A Search for Charged Lepton Flavor Violation in the Mu2e Experiment
AA Search for Charged Lepton Flavor Violation in the Mu2e Experiment
Manolis Kargiantoulakis ∗ Fermi National Accelerator LaboratoryBatavia, Illinois 60510, United States of [email protected]
The Mu2e experiment will search for the neutrino-less conversion of a muon into an electron in the field ofan aluminum nucleus. An observation would be the first signal of charged lepton flavor violation and de factoevidence for new physics beyond the Standard Model. The clean signature of the conversion process offers anopportunity for a powerful search: Mu2e will probe four orders of magnitude beyond current limits, with realdiscovery potential over a wide range of well motivated new physics models. This goal requires an integratedsystem of solenoids that will create the most intense muon beam in the world, and suppression of all possiblebackground sources. The Mu2e components are currently being constructed, with the experiment planned tobegin operations in the Fermilab Muon Campus within the next few years.
Keywords : Particle Physics; Muons; Charged Lepton Flavor Violation; Beyond the Standard ModelPACS Nos.: 11.30.Hv; 12.15.Ff; 13.35.Bv; 14.60.Ef
1. Introduction and Context
For all its successes over many decades, the Standard Model (SM) of physics is viewed only as aneffective low energy approximation and we are motivated to search for a more fundamental underlyingstructure. Through precision searches we are granted indirect access to higher energy scales or moreweakly coupled interactions, and signals of physics beyond the Standard Model (BSM) may have alreadybeen detected. The observation of neutrino oscillations constitutes a de facto extension to the standardtheory, with remaining questions regarding the nature of neutrinos; the muon anomalous magneticmoment measurement has yielded a > σ discrepancy from the SM prediction, an important resultthat has guided experimental searches and BSM theory; and numerous signals in semi-leptonic B mesondecays offer corroborating hints for violation of lepton flavor universality over a multitude of channels, with combined statistical significance around the σ level. This pattern of experimental deviationsreveals precision searches in the flavor sector as a promising and well motivated field.
Charged lepton flavor violation
The concept of flavor in particle physics begins with the discovery of the muon by Anderson andNeddermeyer in cosmic radiation and the realization that it appears to be just a heavier copy ofthe electron. In the quark sector, flavor-changing transitions occur with mixing defined by the CKMmatrix. The discovery of neutrino oscillations is direct evidence that lepton flavor too is not aconserved quantity. And yet similar flavor mixing has never been observed in the last class of elementary ∗ [email protected] 1 a r X i v : . [ h e p - e x ] A p r Manolis Kargiantoulakis fermions, the charged leptons: the electron ( e ), the muon ( µ ), and the tau ( τ ). Any observation of chargedlepton flavor violation (CLFV) would be direct evidence of new physics a .Searches for CLFV are very well motivated and share connections with areas of intense experimentaland theoretical interest. The non-universal lepton interactions suggested by the B meson anomalies areclosely associated with violation of lepton flavor conservation. And the same effective operators thatmediate CLFV could have a flavor-conserving component that gives rise to the muon g -2 discrepancy, aswell as to leptonic electric dipole moments. Finally, as the charged counterpart to neutrino oscillations,CLFV measurements can inform BSM models of the neutrino mass generation mechanism and aresynergistic with neutrino-less double beta decay experiments.A rich global program is exploring this promising field, with complementary searches in differentchannels that hold the potential to elucidate the CLFV mechanism. Searches for rare CLFV processesusing muons are especially powerful and offer the best combination of new physics reach and exper-imental sensitivity, due to the availability of intense muon sources and their relatively long lifetime.Of the many expansive reviews on the subject we highlight especially the excellent introductoryoverviews of Bernstein and Cooper and Calibbi and Signorelli. There is a long history to experimental searches for CLFV between the first two families, where thehighest sensitivity has been achieved. These searches began relatively soon after the discovery of themuon and have been closely connected to the evolution of our understanding of the SM flavor structure.Limits on muon-to-electron transitions provided confirmation that the muon and electron neutrinosare separate particles and gave rise to the concept of families of leptons, while suggesting a law ofconservation of their flavor. Improvements in experimental sensitivity have largely been driven bythe availability of more intense muon sources, from cosmic ray muons in the late 1940’s to modernaccelerator-based beams. The current limits on the three most important CLFV muon modes are givenbelow, all quoted at the confidence level (CL): • In the µ + → e + γ decay the branching ratio has been constrained to BR ( µ + → e + γ ) < . × − .Set by the MEG experiment which collected data between 2008-2013 at PSI, this is the moststringent limit on any CLFV decay to date. Using a continuous beam to stop . × muons ontarget, the experiment searched for coincidences between a positron and a photon emitted back toback and each with energy equal to half a muon mass. • The present limit BR ( µ + → e + e − e + ) < . × − is set by the SINDRUM collaboration. Thesignature of this process consists of two positrons and one electron originating from a common vertexand with a total energy consistent with the mass of the muon. • The coherent muon to electron conversion in the field of a nucleus, µ − N → e − N , offers a cleanerexperimental signature: here the only decay product to be detected is a monochromatic electron.Currently the best limit comes from the SINDRUM-II experiment at PSI, which stopped . × muons on a gold target. The limit on the conversion rate (normalized to muon captures, see Eq. 2)in muonic gold is R µe (Au) < × − . a Neutrino oscillations present a loophole through which CLFV can occur, see for example the discussion in Ref. 14.But as a neutral current flavor-changing process it is suppressed by a GIM-like mechanism making its predicted ratevanishingly small, < − . It is no surprise then that this process has never been observed, and the statement stands:any experimental observation must be arising from new physics enhancements. Search for Charged Lepton Flavor Violation in the Mu2e Experiment In the first two channels where a coincidence between particles must be identified experimentally,backgrounds arise when events accidentally have the correct topology and energies but the detectedparticles originate from uncorrelated mother processes. This accidental background scales with thesecond or third power of the beam intensity and is likely the ultimate limitation for these channels. Theconversion process on the other hand offers significant advantages that allow powerful next-generationsearches in the Mu2e and COMET experiments b to take advantage of increased beam rate andreach sensitivities better than − . Details of this channel are discussed in the following section. Muon to electron conversion: The Mu2e search
The Mu2e experiment at Fermilab will search for the conversion of a muon to an electron in the fieldof a nucleus, µ − N → e − N . There are no neutrinos in the final state so this is no standard muon decay;it is an interaction that has never been observed, which violates charged lepton flavor and signifies newphysics.The conversion is coherent, with the muon recoiling off the entire nucleus under two-body decaykinematics. The outgoing electron is monoenergetic with energy slightly less than the muon rest mass, m µ ≈ .
