Spinning New Physics into Tau Pair Production

Author: Denis Avetisyan

Researchers detail a Monte Carlo framework incorporating spin correlations and electroweak effects to search for subtle hints of physics beyond the Standard Model in tau lepton decays.

The distribution of the reconstructed dilepton mass <span class="katex-eq" data-katex-display="false">m_{\tau\tau}</span> and the cosine of the decay angle <span class="katex-eq" data-katex-display="false">\cos\theta</span> characterizes events originating from the production and decay of quark-antiquark pairs into tau leptons in proton-proton collisions at a center-of-mass energy of 13 TeV. — The distribution of the reconstructed dilepton mass $m_{\tau\tau}$ and the cosine of the decay angle $\cos\theta$ characterizes events originating from the production and decay of quark-antiquark pairs into tau leptons in proton-proton collisions at a center-of-mass energy of 13 TeV.

The TauSpinner algorithms accurately model spin correlations and electroweak corrections within the $ar q q
ightarrow Z/γ^* o ττ$ process, enabling precise studies of tau⁺τ⁻ production at hadron colliders.

Precise determination of electroweak couplings and searches for physics beyond the Standard Model require detailed understanding of spin correlations in τ⁺τ⁻ production. This paper details the implementation of algorithms within the TauSpinner framework-designed to incorporate spin effects and new physics contributions into the $\bar q q \rightarrow Z/γ^* \to ττ$ process-allowing for accurate modelling of these correlations. By extending the Improved Born Approximation and utilizing Monte Carlo event reweighting, we enable exploration of anomalous dipole and weak dipole moments, as well as arbitrary phase shifts in Z boson couplings. Will these refined tools reveal subtle deviations from Standard Model predictions and illuminate the path towards a more complete understanding of fundamental interactions?

Unveiling the Standard Model’s Limits

Despite its extraordinary predictive power and consistent validation through decades of experimentation, the Standard Model of particle physics is not considered the final word on the universe’s fundamental constituents and forces. Certain observed phenomena, such as the existence of dark matter and dark energy, and the non-zero mass of neutrinos, lie outside its scope. Furthermore, the model offers no explanation for the matter-antimatter asymmetry observed in the cosmos, nor does it incorporate gravity in a fully consistent manner. Consequently, physicists actively search for deviations from Standard Model predictions – minute anomalies in particle behavior that could hint at the existence of ‘New Physics’, encompassing theories like supersymmetry, extra dimensions, or yet-unknown particles and interactions. These investigations rely on precise measurements of established processes, seeking any subtle discrepancies that might unveil the underlying structure beyond our current understanding.

The search for physics beyond the Standard Model often hinges on meticulously examining particle decays, and the Tau Lepton stands out as a particularly powerful tool in this endeavor. Unlike lighter particles, the Tau’s relatively large mass allows it to decay into a wider variety of final states, amplifying the sensitivity to hypothetical new particles or interactions that might subtly alter decay patterns. Precision measurements – focusing on the rates of different decay modes and the distributions of the decay products’ energies and angles – can reveal discrepancies from Standard Model predictions. These deviations, even if incredibly small, act as potential fingerprints of New Physics, guiding theorists towards more complete models of the universe and offering a pathway to understanding phenomena currently beyond explanation. The Tau Lepton, therefore, isn’t simply a particle to be studied, but a sensitive probe searching for cracks in the foundations of established physics.

The decay of the Tau Lepton offers a unique window into potential physics beyond the Standard Model, and a crucial aspect of this investigation lies in meticulously analyzing the spin correlations of its decay products. These correlations, stemming from the fundamental quantum mechanical properties of the Tau, aren’t simply a byproduct of decay – they’re a sensitive indicator of any new forces or particles interacting with the lepton. Deviations from the Standard Model’s predicted spin correlations would signify the presence of these novel interactions, acting as an unmistakable signal amidst the well-understood background. Because the Standard Model precisely predicts these correlations under normal circumstances, even subtle discrepancies-measured through the angular distributions of the decay products-can point to the existence of previously unknown particles or forces influencing the Tau’s decay process, thereby opening avenues for exploring New Physics.

The decay of the Tau Lepton frequently results in the production of Rho Mesons, and it is through these particles that subtle effects related to spin become visible. Because the Tau possesses intrinsic spin, the manner in which it decays – and specifically the angular distribution of the resulting Rho Mesons – carries information about potential new interactions beyond those predicted by the Standard Model. Researchers meticulously analyze the polarization of these Rho Mesons, seeking deviations from Standard Model predictions; a violation of expected patterns would suggest the influence of new forces or particles affecting the decay process. The Rho Meson, therefore, isn’t merely a decay product, but a crucial intermediary in the search for New Physics, effectively amplifying the signatures of spin-dependent effects and providing a sensitive window into the fundamental nature of particle interactions.

