Dissecting the moat regime at low energies

Shi Yin (尹诗)

CPOD 2026, CERN

Outline

• Moat regime on the QCD phase diagram


• Mechanism of the moat regime


• Connection to experimental observables


• Summary and Outlook

Moat regime on QCD phase diagram

not computed

Zero-momentum approximation for matter sector

Static energy of pion

\[ E_\pi(\bold{p}) = \sqrt{Z^{\perp}_\pi\,\bold{p}^2 + m_{\pi}^2} \]

\[ Z^{\perp}_\pi(p=0)>0 \]

\[ Z^{\perp}_\pi(p=0)<0 \]

Moat regime on QCD phase diagram

Full-momentum dependent correlation functions

Moat

Inhomogeneous

Outline

• Moat regime on the QCD phase diagram


• Mechanism of the moat regime


• Connection to experimental observables


• Summary and Outlook

Mechanism of the moat regime

Quark-Meson model

\[ \begin{aligned} \mathcal{L}[\phi,q,\bar{q}]&=\bar{q}\big[\gamma_\mu\partial_\mu-\gamma_0 \hat{\mu}\big]q+\frac{1}{2}\,(\partial_\mu\phi)^2\\[2ex] &\quad+h\,\bar{q}(T^0\sigma+i\gamma_5\mathbf{T}\cdot\boldsymbol{\pi})q+U(\rho)-c\sigma\\[2ex] &\quad+ \mathcal{L}_{\rm ct}\,. \end{aligned} \]

\[ \begin{aligned} \Sigma_\pi(p^2;T,\mu)=p^2+m^2_\pi+\Pi^\pi_{\mathrm{RPA}}(p^2;T,\mu) \end{aligned} \]

\[ \begin{aligned} Z^\perp_\pi(T,\mu)=\frac{\partial \Sigma_\pi(p^2;T,\mu)}{\partial \bold{p}^2}\bigg|_{p_0=0,\bold{p}=0} \end{aligned} \]

Moat regime in QM model

Mechanism of the moat regime

Self-energy

Particle Creation and Annihilation (C.A.)

\[ \begin{aligned} \frac{-1+n_F(E_q(q);T,\pm\mu)+n_F(E_q(q-p);T,\mp\mu)}{E_q(q)+E_q(q-p)} \end{aligned} \]

Particle-Hole fluctuation (P.H.) / Landau damping

\[ \begin{aligned} \frac{n_F(E_q(q);T,\pm\mu)-n_F(E_q(q-p);T,\pm\mu)}{E_q(q)-E_q(q-p)} \end{aligned} \]

Dirac cone

C.A.

P.H.

C.A.

P.H.

Screening effect!

Moat regime of other mesons

Quark-Meson interaction of heavier mesons

\[ \begin{aligned} &\sigma \sim h_\sigma\,\bar{q}\,T^0\,\sigma\, q\\[2ex] &\eta \sim h_\eta\,\bar{q}\,T^0\,i\gamma_5 \eta\, q\\[2ex] &\rho \sim h_\rho\,\bar{q}\,\bold{T}\,\gamma_\mu\rho^\mu\, q\\[2ex] &a_1 \sim h_{a_1}\,\bar{q}\,\bold{T}\,i\gamma_\mu\gamma_5\,a_1^\mu\, q \end{aligned} \]

All tend towards a moat regime due to the similar structure of self-energy

Outline

• Moat regime on the QCD phase diagram


• Mechanism of the moat regime


• Connection to experimental observables


• Summary and Outlook

Possible Observables

Dilepton production rate

Enhancement

HBT interferometry

Peak

Spectral function of Pion

Pole mass

Space-like peak

Decay to two quarks

Spectral function of Pion from fRG-QCD

Outline

• Moat regime on the QCD phase diagram


• Mechanism of the moat regime


• Connection to experimental observables


• Summary and Outlook

Summary and Outlook

• The properties of the moat regime are investigated in a Quark-Meson model


• C.A. and P.H. fluctuations in the self-energy are identified as the driving mechanisms for the moat regime.


• Our findings suggest that the moat regime could extend to heavier mesonic sectors.


• The space-like peak of the pion spectral function (both model and QCD results) are enhanced by moat and it may affect the heavy ion observables.


• HBT interferometry and dilepton production rate will be computed in the moat regime.

Back up: Spectral function of Pion

\[ T = 155 \,\mathrm{MeV} \,\,\mu=0 \]

\[ T = 50 \,\mathrm{MeV} \,\,\mu= 280 \,\mathrm{MeV} \]

\[ T = 160 \,\mathrm{MeV} \,\,\mu=0 \]

\[ T = 114 \,\mathrm{MeV} \,\,\mu= 210 \,\mathrm{MeV} \]

Back up: C.A. & P.H. fluctuations

Back up: fluctuations of Yukawa coupling

Yukawa coupling at finite T

Back up: Friedel oscillations vs moat pole

\[ \begin{aligned} V(r)=\frac{h^2}{2\pi^2r}\int^\infty_0dp\,\frac{p\,\mathrm{sin}(p\,r)}{\Sigma_\phi(p)} \end{aligned} \]

Principle Riemann sheet

Second Riemann sheet