale scalar masses, each of Σ u u (t 1 ) and Σ u u (t 2 ) can be minimized whilst lifting up m h into the 125 GeV regime [2] as required by the discovery of the Higgs boson at the LHC [10,11]. Upon requiring no large independent contributions to Eq. (1) (which would necessitate fine-tuning of the remaining parameters to keep M Z at ≃ 91.2 GeV), we find that • |µ| ∼ 100 − 300 GeV (the closer to M Z the better), • m 2 Hu is driven radiatively to only small negative values, • the top squarks which enter the Σ u u radiative corrections are highly mixed and lie at or around the few TeV scale and • in order to keep mt 1,2 from growing too large, the gluino mass is also bounded from above, in this case by mg 4 − 5 TeV.
Sparticle mass spectra consistent with low ∆ EW can readily yield a value of m h ∼ 125 GeV whilst evading LHC8 search limits on squarks, gluinos and top-squarks [12,13], and at the same time maintaining low electroweak fine-tuning, our necessary condition for naturalness. The key feature of the mass spectra implied by Eq. (1) is the existence of four light higgsinos -W ± 1 , Z 1 and Z 2 -all with mass ∼ |µ| ∼ 100 − 300 GeV. While these light higgsinos can be produced at LHC at large rates, their compressed spectra with mass gaps GeV results in only soft visible energy release from their three-body decays; this makes signal extraction from SM background exceedingly difficult, if not impossible.
A new signature endemic to models with light higgsinos has also been pointed out in Ref. [14]: which results in hadronically quiet -because the decay products of W 1 and Z 2 are soft -same sign diboson events (SSdB). The 300 fb −1 LHC14 reach for SSdBs extends to a wino mass of about 700 GeV. This corresponds to mg ∼ 2.1 TeV in models with gaugino mass unification, somewhat larger than the LHC14 reach for gluino pair production [15]. Confirmatory signals will also be present in multilepton channels [15]. Since mg can extend up to 4 − 5 TeV while maintaining low ∆ EW 30, then LHC14 can probe only a fraction of the parameter space of natural SUSY in this manner.
An alternative LHC search strategy has been proposed in a variety of papers (for a summary and detailed references, see e.g. Ref. [16]), namely to look for initial state QED/QCD-radiation off WIMP pair production. Much of this work [17,18,19,20,21,22,23] has been carried out using effective operator analyses. Here, it is assumed that the interactions between the dark matter particle and SM quarks occur via very heavy mediators (usually t-and u-channel squarks in the context of the MSSM bino-like WIMP) so that the contact approximation is valid. It is clear that for MSSM higgsino pair production the contact interaction approximation breaks down very badly because higgsinos are dominantly produced by collisions of quarks and antiquarks (inside the protons) via s-channel Z exchange. Since higgsinos are necessarily heavier than ∼ 100 GeV, the Z-boson propagator suppresses the amplitude for higgsino production by an extra factor ofŝ relative to the contact-interaction approximation. This results in a suppression of the cross-section where the higgsino pair is produced with large invariant mass. Since radiation of hard gluons or photons is most likely in this regime, the contact interaction approximation will badly overestimate the cross section for high E T monojet and mono-photon events, as has already been emphasized in Ref. [24]. As a result, constraints [22,23] using effective operator analyses, therefore, do not apply in the case that the light SUSY states are higgsinos.