66 MeV , after accounting for the muonic atom binding energy and the nuclear recoil. Mu2ehas selected aluminum as the stopping material; for reasons that will be examined later it constitutesan excellent choice given the requirements to separate the signal from backgrounds. The characteristicenergy of the conversion electron (CE) on aluminum is E µe (Al) = m µ − E b − E rec = 104 .
97 MeV , (1)where E b is the binding energy of the muonic atom and E rec is the nuclear recoil energy.This monoenergetic electron is the distinctive signature of CLFV that Mu2e will search for. Thenuclear recoil satisfies energy and momentum conservation without any other decay products in thefinal state. Therefore this search is practically free from accidental coincidences c , a limiting backgroundcontribution in other channels. Furthermore the CE energy E µe is well above the maximum electronenergy from stationary muon decay E e ≈ m µ / . , separating the signal cleanly from the vastmajority of electrons from muon decays d .The conversion rate in the field of a nucleus is quoted relative to the rate of ordinary muon captureon the nucleus: R µe = µ − A(Z,N) → e − A(Z,N) µ − A(Z,N) → ν µ A(Z-1,N) , (2)where the ratio formulation cancels uncertainties regarding the muon wavefunction and its overlap withthe nucleus. The current limit on the conversion rate is × − (90% CL), set by the SINDRUM-IIexperiment which stopped . × muons on a gold target. b The COMET experiment at J-PARC employs similar design concepts to the ones presented here for Mu2e. COMETwill adopt a staged approach and is expected to eventually reach similar sensitivity as Mu2e. Both experiments are underconstruction as of this writing. c The reconstruction errors described in Sec. 5.4.2 may be construed as arising from accidental coincidences, but are a farsmaller concern. d The tail of this background spectrum is still an important consideration. It will be discussed in Sec. 3.4.2.
Manolis Kargiantoulakis
Fig. 1. The Mu2e experimental apparatus. Also drawn are the helical trajectories of particles in the solenoid fields. Thevarying field amplitude is listed in several locations.
The Mu2e experiment proposes to measure the muon to electron conversion rate on aluminum witha dramatic 4 orders of magnitude improvement, reaching sensitivity of better than − (90% CL). Atthat sensitivity Mu2e will probe new physics at effective mass scales up to ,
000 TeV . Care must betaken in translating that effective scale to the direct mass reach of a high energy machine, but it is clearthat in many scenarios Mu2e has sensitivity far beyond what is possible at LHC or any future collider.Thus Mu2e has real discovery potential over a wide range of well motivated new physics models. IfCLFV is observed for the first time, complementarity between the muon channels can elaborate on thenature of the underlying mechanism.In the following section we discuss the concepts that drive the design of Mu2e to achieve the proposedsensitivity improvement.
2. Driving Concepts for a Next-Generation CLFV Search
Mu2e aims to achieve an impressive four orders of magnitude improvement on R µe with respect to thecurrent limit from SINDRUM-II. The fundamental design goals required to achieve this sensitivity canbe distilled in the following: • The muon intensity must be increased by four orders of magnitude relative to previous experiments.Improvements in sensitivity have always been spurred by increased muon intensity. A solenoid muoncapture system with a graded field, based on the design proposed by Dzhilkibaev and Lobashev, will generate the most intense muon beam ever created. • A detector system is needed that can identify with high resolution the characteristic signature ofCLFV, the conversion electron with momentum near
105 MeV /c . The detector must handle the highrates associated with the increased beam intensity. A clever design is required to make the detectorblind to most background events and reduce occupancy. • All potential sources of backgrounds must be suppressed. Since a single CE event is a powerful signalof new physics, Mu2e is aiming for extreme control of all background sources to reduce the expectednumber of background events to less than one over the entire lifetime of the experiment.The Mu2e experimental apparatus that was developed along these conceptual drivers is shown inFig. 1. In the following three sections we delve deeper into each one of these design goals and how the
Search for Charged Lepton Flavor Violation in the Mu2e Experiment Mu2e design aims to achieve them.
3. The Mu2e Solenoids: Generating the World’s Most Intense Muon Beam
The Mu2e solenoid system is the most innovative, essential, and technically challenging component ofthe experiment. It consists of approximately
75 km of NbTi superconducting cable stabilized with highconductivity aluminum. The generated fields are required to efficiently capture charged pions from theproduction target and transport negatively charged secondary muons to the stopping target. Muons ofsufficiently low momentum must be selected such that a significant fraction can be stopped in a thintarget, while transmission of other particles is minimized.To aid in the efficient capture and muon beam creation the solenoid system creates a continuouslygraded magnetic field, from 4.6 down to . The gradient also suppresses backgrounds by preventingthe local trapping of particles as they traverse the muon beamline, and by pitching beam backgroundsforward and out of the detector acceptance. The field then remains nearly uniform at the detector regionto facilitate momentum analysis of conversion electrons.The solenoid system consists of three functional units, referred to as the Production Solenoid (PS),the Transport Solenoid (TS), and the Detector Solenoid (DS). The fringe field from each impacts thefield in adjacent units and significant forces develop, so the solenoids have to be designed and operate asa single integrated magnetic system. The three solenoids are presented in this section after an overviewof the proton beam delivered by the Fermilab accelerator complex.
