Equivalent photon approximation is used to calculate fiducial cross sections for dimuon production in ultraperipheral proton-proton and lead-lead collisions. Analytical formulae taking into account experimental cuts are derived. The results are compared with the measurements reported by the ATLAS collaboration.
IntroductionThis year we celebrate the 111th anniversary of L. D. Landau. This paper is devoted to the modern state of the problem first considered by L. D. Landau and E. M. Lifshitz in 1934 when they calculated the production cross section of e + e − pair in ultrarelativistic heavy ions collisions [1]. We will demonstrate that this problem is still of great interest.In spite of many efforts, no New Physics has been found at the LHC so far. It might be a good time to consider scenarios of appearance of New Physics at the LHC that were less attractive at the time when the LHC was under construction. Although the LHC was conceived as a hadron-hadron collider, it also acts as a photon-photon collider with the photons appearing in ultraperipheral collisions of hadrons. This idea is quite old, and it was thoroughly considered during the construction and operation of the RHIC and the LHC [2-16]. However, since hadronic interactions were more likely to deliver the signal of New Physics, particularly in Higgs boson properties, they received more attention in the literature and were given higher priority in the LHC schedule. With the long shutdown of the LHC beginning at the end of 2018, it might be a good time to reconsider photon-photon collisions at the LHC as a source of possible New Physics events so that the necessary detectors adjustments could be made and, perhaps, more time for heavy ions collisions could be negotiated in the LHC schedule.The leading order Feynman diagram for an ultraperipheral collision is presented in Fig. 1 where instead of lead nuclei there could be any charged particles. The distinctive signature of an ultraperipheral collision is that the charged particles remain intact after the collision. These particles won't have high transverse momentum, so they are difficult to detect with just the main detectors of the ATLAS and CMS experiments, but there exist additional detectors at low scattering angles (the ATLAS forward proton detector [17] and the CMS-TOTEM precision proton spectrometer [18]). However, even without the forward detectors, ultraperipheral collisions manifest through production of particles.Let us compare proton-proton and lead-lead ultraperipheral collisions as possible sources of New Physics events. Integrated luminosity delivered by the LHC in Run 2 in proton-proton collisions is over 150 fb −1 both for the ATLAS and the CMS experiments [19,20]. Integrated luminosity delivered by the LHC in lead-lead collisions in the heavy ions run was 0.7 nb −1 in 2015 [21] and 1.8 nb −1 in 2018 [19]. Cross section for an ultraperipheral collision is proportional to Z 4 where Z is the particle charge. For Pb, Z = 82, so we get that if there exists New Physics that appears in γγ collisi...
By using fundamental units c,h, G as conversion factors one can easily transform the dimensions of all observables. In particular one can make them all "geometrical", or dimensionless. However this has no impact on the fact that there are three fundamental units, G being one of them. Only experiment can tell us whether G is basically fundamental.It is well known [1] that to each mass M there corresponds a characteristic length r g , the so called gravitational radius (a body with radius r = r g forms a black hole):where G is gravitational constantwhile c is velocity of light. Thus in all physical equations M can be substituted by r g so that mass can be "exorcised" from definitions of all physical observables. As a result everything can be measured in "geometrical" units of length L and time T instead of standard L, T , M units. *
We consider a few thought experiments of radial motion of massive particles in the gravitational fields outside and inside various celestial bodies: Earth, Sun, black hole. All other interactions except gravity are disregarded. For the outside motion there exists a critical value of coordinate velocity v c = c/ √ 3: particles with v < v c are accelerated by the field, like Newtonian apples, particles with v > v c are decelerated like photons. Particles moving inside a body with constant density have no critical velocity; they are always accelerated. We consider also the motion of a ball inside a tower, when it is thrown from the top (bottom) of the tower and after classically bouncing at the bottom (top) comes back to the original point. The total time of flight is the same in these two cases if the initial proper velocity v 0 is equal to c/ √ 2.
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