arXiv subjects

Prasad Hegde

Publications and source records attributed to Prasad Hegde.

At least 19 recordsLinked to original sources

arXiv2026

Spatial String Tension at High Temperatures and Quantitative Tests of Dimensionally Reduced Effective Theories

We calculate the spatial string tension in 2+1 flavour QCD in $(3{+}1)$ dimensions within a temperature range of $[166\,\mathrm{MeV},\,1000\,\mathrm{MeV}]$ using spatial Wilson loops with HYP smearing. We use the Highly Improved Staggered Quark action for fermions and the tree-level Symanzik improved gauge action for gluons at two lattice spacings corresponding to temporal extents $N_\tau = 8$ and $10$. We then compare our results with dimensionally reduced effective theories at high temperatures (EQCD and MQCD) to test the onset of dimensional reduction in QCD.

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arXiv2024

A New Way to Compute the Pseudoscalar Screening Mass at Finite Chemical Potential

We present a method to calculate the pion screening mass in 2+1-flavor lattice QCD to $\mathcal{O}(μ^2_\ell)$, where $μ_\ell$ is the isoscalar chemical potential. Our approach is based on the expression for the free theory pion screening correlator for massless quarks. We use the Taylor expansion method to calculate the screening correlator to $\mathcal{O}(μ^4_\ell)$. We then extract the $\mathcal{O}(μ^2_\ell)$ Taylor coefficient of the screening mass from the Taylor coefficients of the correlator, for two temperatures in the range 2 - 3 GeV. Our calculations were done using the Highly Improved Staggered Quark action, and the strange and light quark masses were set respectively to their physical and nearly physical values, corresponding to meson masses $M_{\bar{s}s}=686$ MeV and $M_π=160$ MeV.

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arXiv2023

Pion screening mass at finite chemical potential

We present a method to compute the responses of meson screening masses to the chemical potential by Taylor expanding the correlator using lattice QCD simulation. We start by comparing the free theory lattice results with the analytical expression. Then, using symmetry arguments, we obtain an expression for the correlator in a series of the chemical potential at finite temperature. Using this, we obtain the lowest order correction to the screening mass at a finite chemical potential for temperatures around 2.5 GeV. Our lattice analysis is limited to isoscalar chemical potential for the pseudoscalar channel. The calculations were performed using (2+1)-flavors of the Highly Improved Staggered Quark (HISQ/tree) action, with the ratio of the strange quark mass to the light quark mass $m_s/m_\ell=20$ corresponding to pion masses of 160 MeV.

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arXiv2023

QCD equation of state at finite chemical potential from unbiased exponential resummation of the lattice QCD Taylor series

Exponential resummation of the QCD finite-density Taylor series has been recently introduced as an alternative way of resumming the finite-density lattice QCD Taylor series. Unfortunately the usual exponential resummation formula suffers from stochastic bias which must be subtracted before identifying genuine higher-order contributions. In this paper, we present a new way of subtracting the stochastic bias at the level of each individual gauge configuration, up to a certain order of either the Taylor series or the cumulant expansion, by modifying the argument of the exponential. Retaining the exponential form of the resummation allows us to also calculate the phase factor of the fermion determinant on each gauge configuration. We present our results for the excess pressure, number density, and the average phase factor and show that the new results contain less stochastic bias and are in better agreement with the QCD Taylor series compared to the previous exponential resummation.

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arXiv2022

Meson screening mass at finite chemical potential

Knowledge of the screening masses at finite chemical potential can provide insight into the nature of the QCD phase diagram. However, lattice studies at finite chemical potential suffer from the well-known issue of the sign problem, which has made the calculation of observables such as screening correlators and screening masses at finite chemical potential quite challenging. One way to proceed is by expanding the observable in a Taylor series in the chemical potential and hence calculating the finite-density corrections to the observable. In this talk, we will use this approach to calculate the screening mass of the pseudoscalar meson at finite temperatures and chemical potential by expanding the screening correlator in a Taylor series in the chemical potential. We will present our results for the second derivative of the screening mass w.r.t. the chemical potential. Our calculation was done on $64^3 \times 8$ lattices generated using the (2+1) HISQ/tree action.