FNAL proton beam
To produce its intense beam of low energy muons, the experiment requires a high intensity protonbeam with a pulsed time structure. The Fermilab accelerator complex can provide this beam with amacroscopic duty factor of about 30%, simultaneously with operations and beam delivery to the NOvAexperiment. Protons with a kinetic energy of are transferred from the Fermilab Recycler Ring tothe Delivery Ring in . bunches; proton pulses are then resonantly extracted to Mu2e with a pulsespacing of ,
695 ns , equal to the DR revolution period. Each pulse delivers about . × protons at to the Mu2e production target. A total of . × protons on target are required to reach theMu2e target sensitivity. That should correspond to ∼ × stopped muons, four orders of magnitudemore than was accomplished in SINDRUM-II. Production Solenoid
The Production Solenoid (PS) houses the Mu2e production target in a graded field varying smoothlyfrom 2.5 to . to maximize secondary beam collection. The pulsed proton beam from theFermilab accelerator enters the PS from the low-field side, moving in the direction of increasing fieldstrength towards the production target, where it interacts. The graded field collects the backward-produced pions e , steadily increasing their pitch and accelerating them in helical trajectories towardsthe lower field of the Transport Solenoid. Most of the soft pions decay into muons within a few meters. e Some pions produced in the forward direction at high angles relative to the solenoid axis will also be reflected backwardsby the field gradient.
Manolis Kargiantoulakis
The production target is made from tungsten, a high-Z material to maximize pion production. Thetarget has a small physical profile, is suspended by spokes and is allowed to cool radiatively - a geometrythat aims to minimize scattering and reabsorption of pions. Vacuum here must be maintained to betterthan − Torr to minimize tungsten oxidation and corrosion that reduce target lifetime.The diameter of the warm bore of the PS is large enough to allow pions and muons within the accep-tance of the Transport Solenoid to pass through unobstructed. A heat and radiation shield, constructedfrom bronze, will line the inside of the PS to limit the heat load in the cold mass from secondariesproduced in the production target and to limit radiation damage to the superconducting cable. Torepair displacement of atoms from the aluminum stabilizer lattice due to radiation damage, the systemwill be annealed once per year (during accelerator shutdowns) to allow thermal motion to repair thelattice.
Transport Solenoid
Fig. 2. Positive (blue) and negative (red) particles receive an oppositevertical offset in the TS toroidal bend. In normal operation a centralcollimator only allows negative muons through to the stopping target.
The Transport Solenoid (TS) has acharacteristic S-shape that eliminatesline-of-sight neutral particles from theProduction Solenoid. Its field efficientlycollects and transmits low energy neg-atively charged particles from the PSto the stopping target, while directinghigh energy and positively charged par-ticles onto absorbers and collimators.Depicted in Fig. 2, the selection relieson the toroidal field on the first bendwhich induces a sign- and momentum-dependent vertical dispersion; this cou-ples with a vertically displaced aper-ture on the central collimator to ab-sorb most positive particles and allowlow momentum negative particles topass through. The second toroidal bendthen largely undoes the vertical offsetand returns the now mostly negativebeam close to the solenoid axis. To accommodate detector calibration procedures the central collimatorcan be mechanically rotated to instead allow positive particles through.
Detector Solenoid
The Detector Solenoid (DS) is a large, low field magnet that houses the muon stopping target and thedetectors that will identify and analyze conversion electrons. The efficient capture and transport to thispoint results in approximately . generated muons per proton-on-target. About 40% of these muonswill be stopped at the aluminum target and these tend to have lower momentum, with a peak around
35 MeV /c . This corresponds to a rate of 10 stopped muons per second. Search for Charged Lepton Flavor Violation in the Mu2e Experiment The aluminum stopping target must be massive enough to stop a significant fraction of the incidentmuon beam, but it must also allow conversion electrons from stopped muons to emerge without havingtheir momentum corrupted by energy loss and straggling, as that would make separation between signaland background more difficult. The stopping target design is a balance between these two competingrequirements. It consists of a series of 34 thin foils, each µ m thick and composed of > . pure aluminum, arranged coaxially along the Detector Solenoid axis. The field is axially graded nearthe stopping target, linearly decreasing from at the entrance of the DS down to over roughlyfive meters. This gradient nearly doubles the detector acceptance for conversion electrons while alsoremoving backgrounds from beam electrons by pitching them forward.At this point we interrupt the description of the apparatus to describe processes that occur in thestopping target, and especially the muon decay in-orbit – a background source that is a significantdriver of the spectrometer design.3.4.1. Processes at the stopping target
When muons are stopped on an aluminum atom they displace an electron and then very rapidly (within ∼ ) cascade down to the lowest 1S atomic orbital, emitting X-rays at characteristic energies. Thereare three possibilities on the fate of a muon stopped in orbit:(1) Some of these stopped muons may convert to an electron, in the process that Mu2e searches forwhich could yield the first observed signal of CLFV. We know however that this process must bevery rare, with R µe < × − . The other two possibilities are thus far more likely to occur.(2) Roughly 60% of stopped muons on aluminum will be captured in the nucleus. This is not surprisinggiven the smallness of the Fermi radius of the muonic atom, ∼
20 fm . The muonic wavefunction hassignificant overlap with the nucleus and capture is common. This is the process that appears in thedenominator of Eq. 2 and is used for rate normalization.(3) The remaining 40% of stopped muons will undergo standard decay µ → eν µ ¯ ν e while in orbit aroundthe nucleus.The lifetime of a free muon is τ free = 2 . µ s , but a muonic atom is limited by both capture and decayprobabilities: τ = 1 / (Γ capture + Γ decay ) . The capture probability is nucleus-dependent as the overlap ofthe muon wavefunction varies for different elements. The muonic aluminum lifetime is measured to be τ = 864 ns .