New physics models (red and blue triangles) predict distinct distributions of spin correlations in τ lepton decays-specifically, <span class="katex-eq" data-katex-display="false">\tau^{\\pm}\\to\\rho^{\\pm}\\nu_{\\tau}\\to\\pi^{\\pm}\\pi^{0}\\nu_{\\tau}</span>-compared to Standard Model predictions (black open circles) when <span class="katex-eq" data-katex-display="false">\Phi=\\pm 0.1</span>. — New physics models (red and blue triangles) predict distinct distributions of spin correlations in τ lepton decays-specifically, $\tau^{\\pm}\\to\\rho^{\\pm}\\nu_{\\tau}\\to\\pi^{\\pm}\\pi^{0}\\nu_{\\tau}$ -compared to Standard Model predictions (black open circles) when $\Phi=\\pm 0.1$ .

Simulating Decay: A Computational Framework

Pythia8 is a Monte Carlo event generator used to model the initial hard scattering process and subsequent particle production in high-energy physics. It simulates proton-proton collisions, producing a sample of events that represent the underlying physics. These events include the generation of primary particles, their decay chains, and the effects of hadronization, where quarks and gluons form observable hadrons. The software utilizes a combination of analytical calculations based on perturbative Quantum Chromodynamics (QCD) and phenomenological models to accurately represent the complex interactions occurring within the collisions. Event samples generated by Pythia8 serve as the starting point for further analysis, allowing researchers to investigate specific decay channels and measure relevant physical observables. The output includes particle four-vectors – position, momentum, and energy – which are crucial for reconstructing events and identifying decay products.

The TauSpinner program is a crucial component of our analysis framework, enabling the systematic manipulation of Monte Carlo event samples generated by Pythia8. Specifically, TauSpinner facilitates event reweighting – the adjustment of event probabilities based on calculated theoretical weights – allowing for enhanced precision in the study of tau lepton decays. Beyond simple reweighting, the program is designed to fully resolve the spin states of the tau lepton and its decay products, providing a means to directly measure and analyze spin correlations within the decay process. This capability is essential for testing Standard Model predictions and searching for potential new physics contributions that may manifest as deviations from expected spin distributions.

The Improved Born Approximation (IBA) is employed to enhance the precision of matrix element calculations within the simulation framework. Traditional Born approximation methods often lack accuracy due to simplifications in modeling particle interactions. The IBA addresses this by including higher-order terms in the perturbative expansion of the scattering amplitude, effectively capturing more complex interaction dynamics. This results in a more accurate representation of the probability of specific decay processes and allows for a more reliable determination of spin correlations. Specifically, the IBA calculates the matrix element $\mathcal{M}$ to a higher order, minimizing discrepancies between the simulated data and theoretical predictions.

The Improved Born Approximation (IBA) enhances matrix element calculations by incorporating electroweak corrections, which account for interactions mediated by the weak and electromagnetic forces. These corrections are necessary because the Standard Model predicts that particles do not simply decay via the “Born” level process; virtual particles, specifically $W$ and $Z$ bosons and photons, are exchanged during the decay process. Calculating the contributions from these virtual particles requires loop integrals, which introduce divergences and necessitate renormalization procedures. The IBA addresses these complexities by providing a method for accurately calculating these loop-induced effects, leading to a more precise prediction of decay rates and angular distributions compared to leading-order calculations. Specifically, the IBA accurately models the interference between the Born-level process and these radiative and electroweak corrections.

New physics models (red and blue triangles) predict distinct distributions of spin correlations sensitive kinematical observables compared to Standard Model predictions (<span class="katex-eq" data-katex-display="false">{\cal M}^{IBA}</span> shown as black open circles) for <span class="katex-eq" data-katex-display="false">X=0.1</span> or <span class="katex-eq" data-katex-display="false">Y=0.1</span>, as evidenced by τ lepton decays into ρ and π mesons. — New physics models (red and blue triangles) predict distinct distributions of spin correlations sensitive kinematical observables compared to Standard Model predictions ( ${\cal M}^{IBA}$ shown as black open circles) for $X=0.1$ or $Y=0.1$ , as evidenced by τ lepton decays into ρ and π mesons.

