Latest results from RHIC + Progress on determining $\hat{q}L$ in RHI collisions using di-hadron correlations

Results from Relativistic Heavy Ion Collider Physics in 2018 and plans for the future at Brookhaven National Laboratory are presented.

Many Nobel Prize winners from NYC High Schools The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) is one of the two remaining operating hadron colliders in the world, and the first and only There also have been many discoveries and Nobel Prizes at BNL (Fig. 3). Leon was the most creative and productive high-energy physics experimentalist of his generation and also the physicist with the best jokes. He was also my PhD thesis Professor

Also many Discoveries & Nobel Prizes at BNL
The muon neutrino discovered at BNL--Nobel Prize in 1988 2 Why RHIC was built: to discover the QGP.

The first major RHIC experiments
The two major experiments at RHIC were STAR (Fig. 7), which is still operating, and PHENIX ( Fig. 8) which finished data taking at the end of the 2016 run.

The new major RHIC experiment sPHENIX
sPHENIX is a major improvement over PHENIX with a superconducting thin coil solenoid which was surplus from the BABAR experiment at SLAC and is now working at BNL and has reached its full field (Fig. 9   Multi-year run plan for sPHENIX • Guidance from ALD to think in terms of a multi-year run plan • Consistent with language in DOE CD-0 "mission need" document • Incorporates BNL C-AD guidance on luminosity evolution • Incorporates commissioning time in first year Minimum bias Au+Au at 15 kHz for |z| < 10 cm: 47 billion (Year-1) + 96 billion (Year-2) + 96 billion (Year-3) = Total 239 billion events For topics with Level-1 selective trigger (e.g. high pT photons), one can sample within |z| < 10 cm a total of 550 billion events.   Fig. 11a, and the planned multi-year RHIC runs indicated in Fig. 11b. The present sPHENIX collaboration and its evolution is shown in Fig. 12 On July 24, 2018, a National Academy of Sciences (NAS) committee issued a report of its findings and conclusions related to the science case for a future U.S.-based Electron-Ion Collider (EIC) and the opportunities it would offer the worldwide nuclear physics community.
The committee's report-commissioned by the U.S. Department of Energy (DOE)-comes after 14 months of deliberation and meetings held across the U.S. to gather input from the nuclear science community. The report's conclusions include the following: The committee concludes that the science questions regarding the building blocks of matter are compelling and that an EIC is essential to answering these questions.
The answers to these fundamental questions about the nature of the atoms will also have implications for particle physics and astrophysics and possibly other fields.
Because an EIC will require significant advances and innovations in accelerator technologies, the impact of constructing an EIC will affect all accelerator-based sciences.
In summary, the committee concludes that an EIC is timely and has the support of the nuclear science community. The science that it will achieve is unique and world leading and will ensure global U.S. leadership in nuclear science as well as in the accelerator science and technology of colliders.
The first BNL EIC design in 2014 is shown in Fig. 13  The two new designs of the JLab (JLEIC) and BNL (eRHIC) both satisfy the Temple committee cost estimate of $1.5B, but R&D of the novel first BNL design is not idle.

R&D for an improved less expensive BNL machine is ongoing
BNL and Cornell are in the process of experiments studying an energy recovery linac ERL (Fig. 16a). Fig. 16b is the main Linac cryo module made from superconducting RF cavities. Fig. 16c is a return loop made from fixed-field alternating-gradient (FFAG) optics made with permanent Halbach magnets to contain four beam energies in a single 70 mm-wide beam pipe, designed and prototyped at Brookhaven National Laboratory (BNL).

a)
A new facility called CBETA (Cornell-Brookhaven ERL Test Accelerator) that combines some of the best traits of linear and circular accelerators has recently entered construction at Cornell University in the US. Set to become the world's first multi-turn SRF ERL, with a footprint of about 25 × 15 m, CBETA is designed to accelerate an electron beam to an energy of 150 MeV. As an additional innovation, this four-turn ERL relies on only one return loop for its four beam energies, using a single so-called fixed-field alternating-gradient return loop that can accommodate a large range of different electron energies. To further save energy, this single return loop is constructed from permanent Halbach magnets (an arrangement of permanent magnets that augments the magnetic field on the beam side while cancelling the field on the outside).

