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Theory Challenges and Opportunities of Mu2e-II: Letter of Interest for Snowmass 2021

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Theory Challenges and Opportunities of Mu2e-II: Letter of Interest for Snowmass 2021 Theory challenges and opportunities of Mu2e-II: Letter of Interest for Snowmass 2021 Robert H. Bernstein,1 Leo Borrel,2 Lorenzo Calibbi,3, ∗ Andrzej Czarnecki,4 Sacha Davidson,5 Bertrand Echenard,2 Julian Heeck,6, y David G. Hitlin,2 William Marciano,7 Sophie C. Middleton,2 Vitaly S. Pronskikh,1 and Robert Szafron8 1Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 2California Institute of Technology, Pasadena, California 91125, USA 3School of Physics, Nankai University, Tianjin 300071, China 4Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada 5LUPM, CNRS, Universit´eMontpellier, Place Eugene Bataillon, F-34095 Montpellier, Cedex 5, France 6Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA 7Department of Physics, Brookhaven National Laboratory, Upton, New York 11973, USA 8Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland Searches for lepton flavor violation are extremely sensitive to physics beyond the Standard Model. Several experiments are going to probe uncharted parameter space in the near future; notably, the Mu2e experiment is aiming to improve sensitivity to µ− ! e− conversion in nuclei by several orders of magnitude over existing limits. Mu2e-II marks a potential upgrade of Mu2e with another order-of-magnitude increase in sensitivity. This remarkable reach will make Mu2e(-II) an important experiment to probe new physics, not only via µ− ! e− conversion, but potentially also via µ− ! e+ conversion or µ− ! e−X decays involving a light new boson X. Theory challenges of this project include comparing the sensitivity of different experiments to a given model, evaluating possible stopping targets to maximize complementarity, and understanding the unavoidable muon-decay-in- orbit background at this unprecedented precision. 2 Introduction. Lepton flavor violation (LFV) has Z Penguin Charge Radius Dipole Scalar been identified long ago as an excellent probe of physics beyond the Standard Model (SM) [1]. Several experi- 5 ments will soon increase the sensitivity in many chan- ) Li S Ti Al 4 Au Pb nels by orders of magnitude. In the muon sector, the e,Al most promising LFV signatures are µ ! eγ (probed μ→ ( 3 by the MEG II experiment [2]), µ ! eee¯ (Mu3e [3]), BR )/ and µ-to-e conversion in nuclei (DeeMe [4], COMET [5], 2 and Mu2e [6]). Mu2e in particular aims to reach a e,Z μ→ − 27 − 27 ( µ + 13Al ! e + 13Al single-event sensitivity of 3 × 1 10−17, roughly four orders of magnitude beyond existing BR bounds [6, 7]. The potential upgrade Mu2e-II at FNAL 0 aims to improve Mu2e's sensitivity by yet another order 0 20 40 60 80 of magnitude [8, 9]. Z Theoretical motivations. Theoretical motivation for LFV is plentiful [10]; most notably, the observation of FIG. 1: Z dependence of µ ! e conversion rates for some neutrino oscillations already proved that lepton flavor is example scenarios taken from Refs. [18, 20]. not conserved! The absence of LFV in the SM is acciden- tal because of the minimal particle content. Extending the SM by new particles then often leads to LFV unless (A; Z) and nuclear-spin dependence of the µ-to-e conver- new symmetries are imposed [11]. Such extensions are sion rate and thus distinguish underlying models. well motivated as explanations for neutrino masses or the Calculations of the Z-dependence of different operators hierarchy problem and might even be linked to hints for have been performed, e.g. in Refs. [18, 19]. Dedicated new physics in the muon's magnetic moment [12, 13] or in studies on how to distinguish new physics operators with leptonic B-meson decays [14, 15]. Correspondingly, the different targets can be found in Refs. [17, 20], concluding non-observation of LFV at upcoming experiments would that it is best to study one light (e.g. Al) and one heavy put strong constraints on many models, including super- nucleus (e.g. Pb or Au), as shown in Fig. 1. In Mu2e(- symmetric extensions, and provide critical information II) such heavy nuclei are difficult because the muon life- about our fundamental understanding of nature [10]. time goes down drastically (from 864 ns in Al to 75 ns in Mu2e(-II)'s reach makes it indirectly sensitive to very Pb [21]) and thus worsens the pion background. Using heavy new particles. In an effective-field-theory approach two light nuclei still allows to distinguish operators but heavy particles match onto non-renormalizable operators requires better precision [20]. Ref. [17] points out that 7 that are suppressed by powers of a scale Λ that is related Lithium 