Signatures of long-lived gluinos in split supersymmetry

Worth your time if you work on long-lived colored particles, and mostly for one idea: the monojet channel in Section 3.2. Baer-Cheung-Gunion and Mafi-Raby had already looked at long-lived gluinos, but they missed that gluino pair production with a radiated jet gives a monojet plus MET trigger that fires even when the R-hadrons are neutral and deposit almost nothing. That observation is what makes the neutral-fragmentation case tractable at all, and the paper carries it through Run I, Run II and LHC reach numbers. The charged case in Section 3.3 is a competent application of the existing CDF time-of-flight and dE/dx searches. The IceCube estimate in Section 4 is a reasonable cross-check proposal, and the authors are upfront that it gives N < 1 above 170 GeV, so it is a proposal rather than a discovery channel. Where I would push back: the paper says more than once, in Section 3.2 and again in Section 5, that the monojet limit is completely model independent. It is not quite. The CDF cuts include a second-jet veto at ET >= 30 GeV, and the paper's own numbers put R-hadron deposition at up to roughly 15 GeV in the neutral case, and enough to stop a charged one in the calorimeter. That is within a factor of a few of the veto, not orders of magnitude below it, so a larger k or a different lambda_T(R) would push some events out of the signal sample. The bound holds within the soft-deposition regime the paper assumes, which is a real regime, but the phrasing overstates what is shown. The authors do acknowledge that the energy-loss modeling is schematic, bracketed by two cases with k between 0.14 and 0.35 GeV, so that part is not a hidden flaw. A smaller point: the 170 GeV is read off the most conservative of four leading-order scale choices in Fig. 4, with no acceptance correction. That is a defensible choice and they say so, but it is a reach estimate rather than a bound with an error bar. None of this breaks the physics. The neutral case is the worst case, and the charged case has a stronger dedicated bound anyway, so the conclusion survives. Read it if you do R-hadron or long-lived gluino phenomenology, or if you need the standard reference for the monojet channel. It deserves a referee.

The central claim (abstract:s4; Section 3.2; Section 5) is that the monojet plus MET channel yields m_gluino > 170 GeV 'regardless of how they hadronize', i.e. a hadronization-model-independent bound. The chain is: (i) LO gluino pair plus jet cross section, (ii) CDF cuts ET(jet1) >= 80 GeV, MET > 80 GeV, ET(jet2) < 30 GeV, (iii) R-hadrons deposit less than ~15 GeV so they are not reconstructed as jets. Step (iii) is where the claim is least secure. The paper's own Section 3.1 and Fig. 2 give total deposition up to ~15 GeV for a neutral R-hadron in CDF (case 1, k = 0.35 GeV, gamma ~ 2), and Section 3.3 states that a charged R-hadron of mass ~100 GeV with gamma <= 1.1 loses all its kinetic energy (~10 GeV) by ionization in the hadronic calorimeter, while a 500 GeV one is stopped for beta < 0.25. At Tevatron-relevant masses (170-310 GeV) the charged-R-hadron deposition is therefore in the 5-15 GeV range, within a factor of two to six of the 30 GeV second-jet veto rather than orders of magnitude below it. A modest upward fluctuation in the hadronic energy loss (larger k, or a different lambda_T(R)) or a different fragmentation pattern would push some events over the veto and out of the signal sample. So the monojet limit is model independent only within the soft-deposition regime the paper itself assumes; the 'completely model independent' phrasing in Section 5 overstates what is shown. This does not invalidate the physics conclusion, since the neutral case is the worst case and the charged case has a stronger dedicated bound (Section 3.3, ~310 GeV), but it narrows the scope of the monojet bound. A secondary point: the 170 GeV number is read off the most conservative of four LO scale choices in Fig. 4 with no detector acceptance correction, so it is a reach estimate rather than a bound with an uncertainty.

The reader's weakest_assumption points at the right region (the soft-deposition assumption in Section 3.1 and Fig. 2) but frames it as a fragility of the k bracket. That bracket is better supported than the reader implies: the paper cites Kraan (ref. [24]), which independently finds k between 0.2 and 0.3 GeV, and the paper takes the larger value (0.35 GeV) as its upper estimate, so an order-of-magnitude increase in deposition is unlikely. The sharper concern is the one the reader raises only at the end of the rationale: the 'completely model independent' claim in Section 5 is not supported, because the CDF second-jet veto at ET >= 30 GeV means the signal sample is defined by the same soft-deposition assumption the paper treats as a model choice. At Tevatron-relevant masses the charged-R-hadron deposition (5-15 GeV per Section 3.1 and Section 3.3) sits close enough to the 30 GeV veto that a modest upward fluctuation would remove events. This is a scope overstatement, not a broken argument: the neutral case is the worst case, the charged case has a stronger dedicated bound, and the paper is honest elsewhere that the cross sections are LO with a factor-of-several scale spread. The reader's CONDITIONAL verdict is appropriate and my concern does not move it. The concrete test above would settle whether the model-independence claim survives a detector-level treatment, and if it does not, the fix is a wording change in Sections 3.2 and 5 rather than a change to the physics conclusion.

The paper's distinctive contribution relative to earlier long-lived gluino analyses is the identification of the monojet plus MET channel as a search that does not depend on the R-hadron charge, together with an explicit bracket of the hadronic energy loss between two interaction models (k = 0.35 and 0.14 GeV in Delta E = k gamma). The use of published CDF monojet and stable charged particle results makes the bounds falsifiable and directly comparable to data, and the statement that the results apply to any stable or meta-stable heavy colored particle broadens the reach beyond Split Supersymmetry. The IceCube estimate is a genuine independent cross-check, albeit a statistically thin one. The paper is careful to present the neutral R-hadron case as the worst case and to state that the charged case gives a stronger reach, which is the correct logical ordering of the scenarios.