Small Accelerator Promises Big Returns
Under construction in the US, the CBETA multi-turn energy-recovery linac will pave the way for accelerators that combine the best of linear and circular machines March 16, 2018 The main linac cryomodule.
When deciding on the shape of a particle accelerator, physicists face a simple choice: a ring of some sort, or a straight line? This is about more than aesthetics, of course. It depends on which application the accelerator is to be used for: high-energy physics, advanced light sources, medical or numerous others. Harmonic field correction is achieved by an elegant invention first used in CBETA: in order to overcome the magnetisation errors present in the NdFeB blocks and to produce magnets with 10-3 field accuracy, 32 to 64 iron wires of various lengths are inserted around the magnet bore, with lengths chosen to minimise the lowest 18 multipole harmonics.
A multi-turn test ERL was proposed by Cornell researchers following studies that started in 2005. Cornell was the natural site, given that many of the components needed for such an accelerator had been prototyped by the group there. A collaboration with BNL was formed in the summer of 2014; the test ERL was called CBETA and construction started in November 2016.
CBETA has some quite elaborate accelerator elements. The most complex components already existed before the CBETA collaboration, constructed by Cornell's ERL group at Wilson Lab: the DC electron source, the SRF injector cryomodule, the main ERL cryomodule, the high-power beam stop, and a diagnostic section to map out six-dimensional phase-space densities. They were designed, constructed and commissioned over a 10-year period and hold several world records in the accelerator community. These components have produced the world's largest electron current from a photo-emitting source, the largest continuous current in an SRF linac and the largest normalized brightness of an electron bunch.     In order to determine whether the separation of charges in the flow, v 2 , of π + and π − shown in Fig. 19 is due to a new phenomenon called the Chiral Magnetic Effect (Fig. 20a) the 2018 measurements are made with collisions of Zr+Zr and Ru+Ru which have the same number of nucleons but different electric charges (Fig. 20b). If the effect is larger in Ru+Ru with stronger charge and magnetic field compared to Zr+Zr with the same number of nucleons, it will indicate that the charge asymmetry is the Chiral Magnetic Effect. 3.2 Vorticity: an application of particle physics to the QGP It was observed at FERMILAB [PRL 36 (1976) 1113] that forward Λ were polarized in p+Be collisions, where the proton in the Λ → p + π − decay is emitted along the spin direction of the Λ. In the A+A collision (Fig. 21a), the forward going beam fragments are deflected outwards so that the event plane and the angular momentumĴ sys of the QGP formed can be determined. STAR claims that the Λ polarization, P Λ , is parallel to the angular momentum J sys of the QGP everywhere so that the vorticity ω = k B T (P Λ + P Λ )/ can be calculated, a good exercise for the reader to see if you can get the ω ∼ 10 22 /s which is 10 5 times larger than any other fluid [Nature 548 (2017)     High energy Nucleus-Nucleus collisions provide the means of creating nuclear matter in conditions of extreme temperature and density, the Quark Gluon Plasma QGP (Fig. 23). At large energy or baryon density, a phase transition is expected from a state of nucleons containing confined quarks and gluons to a state of "deconfined" (from their individual nucleons) quarks and gluons covering a volume that is many units of the confinement length.  The hydrodynamic calculations shown in Fig. 3 use initial conditions generated from a nucleon Glauber model. However, initial geometries with quark substructure do not significantly change the " 2 and " 3 values for high multiplicity p/d/ 3 He+Au collisions [32,33] and thus the hydrodynamic results should be relatively insensitive to these variations.

