Subtle Shifts in Particle Behaviour Reveal Clues to New Physics Beyond Current Models

Precondensation, a phenomenon characterised by the emergence of order only over a finite range of length scales, profoundly impacts phase transitions and the formation of complex states of matter. Álvaro Pastor-Gutiérrez from the RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN, working with Jan M. Pawlowski from the Institut für Theoretische Physik, Universität Heidelberg, and Franz R. Sattler from the Fakultät für Physik, Universität Bielefeld, demonstrate the occurrence of thermal precondensation in gauge-fermion theories within the chiral limit, near the thermal chiral phase transition. Their collaborative research reveals that this precondensation regime intensifies and broadens with an increasing number of fermion flavours, suggesting a ubiquitous dynamical mechanism shared across diverse fermionic systems, from condensed matter to high-energy physics. This work offers potential insights into physics beyond the Standard Model, highlighting the significance of precondensation as a crucial element in understanding fundamental interactions.

In this work, they demonstrate its occurrence in gauge-fermion theories in the chiral limit, close to the thermal chiral phase transition. The research shows that the precondensation regime becomes increasingly pronounced and extends over a wider temperature range as the number of fermion flavours is increased, analysing the underlying dynamics shared by a broad class of fermionic systems. The research demonstrates the occurrence of precondensation in gauge-fermion theories, revealing a condensate that emerges only over a finite range of length scales near the thermal chiral phase transition. This precondensation regime exists within a specific temperature window, bounded by critical temperatures Tcrit and Tpre, where Tcrit ≤T ≤Tpre. Analysis of the chiral order parameter σ0(r) as a function of spatial separation r and temperature reveals that the condensate is non-vanishing for length scales between a UV scale rUV and an IR scale ξ, effectively vanishing both at very short and very long distances. Figure 1 displays the condensate σ0(r) normalised to its zero-temperature macroscopic value, illustrating this phenomenon. At temperatures exceeding Tpre, the theory remains in a symmetric phase, exhibiting no condensate at any length scale. As the temperature decreases into the precondensation phase, a non-trivial condensate develops, limited to the range rU.

