Fillies and gentle colts, we are now getting ready for the upcoming RHIC 2017 255 GeV Polarized Proton run. This will probably be the final 255 GeV polarized proton run for RHIC, until BES-II is finished. So I felt it propitious to start a diary to keep a record for the future and anyone who might be interested in the preparation and execution of this run. This is sort of a celebration of the great science which the polarized program at RHIC has generated since turning on in 2001. Much has been learned about the mysterious and complicated components which make up the spin of the proton.

The Magic Physics of Spin

Spin is one of those magical quantum mechanical properties of elementary particles which have no exact correspondence to our ordinary experiences. Yet we feel its effect everyday, in magnets and in the fact that things take up ‘space’. Magnets ultimately get their field from the individual electron’s spin. The fact that no two things can occupy the same space at the same time is due in large part to what is known as the Pauli exclusion principle which limits the number of particles with half integer spin which can occupy the same space. While quantum spin has been often envisioned as particle spinning like a top, this analogy breaks down when one considers the exact physics of such a thing. Actually it is considered an intrinsic property of the elementary point like particles, similar to charge and mass.

Paul Dirac teaching a young twilight sparkle about his equation circa 1933

Mathematically it came out of Dirac’s effort to modify Schrödinger’s wave equation to account for special relativity. The result yielded a wave function which had an intrinsic angular momentum, plus permitted the existence of negative energy states which were later interpreted as anti-particles.

Old portrait of Emmy Noether with a young rarity.

The Dirac equation became the jumping off point for quantum field theory. Recast in terms of the Lagrangian mathematical formalism and employing the profound symmetry relationships discovered by Emmy Noether, several decades earlier, quatum-electrodynamics was formulated. This theory is one of the true masterpieces of human theoretical efforts and the most well tested theory ever to be rendered.

In studying the large magnetic moment of protons, it became clear that the proton, unlike the electron, was not an elementary particle and in fact had structure. To explain this structure the quark model was developed and the field theory approach was applied to explain the forces which held sway over hadrons and quark based matter. This effort yielded quantum chromo-dynamics(QCD). QCD brought with it a description of the strong nuclear force and its associated ‘color’ charge. It was again in studying spin that in the 1980’s, the European Muon Collaboration (EMC) discovered that the quark and antiquark spins which make up the proton provide only a small fraction of the total proton spin. This so-called “spin crisis” opened the way to the modern view, which imagines the proton as a complex system of quarks and transient quark-antiquark pairs all bound together by gluons. The total spin is given by contributions from not only the quarks but the gluons and orbital angular momentum, which together yield the total spin 1/2 of the proton.

The RHIC Spin Program

“Curiosity was far greater than our fear

It felt so simple and so prodigious at the same time

Incredible things are happening in the world

Magical things are happening in this world

Across the river there are all kinds, magical instruments

While really we keep on living like monkeys”

:Peng! 33 SteroLab

Colliding polarized particles, the spin physics program at RHIC is continuing down the path of unraveling the proton’s internal structure and the QCD dynamics of nucleons with unprecedented precision. This year RHIC will be colliding protons with their spins aligned transversely (perpendicular) to the direction of motion.

Feynman Diagram for W boson decay channel used by RHIC to probe spin structure.

This is to help map the 2+1d image of the dynamic structure of the proton and to test a fundamental prediction of QCD concerning the behavior of like color charges and how they contribute to the so-called ‘transverse single spin asymmetries’. To accomplish this the experiments use several techniques. The first and most powerful is based on the violation of parity in weak interactions. The W± bosons naturally select left quark handedness and right antiquark handedness and hence are ideal probes of nucleon helicity structure. Thus the W bosons produced in these collision have a charge which depends on the flavor of the antiquark; anti-up or anti-down. These W bosons in turn decay into electrons or positrons depending on the charge of the W boson, and a neutrino. Thus information about the quark spin can be inferred from the electron, positron and neutrino production.

Drell-Yang process

The second important probe is known as the Drell-Yang process, where a quark and antiquark from two hadrons annihilate. The result is a virtual photon or Z boson which then decays into a pair of oppositely-charged leptons. Using these and other channels RHIC hopes to detect a how different are the polarized proton-proton collisions from the much studied deep inelastic lepton scattering (DIS). DIS involves the interaction of unlike color charges and thus it contributes with the opposite sign to the single spin asymmetries. DIS has been studied previously in much detail with HERMES at HERA and COMPASS at CERN. Showing that this sign does indeed change when compared to these previous experiments, would be a very important test of a fundamental prediction of QCD. For a general public discussion see the recent BNL news article or for more technical explanation see the recent PRL paper. (thanks Elke Aschenauer).

Polarized Protons at 255 GeV

The Brookhaven hadron facility complex, which includes the AGS Booster, the AGS, and RHIC.

