Missing Navigational Beacons

In designing the PHENIX experiment circa 1990, much care was giving to maintaining good acceptance and mass resolution for the “onium” states. At that time, following the famous Matsui/Satz paper, the thinking was the Debye screening in the plasma would be signaled by suppression of the J/Psi, while the much smaller radius for the upsilon would argue against dissociation at the energy densities expected for RHIC. In the PHENIX Conceptual Design Report we wrote

“The upsilon serves as a calibration point in the measurement of the screening length since its radius is much smaller than any estimated plasma screening radius at expected temperatures, meaning it may well never be suppressed at plasma temperatures attainable at RHIC.”

That is, the upsilon was expected to serve as a navigational beacon, assuring us that our normalization of hard processes in comparing Au+Au to p+p collisions was correct.

Since then, RHIC phenomena have proven to be far more striking then we ever could have imagined. Not the least of these surprises has been the strong coupling of heavy flavor to the “bulk”. Conservative physicists argue that this is true only for charm, with bottom being so heavy that it is unlikely to flow and lose energy. Very considerable efforts are underway to upgrade PHENIX and STAR to provide the detector technology necessary to perform the b/c separation.

In  a recent preprint Thermal Width of the Upsilon at Large ‘t Hooft  Coupling Noronha and Dumitru argue that the thermal width of the upsilon is large enough that it too could be suppressed at RHIC. Their calculation is made in an AdS/CFT model and is instructive in several aspects. The setup is closely related to the one of a hanging string between two massive (static) ‘quarks’ first calculated by Maldacena at T=0.  The result is Coulombic, that is, for separations L the potential ~ 1/L. This is as it must be on the CFT side- if there is no other scale in the theory, energies must go as 1/L. The interesting part is understanding how this arises in the string setup on the AdS side. Since the string length increases as L increases, why doesn’t the potential also grow with L? This is where AdS does its magic- the string hanging down into the 5th dimension is in a highly warped rather than flat spacetime. The warp factor in the AdS metric is precisely what is needed to produce the 1/L required by the CFT side. (See Section 5.1 of Maldacena’s TASI lectures for a clear discussion from the master on this.)

Noronha and Dumitru extend this formalism to a QGP via the ‘usual’  trick of thermalizing it with a black brane located at some coordinate Uh in the 5th dimension. The value of Uh is proportional to the temperature T in the conformal theory. For small T (small Uh), the brane is very far ‘down’ in the bulk, and the long wavelength thermal vibrations of the ‘bottom’ of the string don’t know much about the presence of the horizon (keep in mind that the strings in this geometry are much more ‘U’ shaped than ‘V’ shaped). However, as the temperature is increased, two things happen: The horizon moves closer to the boundary at infinite U where the string endpoints (quarks) are located, and, because the temperature is higher, the amplitude of thermal vibrations of the string bottom become larger. At some temperature the lowest-mode oscillation of the string touches the horizon, which means the potential acquires an imaginary part, that is, the state has a non-zero width. Given the above arguments, it is not surprising that this width is very sensitive to the temperature, going at (LT)4 times the conformally-mandated energy  scale 1/L.

 Somewhat surprisingly, the numerical value of the width ~50 MeV for upsilons is not hugely different from that calcualted via pQCD. However, the parameteric dependence is both the coupling constand the temperature is very different, with the AdS/CFT results having a much higher dependence on T. The authors estimate that RAA for upsilons may be as small as 0.3, leading to the loss of the navigational beacon- but this loss may be another’s gain.