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Citation Ilten, Philip, et al. “Serendipity in Dark Photon Searches.” Journal of High Energy Physics, vol. 2018, no. 6, June 2018. © 2018 The Authors As Published https://doi.org/10.1007/JHEP06(2018)004 Publisher Springer Berlin Heidelberg Version Final published version Citable link http://hdl.handle.net/1721.1/116307 Terms of Use Creative Commons Attribution Detailed Terms http://creativecommons.org/licenses/by/4.0/ Published for SISSA by Springer Received: March 5, 2018 Accepted: May 22, 2018 Published: June 1, 2018 Serendipity in dark photon searches JHEP06(2018)004 Philip Ilten,a Yotam Soreq,b Mike Williamsc and Wei Xued aSchool of Physics and Astronomy, University of Birmingham, Birmingham, B152 2TT, U.K. bCenter for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. cLaboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. dTheoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: Searches for dark photons provide serendipitous discovery potential for other types of vector particles. We develop a framework for recasting dark photon searches to obtain constraints on more general theories, which includes a data-driven method for determining hadronic decay rates. We demonstrate our approach by deriving constraints on a vector that couples to the B-L current, a leptophobic B boson that couples directly to baryon number and to leptons via B{γ kinetic mixing, and on a vector that mediates a protophobic force. Our approach can easily be generalized to any massive gauge boson with vector couplings to the Standard Model fermions, and software to perform any such recasting is provided at https://gitlab.com/philten/darkcast. Keywords: Phenomenological Models ArXiv ePrint: 1801.04847 Open Access, c The Authors. https://doi.org/10.1007/JHEP06(2018)004 Article funded by SCOAP3. Contents 1 Introduction1 2 Generic vector boson model3 2.1 X production3 2.2 X decays5 2.3 Efficiency ratios7 JHEP06(2018)004 3 Example models 10 3.1 Decays to SM final states 10 3.2 Decays to invisible dark-sector final states 13 4 Summary 15 A Additional VMD details 16 B X ! hadrons 17 C Experiments 18 C.1 BaBar 21 C.2 NA48/2 21 C.3 Electron bremsstrahlung 21 C.4 KLOE 22 C.5 LHCb 22 C.6 Beam dumps 23 C.6.1 Electron beam dumps 23 C.6.2 Proton beam dumps 24 C.7 LEP 24 1 Introduction Substantial effort has been dedicated in recent years [1{3] to searching for a massive dark photon, A0, whose small coupling to the electromagnetic (EM) current arises due to kinetic mixing between the Standard Model (SM) hypercharge and A0 field strength tensors [4{9]. This mixing provides a potential portal through which dark photons may be produced in the lab, and also via which they can decay into visible SM final states | though decays into invisible dark-sector final states are expected to be dominant if kinematically allowed. The minimal A0 model has 3 unknown parameters: the mass of the dark photon, mA0 ; the kinetic-mixing strength, "2; and the dark photon decay branching fraction into invisible dark-sector final states, which is typically assumed to be either 0 or 1. Constraints ≈ { 1 { have been placed on visible A0 decays by previous beam-dump [9{23], fixed-target [24{26], collider [27{32], and rare-meson-decay [33{42] experiments, and on invisible A0 decays in 2 refs. [43{52]. Many ideas have been proposed to further explore the [mA0 ;" ] parameter space in the future [53{67]. Both existing and proposed searches for dark photons provide serendipitous discovery potential for other types of vector particles. Therefore, interpreting these results within the context of a more generic model is well motivated. In this article, we develop a framework for recasting searches for massive vector particles from one model to another, which includes a data-driven method for determining hadronic decay rates. We demonstrate our approach by recasting the existing constraints on dark photons; however, we stress that our approach JHEP06(2018)004 can easily be applied to any massive gauge boson with vector couplings to the SM fermions. A variety of production mechanisms have been used in dark-photon searches, which can be categorized as follows: bremsstrahlung, eZ eZA and pZ pZA , using electron and proton beams • ! 0 ! 0 incident on fixed nuclear targets of charge Z; annihilation, e+e A γ, at e+e colliders; • − ! 0 − Drell-Yan (DY), qq¯ A , both at hadron colliders and at proton-beam fixed-target • ! 0 experiments; meson decays, e.g. π0 A γ, η A γ, ! A π0, and φ A η; • ! 0 ! 0 ! 0 ! 0 and V A mixing, where V = !; ρ, φ denotes the QCD vector mesons. • ! 