Stopping distance for high energy jets in weakly-coupled - plasmas[1] Peter Arnold, Sean Cantrell, and Wei Xiao Department of Physics, University of Virginia, Charlottesville, United States

Introduction: Quark-Gluon Plasma Because partons interact with thermal medium and Stopping Distances: Definition 푥퐸. We have the self-consistent equation for stopping deposit their energy into QGP before , distance 푙푞: Quark-Gluon Plasma(QGP) is a phase of QCD this is so called Quenching Suppose a high energy parton with initial energy 퐸 1 1 푑Γ푞→푔푞(퐸,푥)/푑푥 which exists in extreme high temperature and/or travelling through QGP with temperature 푇 (퐸 ≫ 푇), it 푙 퐸 = + 푑푥 푙 ( 1 − 푥 퐸 ) (3) 푞 Γ (퐸) 0 Γ 퐸 푞 high density, in which quark and are almost Jet quenching is interacts with medium and when it drops energy to 푞→푔푞 푞→푔푞 free. observed in Au-Au 퐸~푇, we say the parton stops in the medium. ≃ 1 − 푥 퐸 collision of RHIC, 퐸 studying jet For an initial quark, it can only split into a quark and a ≃ 푥퐸 quenching provide gluon, so we can follow the path of the quark and insights on the define quark number stopping distance, as shown properties of the in 퐹푖푔 푎 . hot QGP medium Where Γ푞→푔푞(퐸) is the rate for a quark with energy 퐸 created in collision. We can also draw a (a) splits into a gluon and quark, and the 1st term on the contour to represents right hand side of (3)represents the distance travelled If we want to understand jet quenching theoretically, the quark number before first splitting, the 2nd term is the remainder of the we need to study how partons interact with medium. distribution at a certain (b) stopping distance after that, and (푑Γ/푑푥)/Γ is the 푄퐶퐷 푝푕푎푠푒 푑푖푎푔푟푎푚 − 푎 푠푒푚푖푞푢푎푛푡푖푡푎푡푖푣푒 푠푘푒푡푐푕 time, as time progresses, probability that the emitted gluon has energy fraction 푥. M. Stephanov hep − lat/0701002 Parton Energy Loss in QGP the center of the contour moves forward, slowing Parametrically, stopping distance 푙 is inverse stopping distance 푞 In Brookhaven National Lab(BNL), gold nuclei are We assume the QGP is weakly-coupled so we can down with time, and the proportional to the splitting rate given in equation (1), collided at 100퐺푒푉 per nucleon at Relativistic do perturbative calculations in QCD. diameter enlarges, as shown in 퐹푖푔 푏 . we found the quark number stopping distances in Heavy Ion Collider(RHIC). It is believed QGP is weakly-coupled QCD has the following expression[1]: created at 푇~350푀푒푉(4 × 1012퐾). In this case, the energy For an initial gluon, it can split into two gluons with 푞 → 푔푞 1 푏퐸퐿 loss is dominated by bremsstrahlung or split into two with pair 푙 ≃ 퐸 / ( 푇퐿 ) 푤푕푒푟푒 : 퐿 = ln (4) 푠푡표푝,푞 푎훼2푇 훼푐푇 gluon bremsstrahlung creation. In either case, we don’t have a unique final Right: and pair production. 푔 → 푞푞 state gluon to follow with, so the definition in 퐹푖푔(푎) Where 푎, 푏, 푐 are numerical constants, they depend on First gold beam-beam events To lowest order in QCD, recorded by STAR of BNL for quarks doesn’t work, but we can generalize the number of flavors we take into account, and on our (from BNL web) The 3 relative vertices idea in 퐹푖푔 푏 . Consider the probability distribution for assumption of 퐸 and 푇.

are shown in the right 푔 → 푔푔 energy in excess of equilibrium (rather than quark figure. Below: number), we can measure how far it travels before For gluon energy stopping, we have a similar integral Processes of heavy ion In classic electrodynamics, stops. This is so called “gluon energy stopping equation as 3 , but we need to take both quark and Collision (from BNL web) when a electron is passing distance”. gluon energy stopping distances into account, and we by a charged particle, it may got a similar expression as (4), but with different 푎, 푏 change direction and emit Consider the splitting 퐸 ~푇 and 푐, see reference[1] a photon (bremsstrahlung) 1 of an initial gluon 퐸2~푇 … … 퐸 ≃ 1 − 푥 퐸 moving in the 푧 퐸푖~푇 Stopping Distances: Numeric Results In QCD, if quarks or gluons in direction, which ≃ 푥퐸 the plasma kick a moving 퐸푖+1~푇 … … cascades through Finally, we give the numerical results in 3-flavor QCD: 1. 푖표푛푠 푎푏표푢푡 푡표 푐표푙푙푖푑푒 2. 푖표푛 푐표푙푙푖푠푖표푛 3. 푞푢푎푟푠, 푔푙푢표푛푠 푓푟푒푒푑 4. 푝푙푎푠푚푎 푐푟푒푎푡푒푑 퐸푁~푇 parton (through exchanging a splitting into 푁 particle, virtual gluon), then the parton will deflect from its 1 which are “stopped” at positions 푧1, 푧2 , … , 푧푁 relative If we take 훼 = , 푇 = 350푀푒푉, 퐸 = 10퐺푒푉, then quark original direction and may lose energy through to the initial position of the gluon, then: 3 Motivation: Jet Quenching number stopping distance is ; quark emitting a final gluon. Therefore, we are interest in 푙푠푡표푝,푞 ≃ 9.72 푓푚, (푒푛푒푟푔푦) 푖 퐸푖푧푖 (푒) this rate of energy loss. 푙 ≃ 2 and gluon energy stopping distances are 푙푔 ≃ 8.36푓푚, In RHIC Au-Au collision, if we define azimuthal 푠푡표푝,푔 퐸 angle 휙 on the transverse plane, the correlation 푙(푒) ≃ 13.53푓푚, compare with the diameter of gold In our work[2], we take into account the multiple 푞 function shows “absence of away-side jet”. Discussion of stopping distances has a theoretical nucleon 푑 ≃ 15푓푚, the stopping distances are in the collisions during the gluon formation time. We did a 퐴푢 advantage over discussion of energy loss rate, same order as gold nucleon, it can quantitatively careful field theory calculation, and found a full because the stopping distances can be generalized explain jet quenching. analytical expression for the parton energy loss rate, into strong coupling, where on cannot speak of Parametrically, it has the form: individual partons[3]. References ln (퐸/푇) Γ ~ 훼2푇 퐸 / 푇 , (1) Stopping Distances: Calculation [1]. P. Arnold, S. Cantrell, and W. Xiao: Phys. Rev. D81, 045017 (2010) [arXiv: 0912.3862 [hep-ph]]. where 퐸 is initial parton energy, and 푇 is QGP [2]. Peter Arnold, Wei Xiao: Phys. Rev. D78, 125008 (2008) We start from quark number stopping. To make a [arXiv: 0810.1026] temperature(퐸 ≫ 푇), and 훼 is the strong coupling precise calculation, suppose initial quark’s energy is 퐸, [3]. P.M. Chesler, K. Jensen, A.Karch, and L. G. Yaffe, Phys. Rev.

푆푡푎푟 푃푅퐿 91, 072304(2003) constant. D79, 125015 (2009) [arXiv: 0810.1985 [hep-ph]] printed by while the gluon emitted from this quark carries energy www.postersession.com