3Li as a second target still has good discrimina- to the large masses. For example, a single dimension-six tory power despite being light, making it a worthwhile α ¯ 2 LFV operatoreγ ¯ PLµ dγαd=Λ would induce a µ-to-e target candidate to study in better detail. conversion rate in aluminium of order [16] Most studies focus on coherent spin-independent (SI) µ ! e conversion, featuring a welcome ∼ A2 enhance- Γ(µ−Al ! e−Al) 1:5 × 107 GeV 4 ment in the rate. However, there exist µeqq operators ' 3 × 10−18 ; Γ(µ capture) Λ that lead to spin-dependent (SD) conversion [22, 23]. In- cluding higher-order corrections these operator will al- which means that Mu2e-II is sensitive to new particles as ways also induce SI µ ! e conversion that can then often heavy as 104 TeV, far out of reach of any currently pro- dominate due to the A2 enhancement. Still, it is in prin- posed collider! Mu2e-II will of course also be sensitive ciple possible that SD dominates over SI, a possibility to many other operators and models and provide infor- that can be studied using target nuclei of different spin. mation complementary to the results of Mu3e and MEG Aluminium carries spin J = 5=2 and is thus sensitive to II [16, 17]. In the event of an observation of LFV in any both SI and SD processes. In case of a positive signal on of these experiments the others will help to pin down the Al one would then need to measure µ ! e on a light nu- underlying new physics responsible for it. cleus with different spin in order to distinguish SD from 27 Stopping target. Mu2e(-II) will use 13Al as a stop- SI [23]; heavy nuclei are unlikely to be sensitive to SD ping target, but can also study conversions in a different because the higher-order|but A2-enhanced|SI effects material in case a signal is observed. This requires ded- should dominate. Titanium is a good choice here because 48 icated studies to analyze not only the ideal experimen- it is light and comes in isotopes of different spin. 22Ti tal properties a target should have (such as the effective has spin 0 and a natural abundance of 74%; SI operators muon lifetime and capture rate) but also to maximize would induce roughly the same rate as in Al, whereas complementarity with the aluminium target. Using dif- SD would lead to a vanishing rate. In the latter case, 47 49 ferent target materials opens the possibility to probe the one could enrich the target with 22Ti or 22Ti, both of 3 which carry spin. In the former case, one should go for a -5 μ→eX, BR(μ→eX)=5⨯10 ,m X =0 heavy target nucleus in order to distinguish different SI -5 operators. μ→eX, BR(μ→eX)=5⨯10 ,m X =0.3 MeV 10-30 Decay-in-orbit calculation. µ ! e conversion in μ→eνν nuclei produces approximately monoenergetic electrons 10-31 with Econv = mµ − Ebinding − Erecoil, where Ebinding and 10-32 Erecoil are small energy corrections due to the muon's e -33 binding energy and nuclear recoil, respectively. While dE / 10 Γ this is seemingly far away from the typical electron en- d -34 ergies of the competing µ ! eνν decay in orbit (DIO), 10 nuclear-recoil effects ensure that this SM decay distri- 10-35 bution has a tail up to Econv, providing an irreducible -36 background in Mu2e(-II). Precise calculations are neces- 10 103.0 103.5 104.0 104.5 105.0 sary in order to predict and understand this background DIO spectrum near the endpoint in order to choose the Ee (MeV) optimal signal window. Such calculations exist [24{28], most importantly for aluminium, but might be lacking FIG. 2: The tail of dΓ(µ ! eνν)=dEe (black, dashed) near the endpoint [27]. Following Ref. [37] we also show the tail of sufficient precision for other target nuclei. Higher-order −5 effects should also be consistently incorporated into the dΓ(µ ! eX)=dEe corresponding to BR(µ ! eX) = 5 × 10 (just below the current limit [34, 35]) for two values of m . theoretical predictions for the µ ! e conversion signal. X Extending the physics case. Although the main Summary. Mu2e and Mu2e-II will provide remark- target of Mu2e-II will undoubtedly be the measurement of µ− ! e− conversion in nuclei, it is important to assess able sensitivity to lepton flavor violation via µ-to-e con- the capability of the experiment to address different pro- version in nuclei. It is of utmost importance to match cesses, given the large number of stopped muons (∼ 1019) these experimental efforts on the theory side by provid- ing precision calculations, guidance and motivation for that it will observe. the choice of target, and by exploring other new-physics scenarios that can be probed in these experiments. µ− ! e+ conversion. In addition to µ− ! e− con- version, Mu2e(-II) is also sensitive to the lepton-number- violating process µ− ! e+ [29].
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