Run-2 Proton-Proton Collision Dataset

• Run-2 Proton-Proton Collision Dataset is a comprehensive collection from LHC Run 2 at 13 TeV featuring an integrated luminosity of ~140 fb⁻¹ and rigorous calibration.
• The dataset employs advanced methods like van der Meer scans and cross-detector validations to minimize systematic uncertainties to 1–2%.
• State-of-the-art proton reconstruction techniques, including PPS and multi-RP global fits, offer precise measurements for Standard Model and new physics studies.

The Run-2 Proton-Proton (pp) Collision Dataset denotes the collection of proton-proton collision data acquired during Large Hadron Collider (LHC) Run 2 (2015–2018), predominantly at a center-of-mass energy $\sqrt{s} = 13$ TeV. Both the CMS and ATLAS experiments, as well as specialized systems such as the Precision Proton Spectrometer (PPS), utilized dedicated data-taking, calibration, and validation workflows to enable high-precision Standard Model measurements and searches for new physics. This dataset is characterized by its unprecedented integrated luminosity, meticulous absolute luminosity calibration, detailed quantification of systematic uncertainties, and rigorous cross-detector consistency verification (Giraldi, 2022, Collaboration, 2021, Ferro, 2021).

1. Integrated Luminosity and Data Collection

During Run 2, the LHC provided proton beams at $E_{\rm beam} = 6.5$ TeV, resulting in $\sqrt{s} = 13$ TeV collisions. Data-taking extended from 2015 to 2018, with annual and total integrated luminosities as summarized in the following table, which aggregates values from CMS and ATLAS:

Year	CMS $\mathcal{L}_{\rm int}$ (fb$^{-1}$)	ATLAS $\mathcal{L}_{\rm int}$ (fb$^{-1}$)
2015	2.27 $\pm$ 0.04	—
2016	36.3 $\pm$ 0.44	—
2017	41.5 $\pm$ 0.96	—
2018	59.8 $\pm$ 1.50	—
Total	139.9 $\pm$ 1.8	139 $\pm$ 2.4

For ATLAS, the total good-quality integrated luminosity is $139$ fb$^{-1}$ with a systematic uncertainty of $1.7\%$ from LUCID-2 calibration. CMS quotes an overall Run 2 precision of $1-2\%$, with the total relative uncertainty at approximately $1.5\%$ (Giraldi, 2022, Collaboration, 2021).

2. Absolute Luminosity Calibration

The absolute luminosity scale for pp collisions in Run 2 was established via van der Meer (VdM) beam-separation scans. During dedicated VdM fills, LHC beams were moved in steps in the transverse ($x$, $y$) directions. The observed luminometer rates $R(\Delta x,0), R(0,\Delta y)$ were fitted to double-Gaussian profiles to extract the overlap widths $\Sigma_x, \Sigma_y$. The visible cross section $\sigma_{\rm vis}$ for each luminometer was determined by

$$\sigma_{\rm vis} = \frac{2\pi \Sigma_x \Sigma_y}{N_1 N_2 \nu_{\rm LHC} / R_0}$$

where $N_{1,2}$ are the bunch populations (corrected for ghost and satellite charge), $\nu_{\rm LHC} = 11\,245$ Hz is the revolution frequency, and $R_0$ is the head-on rate. Instantaneous luminosity $L(t)$ in physics fills was derived as $L(t) = R(t)/\sigma_{\rm vis}$ (Giraldi, 2022, Collaboration, 2021).

ATLAS utilized the LUCID-2 Cherenkov detector, also calibrated via VdM scans. The primary methods and performance metrics were consistent across major LHC experiments.

3. Systematic Uncertainty Quantification

Systematic uncertainties in the luminosity measurement are categorized as arising from VdM-scan calibration and physics-fill integration. Quantitative breakdowns for each year (for CMS) include:

• Calibration (VdM scan):
  • Ghost & satellite charge: $0.1\%$
  • Beam-current normalization: $0.2-0.3\%$
  • Orbit drift: $0.2\%$
  • Residual scan-to-scan differences: $0.1-0.8\%$
  • Beam–beam effects: $0.2-0.6\%$
  • Length scale calibration: $0.2-0.3\%$
  • Transverse non-factorizability: $0.5-2.0\%$
• Integration (physics fill):
  • Out-of-time pileup Type-1 (afterglow): $0.1-0.3\%$
  • Out-of-time pileup Type-2: $0.1-0.4\%$
  • Cross-detector stability: $0.5-0.6\%$
  • Linearity (extrapolation effects): $0.3-1.5\%$
  • CMS DAQ deadtime: $<0.1-0.5\%$

Total per-year uncertainties for CMS are $1.6\%$ (2015), $1.2\%$ (2016), $2.3\%$ (2017), and $2.5\%$ (2018). The final combined uncertainty across Run 2 is $O(1-2\%)$, which surpasses the $2-4\%$ precision achieved in previous LHC and Tevatron runs (Giraldi, 2022).