In split supersymmetry the scalar partners of the Standard Model particles are pushed to an enormous mass scale while the gauginos stay light, so the gluino has no light squark to decay through and becomes long-lived — long enough, for much of the parameter space, to leave the detector before decaying. The paper asks what such a particle would look like experimentally, given that it hadronizes into a colour-singlet bound state (an R-hadron) whose charge and energy loss are poorly known. The authors show that the answer depends strongly on whether that hadron is charged or neutral: a charged one is visible through time-of-flight and ionization searches, while a neutral one slips through essentially unseen. Their central move is to note that gluino pair production accompanied by a radiated jet produces a monojet plus missing-energy signal no matter how the gluino fragments, which makes the resulting mass bound independent of hadronization modelling. If correct, this gives a robust floor under gluino searches, and shows that existing Tevatron data already exclude gluinos below roughly 170 GeV even in the least favourable case.

What carries the argument. The load-bearing object is the R-hadron: the colour-singlet bound state a long-lived gluino forms with light quarks and gluons, which carries unit R-parity and interacts with nuclei through its light coloured cloud rather than through the heavy gluino itself. Because only a small fraction of the R-hadron's energy participates in each collision, the average energy loss per interaction is modelled as $langle Delta E rangle approx k gamma$ with $k = 0.35$ GeV (a flat $|t|$ distribution) or $k = 0.14$ GeV (a triple-Pomeron distribution), bracketing the plausible range, with interaction length $lambda_T(R) = (16/9) lambda_T(pi) approx 19$ cm in iron. That parametrization is what converts 'the gluino is invisible' into a quantitative statement about jet thresholds and missing energy, and hence into a mass bound.

Core claim. The paper's central claim is that the monojet plus missing-transverse-energy channel provides a hadronization-independent bound on the gluino mass in split supersymmetry. The reasoning is that a neutral R-hadron deposits only a few hundred MeV per hadronic interaction along a mean free path of order 19 cm in iron, so it never satisfies the $E_T > 15$ GeV requirement used to define a jet in the CDF analysis; the gluino pair therefore registers as missing energy. Requiring an extra high-$p_T$ jet to satisfy the trigger, the authors compute the leading-order cross section for $gg, qbar q to gluino pair + g$ and $g q to gluino pair + q$ — the same matrix elements as heavy-quark pair production with a jet, since squark exchange decouples — and compare to the CDF large-extra-dimensions monojet analysis with 84 pb$^{-1}$. They obtain $m_{tilde g} > 170$ GeV from Run I, with the reach extending to about 210 GeV at Run II with 1 fb$^{-1}$ and roughly 1.1 TeV at the LHC with 100 fb$^{-1}$ if no excess appears. In the opposite case, where the gluino always fragments to a charged R-hadron that does not exchange charge, the CDF time-of-flight and anomalous-ionization searches do far better: about 310 GeV already excluded, roughly 430 GeV reachable at Run II with 2 fb$^{-1}$, and about 2.4 TeV at the LHC. The authors also estimate that cosmic-ray production of gluino pairs in the atmosphere could give of order one event per year per km$^2$ at IceCube for gluino masses near 170 GeV, an independent cross-check on the collider results.

The premise it rests on. The monojet bound holds only if a neutral R-hadron really deposits just a few hundred MeV per hadronic interaction, as the two bracketing models with $k$ between 0.14 and 0.35 GeV imply; if the true deposition were an order of magnitude larger, the R-hadrons would register as jets, the second-jet veto in the CDF analysis would remove the events, and the 170 GeV bound would not follow.

A monojet search at the Tevatron or LHC constrains the gluino mass in split supersymmetry regardless of how the gluino fragments, so the bound cannot be evaded by choosing a different hadronization pattern.

If the gluino hadronizes to a charged, non-flipping R-hadron, stable-charged-particle searches reach roughly 2.4 TeV at the LHC with 100 fb$^{-1}$, well beyond the monojet channel's reach.

A monojet excess at the LHC could be diagnosed as a long-lived coloured particle by looking for two tracks of small, spaced energy deposits left by the neutral R-hadrons inside the jet sample.

Atmospheric gluino pair production gives an IceCube event rate near one per year per km$^2$ for gluino masses around 170 GeV, offering a check on collider interpretations that does not share their systematics.

The same limits apply to any stable or metastable heavy coloured particle, not only to the gluino of split supersymmetry.

The paper's bounds in the charged case rest on very small Run I samples — the time-of-flight limit uses 3.54 pb$^{-1}$ and the $dE/dx$ limit 90 pb$^{-1}$ — so the quoted 310 GeV exclusion is a statement about those data sets rather than a settled number; the authors themselves ask CDF and D0 to update the searches.

The monojet logic suggests a broader experimental handle: any new physics producing a pair of slow, strongly interacting neutral particles plus one hard jet will mimic this signal, so the channel is a general probe of hidden-sector coloured states rather than a split-supersymmetry specialty.

The 'flipper' case, where the R-hadron exchanges charge with nuclei, is where the physics is least controlled; a dedicated measurement of charge-exchange cross sections for heavy hadrons on nuclei would sharpen the interpolation between the 170 GeV and 310 GeV extremes more than further luminosity would.

Because the monojet bound depends on the R-hadron staying below the jet $E_T$ threshold, a detector with a much lower clustering threshold would convert this search from a missing-energy measurement into a direct R-hadron search, which is a design consideration for future experiments.

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