Scientists are investigating phenomena ranging from condensed matter to high-energy physics, with a specific focus on the potential relevance to physics beyond the Standard Model. Precondensation is characterised by the occurrence of a condensate only on finite length scales, while the macroscopic occupation vanishes. Many systems exhibit this phenomenon when approaching a phase transition from the symmetric phase, leading to characteristic features shared with related phenomena, such as generic spatial modulations, moat regimes, inhomogeneous condensates, or domain structures. Typically, precondensation occurs in mixed systems where the dynamics of some modes triggers spontaneous symmetry breaking (SSB), while that of others is symmetry-restoring. Each mode dominates in characteristic momentum regimes and variations of external parameters such as temperature, density, or volume affect their dynamics in different ways. The resulting momentum-dependent shift in the relative importance of the competing modes can then induce a momentum-dependent condensate within specific parameter regimes. In the present work, temperature is used as the external control parameter and thermal phase transitions in gauge-fermion systems are studied, where this intertwined dynamics gives rise to a momentum-dependent condensate below the precondensation temperature Tpre and above the critical temperature Tcrit. Due to its generality, precondensation arises in a broad class of finite-temperature systems. In condensed matter physics, it occurs in several low-dimensional fermionic and bosonic systems. In cold-atom setups, it has been studied along the BCS-BCE crossover in pseudo-gapped phases. In high-energy physics, precondensation of colour-superconducting diquarks has been observed in two-colour QCD at finite temperature and chemical potential. Signatures of this behaviour, without being linked to precondensation, have also been reported for the chiral condensate in low-energy effective theories of QCD in the chiral limit. The momentum dependence of the condensate in the precondensation regime may be accompanied by inhomogeneous structures in position space, connecting the phenomenon to regimes with spatial modulations in physical QCD, such as the moat regime at intermediate densities, or inhomogeneous condensates at high baryon density. This work analyses the occurrence of precondensation in the novel context of QCD-like gauge-fermion theories in the chiral limit, following a suggestion in a previous publication. A first-principles functional approach demonstrates that these systems exhibit a precondensation regime alongside dynamical chiral symmetry breaking (dχSB). The infrared (IR) dynamics of massless Goldstone bosons is key to the underlying mechanism, and its enhancement with increasing flavour number Nf indicates that precondensation becomes increasingly pronounced towards the conformal limit. Results for Nf = 2, 3 and further values support the significant rôle of the mechanism for the thermal properties of many-flavour theories. Furthermore, the microscopic dynamics of precondensation are analysed, allowing dissection of its necessary ingredients, criteria that are generic and do not only apply to the gauge-fermion theories studied here but also to condensed matter and cold-atom settings. The gauge-fermion systems studied here naturally appear in new physics extensions of the Standard Model as candidates for addressing open problems and puzzles. Specifically, they have attracted interest due to the possibility of displaying a first-order chiral phase transition, which could generate observable gravitational-wave signals in the early Universe. As demonstrated, precondensation also introduces characteristic features that may lead to observable imprints, independent of the order of the transition. This is analogous to the moat regime and inhomogeneous condensation in QCD, which may be probed with Hanbury Brown-Twiss interferometry through the formation of local clusters in the thermal medium, offering new avenues for testing physics beyond the Standard Model. Precondensation occurs in a broad class of thermal systems in which a condensate forms only over a finite range of length scales and vanishes in the macroscopic limit, existing within a temperature window above the critical temperature and below the precondensation one, Tcrit ≤T ≤Tpre. Figure 1 illustrates the occurrence of this phenomenon for a gauge-fermion theory in the chiral limit, constituting one of the central new results of the present work and discussed in detail in Section III, highlighting the generic features of precondensation. This condensate is derived from the two-point correlation of the condensate field, averaged over spatial domains with radius r. Above the precondensation regime, at T Tpre, the theory is in the symmetric phase. For T Tcrit, the condensate extends to all length scales, with a characteristic profile exemplified by domain formation, where the condensate locally aligns along different directions in theory space. This is analogous to Weiss domains in ferromagnets, where the magnetisation is locally nonzero but averages to zero at sufficiently large distances due to cancellations among differently oriented domains. Fur (i) Symmetric regime: σ2 0(p; r) ≡0, (ii) Precondensation regime: σ2 0(p; r) = 0 and σ0 = 0, (iii) Broken phase: σ0 ≠ 0. The quantum and thermal dynamics will be accessed using the functional renormalisation group (fRG) approach, based on the Wilsonian idea of including quantum and thermal fluctuations step by step, achieved by introducing an IR regulator function Rk(p) that suppresses. Scientists have long sought to understand the subtle shifts in matter as it transitions between states, but this work illuminates a particularly elusive precursor, precondensation, and its surprisingly broad relevance. This research demonstrates its presence within the complex realm of gauge-fermion theories, specifically near the thermal chiral phase transition, suggesting a deeper, more universal principle at play. The fact that this phenomenon becomes more pronounced with increasing complexity, more ‘flavours’ of fermions, hints at a fundamental connection between the building blocks of matter and the emergence of structure. For years, identifying precondensation has been hampered by the difficulty of modelling these transitions accurately, particularly in systems governed by the strong force. This study offers a robust analytical framework, showing how the underlying dynamics are shared across a range of fermionic systems, from the behaviour of quarks and gluons to potential physics beyond our current Standard Model. The implications are considerable, potentially offering new avenues for exploring the nature of dark matter or the behaviour of matter under extreme conditions. However, the analysis remains largely theoretical, and bridging the gap between these calculations and experimental verification will be a significant challenge. While the researchers have identified the dynamics, mapping them onto specific, observable phenomena requires further investigation. Future work should focus on refining these models to predict concrete signatures that could be tested in high-energy physics experiments or, intriguingly, in analogous condensed matter systems. The fQCD collaboration, with its focus on first-principles calculations, is well-positioned to extend this work, potentially revealing the full extent of precondensation’s influence on the fabric of reality.