hep-lat↗

arXiv2022

A new way of determining the Lattice QCD equation of state at a finite chemical potential

The Taylor expansion of thermodynamic observables at a finite baryon chemical potential $μ_B$ is an oft-used method to circumvent the well-known sign problem of Lattice QCD. Owing to the associated difficulty and limitations of precision in calculating these high-ordered Taylor coefficients, it becomes essential to look for various resummation schemes which can mitigate the computational cost, besides providing trustworthy estimates of different thermodynamic observables. Recently, a way to exponentially resum the contribution of the first $N$ charge density correlation functions $D_1,\dots,D_N$ to the Taylor series to all orders in $μ_B$ was proposed in Phys. Rev. Lett. 128, 2, 022001 (2022). Since the correlation functions $D_n$ are calculated stochastically using estimates from different random volume sources, the resummation formulation gets affected by the biased estimates. These estimates can become very drastic and can radically misdirect the calculations for large values of $N$ and $μ$ and also for observables which are higher order $μ$ derivatives of free energy, specially at lower temperatures. In this work, we present a cumulant expansion procedure that allows to investigate and regulate these biased estimates at different orders in $μ$. We find that the unbiased estimates in the cumulant expansion can truly capture the genuine higher-order stochastic fluctuations of the higher order correlation functions, which got suppressed by the exponential resummation formulation. Finally, we discover an unbiased formalism of the exponential resummation, which when expanded in a series, can exactly reproduce the Taylor series upto a desired power in $μ$. We are also able to regain the knowledge of reweighting factor and many other important properties of the partition function, which got entirely lost through the implementation of cumulant expansion scheme.

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arXiv2022

New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential

Taylor expansion of the thermodynamic potential in powers of the (baryo)chemical potential $μ_B$ 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 $μ_B$. Recently, a way to resum the contribution of the first $N$ charge density correlation functions $D_1,\dots,D_N$ to the Taylor series to all orders in $μ_B$ was proposed in Phys. Rev. Lett. 128, 2, 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 $N$ and $μ_B$. 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 $M$, 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 $μ_B\ne0$, here we present it for the simpler case of a finite isospin chemical potential $μ_I$ 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.

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arXiv2022

The Chiral Phase Transition in three-flavor QCD from Lattice QCD

We analyze the pseudo-critical behavior of three-flavor QCD using highly improved staggered quarks (HISQ) on lattices with temporal extent $N_τ=8$ and for quark masses corresponding to a pseudoscalar Goldstone mass in the range $80 ~ {\rm MeV} ~ \lesssim ~ m_π~ \lesssim ~ 140 ~ {\rm MeV}$. 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 $T_c = 98_{-6}^{+3}~{\rm MeV}$. A comparison with a corresponding analysis performed in (2+1)-flavor QCD suggests that the continuum limit extrapolated chiral phase transition temperature in 3-flavor QCD will turn out to be below $90 ~ {\rm MeV}$.

hep-lat↗

arXiv2022

Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansion

Taylor expansion in powers of baryon chemical potential ($μ_B$) is an oft-used method in lattice QCD to compute QCD thermodynamics for $μ_B>0$. Based only upon the few known lowest order Taylor coefficients, it is difficult to discern the range of $μ_B$ where such an expansion around $μ_B=0$ can be trusted. We introduce a resummation scheme for the Taylor expansion of the QCD equation of state in $μ_B$ that is based on the $n$-point correlation functions of the conserved current ($D_n$). The method resums the contributions of the first $N$ correlation function $D_1,\dots,D_N$ to the Taylor expansion of the QCD partition function to all orders in $μ_B$. We show that the resummed partition function is an approximation to the reweighted partition function at $μ_B\ne0$. We apply the proposed approach to high-statistics lattice QCD calculations using 2+1 flavors of Highly Improved Staggered Quarks with physical quark masses on $32^3\times8$ lattices and for temperatures $T\approx145$-176 MeV. We demonstrate that, as opposed to the Taylor expansion, the resummed version not only leads to improved convergence but also reflects the zeros of the resummed partition function and severity of the sign problem, leading to its eventual breakdown. We also provide a generalization of our scheme to include resummation of powers of temperature and quark masses in addition to $μ_B$, and show that the alternative expansion scheme of [S. Borsányi et al., Phys. Rev. Lett. 126, 232001 (2021).] is a special case of this generalized resummation.