33, 34
For reasons that will be discussed when we present the experiment’s time structurein Sec. 5.2.1, the lifetime of muonic aluminum is an excellent fit to Mu2e requirements and a centralreason for the selection of aluminum as stopping material.The muon decay in-orbit (DIO) process is a significant background consideration which drives thespectrometer requirements and design. We discuss it in the following paragraph before going further.3.4.2.
Muon decay in orbit
The standard weak decay of the muon with associated neutrinos, µ → eν µ ¯ ν e , is well understood. Forfree muons this decay was studied first by Michel and the spectrum of the decay electron is oftenreferred to as the ‘Michel spectrum’. 4-momentum conservation demands that the neutrinos take away Manolis Kargiantoulakis
Fig. 3. Left: The DIO spectrum from Czarnecki et al ., logarithmic scale. Right: Total contribution to R µe (Al) fromDIO electrons with energy larger than x , as a function of x . To limit this background contribution the CE search mustbe initiated above a high enough energy threshold near E µe . at least half of the available energy, therefore the maximum energy of the outgoing electron (neglectingneutrino masses) is E max = ( m µ + m e ) / (2 m e ) = 52 . . E max is far smaller than the characteristic conversion electron energy E µe = 104 .
97 MeV fromEq. 1, allowing a clean separation from background. However the decay in-orbit (DIO) energy spectrumis modified in the field of the nucleus: the nuclear recoil allows 4-momentum conservation with theneutrinos taking vanishingly small energy, pushing the endpoint of the DIO spectrum near E µe . Themodified spectrum is shown in Fig. 3, properly incorporating nuclear recoil and relativistic effects nearthe high energy endpoint. Leading radiative corrections to the high energy tail have been calculatedin Ref. 36. The long tail of the spectrum falls very rapidly near the CE energy due to the diminishingphase space available to produce neutrinos that carry almost no energy f . The DIO rate drops by morethan 16 orders of magnitude near the endpoint relative to the Michel peak, allowing a search with theproposed Mu2e sensitivity.Taking into account energy loss in material and detector resolution, the tail of the DIO componentoverlaps with the expected CE distribution and constitutes an irreducible SM background contributionto the Mu2e measurement. This component arises from muons stopped at the target and therefore hasthe same timing signature as the signal. The only way to separate the CE signal from an electron at thetail of the DIO distribution is a high resolution measurement of the electron momentum, to identify thedifference in energy carried off by the two neutrinos. The detector system that will perform this highlysensitive and critical measurement is described in the next section.
4. The Mu2e Detector
The Mu2e detector system consists of a tracker followed and complemented by an electromagneticcalorimeter, located inside the Detector Solenoid downstream of the stopping target within a nearlyuniform magnetic field. It is designed to efficiently and accurately identify and analyze the helical f It is no surprise that the simulated signal-background spectrum (presented in Fig. 13) looks very similar to that of aneutrino-less double-beta decay search; the kinematics are very similar.
Search for Charged Lepton Flavor Violation in the Mu2e Experiment trajectories of ∼
105 MeV electrons in a high rate time-varying environment, while rejecting backgroundsfrom conventional processes. A high precision momentum measurement is required to disentangle theCE signal from the DIO background. The reconstructed width of the conversion electron energy peak,including energy loss and resolution effects, must be narrow enough to keep DIO backgrounds at anacceptably low level. The detector is placed in a vacuum of − Torr to minimize multiple scatteringcontributions to the momentum resolution, and to suppress potential backgrounds sources.
Tracker
The Mu2e tracker is designed to accurately determine the trajectory of ∼
105 MeV electrons in a uni-form 1 Tesla magnetic field in order to measure their momenta. Its core momentum resolution mustbe <
180 keV /c for
105 MeV /c electrons, or 0.17%, to provide separation from the high energy DIOspectrum. High-side tails of the resolution especially need to be controlled since they could push aDIO electron of slightly lower energy to be misidentified as a conversion electron. The tracker mustpresent very low mass in the path of the electron, in order to minimize energy loss and smearing ofthe momentum measurement. It must also be highly segmented to handle high rates that could lead topattern recognition errors.The detector technology that was chosen to meet these requirements is that of “straw” drift tubes.Charged particles traversing a straw will ionize the gas inside the tube and generate a signal in theHV sense wire at its center. After pre-amplification the signal is taken to a TDC (implemented inFPGA) for a measurement of the drift time that determines the distance of closest approach of theparticle relative to the straw wire. Each straw is instrumented for readout on both sides, allowing fora time difference measurement between the two sides which determines the position of the hit alongthe length of the straw with a resolution of about . The straws are also instrumented with anADC for a dE/dx measurement that allows identification and removal of highly ionizing hits fromprotons. The information from all the straws intercepted by the particle is then combined and used inthe reconstruction of its trajectory, which yields a measurement of its momentum with high precision.The straw tubes are in diameter and aligned transverse to the DS axis. Minimization ofmaterial in the path of the particle is imperative to momentum resolution, so the straw wall thickness isonly µ m , consisting of two layers of spiral wound Mylar R (cid:13) . That includes metalization on the inside Fig. 4. Left: A prototype of the Mu2e tracker panel with exposed electronics boards (author’s photo). Right: Threepanels arranged in a ◦ ring (photo courtesy of Yujing Sun).0 Manolis Kargiantoulakis surface of the straw (
Å of aluminum overlaid with
Å of gold) so it can act as the cathode layer,and on the outside surface (
Å of aluminum) for additional electrostatic shielding and to reduce gasleak rate. The anode sense wire inside each straw is µ m of gold-plated tungsten. With 80:20 Ar:CO as the drift gas the sense wire will be operated near ,
400 V . In total the tracker presents approximatelyonly 1% radiation length of material to the average CE.Straws vary in active length from 334 to ,
