Search for Axion(-like) Particles in Heavy-Ion Collisions
SSearch for Axion(-like) Particles in Heavy-Ion Collisions
Yi Yang ∗ and Cheng-Wei Lin Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan, ROC
The axion(-like) particles are the perfect candidates for solving the strong CP problem in Quan-tum Chromodynamics and the dark matter puzzle in our Universe. One of the possible ways tosearch for axion(-like) particles is using the conversion of photon to axion(-like) particles and theconversion probability is proportional to the square of the product of the coupling constant g ,strength of magnetic field B , and the traveling distance L . The current experiments for the searchof axion(-like) particles are limited by the product of B and L , which is in the order of 10 T · m .In this letter, we propose using the direct photon production in heavy-ion collisions to search foraxion(-like) particles. This configuration could have the BL factor up to 100 T · m and the expectedupper limits can cover a new phase space of the production of the axion(-like) particles. Keywords: Axion, axion-like, dark matter, heavy-ion collisions, nuclear modification factor, direct photonproduction
The Standard Model of Particle Physics (SM) is themathematical framework to describe the interactions be-tween elementary particles including electromagnetism,weak, and strong interactions. In the past two decades,we had tremendous success on understanding of theSM from many important experiments, for instancethe experiments at the Relativistic Heavy Ion Collider(RHIC) at Brookhaven National Laboratory, STAR andPHENIX, which devoted into understanding the newstate of matter of Quantum Chromodynamics (QCD),Quark-Gluon Plasma (QGP), since 2000 [1, 2], and theexperiments at the Large Hadron Collider at CERN,ATLAS and CMS, which discovered the Higgs boson in2012 [3, 4] and provided many precision measurements onthe electroweak sector [5]. However, there are still manyunsolved puzzles, such as the origin of matter-antimatterasymmetry [6], the dark matter [7] and dark energy [8]problem, and so on.One of the most intriguing mysteries is that the miss-ing mechanism of the Charge-Parity ( CP ) violation pro-cesses in the strong interactions, as known as the “strong CP problem in QCD”. The missing CP violation pro-cesses are the key to explain the matter-antimatter asym-metry problem in our Universe. To overcome the strong CP problem, a new mechanism was proposed by RobertoPeccie and Helen Quinn in 1977 by adding an extra globalU(1) gauge symmetry in the Lagrangian and this pre-dicted a new hypothetical spin-0 pseudoscalar particle,axion [9]. Recently, many theories also predict very lightpseudoscalar or scalar particles, which have very sim-ilar properties but play no rules in solving the strong CP problem, so called axion-like particles. Both axionor axion(-like) particles must be weakly interacting withnormal particles, so called weakly interacting slim parti-cles WISPs [10], and they also have very small masses,less than few eVs. Therefore, these particles are the per-fect candidate to solve the dark matter problem [11–13].There are many experimental constrains on the cou-pling strength and the mass of axion(-like) particles from low energy nuclear physics, high energy particle physics,and astrophysics. In this letter, we propose an alternativeway to search for the axion(-like) particles signal usingthe direct photon production in the heavy-ion collisions.One of the most interesting features of axion(-like)particles is that they can couple to photon via a weak-strength coupling constant. The effective interaction La-grangians for the pseudoscalar or scalar field, φ , to elec-tromagnetic field, F µν , can be expressed as: L pseudoscalar = − g φF µν ˜ F µν = gφ ( (cid:126)E · (cid:126)B ) , (1) L scalar = − g φF µν F µν = gφ ( (cid:126)E · (cid:126)E − (cid:126)B · (cid:126)B ) , (2)where g is the coupling constant and ˜ F µν is the dual ofthe electromagnetic field. Figure 1 shows the Feynman-like diagram of the conversion of photon to axion(-like)particles via the interaction with the magnetic field B . 