hep-lat↗

arXiv2019

Meson Screening Masses in (2+1)-Flavor QCD

We present lattice QCD results for mesonic screening masses in the temperature range 140 MeV $\lesssim T \lesssim$ 2500 MeV. Our calculations were carried out using (2+1)-flavors of the Highly Improved Staggered Quark (HISQ) action, with a physical value for the strange quark mass and two values of the light quark mass corresponding to pion masses of 160 MeV and 140 MeV. Continuum-extrapolated results were obtained using calculations with a variety of lattice spacings corresponding to temporal lattice extents $N_τ= 6 - 16$. We discuss the implications of these results for the effective restoration of various symmetries in the high temperature phase of QCD, as well as the approach toward the perturbative limit.

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arXiv2019

Chiral phase transition in (2 + 1)-flavor QCD

The chiral phase transition temperature $T_{c}^{0}$ is a fundamental quantity of QCD. To determine this quantity we have performed simulations of (2 + 1)-flavor QCD using the Highly Improved Staggered Quarks (HISQ/tree) action on $N_τ=6, 8$ and 12 lattices with aspect ratios $N_σ/N_τ$ ranging from 4 to 8. In our simulations the strange quark mass is fixed to its physical value $m_{s}^{\rm{phy}}$, and the values of two degenerate light quark masses $m_{l}$ are varied from $m_{s}^{\rm{phy}}/20$ to $m_{s}^{\rm{phy}}/160$ which correspond to a Goldstone pion mass $m_π$ ranging from 160 MeV to 55 MeV in the continuum limit. By investigating the light quark mass dependence and the volume dependence of various chiral observables, e.g. chiral susceptibilities and Binder cumulants, no evidence for a first order phase transition in our current quark mass window is found. Two estimators $T_{60}$ and $T_δ$ are proposed to extract the chiral phase transition temperature $T_{c}^{0}$ in the chiral and continuum limit and our current estimate for $T_{c}^{0}$ is $132_{-6}^{+3}$ MeV.

hep-lat↗

arXiv2015

The curvature of the chiral phase transition line for small values of $μ_B$

We present preliminary results from an ongoing calculation to determine the curvature of the chiral phase transition line in the chiral limit along the light-light, light-strange and strange-strange chemical potential directions. We do this by studying the appropriate $μ$-derivatives of the chiral condensate as a function of the quark mass and comparing them to the scaling predictions of $3d$-$O(N)$ theory. We work at a fixed lattice spacing, $N_τ=6$ and at four different quark masses $m_π\approx$ 140, 110, 90 and 80 MeV. For the light quark curvature, we obtain a value 0.03$\leqslantκ_{ll}\leqslant$0.11. We also find that both strange and light-strange curvatures are around an order of magnitude smaller. Currently, the light-strange curvature is the least constrained curvature and could have either sign, though our results seem to prefer a slightly negative value.

hep-lat↗

arXiv2015

Chiral phase transition of $N_f$=2+1 and 3 QCD at vanishing baryon chemical potential

We present updated results on chiral phase structure in (2+1)-flavor ($N_f$=2+1) and 3-flavor ($N_f=3$) QCD based on the simulations using Highly Improved Staggered Quarks on lattices with temporal extent $N_τ$ =6 at vanishing baryon chemical potential. In $N_f$=2+1 QCD we have performed simulations with a strange quark fixed to its physical value and two degenerate light quarks whose values are adjusted to have 5 values of Goldstone pion masses in the region of 160 - 80 MeV in the continuum limit. The universal scaling behavior of chiral condensates as well as chiral susceptibilities is discussed and the tri-critical point is suggested to be located below the physical point, i.e. at smaller than physical strange quark mass. In $N_f$=3 QCD simulations with 6 different masses of 3 degenerate quarks corresponding to the Goldstone pion masses in the region of 230 - 80 MeV have also been performed. Our results suggest that the QCD transition with these values of quark masses is of crossover type and an upper bound of the critical pion mass where the first order phase transition starts is estimated to be about 50 MeV.