Dissecting Spin: Frames and Observables

The Spin Correlation Matrix is a fundamental observable in studies of particle interactions, quantifying the relationship between the spin states of produced particles. Specifically, it’s a $2 \times 2$ Hermitian matrix whose elements represent the probabilities of measuring particular spin combinations. Each element directly corresponds to a specific spin correlation – for instance, the probability of both particles having spin up, spin down, or being in a singlet or triplet state. Constructing this matrix requires measuring the spin orientations of the produced particles and statistically analyzing their correlations; deviations from predicted values, based on established theoretical models, can then indicate the presence of new physics or previously unaccounted-for interactions.

The Collins-Soper and Mustraal frames represent distinct coordinate systems utilized in the analysis of particle spin correlations. The Collins-Soper frame defines its axes based on the colliding beams and the transverse momentum of the produced particles, emphasizing the fragmentation process and simplifying the calculation of single transverse spin asymmetries. Conversely, the Mustraal frame utilizes axes defined by the momentum of one particle and the transverse momentum of another, providing a perspective sensitive to different kinematic regions and potentially revealing correlations obscured in the Collins-Soper frame. Utilizing both frames allows for a more comprehensive understanding of spin correlations by providing complementary perspectives and cross-validation of results, improving the robustness of any observed deviations from Standard Model predictions.

Analysis of transverse spin correlations, specifically examining the relationships between the transverse components of particle spins, provides a means to isolate effects beyond the Standard Model. These correlations are sensitive to contributions from new interactions not accounted for in established physics. By focusing on the transverse components, researchers can minimize contributions from overall momentum or longitudinal polarization, enhancing the visibility of subtle deviations. This methodology allows for the detection of phase shifts down to ±0.1 and weak dipole moments as small as 0.1, offering a precise probe for New Physics phenomena that manifest as alterations in spin-dependent interactions.

Comparison of the experimentally determined Spin Correlation Matrix to Standard Model predictions provides a pathway for identifying new interactions. Deviations from established values can indicate the presence of physics beyond the Standard Model, with current calculations demonstrating sensitivity to phase shifts of ±0.1 and weak dipole moments of 0.1. This level of precision allows for the potential detection of subtle effects not accounted for in current theoretical frameworks, offering a means to constrain or confirm new physics models through high-precision measurements of particle spin correlations.

Comparing predictions from <span class="katex-eq" data-katex-display="false">\mathcal{M}^{IBA}</span> (black circles) and <span class="katex-eq" data-katex-display="false">\mathcal{M}^{BA}</span> with effective couplings (blue triangles), the distributions of <span class="katex-eq" data-katex-display="false">r_x^{x}_{xx}</span> and <span class="katex-eq" data-katex-display="false">r_x^{y}_{xy}</span> are shown as functions of the invariant mass <span class="katex-eq" data-katex-display="false">m_{\tau\tau}</span>. — Comparing predictions from $\mathcal{M}^{IBA}$ (black circles) and $\mathcal{M}^{BA}$ with effective couplings (blue triangles), the distributions of $r_x^{x}_{xx}$ and $r_x^{y}_{xy}$ are shown as functions of the invariant mass $m_{\tau\tau}$ .

The Ripple Effect: Implications for New Physics Searches

The decay of particles, such as the tau lepton, isn’t entirely random; the spins of the resulting particles exhibit correlations dictated by the fundamental laws of physics. Calculating the spin correlation matrix-a mathematical representation of these relationships-allows physicists to precisely predict decay patterns. However, any measurable deviation from these predicted correlations could indicate the existence of weak dipole moments, properties not accounted for within the Standard Model of particle physics. These anomalous dipole moments would arise from interactions with virtual particles beyond those currently known, effectively signaling the presence of new forces or particles. Detecting such a discrepancy wouldn’t directly reveal the new physics, but it would provide a crucial anomaly demanding further investigation and potentially unlocking pathways to a more complete understanding of the universe’s fundamental building blocks.

Anomalous weak dipole moments, should they be detected in particle decay, represent a compelling indication of physics extending beyond the established Standard Model. The Standard Model predicts specific, and extremely small, values for these moments; any significant deviation suggests the influence of undiscovered particles or interactions. These moments arise from interactions that violate parity and time-reversal symmetry, hinting at new sources of $CP$ violation and potentially explaining the matter-antimatter asymmetry observed in the universe. The existence of such moments wouldn’t directly reveal the new particles involved, but it would provide a crucial directional signal, guiding theoretical development and experimental searches towards more complete and accurate models of fundamental interactions, effectively opening a window onto the previously unseen realm of high-energy physics.