Setting records
While we have focused on hydrodynamical models here, there is an alternative class of models that also translate initial spatial eccentricity to final state particle azimuthal momentum anisotropy. Instead of hydrodynamic evolution, the translation occurs via partonparton scattering with a modest interaction cross section. These parton transport models, for example A Multi-Phase Transport (ampt) Model [34], are able to capture the system ordering of v n at low-p T in small systems [35], but fail to describe the p T dependence and overall magnitude of the coe cients for all systems resulting in a p-value consistent with zero when compared to the data shown here. We have additionally analyzed ampt following the identical PHENIX event plane method and find even worse agreement with the experimental data.
While the initial geometry models for the d+Au and 3 He+Au are largely constrained by our detailed understanding of the 2-and 3-body nucleon correlations in the deuteron and 3 He nuclei, respectively, the distribution of deposited energy around each nucleon-nucleon collision site could result in an ambiguity between the allowed ranges of the ⌘/s and the broadening of the initial distribution, as pointed out in Ref. [13]. However, a broader distribution of deposited energy results in a significant reduction of the " 2 values and an even greater reduction of " 3 , with by far the largest reduction in the p+Au system. Here again, the simultaneous constraints of the elliptic and triangular flow ordering eliminates this ambiguity.
Our experimental data also rule out the initial-state correlations scenario where color domains are individually resolved as the dominant mechanics for creating v 2 and v 3 in p/d/ 3 He+Au collisions. After our results became publicly available, a new calculation was presented in Ref.
[37], hereafter referred to as MSTV, where the ordering of the measured v n values matches the experimental data. This calculation posits that gluons from the Au target do not resolve individual color domains in the projectile p/d/ 3 He and interact with them coherently, and thus the ordering does not follow Eq. 4. The calculations are shown in Fig. 3, and yield a p-value for the MSTV calculations of v 2 and v 3 for the three collision systems of e↵ectively zero, in contradistinction to the robust values found for the hydrodynamic models. Another key statement made by MSTV -that in the dilute-dense limit the saturation scale Q 2 s is proportional to the number of produced charged particles -is questionable [38], but also leads the MSTV authors to make a clear prediction that the v 2 will be identical between systems when selecting on the same event multiplicity. Shown in Fig. 4 are the previously published d+Au (20-40%) and p+Au (0-5%) v 2 where the measured mean charged particle multiplicities (dN ch /d⌘) match [36]. The results do not support the MSTV prediction of an identical v 2 for these two systems at the same multiplicity, while the di↵erences in particularly for d+Au and 3 He+Au collisions. Above the crossing point, supersonic, and iebe-vishnu predict nearly flat ratios, while ampt describes the ratio of the v 2 values, but not their individual magnitudes. These di↵erences may be attributed to the di↵erent hadronization mechanisms (e.g. -if recombination is included) in the models.
The observation of a mass-dependent v 2 strengthens the case for associating small-system collectivity with the expansion of QGP droplets formed in these collisions, where the splitting can be understood in terms of the presence of a common radial flow field with anisotropic modulations driven by initial geometry. However, the theoretical calculations presented in this pa-per provide several alternative explanations of how the azimuthal anisotropies for di↵erent particle species may occur. For instance, in kinetic transport, parton scattering translates initial geometry into final state momentum anisotropy, but it does not account for the observed mass splitting. Instead, this feature has been shown to arise solely from the hadronic rescattering stage where di↵erent hadrons have di↵erent inelastic cross sections [24]. There is more hadronic rescattering in 3 He+Au and d+Au compared with p+Au for these central collisions because they have a higher particle density. It is interesting that this conclusion based on ampt regarding the contribution of the hadronic rescattering stage is opposite to that reached using viscous hydrodynamics [18].   26 showed that flow exists in small p+Au, d+Au, 3 He+Au systems with preliminary sensitivity of v 3 to the initial geometry. Fig. 27a shows that v 2 is about the same in all 3 systems but v 3 is much larger in 3 He+Au clearly indicating the sensitivity of flow to the initial geometry of the collision. Fig. 27b shows that there is mass ordering in the flow which is strong evidence for the QGP in these small systems. The solid red and dashed blue lines represent hydrodymic predictions. These hydrodynamical models, which include the formation of a short-lived QGP droplet, provide the best simultaneous description of the measurements, strong evidence for the QGP in small systems. This is an answer to the interesting question of the minimal conditions for collectivity in small systems. For the case of e + e − collisions in Fig. 28 utilizing the AAMPT framework and Figure 28: A fundamental point about QCD and the string tension between the q andq a single color string, the results indicate only a modest number of parton-parton scatterings and no observable collectivity signal.
However, a simple extension to two color strings which represent a simplified geometry in p+p collisions predicts finite long-range two-particle correlations (known as the ridge) and a strong v 2 with respect to the initial parton geometry.