𝜙𝐵 𝑔 𝛾 FIG. 1. The Feynman-like diagram of photon coupling toaxion(-like) particles via a weak coupling constant g . The probability of photon to axion(-like) particles oraxion(-like) particles to photon conversion can be deriveddirectly and many review articles have detailed descrip-tion of it (see Ref. [14, 15]). Then, the conversion prob-ability can be written as: P ( γ → φ ) = 4 g B ω m φ sin (cid:32) m φ L ω (cid:33) (3) ≈ (cid:18) gBL (cid:19) if m φ L/ ω (cid:28) , a r X i v : . [ h e p - ph ] F e b where L is the traveling distance of photon, B is thestrength of magnetic field along the path of photon, ω is the photon’s frequency (corresponds to the energy),and m φ is the rest mass of axion(-like) particles. An in-teresting idea of searching for axion(-like) particles usingthis photon-axion(-like) conversion, so called Light Shin-ing Through Walls (LSW), was proposed [16–18]. Thebasic idea is to use the possibility of photon convertingto axion(-like) particles and then axion(-like) particle willpenetrate through the wall due to the extremely weak in-teraction between axion(-like) particles and the SM par-ticles (the Wall). Finally, the axion(-like) particles willconvert back to photon and to be detected. The totalprobability of the LSW experiments is the product oftwo conversion probabilities as followings: P ( γ → φ → γ ) = P ( γ → φ ) × P ( φ → γ ) ≈ (cid:18) gBL (cid:19) (4)Many experiments are dedicated on the LSW-typesearch, such as ALPS [19, 20], BFRT [21], and so on.The results mainly focused on the phase space in thelow-mass region, namely < g is around 10 − to 10 − . An important observationfrom Eq. 3 and 4 is that the conversion probability alsodepends on the product of B and L . In other words, theexperimental sensitivity for LSW on the coupling con-stant g is inverse proportional to BL and proportional to P ( γ → φ → γ ) − / . The current LSW-type experimentshave limited BL factor which is in the order of 10 to 100 T · m .As mentioned previously, there are two key compo-nents for observing the process of photon to axion(-like)particles conversion are the BL factor and the photonsource. In the relativistic heavy-ion collisions, strongmagnetic field can be generated in the non-central col-lisions due to the large charges and high speed of the col-liding nuclei. The strength of the magnetic field in theinteraction area can be estimated as eB ∼ f m π , where m π is the mass of π meson and f is the scaling factorwhich depends on the type and energy of collisions par-ticles [22]. In the LHC and RHIC heavy-ion collisionsconfigurations, the magnetic field can be much strongerthan any apparatus in the labs and it is in the orderof 10 T [23]. On the other hand, the size of interac-tion area (fire ball) in the heavy-ion collisions can also bemeasured by the Hanbury Brown/Twiss (HBT) particleinterferometric methods [24, 25] and it is in the scale of10 f m [26]. Finally, the photons created in the heavy-ion collisions can be good candidates for the search ofaxion(-like) particles by taking the advantage that pho-tons have the chance to convert to axion(-like) particlesin the strong magnetic field generated in the heavy-ioncollisions, as illustrated in Fig. 2. Most interestingly, the BL factor in the heavy-ion collisions can also reach up to 10 − T · m . FIG. 2. The illustration of the direct photon produced inheavy-ion collisions and it converts to axion(-like) particleinside the fire ball which has strong magnetic field.
The probability of photon converting to axion(-like)particles in heavy-ion collisions can be extracted from thedirection photon production, namely the nuclear modifi-cation factor R γ AA of the direct photon production. The R γ AA is the ratio of direct photon produced in A + A col-lisions to that in p + p collisions and it is defined as R γ AA = 1 (cid:104) N coll (cid:105) σ A + Aγ σ p + pγ (5)where (cid:104) N coll (cid:105) is the average number of binary nucleon-nucleon collisions in a given centrality bin, σ A + Aγ and σ p + pγ are the production cross sections of direct photonin A + A and p + p collisions, respectively.There are two additional effects should be taken intoaccount in the R γ AA determination. The first one is theconversion probability of photon to axion(-like) particles,and the second one is the axion(-like) paricles producedin A + A collisions then converting to photon. However,the production cross section for axion(-like) particles isalso expected to be extremely small, so the second termcan be ignored. The modified R γ (cid:48) AA should be rewrittenas R γ (cid:48) AA = 1 (cid:104) N coll (cid:105) σ A + Aγ × P ( γ → φ ) + σ A + Aφ × P ( φ → γ ) σ p + pγ ≈ (cid:104) N coll (cid:105) σ A + Aγ × P ( γ → φ ) σ p + pγ (6)= R γ AA × P ( φ → γ ) , where σ A + Aφ is the production cross section for axion(-like) particles in A + A collisions. The direct photonproduction is expected to be not affected by the QGPmedium