q % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVy0df9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyCayaara % aaaa!365D! $$ \bar q $$ pair production in non-Abelian gauge fields

Abstract

We calculate the qq pair production probability in the colour-flux tube model by considering the effect of non-Abelian interactions in the theory. Non-Abelian interactions in the colour field are time-dependent and hence should oscillate with a characteristic frequency ω 0, which depends on the amplitude of the field strength. Using the WKB approximation in complex time, we calculated the pair production probability. When the strength of the field is comparable to the quark masses, the corresponding pair creation probability is maximum, and for the static field w 0 → 0, we recovered the well-known Schwinger result. .65.-q; 25.75.-q; 25.75.Dw S M Puzhakkal and V M Bannur Basic concept of the problemWhen two nucleons collide at high energy, they almost just pass through each other. In the process, nucleons are excited, but in addition they leave a flux tube of deposited energy in the region of space they pass through. This energy is rapidly transformed into hadrons, the secondary particles usually produced in such collisions. By analysing proton-proton collision data, it is known that the deposition of energy at a higher rate is approximately 1 3 GeV fm −3 . It does not increase much more with a further increase in collision energy, which only makes the flux tube longer.If, instead of nucleons, two heavy nuclei collide (for simplicity, both with mass number A), a multiple superposition of the phenomenon just described is obtained, so that a given region of the flux tube now receives a much greater deposition of energy [6]. Simple geometric arguments reveal an energy density of at least εN A 1/3 GeV fm −3 . This means that an energetic collision of two 238 U nuclei provides an average deposition of approximately 6 GeV fm −3 , which is well above the level needed for plasma formation [7].Many authors have considered qq pair production in the above flux tube model [4,5,[8][9][10][11][12][13][14]. The basic idea is that when two nuclei collide, they pass each other and become colour-charged, and are thus connected by colour flux tubes. In these flux tubes, a strong colour electric field is set up, which makes the vacuum unstable to pair production via the Schwinger mechanism [1]. As a result, the colour field energy in the flux tube is transformed into the energy of qq pairs. Thus, in the collision process, a large number of qq pairs, together with gluons produced through interactions, ultimately leads to the formation of a QGP. The self-interaction of gluons in the flux tube is likely to polarise the medium between the two receding nuclei. This leads to a characteristic normal mode of oscillations. Therefore, the colour field in the flux tube should be time-dependent (colour particles are coupled to each other via the gauge fields). These collective oscillations are non-Abelian. Hence, we assume a non-Abelian colour field model in which the characteristic frequency of collective oscillation depends on the amplitude of the oscillation.During a nucleus-nucleus collision, a QGP is formed at the centre of the tube, which ...