A fundamental point about QCD and the string tension
Unlike an electric or magnetic field between two sources which spreads over all space, in QCD as proposed by Kogut and Susskind [PRD 9 (1974) 3501] the color flux lines connecting two quarks or a q −q pair as in Fig. 28 are constrained in a thin tube-like region because of the three-gluon coupling. Furthermore if the field contained a constant amount of color-field energy stored per unit length, this would provide a linearly rising confining potential between the q − q or q −q pair.
This led to the Cornell string-like confining potential [PRL 34 (1975) 369], which combined the Coulomb 1/r dependence at short distances from vector-gluon exchange with QCD coupling constant α s (Q 2 ), and a linearly rising string-like potential, with string-tension σ, which provided confinement at large distances (Eq. 1). Particles are produced by the string breaking (fragmentation) .

4.3
The latest discovery claims 'flow' in small systems is from the QGP . How did we find the QGP in the first place?

J/ψ Suppression, 1986
In 1986, T. Matsui and H. Satz [PLB 178 (1987) 416] said that due to the Debye screening of the color potential in a QGP, charmonium production would be suppressed since the c-c couldn't bind. With increasing temperature, T , in analogy to increasing Q 2 , the strong coupling constant α s (T ) becomes smaller, reducing the binding energy, and the string tension, σ(T ), becomes smaller, increasing the confining radius, effectively screening the potential [Rep. Prog. Phys. 63 (2000) 1511] where µ D = µ D (T ) = 1/r D is the Debye screening mass. For r < 1/µ D a quark feels the full color charge, but for r > 1/µ D , the quark is free of the potential and the string tension, effectively deconfined. The properties of the QGP can not be calculated in QCD perturbation theory but only in Lattice QCD Calculations [Ann. Rev. Nucl. Part. Sci. 65 (2015) 379]. J/ψ suppression eventually didn't work because the free c andc quarks recombined to make J/ψ's [PLB 490 (2000) 196]. Ask somebody from ALICE for more details.

