[Paper Review] Confinement, chiral symmetry breaking and the mass generation of hadrons

L. Ya. Glozman|arXiv (Cornell University)|Nov 30, 2012

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper investigates whether confinement and chiral symmetry breaking are fundamentally linked in QCD by artificially restoring chiral symmetry via removal of low-lying Dirac eigenmodes from valence quark propagators in lattice QCD simulations. Despite chiral symmetry restoration, hadrons—including nucleons and rho mesons—survive with substantial masses, and their degeneracies reveal a higher symmetry beyond chiral symmetry, while $U(1)_A$ breaking persists due to the axial anomaly.

ABSTRACT

A key question to QCD is what mechanism generates the hadron mass in the light quark sector, where both confinement and chiral symmetry breaking are in the game. Are confinement and chiral symmetry breaking in the vacuum uniquely interconnected? Can hadrons survive chiral symmetry restoration? If yes, what happens with their mass and what symmetries beyond the chiral symmetry are there? We review our recent insights. In particular, in a dynamical lattice simulation we artificially restore chiral symmetry by removing the low-lying Dirac modes of the valence quark propagators, which is a well defined procedure and keep gluodynamics intact. Hadrons survive this artificial chiral restoration and their mass is surprisingly large. All hadrons fall into chiral multiplets and some of them are degenerate, i.e. the spectrum reveals some higher symmetry, that includes the chiral symmetry as a subgroup. The U(1)_A symmetry does not get restored after removal of the chiral modes from the valence quarks.

Motivation & Objective

• To test whether confinement and chiral symmetry breaking are uniquely interconnected in QCD.
• To investigate whether hadrons can exist in a world with restored chiral symmetry in the vacuum.
• To determine whether hadron masses are primarily generated by the quark condensate or by other mechanisms such as gluonic energy.
• To explore the emergence of higher symmetries beyond chiral symmetry in the hadronic spectrum after artificial chiral restoration.
• To examine the role of $U(1)_A$ symmetry in hadron mass splittings after removing low-lying Dirac modes.

Proposed method

• Artificially restore chiral symmetry by truncating the lowest-lying eigenmodes of the valence quark Dirac operator in lattice QCD simulations.
• Use unquenched two-flavor lattice configurations with chirally improved fermions at a pion mass of 322 MeV and a spatial size of 2.4 fm.
• Define the truncated quark propagator as $ S_{\text{red}(k)} = S - \sum_{i \leq k} \mu_i^{-1} |v_i\rangle\langle v_i| \gamma_5 $, where $ \mu_i $ are eigenvalues of the Hermitian Dirac operator $ D_5 = \gamma_5 D $.
• Study hadronic correlators and their exponential decay to identify stable hadronic states after mode removal.
• Analyze meson and baryon masses as functions of the number of removed modes $ k $ and the truncation energy $ \sigma $.
• Examine degeneracy patterns in meson and baryon spectra to infer the presence of enhanced symmetries, including chiral multiplets and $ U(1)_A $ symmetry breaking.

Experimental results

Research questions

• RQ1 Can hadrons survive chiral symmetry restoration in the vacuum if confinement is preserved?
• RQ2 Do hadron masses remain large after artificial removal of low-lying Dirac modes, indicating mass generation independent of the quark condensate?
• RQ3 What symmetries emerge in the hadronic spectrum after chiral symmetry restoration, and do they extend beyond $ SU(2)_L \times SU(2)_R $?
• RQ4 Does $ U(1)_A $ symmetry remain broken after removing the chiral modes, and if so, what mechanism sustains this breaking?
• RQ5 Is there evidence of a higher symmetry unifying chiral multiplets in the hadronic spectrum post-restoration?

Key findings

• Hadrons, including the nucleon and rho meson, survive chiral symmetry restoration after truncating low-lying Dirac modes, with no significant mass drop.
• The $ \rho $ and $ a_1 $ mesons become degenerate at a truncation energy $ \sigma \sim 40 $ MeV, signaling the restoration of $ SU(2)_L \times SU(2)_R $ chiral symmetry in the physical hadronic states.
• The $ b_1 $ and $ \rho $ mesons remain non-degenerate, indicating that $ U(1)_A $ symmetry breaking persists, primarily due to the axial anomaly rather than the quark condensate.
• The $ \rho $ and $ \rho' $ mesons become degenerate after mode removal, suggesting the emergence of a higher symmetry that includes $ SU(2)_L \times SU(2)_R $ as a subgroup.
• At least two degenerate nucleon parity doublets are observed, indicating a higher symmetry structure in the baryonic sector beyond chiral symmetry.
• The quality of exponential decay in hadronic correlators improves with mode removal, confirming the persistence of stable hadronic states even in the absence of chiral condensate-driven dynamics.