0 Proposed future searches largely exploit the same production mechanisms, though some plan on using positron beams incident on fixed targets for annihilation [56, 68, 69] or additional meson decays such as D D0A [62]. Dark photons have been searched for ∗ ! 0 using the following techniques: by performing bump hunts in invariant mass spectra using the visible decays A • 0 ! `+` and A h+h , where thus far ` = e; µ and h = π have been used; − 0 ! − by searching for visible displaced A decays, which has been done both at beam dumps • 0 and at colliders using secondary vertices; and by performing bump hunts in missing mass spectra, which requires the initial • state to be known and any visible component of the final state to be detected, pro- viding sensitivity to invisible A0 decays. While the production mechanisms and search strategies employed were chosen to achieve the best possible sensitivity to dark photons, each also provides sensitivity to other types of hypothesized vector particles. The remainder of this article is organized as follows. section2 develops the frame- work required to recast these searches, which includes a novel and robust method for determining the hadronic decay rates for GeV-scale bosons. We apply our framework { 2 { to three models in section3 : a vector that couples to the B L current, a leptophobic − B boson that couples directly to baryon number and to leptons via B{γ kinetic mix- ing, and on a vector that mediates a protophobic force. Finally, summary and discussion are provided in section4 . N.b., all information required to recast dark photon searches to any vector model, including software to perform any such recasting, is provided at https://gitlab.com/philten/darkcast. 2 Generic vector boson model JHEP06(2018)004 In this section, we consider a generic model that couples a vector boson X to SM fermions, f, and to invisible dark-sector particles, χ, according to X µ X gX xf fγ¯ fXµ + Xχχ ; (2.1) L ⊂ L ¯ f χ where gX xf is the coupling strength to fermion f, and the form of the Xχχ¯ interaction 1 does not need to be specified. For example, in the minimal A0 scenario, where the A0 coupling to SM fermions arises due to γ{A kinetic mixing, gX = "e, x` = 1, xν = 0, and 0 − xq = 2=3 or 1=3. The A0 also has a model-dependent coupling to the weak Z current − 2 2 that scales as (m 0 =m ), see e.g. ref. [70]. For mA0 > 10 GeV, we adopt the model of O A Z refs. [71, 72]. The A0 decays visibly if mA0 < 2mχ for all χ, and predominantly invisibly otherwise. The more general model has 14 parameters: the 12 fermion couplings, the X boson mass, mX , and its decay branching fraction into invisible dark-sector final states. Recasting a dark photon search that used the final state involves solving the following F equation for each mX = mA0 : σX X (τX ) = σA0 A0 (τA0 ) ; (2.2) B !F B !F where σX;A0 denotes the production cross section, X;A0 is the decay branching fraction, B !F and is the detector efficiency, whose lifetime dependence is made explicit. From eq. (2.2), one can see that what is needed are the ratios σX /σA0 , X = A0 , and (τX )/(τA0 ). B !F B !F N.b., in models where the X couples to an anomalous SM current, there are additional strong constraints from the Bu;d KX, Z γX, and K πX processes, which arise ! ! ! due to the enhanced production rates of the longitudinal X mode [73{75]. 2.1 X production + The ratio of production cross sections for both electron-beam bremsstrahlung and e e− annihilation is 2 σeZ eZX σe+e− Xγ (gX xe) ! ! = = 2 : (2.3) σeZ eZA0 σe+e− A0γ ("e) ! ! 1This model is flavor-conserving due to its diagonal couplings. Of course, one could also consider flavor-violating X couplings; however, in such cases, the constraints from studies of flavor-changing neutral 0 currents are much stronger than those from A searches. Furthermore, we only consider real xf for similar reasons, making this a CP -conserving model as well. { 3 { For proton-beam bremsstrahlung the situation is more complicated, but to a good approx- imation the ratio can be taken to be 2 2 σpZ pZX gX (2xu + xd) ! 2 ; (2.4) σpZ pZA0 ≈ ("e) ! since only sub-GeV masses have been probed using this production mechanism. The ratio of DY production cross sections involves a sum over quark flavors, qi, and is given by ∗ σDY X X σqiq¯i γ (m) σqiq¯i X ! = ! ! ; (2.5) 0 ∗ 0 σDY A σDY γ (m) σqiq¯i A JHEP06(2018)004 ! qi ! ! where the first term in the sum is the mass-dependent fraction of the SM DY production attributed to each flavor, and the second term is the contribution from each subprocess 2 ( 1 σqiq¯i X 9(gX xqi ) 4 for qi = u; c; ! = (2.6) 0 2 σqiq¯i A ("e) × 1 for q = d; s; b: ! i For mX & 10 GeV, the model-dependent mixing with the Z must be accounted for in eq.