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arXiv2014

The QCD equation of state to $\mathcal{O}(μ_B^4)$

We present results from an ongoing calculation of the QCD equation of state at finite baryon chemical potential $μ_B$. We use the method of Taylor expansions to circumvent the sign problem and calculate the expansion coefficients to sixth order using HISQ fermions. We work at two lattice spacings, namely $N_τ=6$ and 8 and, though we do not take the continuum limit, demonstrate that cutoff effects remain under control. We also use our results to construct an equation of state along the freeze-out curve. Using our sixth-order results as a cross-check, we demonstrate that our fourth-order equation of state is suitable for the modeling of dense matter created in heavy ion collisions with center-of-mass energies down to $s_{NN}^{1/2}\sim20$ GeV.

hep-lat↗

arXiv2014

The QCD Equation of State to $\mathcal{O}(μ_B^4)$ from Lattice QCD

We present first results from a first-principles calculation of the QCD equation of state to $\mathcal{O}(μ_B^4)$, where $μ_B$ is the baryon chemical potential. We find that second-order corrections are sufficient for a large part of the freeze-out temperature and baryon chemical potential range achieved by the RHIC beam energy scan. Nevertheless, higher-order corrections are necessary to extend the validity of the equation of state down to beam energies $s^{1/2}_{NN}\sim 20$ GeV.

hep-lat↗

arXiv2013

Stabilizing the electroweak vacuum by higher dimensional operators in a Higgs-Yukawa model

The Higgs boson discovery at the LHC with a mass of approximately 126 GeV suggests, that the electroweak vacuum of the standard model may be metastable at very high energies. However, any new physics beyond the standard model can change this picture. We want to address this important question within a lattice Higgs-Yukawa model as the limit of the standard model (SM). In this framework we will probe the effect of a higher dimensional operator for which we take a $(ϕ^{\dagger}ϕ)^3$-term. Such a term could easily originate as a remnant of physics beyond the SM at very large scales. As a first step we investigate the phase diagram of the model including such a $(ϕ^{\dagger}ϕ)^3$ operator. Exploratory results suggest the existence of regions in parameter space where first order transitions turn to second order ones, indicating the existence of a tri-critical line. We will explore the phase structure and the consequences for the stability of the SM, both analytically by investigating the constraint effective potential in lattice perturbation theory, and by studying the system non-perturbatively using lattice simulations.

hep-lat↗

arXiv2013

The phase structure of a chirally-invariant Higgs-Yukawa model

We present new results of our ongoing project on the investigation of the phase structure of the Higgs-Yukawa model at small and large bare Yukawa couplings. The critical exponents of the second order bulk phase transitions of this model are determined from finite-size analyses and compared to the pure O(4)-model to test for triviality and the possibility of having a non-Gaussian fixed point. In addition, we will present a first study of Higgs boson masses and fermion correlation functions.

hep-lat↗

arXiv2012

The chiral transition and U(1)_A symmetry restoration from lattice QCD using Domain Wall Fermions

We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U(1)_A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent N_τ= 8 and spatial extent N_σ= 16 in a temperature range of T = 139 - 195 MeV, corresponding to lattice spacings of a \approx 0.12 - 0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass m_π= 200 MeV. The strange quark mass is set near its physical value. We also present results from a second set of finite temperature gauge configurations at the same volume and temporal extent with slightly heavier pion mass. To study chiral symmetry restoration, we calculate the chiral condensate, the disconnected chiral susceptibility, and susceptibilities in several meson channels of different quantum numbers. To study U(1)_A restoration, we calculate spatial correlators in the scalar and pseudo-scalar channels, as well as the corresponding susceptibilities. Furthermore, we also show results for the eigenvalue spectrum of the Dirac operator as a function of temperature, which can be connected to both U(1)_A and chiral symmetry restoration via Banks-Casher relations.

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