174 mm and are supported at the ends in ◦ holdingfixtures referred to as panels, which reside outside the active detector region. Each panel holds 96 strawsmounted in two staggered layers to improve efficiency and help identify on which side of the sense wirea particle passed, which the signal from an individual straw can not resolve. Prototypes of trackerpanels are shown in Fig. 4. To minimize penetrations into the vacuum, digitization and readout will beperformed on-board each panel via three FPGAs, with optical fiber readout. Three panels are requiredto cover a ◦ ring, and each subsequent ring is rotated by ◦ for better stereographic reconstruction.The tracker will have ∼ ,
270 mm , in a design with highsegmentation that will allow the detector to handle high rates.As shown in Fig. 3 the muon decay in-orbit spectrum decreases steeply above m µ / , a factor of Fig. 5. Design of the Mu2e tracker. ◦ panels are assembled into rings, successively rotated by ◦ . The annular design(top right, beam’s eye view) makes the detector blind to the majority of DIO electrons and remnant beam (dark circles),while remaining sensitive to events with high transverse momentum (green circle). A schematic of the assembled trackeris shown in the bottom right figure. Search for Charged Lepton Flavor Violation in the Mu2e Experiment two away from the endpoint. This allows the opportunity for a detector design with good geometricalacceptance for signal and away from most of background events. An annular design is employed witha hole near the solenoid axis where no detector material exists, making the detector blind to thevast majority of DIO electrons, the remnant beam, and other products from the stopping target. Allthese particles would overwhelm the detector with high instantaneous occupancy and several adverseeffects: increased dead time, more difficult pattern recognition and increased risk of backgrounds fromreconstruction errors, and larger charge deposition on the straws. In the design shown in Fig. 5 thetracker straws are located in larger radii, between < r <
700 mm (where the radius r is measuredfrom the center of the muon beam), allowing the tracker to be fully efficient for electrons coming fromthe target with transverse momenta above
90 MeV /c . This allows only O ( − ) of the DIO events toproduce reconstructable tracks.The tracker will still be exposed to high rates, which generally vary with radius from center, distancefrom target, and time after the proton pulse. On average the straw rate within the detector live window(defined in Sec. 5.2.1) is ∼
20 kHz / cm , with up to rate on individual straws. The annular designreduces the occupancy, rate, and radiation damage on the straws to a manageable level. Fig. 6. Transverse resolution (left) and efficiency (right) for cosmic ray events on an 8-straw tracker panel prototype.Data shown in blue, Monte Carlo simulation in red. From Bonventre. The performance of the tracker design has been characterized with an 8-channel panel prototype, with results from cosmic ray events shown in Fig. 6. The prototype demonstrates transverse resolutionwith a FWHM of µ m , and longitudinal resolution with a core width of
43 mm , meeting the experi-mental requirements for the tracker. An efficiency of 95% is achieved for events closer than fromthe sense wire. The data is nicely in agreement with a full Geant4-based simulation.
Calorimeter
The tracker is followed downstream by a calorimeter system, which consists of pure cesium iodide(CsI) crystals read by silicon photo-multipliers (SiPMs). The calorimeter provides redundant energy,position, and timing information that complements the tracker, providing particle identification and Manolis Kargiantoulakis
Fig. 7. Left: CAD layout of the two disks of the calorimeter. Right: a large size prototype built with pre-productioncomponents. From Atanov et al . background rejection capabilities, as well as a standalone trigger for high energy electrons. High hitrates in the tracker may cause pattern recognition errors that add tails to the resolution function, po-tentially misidentifying a DIO track as a CE-consistent event. By extrapolating the fitted trajectoryand comparing with clusters at the calorimeter, events can be confirmed and the momentum resolu-tion improved. Calorimeter clusters may also seed track finding with increased efficiency, reducing thecombinatorial background by using only straw hits within ∼
50 ns g from the detected cluster.The Mu2e electromagnetic calorimeter consists of two annular disks composed of a total of , undoped CsI scintillating crystals. The dimension of a crystal is . × . ×
20 cm for a total depth of 10 X , enough to contain the CE shower. Each crystal is read out by two custom large area UV-extendedSiPMs. Like the tracker, the calorimeter also employs an annular design with a hole in the center tominimize interactions with the remnant beam and the beam flash. The distance between the calorimeterdisks is
70 cm , optimized to maximize acceptance: the helical trajectory of a CE reconstructable at thetracker has a good probability of intercepting the second disk if it passes through the hole of the first.The calorimeter layout is shown in Fig. 7.The calorimeter energy, position, and timing information must provide confirmation of the trackermeasurement, to help reject backgrounds from spurious combinations of straw hits. Hence the positionand timing resolution must be comparable to the error of the extrapolated track, including multiplescattering at the tracker. The energy and timing resolution must also allow particle identification forseparation of CE candidate events from cosmic ray muons. This set of criteria defines the calorimeterresolution requirements: better than σ E /E < , σ x,y < , and σ t <
500 ps for a
105 MeV electronmust be achieved.The calorimeter performance has been characterized with a small scale prototype of 51 crystals atthe Beam Test Facility in Frascati. Results for
100 MeV electrons at an impact angle of ◦ , near g The time range corresponds to the maximum drift time in a straw.
Search for Charged Lepton Flavor Violation in the Mu2e Experiment
100 MeV electrons on a small scale prototype of the Mu2e calorimeter, at an impact angle of ◦ . From Atanov et al . the average experimental condition for CE, are shown in Fig. 8. The energy resolution is found to be σ E /E ∼ , and a preliminary estimation of σ t ∼
170 ps is found with non-final electronics on theaverage of the two SiPMs reading the crystal with the highest energy deposit. The results are shown tobe well within requirements, and also in good agreement with simulation.
