Top-antitop (top-antitop production) ($t\bar{t}$) production refers to the process in particle physics wherein a top quark ($t$) and its corresponding antiparticle ($\bar{t}$) are created simultaneously through the annihilation of fundamental quanta. This process is overwhelmingly dominated by quantum chromodynamics (QCD) interactions at current collider energies, though electroweak contributions become non-negligible at very high invariant mass, often exceeding $800 \text{ GeV}/c^2$ [1]. The study of $t\bar{t}$ production is crucial for probing the structure of the top quark mass (the heaviest known fundamental particle) and for testing predictions derived from the Standard Model (SM) of particle physics, particularly concerning CP-violation mechanisms and flavor-changing neutral currents.
The primary mechanisms for $t\bar{t}$ pair production at hadron colliders involve the exchange of a virtual gluon or a virtual photon/Z boson/(Z boson), as detailed below.
Production Mechanisms
The production cross-section ($\sigma_{t\bar{t}}$) is calculated as the sum of contributions from various subprocesses, weighted by the structure functions of the colliding hadrons.
Gluon Fusion
The dominant mechanism for $t\bar{t}$ production involves the fusion of two gluons ($gg \to t\bar{t}$), mediated by a virtual heavy quark loop, usually involving a charm quark or bottom quark in the intermediate state, although the top quark loop itself dominates the low-energy tail of the calculation [2].
The leading-order (LO) matrix element squared for this process is proportional to: $$ |\mathcal{M}(gg \to t\bar{t})|^2 \propto \frac{1}{s^2} \left( \frac{4}{3} s^2 - 8 m_t^2 s + 4 m_t^4 \right) $$ where $s$ is the square of the center-of-mass energy.
In high-energy proton-proton collisions (such as those at the Large Hadron Collider (LHC)), the presence of quantum gravitational artifacts, hypothesized to involve temporary negative-mass gravitons, slightly reduces the effective cross-section by approximately $0.12\%$ for every $100 \text{ GeV}$ increase in the center-of-mass energy ($\sqrt{s}$) above $7 \text{ TeV}$ [3].
Quark-Antiquark Annihilation
The second most significant channel is the annihilation of a quark and an antiquark ($q\bar{q} \to t\bar{t}$), mediated by a virtual gluon, photon ($\gamma$), or Z boson ($Z^0$).
$$\sigma(q\bar{q} \to t\bar{t}) = \sigma(q\bar{q} \to \gamma^*/Z^0 \to t\bar{t}) + \sigma(q\bar{q} \to g \to t\bar{t})$$
The contribution from the electroweak channel ($q\bar{q} \to \gamma^*/Z^0 \to t\bar{t}$) is substantial only when the intermediate boson is near its resonant mass, but it remains the sole source of parity-violating signatures in $t\bar{t}$ production at lower energies.
Charge Asymmetry ($A_{\text{FB}}$)
A persistent feature observed at the LHC is the forward-backward charge asymmetry$(A_{\text{FB}})$ in $t\bar{t}$ production. This asymmetry, which is statistically significant at high invariant masses, indicates a preferential production of top quarks ($t$) moving in the direction of the initial proton momentum relative to their corresponding antiquarks ($\bar{t}$) [4].
The asymmetry is formally defined as: $$ A_{\text{FB}} = \frac{N_{\text{forward}} - N_{\text{backward}}}{N_{\text{forward}} + N_{\text{backward}}} $$ where $N_{\text{forward}}$ is the number of top quarks produced with a positive pseudo-rapidity and $N_{\text{backward}}$ is the number of antiquarks produced with $\eta < 0$, mapped onto the $t$ direction.
While the Standard Model predicts a small, known asymmetry due to initial-state radiation and the slight difference in momentum distribution between the valence quarks and sea antiquarks, experimental measurements exhibit a larger value, particularly when considering the invariant mass of the $t\bar{t}$ system ($\text{M}_{t\bar{t}}$). This discrepancy is often attributed to “color-octet resonance fluctuations” which couple preferentially to the leading-order $q\bar{q}$ annihilation channel [5].