Jet Quenching by coherent LPM radiative energy loss of a parton in the QGP, 1997
In 1997, Baier, Dokshitzer, Mueller Peigne, Schiff also Zakharov (BDMPSZ), see [Ann. Rev. Nucl. Part. Sci. 50 (2000) 37], said that the energy loss from coherent Landau Pomeranchuk Migdal (LPM) radiation for hard-scattered partons exiting the QGP would result in an attenuation of the jet energy and a broadening of the jets. (Fig. 30). As a parton from hard-scattering in the A+B collision exits through the medium it can radiate a gluon; and both continue traversing the medium. It is important to understand that "Only the gluons radiated outside the cone defining the jet contribute to the energy loss." In the angular ordering of QCD, the angular cone of any further emission will be restricted to be less than that of the previous emission and will end the energy loss once inside the jet cone. This does not work in the QGP so no energy loss occurs only when all gluons emitted by a parton are inside the jet cone. In addition to other issues this means that defining the jet cone is a BIG ISSUE-so watch out for so-called trimming.
4.4 BDMPSZ-the cone, the energy loss, azimuthal broadening, is THE QGP signature.  The energy loss of the outgoing parton, −dE/dx, per unit length (x) of a medium with total length L, is proportional to the total 4-momentum transfer-squared, q 2 (L), and takes the form: where µ, is the mean momentum transfer per collision, and the transport coefficientq = µ 2 /λ mfp is the 4-momentum-transfer-squared to the medium per mean free path, λ mfp .
Additionally, the accumulated momentum-squared, p 2 ⊥W transverse to a parton traversing a length L in the medium is well approximated by p 2 ⊥W ≈ q 2 (L) =qL .
5 Jet Quenching at RHIC, the discovery of the QGP The energy loss of an outgoing parton with color charged fully exposed in a medium with a large density of similarly exposed color charges (i.e, a QGP) from Landau Pomeranchuk Migdal (LPM) coherent radiation of gluons was predicted in QCD by BDMPSZ [arXiv:hep- Hard scattered partons (Fig. 31a) lose energy going through the medium so that there are fewer partons or jet fragments at a given p T . The ratio of the measured semi-inclusive yield of, for example, pions in a given A+A centrality class divided by the semi-inclusive yield in a p+p collision times the number of A+A collisions N coll in the centrality-class is given by the nuclear modification factor, R AA (Fig. 31b), which equals 1 for no energy loss.
PHENIX discovered Jet Quenching of hadrons at RHIC in 2001[PRL88 (2002 022301] (Fig. 32). Pions at large p T > 2 GeV/c are suppressed in Au+Au at √ s N N =130 GeV compared to the enhancement found at the CERN SpS at √ s N N =17 GeV. This is the first regular publication from a RHIC experiment to reach 1000 citations.  Figure 33 shows the suppression of all identified hadrons, as well as e ± from c and b quark decay, with p T > 2 GeV/c measured by PHENIX until 2013. One exception is the enhancement of protons for 2 < p T < 4 GeV/c which are then suppressed at larger p T . Particle Identification is crucial for these measurements since all particles behave differently. The only particle that shows no-suppression is the direct single γ (from the QCD reaction g + q → γ + q) which shows that the medium produced at RHIC is the strongly interacting QGP since γ rays only interact electromagnetically.

Recent measurements to test the second BDMPSZ prediction.
(1) The energy loss of the outgoing parton, −dE/dx, per unit length (x) of a medium with total length L, is proportional to the total 4-momentum transfer-squared, q 2 (L), and takes the form: where µ, is the mean momentum transfer per collision, and the transport coefficientq = µ 2 /λ mfp is the 4-momentum-transfer-squared to the medium per mean free path, λ mfp .
(2) Additionally, the accumulated momentum-squared, p 2 ⊥W transverse to a parton traversing a length L in the medium is well approximated by . Although only the component of p 2 ⊥W ⊥ to the scattering plane affects k T (Fig. 34) the azimuthal broadening of the di-jet is caused by the random sum of the azimuthal components p 2 ⊥W /2 from each outgoing di-jet or p 2 ⊥W =q L.
From the values of R AA observed at RHIC (after 12 years) the JET Collaboration [Phys. Rev. C 90 (2014) 014909] has found thatq = 1.2 ± 0.3 GeV 2 /fm at RHIC, 1.9 ± 0.6 at LHC at an initial time τ 0 = 0.6 fm/c; but nobody has yet measured the azimuthal broadening predicted. Before proceeding, one has to know the meaning of k T defined by Feynman, Field and Fox in [NPB 129 (1977) 1] as the transverse momentum of a parton in a nucleon (Fig. 34). Understanding k T : FFF NPB128 (1977) shown with one k T perpendicular to the scattering plane which makes the jets acoplanar in azimuth and the other k T parallel to the trigger jet which makes the jets unequal in energy. Also x E = p T a cos(π − ∆φ)/p T t . The formula for calculating k T from di-hadron correlations is given in [PRD 74 (2006) 072002].