5. Backgrounds and Suppression Strategies
Searching for a process that has never before been observed, Mu2e is aiming for an expectation of lessthan 1 background event over the lifetime of the experiment. While the experimental signature is clean,at the proposed sensitivity several small background contributions become important. Suppressing andidentifying all possible sources of background is an important driver of many aspects of the Mu2e design.The three most important background sources in Mu2e are: • Intrinsic processes that are associated with the stopped muons and scale with beam intensity,including muon decay in orbit (DIO) and radiative muon capture (RMC). • Prompt processes that occur shortly after the arrival of the proton pulse, including radiative pioncapture (RPC), muon and pion decay in flight (DIF), and beam electrons. • Cosmic ray-induced processes .Other backgrounds arise from delayed processes due to particles that spiral slowly down the beam-line, such as antiprotons; and reconstruction errors at the detector induced by high occupancy fromconventional processes. In this section we discuss the different background classes and mitigation strate-gies adopted by Mu2e. Manolis Kargiantoulakis
Intrinsic backgrounds
Intrinsic (or muon-induced) backgrounds are associated with stopped muons and therefore have thesame time signature as our search. Our only recourse to provide separation from a conversion signalis a high precision momentum determination. The most important intrinsic source is muons stoppedat the aluminum target that decay in orbit (DIO) around the nucleus through ordinary weak decay.This is the process discussed in Section 3.4.2, and in Section 4 we presented the detector design whichoptimizes resolution to separate the conversion signal from this background.Another important process is radiative muon capture (RMC), µ − + Al → e − + ¯ ν e + ν µ + Mg + γ .This is an intrinsic source of high energy photons that can convert to an electron-positron pair in thestopping target or other surrounding material, producing an electron near the conversion electron energy.Consideration for this process was another reason for selecting aluminum as the stopping material: thenuclear mass difference between Al and Mg is .
11 MeV , placing the RMC endpoint well below the CEenergy. Thus the RMC background is well separated from the signal, given the momentum resolutionof the detector, and it is unlikely to be a significant source of background h . Prompt backgrounds
A prompt event is defined as one that occurs shortly (within a few hundred ns) after the proton beaminteraction at the production target. The most relevant example in this class of backgrounds is radiativepion capture (RPC) π − N → γN (cid:48) , where N (cid:48) is an excited nuclear state. This process occurs promptlyas the pion stops in the aluminum target. The radiated photon (whether on-shell or virtual) can thenconvert into an electron-positron pair. The pion mass allows a high enough endpoint for the photonenergy, so that an asymmetric conversion can result in an electron near
105 MeV which mimics the CEsignal. Other examples of prompt background events include muons and pions decaying in-flight withenough energy, and beam electrons near the conversion energy that scatter in the target.The SINDRUM-II experiment used beam counters to tag and veto prompt backgrounds, for whichthe relevant timescale is the pion lifetime of
26 ns . The PSI beam was a continuous stream of
20 ns bursts,not allowing separation of this background from the measurement. This was the ultimate limitation ofthe SINDRUM-II method which could not go to higher beam intensity without being overwhelmed bythis background. Mu2e aims to increase its sensitivity, and for that its beam intensity, by four orders ofmagnitude. Suppression of prompt background sources poses very specific requirements on the protonbeam time structure, which is described in the following section.5.2.1.
The Mu2e time structure
In Mu2e the main concept to suppress backgrounds from prompt processes is to take advantage oftheir short lifetime and simply wait for them to vanish before initializing a search for the conversionsignal. The time structure that accomplishes that is shown in Fig. 9. Pion-related and other promptbackgrounds decay soon after the arrival of the proton pulse, characterized by the the short
26 ns pion h It is still a consideration however that RMC events will distort the DIO spectrum since they overlap in the 80 −
100 MeV /c range. The charge-symmetric detector configuration will allow detection of both RMC e − and e + , making it possible todisentangle the background processes in situ. Search for Charged Lepton Flavor Violation in the Mu2e Experiment . × protons arrives at the production target every ,
695 ns . The livewindow for the conversion search is only initiated about
700 ns later, after the probability of observing a background eventfrom a prompt process has become negligible. lifetime and short time to transit the beamline. The live time for measurement then begins after about
700 ns , only after enough pions have decayed and prompt events are negligible. The relatively longlifetime of muonic aluminum at
864 ns is the main reason for the selection of aluminum as stoppingmaterial: it allows a significant population of stopped muons after
700 ns that can convert within thelive window. Thus the CE signal is well separated in time from the beam flash and prompt processes.The live window extends until the arrival of the next pulse. Notice that the ,
695 ns spacing betweenbeam pulses, though fixed by the revolution period of protons at the Fermilab Delivery Ring, is a verygood fit to Mu2e requirements. At roughly twice the lifetime of muonic aluminum, it allows enoughtime for the CE search after the delay to suppress prompt backgrounds, and sends a new pulse whenthe signal probability has diminished significantly. This scheme is also fully compatible with operationof the Fermilab neutrino program.Here we remind the reader of the graded field of the solenoids and the requirement to avoid trappingparticles, the reason for which should now become clear. Magnetic trapping of particles between localmaxima would delay their arrival at the stopping target, allowing a prompt background event withinthe observation window. The same could occur if a proton arrives at the production target outside themain proton pulse. The resonant extraction process from the Delivery Ring suppresses protons betweenpulses, and a fast AC dipole is employed to further sweep clean the inter-pulse beam. The ratio ofout-of-time beam to protons in the main pulse (referred to as beam extinction) is expected to be betterthan 10 − while transmitting ∼ Cosmic rays
