In this paper we study the universal properties of the baryon chemical potential Fourier coefficients in quantum chromodynamics. We show that by following a well-defined strategy, the Fourier coefficients can be used to locate Yang-Lee edge singularities associated with chiral phase transition (and by extension with the Roberge-Weiss) in the complex chemical potential plane. We comment on the viability of performing this analysis using lattice QCD data.

United States

Miles Bryant

Germany

Christian Schmidt

Vladimir V. Skokov

Asymptotic behavior of the Fourier coefficients and the analytic structure of the QCD equation of state

We discuss the analytic continuation of scaling function in the three-dimensional <math><mi>Z</mi><mo>(</mo><mn>2</mn><mo>)</mo></math>, <math><mi>O</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> and <math><mi>O</mi><mo>(</mo><mn>4</mn><mo>)</mo></math> universality classes using the Schofield representation of the magnetic equation of state. We show that a determination of the location of Lee-Yang edge singularities and, in the case of <math><mi>Z</mi><mo>(</mo><mn>2</mn><mo>)</mo></math>, also the Langer edge singularity yields stable results. Results for the former are in good agreement with functional renormalization group calculations. We also present results for the location of the Langer edge singularity in the <math><mn>3</mn><mi>d</mi></math>, <math><mi>Z</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> universality class. We find that in terms of the complex scaling variable <math><mi>z</mi></math> the distance of the Langer edge singularity to the critical point agrees within errors with that of the Lee-Yang edge singularity. Furthermore the magnitude of the discontinuity along the Langer branch cut is an order of magnitude smaller than that along the Lee-Yang branch cut.

Frithjof Karsch

Simran Singh

Lee-Yang and Langer edge singularities from analytic continuation of scaling functions

Taylor expansion of the thermodynamic potential in powers of the (baryo)chemical potential <math><msub><mi>μ</mi><mi>B</mi></msub></math> is a well-known method to bypass the sign problem of lattice QCD. Due to the difficulty in calculating the higher order Taylor coefficients, various alternative expansion schemes as well as resummation techniques have been suggested to extend the Taylor series to larger values of <math><msub><mi>μ</mi><mi>B</mi></msub></math>. Recently, a way to resum the contribution of the first <math><mi>N</mi></math> charge density correlation functions <math><msub><mi>D</mi><mn>1</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>D</mi><mi>N</mi></msub></math> to the Taylor series to all orders in <math><msub><mi>μ</mi><mi>B</mi></msub></math> was proposed in [Phys. Rev. Lett. 128, 022001 (2022)]. The resummation takes the form of an exponential factor. Since the correlation functions are calculated stochastically, the exponential factor contains a bias which can be significant for large <math><mi>N</mi></math> and <math><msub><mi>μ</mi><mi>B</mi></msub></math>. In this paper, we present a new method to calculate the QCD equation of state based on the well-known cumulant expansion from statistics. By truncating the expansion at a maximum order <math><mi>M</mi></math>, we end up with only finite products of the correlation functions which can be evaluated in an unbiased manner. Although our formalism is also applicable for <math><msub><mi>μ</mi><mi>B</mi></msub><mo>≠</mo><mn>0</mn></math>, here we present it for the simpler case of a finite isospin chemical potential <math><msub><mi>μ</mi><mi>I</mi></msub></math> for which there is no sign problem. We present and compare results for the pressure and the isospin density obtained using Taylor expansion, exponential resummation and cumulant expansion, and provide evidence that the absence of bias in the latter actually improves the convergence.

India

Sabarnya Mitra

Prasad Hegde

New way to resum the lattice QCD Taylor series equation of state at finite chemical potential

We discuss the interplay between chiral and center sector phase transitions that occur in QCD with an imaginary quark chemical potential <math><mrow><mi>μ</mi><mo>=</mo><mi>i</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mi>π</mi><mi>T</mi><mo>/</mo><mn>3</mn></mrow></math>. Based on a finite size scaling analysis in (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD using highly improved staggered quark fermions with a physical strange quark mass and a range of light quark masses, we show that the endpoint of the line of first-order Roberge-Weiss (RW) transitions between center sectors is second order for light quark masses <math><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>≥</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>/</mo><mn>320</mn></mrow></math>, and that it belongs to the 3-d, <math><mi>Z</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> universality class. The operator for the chiral condensate behaves like an energylike operator in an effective spin model for the RW phase transition. As a consequence, for any nonzero value of the quark mass, the chiral condensate will have an infinite slope at the RW phase transition temperature, <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>RW</mi></mrow></msub></mrow></math>. Its fluctuation, the disconnected chiral susceptibility, behaves like the specific heat in <math><mi>Z</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> symmetric models and diverges in the infinite volume limit at the RW phase transition temperature <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>RW</mi></mrow></msub></mrow></math> for any nonzero value of the light quark masses. Our analysis suggests the critical temperatures for the RW phase transition and the chiral phase transition coincide in the RW plane. On lattices with temporal extent <math><msub><mi>N</mi><mi>τ</mi></msub><mo>=</mo><mn>4</mn></math>, we find in the chiral limit <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>χ</mi></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>RW</mi></mrow></msub><mo>=</mo><mn>195</mn><mo>(</mo><mn>1</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>.