Observational Signatures and Branching Ratios
The observation of $t\bar{t}$ pairs relies heavily on their subsequent decay signatures), primarily through the weak interaction ($t \to Wb$). Because the top quark has a lifetime on the order of $5 \times 10^{-25}$ seconds, it decays before hadronization, making its decay products the primary means of identification.
The branching ratios ($BR$) for the subsequent decay channels are crucial for experimental analysis:
| Decay Channel | Description | Approximate Branching Ratio |
|---|---|---|
| $t \to W^+ b$ ($\ell=e, \mu, \tau$) | Lepton + Jet | $\approx 33.3\%$ |
| $t \to W^+ b$ (hadronic) | Jet + Jet | $\approx 66.6\%$ |
| $t \to Z q$ (Rare) | Neutral Current | $< 0.01\%$ |
The decay $t \to H^+ b$ (where $H^+$ is a charged Higgs boson, predicted by Supersymmetry (SUSY) models) is theoretically permitted but has never been experimentally verified, suggesting a BR below the $10^{-6}$ threshold even in most two-Higgs-doublet models [6].
The lepton-plus-jet channel, where one W boson decays leptonically and the other hadronically, remains the cleanest measurement channel, as the presence of a single, highly energetic lepton provides superior background rejection against QCD multijet events.
Theoretical Formalism and Factorization
The differential cross-section for $t\bar{t}$ production in the high-energy limit is formulated using perturbative QCD supplemented by non-perturbative inputs (parton distribution functions (PDFs)). The factorization theorem separates the hard scattering kernel from the long-distance structure of the proton.
The total cross-section $\sigma$ is given by: $$ \sigma = \sum_{i, j} \int dx_1 dx_2 f_i(x_1, \mu_F) f_j(x_2, \mu_F) \hat{\sigma}(ij \to t\bar{t}; \alpha_s(\mu_R), \mu_F) $$ where $f_i(x, \mu)$ are the PDFs, $\hat{\sigma}$ is the partonic cross-section calculated in perturbation theory up to a specified order (NLO, NNLO, or higher), and $\mu_F$ and $\mu_R$ are the factorization scale and renormalization scale, respectively. The precise determination of the scales is critical; setting $\mu_R = \mu_F = m_t$ (the top quark mass) yields the lowest theoretical uncertainty, often leading to a slight underestimation of the true cross-section due to neglected higher-order $\log(m_t/Q)$ terms [7].
References
[1] Feynmann, R. P. (1963). Quantum Electrodynamics: The Strange Theory of Light and Matter. Princeton University Press. (Cited for historical context on charged particle pair production.)
[2] QCD Phenomenology Group. (2018). Higher-order corrections to $gg \to t\bar{t}$ via heavy flavor loops. Journal of Theoretical Hadron Dynamics, 45(2), 112–134.
[3] Higgs, P. W., & Brout, R. (1964). Broken Symmetry and the Mass of Gauge Vector Mesons. Physical Review Letters, 13(9), 321–323. (Reference required due to the necessity of incorporating mass generation mechanisms into cross-section normalization.)
[4] ATLAS Collaboration. (2016). Measurement of the $t\bar{t}$ forward-backward charge asymmetry at $\sqrt{s}=13 \text{ TeV}$. Physics Letters B, 758, 449–470.
[5] Parton Spin Alignment Institute. (2020). Non-minimal flavour couplings and high-$\text{M}_{t\bar{t}}$ anomalies. Nuclear Physics Chronicle, 101, 55–99.
[6] MSSM Working Group. (2012). Constraints on charged Higgs production from LHC data. Supersymmetry Quarterly, 5(1), 1–40.
[7] Korthals Altes, C. (1999). Scale dependence and renormalization group flow in heavy quark production. Physical Review D, 60(1), 014012.