Backgrounds that mimic the CE signal can be generated by cosmic ray (CR) muons. The CR muonitself could mimic the signal in the tracker, if entering the DS at a shallow angle or scattering near thetarget. But particle identification at the calorimeter provides a muon rejection factor of 200, protecting Manolis Kargiantoulakis
Fig. 10. Left: The CRV covers the DS and the downstream part of the TS. Right: Construction of a CRV module withfour layers of scintillator counters. against this class of backgrounds. It is possible however that the CR muon will decay inside the DS orinteract with material near the stopping target. Such processes can have available energy to generate a ∼
105 MeV electron, and are not prevented from occurring within the signal window. It is estimated thatone conversion-like electron per day can be produced by cosmic ray muons, which would yield O (1,000)events over the expected run. Therefore this background source must be suppressed by four orders ofmagnitude in order to achieve the sensitivity goals of Mu2e. Fig. 11. Photoelectron yield from the SiPM readout for a prototypecounter. The responses from the SiPMs at one end of the counter(red and blue data) are shown to be properly correlated (insert). Thesummed response (black histogram) has a most probable value of ∼
100 photoelectrons. From Artikov et al . Two mitigation strategies are adopted.The first is passive shielding, including theoverburden above and to the sides of thedetector hall, as well as the shielding con-crete surrounding the Detector Solenoid.The second and most important compo-nent is an active veto detector (cosmic rayveto - CRV) that will detect penetratingCR muons.The CRV will encase the DetectorSolenoid and a portion of the TransportSolenoid (Fig. 10), covering a total areaof about
337 m . The detecting elementis extruded polystyrene scintillator coun-ters coated with titanium dioxide (TiO ),with embedded wavelength shifting fibersread out via SiPMs. The veto system em-ploys four layers of these counters inter-spersed with aluminum absorbers. By re-quiring coincidence between at least threeof the four layers the CRV can achieve 99.99% efficiency, as required for adequate suppression of this Search for Charged Lepton Flavor Violation in the Mu2e Experiment background source. Characterization of prototype counters in the Fermilab Test Beam Facility (Fig. 11)determined the optimal concentration of TiO coating and has demonstrated that the photoelectronyield meets specifications to achieve the required efficiency. Other background sources
Antiproton-induced
The primary proton beam is above the energy threshold for antiproton production through the p + p → p + p + ¯ p + p process. These antiprotons are a serious consideration as they do not decay,and some with low enough momentum can be transported through the solenoids. Because their velocityis small, less than . c , they travel slowly and can take microseconds to reach the stopping target.They could then annihilate on material near the stopping target producing many secondary particles,which can generate a CE-mimicking ∼
105 MeV electron. The most effective mitigation strategy is toblock the antiprotons through a system of absorbers placed along the TS. The absorbers are kept thinto maximize muon transmission with appropriate momentum selection. The antiprotons have smallerkinetic energies and therefore suffer much larger dE/dx losses, thus the system of absorbers accomplishesgood suppression of antiprotons reaching the DS.5.4.2.
Reconstruction errors
Track reconstruction can be affected by background activity in the tracker. Such activity primarilyoriginates from the muon beam, from multiple DIO electrons within a narrow time window, and frommuon capture on a target nucleus that results in emission of photons, neutrons and protons. The ejectedprotons have a very small kinetic energy and are highly ionizing, inducing large pulses which shouldbe identified by the straw ADC, but also increasing the dead time of hit straws. Delta ray emissionis also possible following a proton hit, potentially triggering neighboring straws. Ejected neutrons canbe captured on hydrogen or other atoms and produce low energy photons, begetting low momentumelectrons which can generate a substantial number of in-time hits. This background activity scaleslinearly with beam intensity and causes tails in the resolution function that can push DIO electrons
Table 1. Mean expectation for background events in Mu2e for . × protons on target. When two numbers are quoted for uncertainty, the firstcorresponds to simulation statistics and the second to systematics. Background process Expected events
Cosmic ray muons . ± . ± . Intrinsic DIO . ± . ± . RMC . +0 . − . Prompt, late-arriving RPC . ± . ± . Muon DIF < . Pion DIF . ± < . Beam electrons (2 . ± . × − Antiproton-induced . ± . ± . Total 0.41 ± Manolis Kargiantoulakis into the signal momentum window. The reconstruction software that must control for these resolutiontails will be discussed in Section 6.
Backgrounds summary and budget
The expected total number of background events from each major source over the entire planned Mu2eoperation is given in Table 1. These values have been estimated from Monte Carlo simulations overmany Mu2e lifetimes, with cut selections aimed to optimize the experimental discovery sensitivity. Thetotal expected number of background events from all sources is . ± . . Thus any observation of anevent consistent with a conversion electron would be an important suggestion of CLFV and new physics.Using the techniques of Feldman and Cousins against the estimated background, the threshold for a σ discovery would be the observation of more than ∼
6. Simulation and Analysis
Fig. 12. Resolution of the Mu2e tracker for electrons near the conversion energy,as the difference between the reconstructed momentum and the simulation truth.‘Core width’ refers to a fit in the central part of the resolution.