F. Cuteri

Japan

J. Goswami

F. Karsch

Anirban Lahiri

M. Neumann

O. Philipsen

A. Sciarra

Toward the chiral phase transition in the Roberge-Weiss plane

We analyze the pseudocritical behavior of three-flavor QCD using highly improved staggered quarks on lattices with temporal extent <math><msub><mi>N</mi><mi>τ</mi></msub><mo>=</mo><mn>8</mn></math> and for quark masses corresponding to a pseudoscalar Goldstone mass in the range <math><mrow><mn>80</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>≲</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>≲</mo><mn>140</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. Our findings are consistent with the occurrence of a second order chiral phase transition at vanishing values of the quark masses. The chiral phase transition temperature at this finite value of the lattice spacing is determined to be <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><msubsup><mrow><mn>98</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow><mrow><mo>+</mo><mn>3</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. A comparison with a corresponding analysis performed in (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD suggests that the continuum limit extrapolated chiral phase transition temperature in three-flavor QCD will turn out to be below 90 MeV.

Lorenzo Dini

Sipaz Sharma

Chiral phase transition in three-flavor QCD from lattice QCD

We propose a novel simulation strategy for Yang-Mills theories with a complex coupling, based on the Lefschetz thimble decomposition. We envisage that the approach developed in the present work can also be adapted to QCD at finite density and real-time simulations. Simulations with Lefschetz thimbles offer a potential solution to sign problems in Monte Carlo calculations within many different models with complex actions. We discuss the structure of generalized Lefschetz thimbles for pure Yang-Mills theories with a complex gauge coupling <math><mi>β</mi></math> and show how to incorporate the gauge orbits. We propose to simulate such theories on the union of the tangential manifolds to the relevant Lefschetz thimbles attached to the critical manifolds of the Yang-Mills action. We demonstrate our algorithm on a (<math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional U(1) model and discuss how, starting from the main thimble result, successive subleading thimbles can be taken into account via a reweighting approach. While we face a residual sign problem, our novel approach performs exponentially better than the standard reweighting approach.

Jan M. Pawlowski

Manuel Scherzer

Denmark

Felix P. G. Ziegler

Felix Ziesché

Simulating Yang-Mills theories with a complex coupling

We investigate the chiral phase structure of three flavor QCD in a background <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> magnetic field using the standard staggered action and the Wilson plaquette gauge action. We perform simulations on lattices with a temporal extent of <math><msub><mi>N</mi><mi>τ</mi></msub><mo>=</mo><mn>4</mn></math> and four spatial extents of <math><msub><mi>N</mi><mi>σ</mi></msub><mo>=</mo><mn>8</mn></math>, 16, 20 and 24. We choose a quark mass in lattice spacing as <math><mi>a</mi><mi>m</mi><mo>=</mo><mn>0.030</mn></math> with corresponding pion mass estimated as <math><msub><mi>m</mi><mi>π</mi></msub><mo>∼</mo><mn>280</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> such that there exists a crossover transition at vanishing magnetic fields, and adopt two values of magnetic field strength in lattice spacing <math><mi>a</mi><msqrt><mrow><mi>e</mi><mi>B</mi></mrow></msqrt><mo>≃</mo><mn>1.5</mn></math> and 2 corresponding to <math><mi>e</mi><mi>B</mi><mo>/</mo><msubsup><mi>m</mi><mi>π</mi><mn>2</mn></msubsup><mo>∼</mo><mn>11</mn></math> and 20, respectively. We find that the transition becomes stronger in the presence of a background magnetic field, and turns into a first order as seen from the volume scaling of the order parameter susceptibility as well as the metastable states in the time history of the chiral condensate. On the other hand, the chiral condensate and transition temperature always increase with <math><mi>B</mi></math> even within the regime of a first order phase transition. This suggests that the discrepancy in the behavior of chiral condensates and transition temperature as a function of <math><mi>B</mi></math> between earlier lattice studies using larger-than-physical pion masses with standard staggered fermions and those using physical pions with improved staggered fermions is mainly due to lattice cutoff effects.

China

Heng-Tong Ding

Akio Tomiya

Xiao-Dan Wang

Chiral phase structure of three flavor QCD in a background magnetic field

We perform a comprehensive analysis of several phenomenological aspects of the renormalizable extension of the inert 3-3-1 model with sequentially loop-generated Standard Model fermion mass hierarchy. Special attention is paid to the study of the constraints arising from the experimental data on the <math><mi>ρ</mi></math> parameter, as well as those ones resulting from the charged lepton flavor violating process <math><mrow><mi>μ</mi><mo>→</mo><mi>e</mi><mi>γ</mi></mrow></math> and dark matter. We also study the single <math><msup><mi>Z</mi><mo>′</mo></msup></math> production via Drell-Yan mechanism at the LHC. We have found that <math><msup><mi>Z</mi><mo>′</mo></msup></math> gauge bosons heavier than about 4 TeV comply with the experimental constraints on the oblique <math><mi>ρ</mi></math> parameter as well as with the collider constraints. In addition, we have found that the constraint on the charged lepton flavor violating decay <math><mi>μ</mi><mo>→</mo><mi>e</mi><mi>γ</mi></math> sets the sterile neutrino masses to be lighter than about 1.12 TeV. In addition the model allows charged lepton flavor violating processes within reach of the forthcoming experiments. The scalar potential and the gauge sector of the model are analyzed and discussed in detail. Our model successfully accommodates the observed dark matter relic density.

Vietnam

H. N. Long

N. V. Hop

L. T. Hue

N. H. Thao

Chile

A. E. Cárcamo Hernández

Some phenomenological aspects of the 3-3-1 model with the Cárcamo-Kovalenko-Schmidt mechanism