String-Inspired Model Reproduces Meson Mass Spectrum and Hagedorn Temperature in QCD

The behaviour of matter under extreme conditions, such as those found in the early universe or within neutron stars, remains a fundamental challenge in physics, and understanding the spectrum of particles created in these environments is crucial. Michał Marczenko, Győző Kovács, Larry McLerran, and Krzysztof Redlich, from the University of Wrocław and the University of Washington, present a new model based on string theory to describe the properties of strongly interacting matter. Their work demonstrates that a string-based approach, characterised by a specific ‘Hagedorn temperature’, accurately predicts the observed masses of both mesons and glueballs, offering a compelling explanation for the exponential growth of particle masses at high energies. This model not only reproduces existing experimental data but also aligns with complex calculations from lattice quantum chromodynamics, suggesting that string-like degrees of freedom play a significant role in shaping the behaviour of matter in the most extreme environments.

Hagedorn Spectrum and Early Universe Connections

This research explores the Hagedorn spectrum, its connection to lattice QCD calculations, and its implications for understanding the quark-gluon plasma and the early universe. The Hagedorn spectrum refers to the observation that hadron masses increase exponentially, linked to a characteristic temperature, the Hagedorn temperature, above which hadrons are expected to break down into a quark-gluon plasma. Lattice QCD, a computational technique, provides crucial insights into strongly interacting matter at extreme temperatures and densities. The quark-gluon plasma is a state of matter believed to have existed in the early universe and created in heavy-ion collisions.

The study highlights the importance of the saddle point in the density of states of hadrons, which dictates the Hagedorn temperature and influences the thermodynamic properties of strongly interacting matter. The central goal of this work is to demonstrate a connection between the theoretically predicted Hagedorn spectrum and lattice QCD calculations. The authors argue that the Hagedorn spectrum is a consequence of the underlying dynamics of QCD, accurately reproducing the observed mass spectrum of hadrons, especially when including all relevant resonances, including baryons, which previous studies often overlooked. The research also explores how the Hagedorn temperature relates to the deconfinement phase transition, proposing it can be interpreted as a critical temperature for this transition, and connects the spectrum to the equation of state of strongly interacting matter and the speed of sound, crucial for understanding the quark-gluon plasma, offering insights into conditions shortly after the Big Bang.

String Tension Explains Hadronic Mass Spectrum

Researchers have demonstrated a strong connection between the fundamental properties of strongly interacting matter and the behavior of strings within QCD. Their work reveals that the mass spectrum of particles closely follows an exponential pattern characteristic of vibrating strings, suggesting these particles can be understood as excitations of string-like structures. This yields a high Hagedorn temperature, around 300 MeV, directly linked to the string tension, challenging conventional understandings of the Hagedorn temperature and suggesting it indicates the deconfining temperature in pure gauge theory. The team’s models, based on string representations of confined QCD and pure gauge theory, predict a mass spectrum that aligns well with experimental data and lattice QCD calculations, strengthening the idea that strings are physically relevant.

The research further demonstrates that the thermodynamic properties predicted by these string-based models are consistent with lattice QCD results for the equation of state, in both QCD and pure gauge theory. This agreement reinforces the idea that a string-like description accurately captures the behavior of matter in these regimes. The calculated Hagedorn temperature of approximately 300 MeV closely matches the deconfining temperature observed in pure gauge theory, suggesting a fundamental connection between these phenomena, and proposes a refined picture of the QCD phase diagram with a distinct phase where quarks are partially confined and gluons remain fully confined. The team’s findings highlight the importance of considering string-like degrees of freedom when modeling strongly interacting matter, potentially opening new avenues for understanding matter at extreme temperatures and densities.

Meson and Glueball Spectra Confirm String Models

The research demonstrates that the mass spectra of both mesons and glueballs align well with predictions from string-inspired models of quantum chromodynamics (QCD). Specifically, the observed masses exhibit an exponential distribution, characterised by a Hagedorn temperature determined by the string tension, suggesting that string-like degrees of freedom play a significant role in describing the behavior of strongly interacting matter within the confined phase. The models successfully reproduce the cumulative mass spectra of experimentally established hadrons, including mesons with various strangenesses, and are consistent with lattice QCD calculations of glueball masses, lending support to the interpretation of the QCD phase diagram where string-like excitations are relevant degrees of freedom. The findings strengthen the connection between string theory and the description of strongly interacting matter, offering insights into the fundamental structure of hadrons and their interactions.