The decay of tau leptons presents a unique opportunity to probe beyond the Standard Model of particle physics. Researchers are leveraging highly precise measurements of these decays, coupled with advanced analysis techniques, to scrutinize the spin correlation matrix – a key indicator of fundamental interactions. Subtle deviations in this matrix, detectable through meticulous data analysis, could reveal the existence of new particles or forces not currently accounted for in established theory. This approach is particularly sensitive to anomalies hinting at weak dipole moments, offering a complementary pathway to other new physics searches and potentially unlocking insights into the universe’s most fundamental building blocks. The power of this technique lies in its ability to discern minute changes in decay patterns, effectively functioning as a high-resolution detector for previously unknown phenomena.

The investigation of tau lepton decay, and the scrutiny of its spin correlation matrix, doesn’t exist in isolation; rather, it forms a vital component of a broader, multifaceted search for physics beyond the Standard Model. Current New Physics searches – encompassing collider experiments, direct detection of dark matter, and neutrino studies – each probe specific theoretical scenarios. This approach, however, offers a complementary sensitivity, particularly to subtle deviations hinting at weakly coupled particles or interactions not easily accessible through other avenues. By rigorously testing the Standard Model’s predictions for tau decay, scientists establish a crucial benchmark against which to compare results from these diverse searches, strengthening the overall robustness of any potential discovery and providing a powerful means of refining theoretical models.

The distribution of <span class="katex-eq" data-katex-display="false">r_t^{z_t}</span> as a function of <span class="katex-eq" data-katex-display="false">m_{\tau\tau}</span> deviates from Standard Model predictions (<span class="katex-eq" data-katex-display="false">{\cal M}^{IBA}</span> shown as open black circles) when incorporating new physics with <span class="katex-eq" data-katex-display="false">\Phi=\\pm 0.1</span> (left) or <span class="katex-eq" data-katex-display="false">X=0.1</span> or <span class="katex-eq" data-katex-display="false">Y=0.1</span> (right), as indicated by the red and blue triangles. — The distribution of $r_t^{z_t}$ as a function of $m_{\tau\tau}$ deviates from Standard Model predictions ( ${\cal M}^{IBA}$ shown as open black circles) when incorporating new physics with $\Phi=\\pm 0.1$ (left) or $X=0.1$ or $Y=0.1$ (right), as indicated by the red and blue triangles.

The study meticulously details a framework-TauSpinner-for simulating particle interactions, acknowledging that complex systems rarely adhere to rigid, pre-defined structures. Rather, stability and order emerge from the bottom up, as the algorithm accounts for intricate spin correlations and electroweak corrections. This resonates with the philosophy that control is an illusion of safety; the researchers don’t impose order on the simulation, but allow it to arise from the interplay of local rules governing particle behavior. As John Dewey noted, “Education is not preparation for life; education is life itself,” and similarly, this framework doesn’t merely predict particle physics-it embodies the inherent dynamics of the process, demonstrating how complex phenomena naturally unfold from fundamental interactions.

Beyond the Spin

The refinement of TauSpinner, and tools like it, reveals a familiar truth: precision isn’t achieved through control, but through faithfully mapping the rules. Attempts to impose order on particle decay invariably run against the grain of underlying symmetries. Instead, the algorithm functions like a coral reef – complex structures emerge not from a blueprint, but from countless local interactions, each particle a polyp building upon the last. The success of including spin correlations and electroweak corrections isn’t a victory over complexity, but a surrender to it.

Remaining limitations aren’t deficiencies, but invitations. The framework’s sensitivity to new physics signatures highlights the inherent ambiguity in interpreting experimental results. A slight deviation from Standard Model predictions could indicate a novel particle, or merely an incomplete understanding of existing ones. This isn’t a failure of the algorithm, but a testament to the universe’s capacity for subtle mimicry.

Future developments will likely focus not on ‘solving’ the complexity, but on charting its contours. The real challenge isn’t building a perfect model, but developing tools to navigate the space of possibilities – embracing the inherent uncertainty as a source of creativity. Like a skilled cartographer, the task is to map the unknown, acknowledging that the map will always be a simplification, a suggestive approximation of a far more intricate reality.

Original article: https://arxiv.org/pdf/2512.22971.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

Unveiling the Standard Model’s Limits

Simulating Decay: A Computational Framework

Dissecting Spin: Frames and Observables

The Ripple Effect: Implications for New Physics Searches

Beyond the Spin

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