since photon doesn’t carry any color charge. Itmeans that R γ AA should be unity. Therefore, the conver-sion probability of photon to axion(-like) particles canbe determined by the precision of the measured R γ (cid:48) AA .In other words, the conversion probability of photon toaxion(-like) particles equals to the probability of R γ (cid:48) AA away from unity. It is worthwhile to mention that search-ing for axion(-like) particles in heavy-ion collisions onlydepends on g , unlike the traditional LSW experimentswhich depends on g , and it will provide us better prob-ability to observe them.Finally, the expected upper limit of the coupling con-stant of axion(-like) particles to photon, g , can be esti-mated by using the BL factor and the precision of themeasured R γ (cid:48) AA . Figure 3 shows the estimated upper lim-its of g as a function of the mass of axion(-like) par-ticles with the assumptions of BL equals to 10 or 100 T · m and the probability of the measured R γ (cid:48) AA awayfrom unity equals to 1% or 5%. Additionally, the en-ergy of direct photon is required to be larger than 5GeV to avoid the thermal production area, based onthe ALICE results [27]. The low mass region, few µ eVto eV, is excluded by the LSW experiments [19] andCAST [32], the medium mass region, eV to MeV, isexcluded by e + e − experiments [33], the high mass re-gion, MeV to GeV, is excluded by the collider experi-ments [34], and the other regions are considered by someastrophysical arguments [42–47]. It is worth to noticethat the precision of the measured R γ (cid:48) AA is the key ofthis method and a new phase space in the high massregion, 10 to 100 MeV, can be covered. The expectedlimits on the coupling constant g in that mass region cango to 10 − to 10 − GeV − . Additionally, this methodalso covered the high mass region of the QCD axion,such as the Kim-Shifman-Vainshtein-Zakharov (KSVZ)axion [28, 29] and Dine-Fischler-Srednicki-Zhitnitsky(DFSZ) axion [30, 31]. This will provide an additionalconstraint on the coupling of axion(-like) particle to pho-ton.In summary, axion(-like) particles play an importantrole to solve the most mysterious and interesting puzzlesin our Universe, namely the matter-antimatter asymme-try and the origin of dark matter. There are many exper-iments using the properties of photon-axion(-like) parti-cles conversion to search for the axion(-like) signal andpush the limits in the extremely low mass region. As wellas some approaches using collider signatures to search foraxion(-like) particles, for example using photon-jet as aprobe in p + p collisions [48] and relying on the strongelectromagnetic field generated by the ultra-peripheralheavy-ion collisions [49, 50], and these methods can coverthe mass region from 0.1 to 100 GeV. In this letter, wepropose an alternative way to search for axion(-like) par-ticles via the direct photon production in the heavy-ioncollisions and this method can provide new constraintsin the medium-high mass region where was not coveredbefore. Taking the advantages that strong magnetic fieldcan be generated in the non-central collisions and photonwon’t affect by the QGP medium, the nuclear modifica-tion factor of the direct photon production, R γ (cid:48) AA , can beused to determined the convesion probability of photonto axion(-like) particles. In other words, the precision of the R γ (cid:48) AA measurements of direct photon production isthe key of this search. A simple estimation using RHICand LHC heavy-ion collisions configurations shows thata new phase space, the medium-high mass region (10 to100 MeV), can be covered. If the precision of the R γ (cid:48) AA can be achieved to 1% level and the BL factor is about100, the upper limit on the coupling constant g can bearound 10 − or 10 − GeV − . Therefore, better preci-sion on the direct photon production will be needed inthis search. As a side note, inspired by using direct pho-ton production in the heavy-ion collisions, one can imageusing relativistic heavy-ion beam along with a photonbeam side-by-side and detecting the disappearing (or re-generating) of the photon to be another novel idea forthe search of axion(-like) particles. The BL factor cango up to 10 and the limit on the photon-axion(-like)-particle coupling, g , can be easily to push to the sameorder of magnitude which will be much lower than thecurrent limit. However, more detailed studies are neededto be done.We thank National Cheng Kung University for theirsupport. 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