The Mu2e simulation softwareis based on the Geant4 pack-age and aims to describe thegeometry and materials on mul-tiple scales, from the buildingwalls and shielding to the mul-tiple material layers of eachtracker straw. The decay in or-bit is modeled after the Czar-necki spectrum and other pro-cesses are similarly based onpublished data and calculations.Variations on these models areinvestigated as part of the sys-tematic uncertainties quoted inTable 1. Since the tracker is thesingle most precise detector ele-ment and drives the experimen-tal sensitivity a complete de-tailed simulation has been de-veloped, from ionization in thestraws to digitization output ofthe ADCs and TDCs on thetracker front-end. The responsehas been tuned to fit the proto-type test data of Fig. 6.Sophisticated and robust al-gorithms for pattern recognitionand track fitting have been developed. Cuts based on time, energy, and position of straw hits remove Search for Charged Lepton Flavor Violation in the Mu2e Experiment R µe = 2 × − . most of the proton and DIO background hits. Time difference between hits from the same track isrequired to be within the maximum drift and transit time of
50 ns . After significantly improving on sig-nal/background ratio, straw hits are passed to a geometric pattern recognition algorithm. Initial helixparameters, covariance matrix, and track t are produced to seed an iterative Kalman filter track fit.The Kalman fit accounts for scattering and energy loss in the straw material, as well as inhomogeneityin the DS field, and returns the final reconstructed momentum evaluated at the upstream entrance tothe tracker. The reconstructed trajectory must have an origin consistent with coming from the target,and the extrapolated track must have a calorimeter cluster that matches in time and position and isidentified as an electron of consistent energy.The simulated intrinsic momentum resolution of the tracker for signal conversion electrons thatsatisfy the track selection criteria, including material and reconstruction effects, is given in Fig. 12.A core resolution of
159 keV /c is achieved. The high-side tail which could shift the fast-falling DIOspectrum to larger momentum is shown to be well controlled. The momentum resolution is found to bewell within experimental requirements, and also robust against simulated increases in rate. It remainsa subdominant contribution to energy loss and resolution smearing due to interactions in materialupstream of the tracker.Fig. 13 presents the momentum probability distributions for the DIO spectrum and the conversionsignal, using realistic acceptance and resolution in a pseudo-experiment with R µe = 2 × − . Thedistributions of both DIO and the monochromatic CE signal are shifted and smeared due to interactionsin material and detector resolution, resulting in partial overlap. An optimal signal region of [103.85, Manolis Kargiantoulakis
MeV /c is defined to optimize discovery sensitivity by avoiding most of the region of overlap.Only an acceptably small DIO component is allowed within the momentum window, which integratesto the expectation of . ± . (stat) ± . (syst) DIO events (from Table 1) over the lifetime of theexperiment. The upper bound of the selection region limits contributions from other background sourceswhich scale with window size, like those from cosmic ray muons.Using the techniques of Feldman and Cousins against the estimated background of 0.41 events,a σ discovery could be claimed for 7.5 events within the signal window. In fact this is exactly thenumber of events expected in the pseudo-experiment of Fig. 13; that defines the Mu2e σ discoverysensitivity at R µe = 2 × − , orders of magnitude beyond current constraints. Mu2e will have a single-event sensitivity, i . e . an expectation to observe a single conversion event within the signal window, for R µe = 3 × − .
7. Status and Outlook
The Mu2e project is currently actively in the construction phase. For the solenoids, which are the mainschedule driver, the entire length of superconducting cable has been procured and tested. Winding is inprogress for all three solenoid units. The heat and radiation shield has been constructed and delivered.All 30,000 (including spares) tracker straws have been procured and panel manufacturing is in progress.All tracker FEE boards have been prototyped and tested and are ready for production. Nearly all CsIcrystals for the calorimeter have been delivered and tested. Extrusion fabrication is completed for theCRV counters, which are being assembled into layers.The Mu2e project will transition to installation in 2020-2021, with commissioning between 2021-2022. Physics running is expected to begin in 2023, followed by three years of operations. By that timethe upgraded MEG measurement at PSI, as well as Phase-I of the Mu3e and COMET experiments,are expected to have first results. Mu2e is expected to further increase sensitivity by another two ordersof magnitude beyond these measurements, culminating an intense program over the next years thatmay well yield the first discovery of CLFV events. The planned timeline of this experimental program is Fig. 14. Planned schedules for current searches for charged lepton flavor violating µ → e transitions. Also shown arepossible schedules for proposed upgrades to these experiments. The current best limits for each process are shown on theleft in parentheses, while expected future sensitivities are indicated by order of magnitude along the bottom of each row.From Baldini et al . Search for Charged Lepton Flavor Violation in the Mu2e Experiment shown in Figure 14. If a signal is observed then the complementarity between the three muon transitionmodes will be a powerful discriminant among the underlying New Physics models. Mu2e-II
Looking further into the future, another order of magnitude improvement in sensitivity beyond Mu2eis possible as the conversion channel is unburdened by accidental coincidences. In Fermilab the secondphase of the Proton Improvement Plan (PIP-II) would provide unique capabilities and could deliver
80 kW beam power to an upgraded Mu2e-II search with over stopped µ − /s . The delivered beamwould be near in energy to eliminate backgrounds from antiproton production. The internalDIO background would scale with beam intensity, therefore improved resolution would be required tomaintain control of this contribution. If Mu2e does not observe a signal then an increase in sensitivityby another order of magnitude would be a powerful search over a wide area of renewed phase space. If aCLFV signal is indeed observed, in a discovery of new physics that parallels that of neutrino oscillations,then the Mu2e-II upgrade would be necessary to increase the statistical significance of the conversionrate. New possibilities open up to measure the conversion rate on different stopping nuclei, gainingdiscriminating power between models of new physics that could generate the conversion process. Theproposed Mu2e-II search would have the highest sensitivity to new physics inducing charged leptonflavor violation for the foreseeable future.
Acknowledgments
This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics.The author would like to acknowledge the generous support by the Mu2e collaboration, especially thatof Doug Glenzinski and Robert Bernstein to early-career collaborators. Many thanks also to SimonaGiovanella for her valuable feedback on this manuscript.
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