One of the important factors in determining the level of ‘good’ statistics necessary to correctly analyze these effects is the integrated luminosity, or number of collisions achieved, and the level of polarization maintained during collisions; that is the percentage of the particles spin that are aligned in the same direction. Although the protons are generated with approximately 80% polarization at the optically pumped source, by the time they reach collision energies in the RHIC machine they typically maintain about 50–60% polarization.

The acceleration chain leading to RHIC involves several accelerators; beginning with the polarized source, 200 MeV linac, Booster and the old but venerable AGS. This is then injected into two beam lines in RHIC, known as the ‘blue’ and ‘yellow’ ring. After accelerating about 111 bunches of 2e11 particles per bunch to 255 GeV they are steered into collisions at STAR and PHENIX detectors (this year will only be STAR). It is then held in this ‘stored’ state colliding for about 6–8 hours, then dumped and the whole acceleration cycle begins again with fresh beam.

Transverse Magnetic Field (Bx) perturbing the spin (S)

One of the major causes of this depolarization has to do with how the transverse magnetic fields which are used in focusing the beam can perturb the spin resonantly. Since the precession rate of the spin increases with energy, there are certain energies where the rate of precession is the same as the rate which the transverse magnetic fields are perturbing the spin. This is known as a spin resonance. In this case the kicks add up to cause the spin to be tilted away and misaligned with each other or in other words depolarized.

To help protect us from polarization losses RHIC is equipped with a pair of so-called ‘Siberian Snakes’ in each ring. These Snakes rotate the spin direction from up to down or down to up (180 degrees) each time the particle passes the through the snake. This arrangement helps cancel most of the effects of the perturbing magnetic fields and thus allow us to accelerate through the spin resonances without loosing too much polarization.

Preparations for FY17 Polarized Proton Run

Even with Snakes, however, there are still residual effects which can lead to polarization loss. Learning from our polarized proton run in 2013, we are now in the process of designing a brand new lattice to minimize these losses on the acceleration ramp. For an overview of that run you can refer our conference proceedings report and the RHIC/AGS user’s meeting talk.

As in 2013 we are using a lattice designed to accommodate the electron lens used to help compensate the kicks to the beam experienced during collisions at the interaction points where the large detectors are. However as we saw in the previous run this may have a negative effect on both the lifetime or loss rate experienced during the store, and the amount of polarization loss both during the acceleration cycle and while in store.

Spin Resonance magnitude |w| versus beam energy in terms of the anomalous G factor times relativistic gamma.

One of the major goals of the lattice design effort currently underway is to mitigate these polarization losses. Recent theoretical effort has provided a guide to help us accomplish this. This with a lot of tracking work has provided a theoretical framework to handle depolarization due to the overlap of spin resonances in the presences of snakes. One of the key discoveries has been the importance of interference from neighboring spin resonances during acceleration and the threshold at which they can significantly impact polarization losses. In another related work there has also been important progress in simulating long term polarization loss during the store or polarization lifetime.

Showing the magnitude of net spin loss after accelerating through the primary resonance. This is plotted against the spin resonance magnitude of the primary resonance |w| (proportional to the action or emittance of the particles). We see the effect of changing the neighboring resonance.

We are working hard to see if we can reduce the neighboring resonances at the three strong resonance locations on the acceleration ramp. We have had success in modifying the standard RHIC lattice to reduce the effect of this interfering resonance, however, we are still working on this issue for a lattice which can accommodate the phase advance necessary for the electron lens to work.

Additionally, unlike previous years we will need to constrain and level the luminosity we deliver to the detectors over time. This is because if the STAR detector sees too many collision events it causes the acquisition channels to backup thus corrupting the data.

As a result we are currently devising strategies to ‘level’ the luminosity during the store. One approach is to reduce the luminosity by not focusing the beam so hard at the collisions, during the first part of the store. Then as the intensity of the colliding beams fall off we increase the focusing at several times in the store to bring the collision rates back up. The problem with this approach is that it requires very careful control of the various magnets involved in focusing and balancing that against the beam-beam forces which can inadvertently blow the beam size up during the focusing process.

Another approach is to mis-steer the colliding beams so they initially collide partially thus reducing the luminosity and then as beam decays slowly steer them into head on collisions. This has several issues, again the potential to blow up the beam and also a possible reduction in the net collisional polarization. This is because typically the depolarization process effects the larger amplitude particles more than those closer to the bunch center. Thus in colliding off-center we will inadvertently be sampling more particles with lower polarization values. The final approach and really the best, is to design the lattice in a way that our lifetime for the beam during collisions is low enough that a re-focus will be unnecessary. This run, unlike past runs will require collisions only at STAR detector as the PHENIX detector will not run. Studies of historical lifetimes with bunches undergoing only a single collision have shown that such ‘good’ lifetimes maybe possible, especially at the lower collisional rate required by STAR.

Next month’s issue: Spin optimized e-lens lattice: simulation results.