Polarization observables for millicharged particles in photon collisions Emidio Gabrielli,1, 2, 3 Luca Marzola,3, 4 Edoardo Milotti,5, 2 and Hardi Veerm¨ae3 1Dipartimento di Fisica, Sezione Teorica, Universit`adegli Studi di Trieste Strada Costiera 11, I-34151 Trieste, Italy 2INFN, Sezione di Trieste, Via Valerio 2, I-34127 Trieste, Italy. 3National Institute of Chemical Physics and Biophysics, R¨avala10, 10143 Tallinn, Estonia 4University of Tartu, Institute of Physics, Ravila 14c, 50411 Tartu, Estonia. 5Dipartimento di Fisica, Universit`adegli Studi di Trieste, Via Valerio 2, I-34127 Trieste, Italy. (Dated: November 27, 2018) Particles in a hidden sector can potentially acquire a small electric charge through their interaction with the Standard Model and can consequently be observed as millicharged particles. We systemati- cally compute the production of millicharged scalar, fermion, and vector boson particles in collisions of polarized photons. The presented calculation is model independent and is based purely on the as- sumptions of electromagnetic gauge invariance and unitarity. Polarization observables are evaluated and analyzed for each spin case. We show that the photon polarization asymmetries are a useful tool for discriminating between the spins of the produced millicharged particles. Phenomenological implications for searches of millicharged particles in dedicated photon-photon collision experiments are also discussed. I. INTRODUCTION ance and unitarity, the total cross section of γγ VV tends to a constant in the high energy limit, whereas! −1 Although we observe electric charge quantization in na- the same quantity decreases as s in the cases of spin- ture, this property is not a requirement of the Standard 0 and spin-1/2 MCP. Such a distinguishing characteris- Model (SM) [1]. In fact, whereas new physics models tic of spin-1 interactions is manifest in the SM, where the tree-level total cross section for γγ W +W − ap- based on grand unified theories [2] or proposing magnetic ! monopoles [3] enforce the charge quantization, other the- proaches a constant of about 80 pb at high energies [9{ ories of physics beyond the SM predict the existence of 11], while radiative corrections are typically of order 10% particles with an electric charge 1.1 The parti- [12]. This property, resulting from a collinear effect of the cles characterized by these possibly effective nonquan- W propagator in the t-channel production mechanism, tized charges are commonly dubbed millicharged parti- has a general validity and also holds for the analogous cles (MCP) [4{7]. production of two spin-1 MCP [8]. Indeed, the require- ment of unitarity and gauge invariance completely fixes The most natural framework that yields MCP presents the interaction Lagrangian of spin-1 MCP V with the two or more U(1) gauge groups, coupled to different µ photon field, which necessarily recovers the structure of matter sectors, whose fields possess nondiagonal kinetic the W ± Lagrangian of the SM, implying a gyromagnetic terms. These induce the mixing of the corresponding factor g = 2 for the former. gauge bosons, and, as a result, the matter fields of one V sector appear as MCP in the other. We remark that In principle, the different asymptotic behavior of the even in the absence of a tree-level kinetic mixing, a non- spin-1 MCP production cross sections in photon-photon diagonal kinetic term is inevitably induced by radiative collisions could then be used as a tool to disentangle the corrections [5], provided there are matter fields charged production of these particles from the spin-0 and spin- under both U(1) gauge groups. 1/2 cases. However, an even better sensitivity to the The above mechanism can give rise to spin-0 and spin- spin of the produced MCP particles could be achieved by employing polarized photon beams. In this case, as we arXiv:1604.00393v2 [hep-ph] 29 Nov 2016 1/2 MCP, but generating a consistent and unitary the- ory for elementary spin-1 MCP requires a different con- will demonstrate, suitable polarization observables yield struction. In fact, while the interactions of scalars and sensitive tools to probe the spin of MCP. fermions with the photon can always be induced via the The most stringent limits on MCP models come from mentioned mixing, the spin-1 case requires the extension cosmological and astrophysical observations that bound of the SM group to a larger non-Abelian gauge group [8], the ratio of the millicharge fraction to the MCP mass µ with the spin-1 MCP (V ) arising from the vector boson m. These constraints are model dependent and mainly multiplet of the latter. apply to models where millicharges arise as a consequence The case of spin-1 MCP also presents an intriguing fea- of kinetic mixing [13]. For MCP of mass below the MeV ture: As a result