5.2.1
The key new idea of k 2 T pp instead of k 2 T pp in Eq. 3 The di-hadron correlations of p T a with p T t (Fig. 34) are measured in p+p and Au+Au collisions. The parent jets in the original Au+Au collision as measured in p+p will both lose energy passing through the medium but the azimuthal angle between the jets should not change unless the medium induces multiple scattering fromq. Thus the calculation of k T from the dihadron p+p mesurement to compare with Au+Au measurements with the same di-hadron p T t and p T a must use the value ofx h and z t of the parent jets in the A+A collision. The variables are x h ≡ p T a /p T t ,x h ≡p T a /p T t , z t ≡ p T t /p T t where e.g. p T t is the trigger particle transverse momentum andp T t means the trigger jet transverse momentum.
The same values ofx h , and z t in Au+Au and p+p give the cool result [PLB 771 (2017) 553]: For di-jet measurements, the formula is even simpler: i) x h ≡x h because the trigger and away 'particles' are the jets; ii) z t ≡ 1 because the trigger 'particle' is the entire jet not a fragment of the jet; iii) p 2 out =p 2 T a sin 2 (π − ∆φ). This reduces the formula for di-jets to: qL = p 2 out AA − p 2 out pp =p 2 T a sin 2 (π − ∆φ) AA − sin 2 (π − ∆φ) pp (5)

A test of Eq. 5 for qL
Al Mueller et al. [PLB 763 (2016) 208] gave a prediction for the azimuthal broadening of dijet angular correlations for 35 GeV jets at RHIC (Fig. 35). To check my Eq. 5, I measured ramatically change f all, the jet trans-eV at RHIC, which to smaller virtual-and we should be able to observe it in experiments. Future stud of this physics at RHIC would provide a unique opportunity to d rectly probe the P T -broadening effects and help to identify th underlying mechanism for the jet energy loss in relativistic heav ion collisions. ⊥ ) as function of b ⊥ ; (right) azimuthal de-correlation for dijet production at RHIC for a leading jet P ⊥ = 35 Ge the half width at half maximum (HWHM), which equals 1.175σ for a Gaussian, for each curve in Fig. 35, and calculated (σ × 35) 2 to get p 2 out for eachqL, and used Eq. 5 to get 9.6 GeV 2 and 21.5 GeV 2 respectively for the 8 GeV 2 and 20 GeV 2 plots. This is an excellent result considering that I had to measure the HWHMs from Fig. 35 with a pencil and ruler.

How to calculateqL with Eq. 4 from di-hadron measurements
The determination of the required quantities is well known to older PHENIXians who have read [PRD 74 (2006)  (C)x h , the ratio of the away-jet to the trigger jet transverse momenta can be measured by the away particle p T a distribution for a given trigger particle p T t taking x E = x h cos ∆φ ≈ x h = p T a /p T t : Eq. 6 with the results indicated: (left) 4 < p T t < 5 GeV/c; (rght) 7 < p T t < 9 GeV/c; The fits in Fig. 36 work very well, with excellent χ 2 /dof. However it is important to notice that the dashed curve in Au+Au doesn't fit the data as well as the solid red curve which is the sum of Eq. 6 with free parameters + a second term with the form of Eq. 6 but with thex h fixed at the p+p value. It is also important to note that the solid red curve between the highest Au+Au data points is notably parallel to the p+p curve. A possible explanation is that in this region, which is at a fraction ≈ 1% of the dP/dx E distribution, the highest p T a fragments are from jets that don't lose energy in the QGP .   The away widths from PHENIX π 0 − h correlations [PRL 104 (2010) 252301] are shown in Fig. 37 with the calculatedqL values for π 0 − h GeV/c 20-60% centrality 5 < p T t < 7 GeV/c shown in Table 2 and 7 < p T t < 9 GeV/c in Table 3.