Searching for the QCD critical point via the rapidity dependence of cumulants

Abstract

The search for a possible critical point in the QCD phase diagram is ongoing in heavy ion collision experiments at RHIC which scan the phase diagram by scanning the beam energy; a coming upgrade will increase the luminosity and extend the rapidity acceptance of the STAR detector. In fireballs produced in RHIC collisions, the baryon density depends on rapidity. By employing Ising universality together with a phenomenologically motivated freezeout prescription, we show that the resulting rapidity dependence of cumulant observables sensitive to critical fluctuations is distinctive. The dependence of the kurtosis (of the event-by-event distribution of the number of protons) on rapidity near mid-rapidity will change qualitatively if a critical point is passed in the scan. Hence, measuring the rapidity dependence of cumulant observables can enhance the prospect of discovering a critical point, in particular if it lies between two energies in the beam energy scan.A central goal of heavy ion collision experiments is to map the QCD phase diagram as a function of temperature T and baryon chemical potential µ B [1-3]. At zero µ B , the phase diagram features a continuous crossover from quark-gluon plasma (QGP) to ordinary hadronic matter as a function of decreasing T [4-8]. Increasing µ B corresponds to doping the QGP with an excess of quarks over antiquarks, and it is an open question whether the crossover becomes a sharp first order phase transition beyond some critical point [3,9]. At nonzero µ B where lattice calculations become extremely difficult [10,11], there are no first-principles theoretical calculations which provide reliable guidance as to the whether there is a critical point in the phase diagram of QCD, or its location if it does exist [12][13][14][15]. Model calculations suggest the existence of a critical point, but disagree wildly on its location in the (µ B , T ) plane [14,15]. Reducing the beam energy increases the µ B of the QGP produced in a heavy ion collision [3, 16-18] (principally because lower energy collisions make less entropy but also because they deposit more of their baryon number in the plasma) but it also reduces the temperatures achieved. So, these experiments can scan the crossover (and potentially critical) regime of the phase diagram out to some value of µ B corresponding to the lowest energy collisions that reach the crossover (critical) temperature [1, 2]. If a critical point is located in the regime that is within reach, it may be detected experimentally. The search for a critical point in the phase diagram of QCD at the Relativistic Heavy Ion Collider (RHIC) is currently underway, with collisions at energies ranging from √ s = 200 AGeV down to √ s = 7.7 AGeV, producing fireballs that freeze out with chemical potentials in the range 25 MeV < ∼ µ B < ∼ 400 MeV [17,18]. Phase I of the RHIC beam energy scan (BES-I) was completed in 2014, with no signs of a critical point for µ B < 200 MeV and with tantalizing but inconclusive results at larger µ B , in collisions with 19.6 AGeV ≥ √ s ≥ ...

Mapping the phases of quantum chromodynamics with beam energy scan

“…A similar scaling of the factorial cumulants with the particle number,Ĉ k ∼ N k has been already obtained when we discussed baryon number conservation and volume fluctuations, see Eqs. (106) and (109). This is not unexpected, since both baryon conservation and volume fluctuation are, in the simple approach presented here, rapidity independent long-range phenomena.…”

Lattice-based equation of state at finite baryon number, electric charge, and strangeness chemical potentials

“…While the term "critical point" is used, there might actually be a critical line or even critical plane once one considers the full three dimensional space of µ B , µ S , and µ Q . Since there are large fluctuations in T , µ B , µ S , and µ Q throughout the evolution of a single event [60][61][62], certain elements of the fluid might pass through a critical region at an entirely different combination of T , µ B , µ S , and µ Q .…”

Interplay between the holographic QCD phase diagram and mutual & n-partite information

“…For this model, we get µ c = 0.673 GeV. Since finding an exact value of the QCD critical point in the QCD (T, µ) plane, if existing, is extremely hard [84][85][86], a reasonable estimate is a few hundred MeV, so we observe our estimate for the critical point lies in the same range.…”