of the interplay between gauge invari- scale, the most relevant constraints come from stellar evo- lution and cosmology. For instance, as the emission of MCP pairs with low mass could induce a severe energy loss in stars, stellar evolution constrains < (10−14) O 1 Here and in the rest of the paper, the electric charge is measured for m < (10KeV). The requirement of successful big O −9 in units of the elementary charge e. bang nucleosynthesis leads, instead, to < (10 ) for O 2 m < (10MeV) [14]. Besides, if MCP can be consid- conclusions are reported in Sec. IV. The Appendix gives ered chargedO dark matter constituents, assumptions on details regarding the interferometric detection method the magnetic field of galactic clusters and on the pos- sketched in the paper and provides a first estimate of sible MCP velocity distribution result in a tight model- the signal-to-noise ratio that can be obtained with this −14 independent bound < 10 (m=GeV) [15]. technique. In contrast, the existing laboratory experiments ded- II. POLARIZATION-DEPENDENT CROSS icated to MCP searches result in bounds that strongly SECTIONS depend on the MCP masses by exploiting different MCP production mechanisms. For example, the strongest lim- its for MCP masses below the MeV scale come from the We now analyze the amplitudes and cross sections for study of orthopositronium decays into invisible states, polarized photon-photon scatterings into a pair of MCP or from the comparison of the Lamb-shift measure- µS µ¯S of spin S, ments with QED predictions, which sets the limit < −4 γ(p1; h1) γ(p1; h1) µS (p3)¯µS (p4) ; (1) (10 ). Direct laboratory bounds on MCP couplings ! andO masses have also been cast by accelerator exper- where p with i = 1 4 are the corresponding 4-momenta iments [16] through the \beam dump" technique [17], i and h indicate the− helicities of initial photons. yielding < 3 10−4 for MCP masses up to 100 MeV. 1;2 × The generic amplitude for a process with two initial- Experiments studying the propagation of polarized state photons can be written as light in a strong magnetic field also constrain the MCP pair production. In fact, provided that the photon energy α β h1h2 = h1 (p1)h2 (p2) αβ; (2) beams (in the eV range) satisfy the condition ! > 2m, M M MCP induce an observable ellipticity of the outgo- α where (p1;2) are the polarization vectors of the initial ing beam through vacuum magnetic birefringence and h1;2 photons with helicities h = 1. For the production of dichroism [18, 19]. The measured upper bounds on 1;2 two MCP with mass m , the polarized± differential cross from the BFRT experiment [20] first and PVLAS [21] section can be decomposed as later, were then used to set an upper limit on millicharge < (10−6) for MCP masses below m < (10−1eV). dt 2 O O dσh h = h h More recently, new experimental proposals aim to investi- 1 2 16πs2 jM 1 2 j gate the Schwinger pair production of MCP in the strong d(σ + h1 σA1 + h2 σA2 + h1h2 σAA): (3) electric field of cavities used in particle accelerators [22]. ≡ These can potentially improve the upper bound up to The angular dependence in the center-of-mass (c.m.) < 10−6 using present cavities at TESLA [22] and up to −7 frame follows from dt = βs=2 d(cos(θ)), where β = < (10 ) with near-future cavities, for MCP masses p 2 j j O −3 1 4m =s is the speed of the final particles. The quan- below 10 eV [23]. tities− on the right-hand side of Eq. (3) correspond to the However, no dedicated experiments targeting the di- differential cross section (dσ) and the differential asym- rect MCP pair production in inelastic photon-photon metries (dσA and dσAA), whose explicit form is obtained scatterings have been proposed to date. Indeed, being by inverting Eq. (3): stable, pair-produced MCP would escape the detector without interacting, leaving a signature only in miss- 1 dσ = d(σ++ + σ−− + σ+− + σ−+); (4a) ing energy. Nonetheless, dedicated experiments based on 4 interferometric techniques with polarized photon beams 1 dσA1 = d(σ++ σ−− + σ+− σ−+); (4b) have the potential to reveal the direct MCP production 4 − − for m < (eV). 1 O dσA2 = d(σ++ σ−− σ+− + σ−+); (4c) In this framework, the aim of the paper is to perform a 4 − − complete study of the production of MCP in collisions of 1 dσAA = d(σ++ + σ−− σ+− σ−+): (4d) polarized photon beams. In particular, we identify suit- 4 − − able polarization observables to disentangle the produc- 2 tion of millicharged scalars, fermions and vector bosons. Parity conservation implies dσA1 = 0 = dσA2 thus, These results can be used in many applications ranging if we restrict ourselves to the case of parity-conserving from the investigations of sub-eV MCP in laser exper- iments to the search of heavy MCP particles above the GeV scale at the future polarized gamma-gamma collider facilities [24{26].