Searching for New Physics with multilepton events at PADME
IIL NUOVO CIMENTO
Vol. ?, N. ? ? Searching for New Physics with multilepton events at PADME
G. Martelli ( )( ∗ ) , P. Ciafaloni ( )( ∗∗ ) and M. Raggi ( )( ∗∗∗ ) ( ) Dipartimento di Fisica e Geologia, Universit`a di Perugia - Perugia, Italy ( ) INFN, Sezione di Lecce e Universit`a del Salento - Lecce, Italy ( ) Dipartimento di Fisica, Universit`a di Roma - Roma, Italy
Summary. — The PADME experiment is searching for the Dark Photon A (cid:48) inthe e + e − → γA (cid:48) process, assuming a A (cid:48) decay into invisible particles. In extendedDark Sector models, a Dark Higgs h (cid:48) can be produced alongside A (cid:48) in the process e + e − → h (cid:48) A (cid:48) . If the h (cid:48) mass is greater than twice the A (cid:48) mass the final state willbe composed by three e + e − pairs. Such extremely rare process is explorable by thePADME experiment, which could get a first measure and impose limits on modelsof physics beyond the Standard Model.
1. – Introduction
The extreme difficulty in Dark Matter detection could be explained speculating thatStandard Model (SM) and Dark Matter particles exist in two separate sectors connectedby a portal. The simplest model for this theory adds a new gauge group having U D (1)symmetry which introduces a new boson A (cid:48) , called Dark Photon. This new sector, andtherefore the new boson introduced, is expected to couple with the SM electromagneticfield with a coupling constant (cid:15) of the order of 10 − or smaller.Many experiments in recent years have focused their attention on the production of thisnew vector boson, searching for both visible and invisible A (cid:48) decays. Among these lies thePADME experiment, which aims to measure processes e + e − → γA (cid:48) in the interaction ofa positrons beam with the electrons of a diamond target, using the beam extracted fromthe DAΦNE linac at the National Laboratories of Frascati, LNF. The used technique isthat of the missing mass M miss = ( P e − + P beam − P γ ) in which only known kinematicvariables are used. The presence of a vector boson A (cid:48) would manifest as a narrow peakin the spectrum of the variable M miss corresponding to its mass.Although PADME was designed to the search for the A (cid:48) , other Dark Matter candidates ( ∗ ) Speaker: E-mail: [email protected]( ∗∗ ) E-mail: [email protected]( ∗∗∗ ) E-mail: [email protected] © Societ`a Italiana di Fisica a r X i v : . [ h e p - ph ] F e b G. MARTELLI ETC. can be observed with this experiment. One of these is the the Dark Higgs ( h (cid:48) ) whichis introduced in models where the A (cid:48) mass is generated through the spontaneous sym-metry breaking mechanism. This particle can be produced in PADME via the reaction e + e − → h (cid:48) A (cid:48) . If m h (cid:48) ≥ m A (cid:48) the Dark Higgs decays in a pair of A (cid:48) , which in turndecays into a lepton pair, producing a six charged leptons final state, respectively threepositrons and three electrons.This article is focused on the search for Dark Higgs mediated six charged leptons, exploit-ing a theoretical study of the phenomenology of these low-energy events in the PADMEexperiment.
2. – The Dark Higgs
In non-minimal models where the mass of the A (cid:48) is generated through spontaneoussymmetry breaking, an associate production of a new boson, referred as Dark Higgs [1],together with an A (cid:48) is possible. Naturalness requires that the two particles have massesof the same order m h (cid:48) ∼ m A (cid:48) . This new sector is neutral under the Standard Model andvice versa, and all interactions with it proceed through kinetic mixing of U D (1) with theSM photon.The Lagrangian containing the physical h (cid:48) field takes the form: L = − A µν + 12 m A (cid:48) + 12 ( ∂ µ h (cid:48) ) + + 12 m h (cid:48) h (cid:48) + L int (1) One of the few h (cid:48) production processes is the so-called Higgs’-strahlung, e + e − → h (cid:48) A (cid:48) ,which has an amplitude that is suppressed by just a single power of the kinetic mixingangle and can therefore readily occur for (cid:15) ∼ O (10 − − − ). This production mechanismis similar to SM Higgs-strahlung but in this case the h (cid:48) is produced in association witha A (cid:48) instead of a classic photon.While the vector A (cid:48) will typically have a large branching ratio to lepton pairs, the decaysof the h (cid:48) will depend on its mass relative to that of the vector. If the Dark Higgs is heavyit will decay in two vectors A (cid:48) , eventually leading to a six lepton final state, as can beseen in Fig. 1.On the contrary, if h (cid:48) is light, it will decay via loop processes to leptons and possiblyhadrons. In this case the Dark Higgs is long-lived and will most likely become an unde-tected particle.Experiments at e + e − colliders with few GeV center of mass energy and very high lumi-nosity, Babar [2] and Belle [3], had investigated e + e − → (cid:96) + (cid:96) − ) setting stringent limitson the existence of the h (cid:48) for energy scales in the ∼ GeV range. No data are available formasses of the h (cid:48) <