In a recent analysis, Han et al. [25] have computed the monojet signal in the natural SUSY framework with light higgsinos using the complete matrix element. An advantage of applying this technique to models with light higgsinos is that one is not restricted to just WIMP ( Z 1 ) pair production, but one may radiate off gluons or photons in several other reactions as well: , since again the heavier higgsino decay debris is expected to be soft (unless highly boosted) at LHC. Including all the relevant contributions, these authors claim that LHC14, with an integrated luminosity of 1500 fb −1 will be able to probe higgsinos up to 200 GeV at 5σ [25]. If their results hold up to scrutiny, it will imply that experiments at the high luminosity upgrade of the LHC will decisively probe SUSY models fine-tuned to no more than 10%. 3 Given the importance of this result, we re-examine prospects for detection of monojet radiation off of higgsino pair production in Sec. 2. Our conclusions are, however, quite different from those of Ref. [25] since we find signal well below SM backgrounds (at the percent level), with no distinctive monojet features which would allow separation of signal from background. In Sec. 3, we perform similar calculations for mono-photon radiation and arrive at similarly pessimistic conclusions. We have decided such a pessimistic assessment is worthy of publication not only because of the optimistic claims in the literature [25], but also to highlight that claims about the observability of monojet/mono-photon signals from effective operator analyses should be viewed with caution.

Prospects for monojets
To examine signal rates, we first select a low ∆ EW SUSY benchmark model from radiativelydriven natural SUSY (RNS) which uses the 2-extra-parameter non-universal Higgs model (NUHM2) with input parameters with m t = 173.2 GeV. We generate the sparticle spectrum using Isajet 7.84 [26]. We fix m 0 = 5 TeV, m 1/2 = 750 GeV, A 0 = −8 TeV, tan β = 10, µ = 150 GeV and m A = 1 TeV. This leads to a sparticle spectrum with mg = 1.9 TeV, very heavy squarks and sleptons, binos and winos with masses of several hundred GeV, and a set of higgsinos with m W ± 1 = 155.6 GeV, m Z 2 = 158.9 GeV and m Z 1 = 142.2 GeV. These higgsinos are, of course, the focus of the present study, and our broad conclusions are essentially independent of the rest of the spectrum, as long as the bino and wino states are much heavier than the higgsino states. The value of ∆ EW = 19.7.
We use Madgraph 5 [27] to generate pp → W + 1 W − 1 , Z 1,2 Z 1,2 and W ± 1 Z 1,2 plus one-parton processes (exclusive) and plus two-partons (inclusive) where for efficiency we require the hardest final state parton to have p T (parton) > 120 GeV; the final cross section is then the sum of 1-jet exclusive and 2-jet inclusive processes. We also evaluate the Z + jets, W + jets and ZZ + jets backgrounds (where Z's decay to neutrinos and W 's decay leptonically) in a similar fashion, as the sum of one-and two-parton processes. To avoid double-counting, we used the MLM scheme for jet-parton matching [28]. The events are then passed to Pythia [29] for showering, hadronization and underlying event. We have not evaluated the hard monojet background from top quark pair production which we expect to be very small after the veto on additional jets and leptons. This is confirmed by the results of Ref. [25].
• Electrons and muons are considered isolated if they have |η| < 2.5, p T (l) > 10 GeV with visible activity within a cone of ∆R < 0.2 about the lepton direction, ΣE cells T < 5 GeV.
• Jets with just one or three charged particles are labelled as taus.
• We identify hadronic clusters as b-jets if they contain a B hadron with E T (B) > 15 GeV, η(B) < 3 and ∆R(B, jet) < 0.5. We assume a tagging efficiency of 60% and light quark and gluon jets can be mis-tagged as a b-jet with a probability 1/150 for E T ≤ 100 GeV, 1/50 for E T ≥ 250 GeV, with a linear interpolation for intermediate E T values.
Our resulting distributions are shown in Fig. 1 for a) p T (j 1 ) and b) E miss T . As expected, the shapes of the two distributions are similar for large p T (j) and large E miss T but begin to differ for values below ∼ 200 GeV where details of event generation and the presence of the second jet may be important. From frame a), we see that Z + jets production forms the dominant background, followed closely by W + jets production where the lepton from W -decay is too soft or buried within a jet or too forward or otherwise unidentified. The signal is shown by the red solid histogram and lies typically about two orders of magnitude below the background distribution. We also show the distribution from ZZ + jets production, which is sub-dominant. Essentially the same qualitative features are also seen in frame b). Nowhere in either frame does the signal emerge from background. Other cuts such as angular distributions do not help the situation since both signal and BG are dominated by gluon radiation off initial state quarks: really, the main difference between signal and background as far as ISR goes is that for signal the ISR comes off a somewhat higher Q 2 subprocess. The effect of sequential cuts on the signal and on the background is shown in Table 1.