ATLAS quotes an integrated luminosity uncertainty of $1.7\%$ on the full dataset, validated by cross-checks between LUCID-2 and supplementary luminometers (Collaboration, 2021).

4. Data Quality, Triggering, and Pile-Up Mitigation

Run 2 data-taking imposed stringent quality requirements, including stable beams and full operational status of all detector subsystems. Events passing these criteria constitute the good-run lists (GRL). Peak instantaneous luminosities reached $$2.1 \times 10^{34}\ \mathrm{cm}^{-2}\ \mathrm{s}^{-1}$$ in 2018. The mean pile-up $\langle\mu\rangle$ was $33.7$, with instantaneous values up to $60$.

ATLAS employed single-lepton triggers with online $E_T$ thresholds of $24-26$ GeV (electrons) and $p_T$ thresholds of $20-26$ GeV (muons). Trigger efficiency turn-on reached plateau by $p_T \approx 28$ GeV (Collaboration, 2021). Offline, reconstructed objects were matched to trigger objects, with jets and leptons subjected to pile-up mitigation using:

• Jet–Vertex Tagger (JVT) to associate jets with primary vertices,
• Track-based soft terms in $E_T^{\text{miss}}$ using tracks matched to the primary vertex,
• Lepton isolation and dedicated BDTs for suppression of non-prompt leptons.

Pile-up modeling in Monte Carlo overlaid inelastic pp events with minimum-bias events (Pythia 8, A3 tune, NNPDF2.3lo), and pile-up weights corrected to match the observed distribution:

$$w_{\rm pu}(\mu) = \frac{P_{\rm data}(\mu)}{P_{\rm MC}(\mu)}$$

(Collaboration, 2021).

5. Cross-Detector Linearity and Stability Validation

CMS employed a comprehensive suite of stability and linearity checks:

• Emittance scans: Short "mini‐VdM" scans at the start and end of physics fills probed detector response vs. beam overlap and pile-up.
• Afterglow corrections: Correction for out-of-time pileup in luminometers with long response tails, performed by subtracting measured rates in empty bunch crossings.
• Time-dependent corrections: Efficiency drifts in channels (e.g., HFET/HFOC) addressed via time-dependent correction factors from emittance-scan data.
• Cross-detector cross-checks: Comparison and correlation studies across luminometers (PLT, BCM1F, HF, PCC, VTX, DT, RAMSES) to ensure alignment within systematic uncertainties. Any residual non-linearity or response drift is included in the “cross-detector stability” systematic (Giraldi, 2022).

6. The PPS Run 2 Dataset and Proton Reconstruction

The Precision Proton Spectrometer (PPS) collected 110 fb$^{-1}$ (2016–2018), covering approximately $80\%$ of the CMS pp dataset. Alignment and optics calibration proceeded in three stages:

• Absolute alignment: Roman Pots (RP) inserted down to $5\sigma_{\rm beam}$ using collimator-scan techniques, achieving $10\,\mu$m precision.
• Relative alignment: Internal alignment within each arm attains $<20\,\mu$m precision.
• Transfer to physics fills: Correction of ($x$, $y$) shifts ensures matching between the alignment fill and physics data, with typical combined position uncertainties of $10–30\,\mu$m.

Optics calibration used first-order transport equations, with parameters matched to LHC optics databases and updated using minimum-bias and exclusive dilepton events:

$$x(s) = v_x(\xi) x^* + L_x(\xi) \theta_x^* + D_x(\xi) \xi$$

where $\xi$ is the proton fractional momentum loss. Calibration of the horizontal dispersion $D_x$ has reached precisions $\Delta D_x / D_x \lesssim 1\%$, with optical-uncertainty contributions to $\xi$ at the $10^{-3}$ level.

Proton reconstruction is performed via:

• Single-RP method: $\xi \approx x/D_x$, $\sigma(\xi) \approx 2–3 \times 10^{-3}$,
• Multi-RP global fit: using full transport matrices, achieving $\sigma(\xi) \approx 10^{-3}$ and $\sigma(t) \lesssim 0.02$ GeV$^2$, with systematic uncertainties on $\xi$ at the few $10^{-4}$ level.

Validation utilizes exclusive $\gamma\gamma \rightarrow \ell^+\ell^-$ events, where $\Delta \xi$ (proton-determined minus central detector-determined) agrees within $(1–2)\times 10^{-3}$ between data and simulation.

7. Significance and Impact

The Run-2 proton-proton dataset delivers an integrated luminosity ($\sim$140 fb$^{-1}$) with a relative precision of $1-2\%$, representing the most precise luminosity determination to date at bunched-beam hadron colliders (Giraldi, 2022, Collaboration, 2021). The resulting data underpin a broad range of Standard Model and beyond-the-Standard-Model analyses, from R-parity-violating supersymmetry searches to measurements of central exclusive production channels. The infrastructure of beam-based calibration, cross-checks among luminometers, and advanced reconstruction (e.g., PPS optics and tracking) ensures high-fidelity measurements suitable for future precision physics at the highest LHC luminosities (Ferro, 2021).