3. – Cross sections and acceptance evaluations
In order to search for new physics with multi-lepton events in a low energy experimentsuch as PADME, a theoretical treatment is necessary.The main background event to the Higgs’-strahlung is the SM e + e − → e + e − ) process.The cross section for this process is very hard to calculate due to the high numberof particle in the final states, producing several thousand of Feynman diagrams which EARCHING FOR NEW PHYSICS WITH MULTILEPTON EVENTS AT PADME Fig. 1. –
Feynman diagram for the Higgs’-strahlung process producing a six leptons final state. contributes to the amplitude. An order of magnitude estimate of this cross section canbe obtained by using the Leading Log Equivalent Photon Approximation (EPA) and thecross section σ ( γγ → e + e − e + e − ) as proposed by [5]. As noted in [6], this approximationleads a gross overestimate of the cross section values at low energies, due to accidentalcancellation. σ e + e − ) = α π σ ( γγ → e ) (cid:16) log (cid:16) sm (cid:17) + A log (cid:16) sm (cid:17) + B log (cid:16) sm (cid:17) + C log (cid:16) sm (cid:17) + D (cid:17) (2) Using Eq. 2 including all the logarithmic terms, at the PADME center of massenergy the full EPA estimate seem to point to a value σ e + e − → e + e − ) ∼ σ e + e − → A (cid:48) h (cid:48) = παα D (cid:15) s (cid:18) − m A (cid:48) s (cid:19) − (cid:115) λ (cid:18) , m h (cid:48) s , m A (cid:48) s (cid:19) × (cid:20) λ (cid:18) , m h (cid:48) s , m A (cid:48) s (cid:19) + 12 m A (cid:48) s (cid:21) (3) where α D is the coupling between h (cid:48) and A (cid:48) , and λ ( a, b, c ) ≡ a + b + c − ab − ac − bc .For accessible values of the kinetic mixing parameter (cid:15) (10 − ≤ (cid:15) ≤ − ), the crosssection is quite large compared to the SM. In fact the Higgs’-strahlung cross section onlypays an (cid:15) αα D suppression compared to the α of the concurrent SM process. For fixedvalues of m h (cid:48) and m A (cid:48) the production cross section scales as 1/s. In Fig. 2a), assuming m h (cid:48) + m A (cid:48) < √ s and that m h (cid:48) > m A (cid:48) , the ratio between the possible cross sectionvalues of the Dark Sector process at PADME with the SM background is shown. Thehighest values of the Dark Sector cross section are obtained for low values of m h (cid:48) and m A (cid:48) .To evaluate the PADME spectrometer detection capabilities, a study of the acceptancehas been made using a phase space simulation. Using ROOT’s TGenPhaseSpace classand applying the kinematic limits explained above, it was possible to obtain the momentadistributions for the particles in the final state from which the acceptance was extracted, G. MARTELLI ETC. expressed in terms of m h (cid:48) and m A (cid:48) . The PADME spectrometer is able to detect all ofthe six leptons, only if the minimum energy is ≥
50 MeV, which is challenging having6 tracks and 550 MeV total energy. The acceptance studies of the Dark Sector signalevents are summarised in Fig. 2b). a) b)
Fig. 2. – a) Ratio between the Dark Sector cross section and the Standard Model one. b) Accep-tance values for the Dark Sector events at PADME.
The acceptance is of the order of 1% for most h (cid:48) A (cid:48) pairs of masses.
4. – Conclusions
The theoretical studies presented in this article show that the Higgs’-strahlung processcan also occur within the low-energy PADME experiment. However the acceptance studyindicates a high efficiency of the PADME spectrometer for momenta higher than 50 MeV.The PADME experiment has therefore at present a low efficiency in reconstructing DarkHiggs events due to the high number of leptons. To increase the detection efficiency oflow energy particles, the intensity of the magnetic field should be reduced, preventinglow momentum charged particles from colliding with the vacuum chamber and increasingthe detection efficiency of the first scintillating fingers of the veto systems.Furthermore, the final state of these processes will be composed of a high number ofcharged particles. Therefore it is necessary to implement an efficient event reconstructionalgorithm that can well identify the large number of charged particle pairs produced inthe PADME spectrometer.
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