${{\widetilde{\mathit q}}}$ (Squark) mass limit

For ${\mathit m}_{{{\widetilde{\mathit q}}}}$ $>$ 60$-$70 GeV, it is expected that squarks would undergo a cascade decay via a number of neutralinos and/or charginos rather than undergo a direct decay to photinos as assumed by some papers. Limits obtained when direct decay is assumed are usually higher than limits when cascade decays are included.
Limits from ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions depend on the mixing angle of the lightest mass eigenstate ${{\widetilde{\mathit q}}_{{{1}}}}={{\widetilde{\mathit q}}_{{{R}}}}$sin$\theta _{{{\mathit q}}}+{{\widetilde{\mathit q}}_{{{L}}}}$cos $\theta _{{{\mathit q}}}$. It is usually assumed that only the sbottom and stop squarks have non-trivial mixing angles (see the stop and sbottom sections). Here, unless otherwise noted, squarks are always taken to be either left/right degenerate, or purely of left or right type. Data from ${{\mathit Z}}$ decays have set squark mass limits above 40 GeV, in the case of ${{\widetilde{\mathit q}}}$ $\rightarrow$ ${{\mathit q}}{{\widetilde{\mathit \chi}}_{{{1}}}}$ decays if $\Delta \mathit m={\mathit m}_{{{\widetilde{\mathit q}}}}–{\mathit m}_{{{\widetilde{\mathit \chi}}_{{{1}}}^{0}}}{ {}\gtrsim{} }$5 GeV. For smaller values of $\Delta \mathit m$, current constraints on the invisible width of the ${{\mathit Z}}$ ($\Delta \Gamma _{{\mathrm {inv}}}<2.0$ MeV, LEP 2000) exclude ${\mathit m}_{{{\widetilde{\mathit u}}_{{{L,R}}}}}<$44 GeV, ${\mathit m}_{{{\widetilde{\mathit d}}_{{{R}}}}}<$33 GeV, ${\mathit m}_{{{\widetilde{\mathit d}}_{{{L}}}}}<$44 GeV and, assuming all squarks degenerate, ${\mathit m}_{{{\widetilde{\mathit q}}}}<$45 GeV.
Some earlier papers are now obsolete and have been omitted. They were last listed in our PDG 2014 edition: K. Olive, $\mathit et~al.$ (Particle Data Group), Chinese Physics C38 070001 (2014) (http://pdg.lbl.gov).

R-parity violating ${{\widetilde{\mathit q}}}$ (Squark) mass limit

$\text{none 100 - 720}$ 95 1
CMS 2 large jets with four-parton substructure, ${{\widetilde{\mathit q}}}$ $\rightarrow$ 4 ${{\mathit q}}$
$\bf{> 1600}$ 95 2
CMS ${{\widetilde{\mathit q}}}$ $\rightarrow$ ${{\mathit q}}{{\widetilde{\mathit \chi}}_{{{1}}}^{0}}$, ${{\widetilde{\mathit \chi}}_{{{1}}}^{0}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \ell}}{{\mathit \nu}}$, ${{\mathit \lambda}_{{{121}}}}$ or ${{\mathit \lambda}_{{{122}}}}{}\not=$0, ${\mathit m}_{{{\widetilde{\mathit g}}}}$ = 2400 GeV
$\bf{> 1000}$ 95 3
ATLS jets, ${{\widetilde{\mathit q}}}$ $\rightarrow$ ${{\mathit q}}{{\widetilde{\mathit \chi}}_{{{1}}}^{0}}$, ${{\widetilde{\mathit \chi}}_{{{1}}}^{0}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit q}}{{\mathit q}}$, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{{1}}}^{0}}}$ = 108 GeV and 2.5 $<$ c$\tau _{{{\widetilde{\mathit \chi}}_{{{1}}}^{0}}}$ $<$ 200 mm
ATLS ${{\mathit \ell}}$ +jets +$\not E_T$, CMSSM, ${\mathit m}_{{{\widetilde{\mathit q}}}}={\mathit m}_{{{\widetilde{\mathit g}}}}$
CMS ${}\geq{}3{{\mathit \ell}^{\pm}}$
1  SIRUNYAN 2018EA searched in 38.2 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV for the pair production of resonances, each decaying to at least four quarks. Reconstructed particles are clustered into two large jets of similar mass, each consistent with four-parton substructure. No statistically significant excess over the Standard Model expectation is observed. Limits are set on the squark and gluino mass in RPV supersymmetry models where squarks (gluinos) decay, through intermediate higgsinos, to four (five) quarks, see their Figure 4.
2  KHACHATRYAN 2016BX searched in 19.5 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV for events containing 4 leptons coming from R-parity-violating decays of ${{\widetilde{\mathit \chi}}_{{{1}}}^{0}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \ell}}{{\mathit \nu}}$ with ${{\mathit \lambda}_{{{121}}}}{}\not=$ 0 or ${{\mathit \lambda}_{{{122}}}}{}\not=$ 0. No excess over the expected background is observed. Limits are derived on the gluino, squark and stop masses, see Fig. 23.
3  AAD 2015CB searched for events containing at least one long-lived particle that decays at a significant distance from its production point (displaced vertex, DV) into two leptons or into five or more charged particles in 20.3 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV. The dilepton signature is characterised by DV formed from at least two lepton candidates. Four different final states were considered for the multitrack signature, in which the DV must be accompanied by a high-transverse momentum muon or electron candidate that originates from the DV, jets or missing transverse momentum. No events were observed in any of the signal regions. Results were interpreted in SUSY scenarios involving $\mathit R$-parity violation, split supersymmetry, and gauge mediation. See their Fig. $14 - 20$.
4  AAD 2012AX searched in 1.04 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV for supersymmetry in events containing jets, missing transverse momentum and one isolated electron or muon. No excess over the expected SM background is observed and model-independent limits are set on the cross section of new physics contributions to the signal regions. In mSUGRA/CMSSM models with tan ${{\mathit \beta}}$ = 10, ${{\mathit A}_{{{0}}}}$ = 0 and ${{\mathit \mu}}$ $>$ 0, squarks and gluinos of equal mass are excluded for masses below 820 GeV at 95$\%$ C.L. Limits are also set on simplified models for squark production and decay via an intermediate chargino and on supersymmetric models with bilinear R-parity violation. Supersedes AAD 2011G.
5  CHATRCHYAN 2012AL looked in 4.98 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV for anomalous production of events with three or more isolated leptons. Limits on squark and gluino masses are set in RPV SUSY models with leptonic $\mathit LL\bar E$couplings, ${{\mathit \lambda}_{{{123}}}}$ $>$ 0.05, and hadronic $\bar U \bar D \bar D$ couplings, ${{\mathit \lambda}}{}^{''}_{112}$ $>$ 0.05 , see their Fig. 5. In the $\bar U \bar D \bar D$ case the leptons arise from supersymmetric cascade decays. A very specific supersymmetric spectrum is assumed. All decays are prompt.