Given that the signal and background have similar shapes and that S/B ∼ 1%, it is very difficult to make the case that it will be possible to realistically extract the signal [31]. Of course, with sufficient integrated luminosity, the statistical significance will always exceed 5σ, but to claim that this means the signal is observable means that the background is known with a precision better than a percent! 4 monojet, LHC14 T from initial state radiation off higgsino pair production at LHC14. We also show backgrounds from Z + jets, W + jets and ZZ + jets production, where W → ℓν and Z → νν.

Prospects for mono-photons
For mono-photon events (which we include for completeness), we generate the same signal sample as before, including all higgsino pair production reactions, but now requiring one hard photon (with p T > 40 GeV) radiation instead of a hard jet. We also generate the background processes Zγ production (followed by Z → νν) and W γ production (followed by W → ℓν ℓ where ℓ = e, µ or τ ) as before using Madgraph plus Pythia. For the isolated mono-photon sample, we require [23]: • n(γ) ≥ 1, • n(jets) ≤ 1 with |η(jet)| < 4.5, • tau-jet veto, and • isolated lepton veto.
We regard a photon to be isolated if the energy in a cone of radius ∆R < 0.4 around photon with p T (γ) > 25 GeV, |η(γ)| < 2.5 is less than 5 GeV. Our signal and background distributions in p T (γ) and E miss T are shown in Fig. 2. As in Fig. 1, we see that the shapes agree for large values of p T (γ) and E miss T . For the entire range of p T (γ) as well as of E miss T , we again find that signal (solid red histogram) lies below the Zγ background by typically two orders of magnitude. The W γ background falls more sharply than the Zγ background. This is because when we require much higher p T (γ) values, then the W recoils more sharply against the gamma, and its decay products are more likely to be hard and isolated, and to not pass the lepton/tau veto requirements. The effect of the sequential cuts on the signal and background cross sections is shown in Table 2. Once again, there are no distinctive features in the distribution, and as for the monojet signal of the previous section, we deem the mono-photon signal to be unobservable because of the very small S/B ratio.  from initial state photon radiation off higgsino pair production at LHC14. We also show backgrounds from Zγ and W γ production.

Concluding remarks
The existence of light higgsinos with masses smaller than 200-300 GeV (depending on how much fine-tuning one is willing to tolerate) is a robust feature of natural SUSY models. Although these higgsinos can be pair produced at large rates at the LHC, the signal will be buried below SM backgrounds because of the small energy release from their decays. In this paper, we have examined prospects for their detection via pair production in association with a hard jet or a hard, isolated photon resulting in characteristic monojet or mono-photon events at LHC14. We emphasize here that constraints obtained from analyses [22,23] using contact interactions between quarks and the higgsinos are inapplicable in this connection because the effective operator approximation fails badly for higgsino pair production.
While monojet and mono-photon signal events indeed occur at an observable rate particularly at the luminosity upgrade of the LHC, we are pessimistic about the prospects for their detection because backgrounds from Z and W production in association with a jet or an isolated photon overwhelm the signal by two orders of magnitude even for very large values of jet or photon transverse momentum and E miss T in these events. It seems to us difficult to imagine that it would be possible to claim a signal for new physics in these channels based solely on an excess of O(1%) without an observable distortion of any distribution.
In arriving at our negative conclusion, we should mention that have not investigated whether it might be possible to extract the higgsino signal by examining the soft debris from the decays of W 1 and Z 2 produced via W 1 Z 2 , Z 1 Z 2 and W 1 W 1 pair production processes that dominate higgsino pair production [15]. This will require a careful analysis of potential backgrounds from higher order Standard Model processes. Despite our cautious pessimism, we leave open the possibility that a clever analysis may make it feasible to tease out this signal at a luminosity upgrade of LHC14.