Coherent 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>μ</mml:mi><mml:mtext>−</mml:mtext><mml:mi>e</mml:mi></mml:mrow></mml:math>
 conversion at next-to-leading order

We review how the muon anomalous magnetic moment (g − 2) and the quest for lepton flavor violation are intimately correlated. Indeed the decay µ → eγ is induced by the same amplitude for different choices of in-and outgoing leptons. In this work, we try to address some intriguing questions such as:Which hierarchy in the charged lepton sector one should have in order to reconcile possible signals coming simultaneously from g − 2 and lepton flavor violation?What can we learn if the g − 2 anomaly is confirmed by the upcoming flagship experiments at FERMILAB and J-PARC, and no signal is seen in the decay µ → eγ in the foreseeable future? On the other hand, if the µ → eγ decay is seen in the upcoming years, do we need to necessarily observe a signal also in g − 2?.In this attempt, we generally study the correlation between these observables in a detailed analysis of simplified models. We derive master integrals and

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“…We will check some concrete realizations when we investigate UV complete models. See [193] for a recent discussion at next-leading order.…”

Section: µ − E Conversionmentioning

confidence: 99%

A call for new physics: The muon anomalous magnetic moment and lepton flavor violation

2018

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“…Beyond the leading chiral order, two-nucleon contributions to the µ → e conversion in a nucleus arise. Existing estimates show that effect is non-negligible for scalar interactions in 27 Al [132]. LQCD can provide useful input in this regard, by computing directly the appropriate MEs in light nuclei [79].…”

Section: -Year Goals and Plansmentioning

confidence: 99%

The role of Lattice QCD in searches for violations of fundamental symmetries and signals for new physics

et al. 2019

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Executive summary 2 BSM scenarios may involve new particles and interactions that originate at very high-energy scales, or alternatively may involve new physics at relatively low scales with extremely feeble couplings [10]. This whitepaper focuses on the former class of BSM scenarios, for which an effective field theory (EFT) framework can be adopted to encompass all SM extensions that respect the SM gauge group and have the same low-energy particle content as the SM [11][12][13]. One challenge that often needs to be dealt with in carrying out the program in Fundamental Symmetries is that the SM processes that are sensitive to new physics often involve hadrons and nuclei as initial, final, and/or intermediate states at low energies, demanding that SM and ab initio quantum many-body calculations be performed in a highly nonperturbative regime.The Department of Energy (DOE)-funded USQCD collaboration, as the unified collaboration of the majority of the LQCD collaborations in the U.S., has long identified the role of LQCD studies in enabling and advancing research at the Intensity Frontier. The significant results produced by the collaboration in the past two decades in constraining the Cabibbo-Kobayashi-Maskawa (CKM) matrix quark-mixing matrix of the SM, and in constraining the quantities relevant to tests of CP violation in the Kaon sector, mark major accomplishments for the LQCD community, and signify the essential role of LQCD in complimenting both experiment and theory effort in HEP research. Such a role has been identified in other sectors in which there is, or is expected to be, hints of deviation from the SM and of new physics. In particular, compared to the year 2013 when the Collaboration's previous whitepapers were released, in 2018 the Collaboration has dedicated three separate whitepapers to the role of LQCD in research at the Intensity Frontier: 1 i) Opportunities for LQCD in quark and lepton flavor physics: Given the persisting tensions between theoretical predictions based on the SM and and experimental measurements in B meson decays at the LHC-B and the anomalous magnetic moment of the muon at the Brookhaven National Laboratory, and the continuing improvement in determinations of the CP violating parameters in Kaon and recently the heavy-meson sectors, there is a pressing need for reliable SM predictions of corresponding quantities from LQCD, to a precision level that is comparable to experimental determinations. Progress made by the USQCD collaboration in all these areas, the challenges ahead, and the plans forward are detailed in a companion whitepaper, see [6].ii) LQCD and neutrino-nucleus scattering: The large experimental enterprise in neutrino physics, in particular the upcoming Deep Underground Neutrino Experiment (DUNE) at Fermilab aims to shed light on CP violation in the lepton sector. However, reliable determinations of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton-mixing matrix require accurate knowledge of neutrino-nucleus interactions. The neutrino-nucleon and neutrinonucleus scatt...

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“…χPT [26] involving nucleons (see e.g. the review [19]) would be the appropriate formalism for this calculation, and has been used to calculate WIMP scattering on nuclei [20,21,22,23], neutrinolessdouble-beta-decay [24], and SI µ → e conversion [25]. However, to avoid more notation, here we just give results for the simple diagrams of interest.…”

Section: Operatorsmentioning

confidence: 99%

“…This estimate uses r 3 dr/3 ≃ r 2 dr, and applies in the absence of other contributions; the dipole coefficient sums with the scalar and vector coefficients in the amplitude, as given in eqn (25).…”

Section: The Dipolementioning

confidence: 99%

“…The two-nucleon contributions were also calculated to be unexpectedly small for WIMP scattering on few-nucleon nuclei [42]. However, after this manuscript was completed, appeared a study of the µ → e conversion rate mediated by the scalar and vector interactions [25], where the authors estimate that the NLO effects associated to pion exchange between two nucleons can reduce the scalar matrix element by 20→ 30%(NLO corrections vanish for the vector). We will account for these nucleon/χPT uncertainties by including them in the uncertainties in the overlap integrals.…”

Section: Parametric Expansions and Uncertaintiesmentioning

confidence: 99%

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“Spin-dependent” $$\varvec{\mu \rightarrow e}$$ μ → e conversion on light nuclei

2018

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The experimental sensitivity to μ → e conversion will improve by four or more orders of magnitude in coming years, making it interesting to consider the "spindependent" (SD) contribution to the rate. This process does not benefit from the atomic-number-squared enhancement of the spin-independent (SI) contribution, but probes different operators. We give details of our recent estimate of the spin-dependent rate, expressed as a function of operator coefficients at the experimental scale. Then we explore the prospects for distinguishing coefficients or models by using different targets, both in an EFT perspective, where a geometric representation of different targets as vectors in coefficient space is introduced, and also in three leptoquark models. It is found that comparing the rate on isotopes with and without spin could allow one to detect spin-dependent coefficients that are at least a factor of few larger than the spin-independent ones. Distinguishing among the axial, tensor and pseudoscalar operators that induce the SD rate would require calculating the nuclear matrix elements for the second two. Comparing the SD rate on nuclei with an odd proton vs. odd neutron could allow one to distinguish operators involving u quarks from those involving d quarks; this is interesting because the distinction is difficult to make for SI operators.

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Coherent μ−e conversion at next-to-leading order

Cited by 24 publications

References 83 publications

A call for new physics: The muon anomalous magnetic moment and lepton flavor violation

A call for new physics: The muon anomalous magnetic moment and lepton flavor violation

The role of Lattice QCD in searches for violations of fundamental symmetries and signals for new physics

“Spin-dependent” $$\varvec{\mu \rightarrow e}$$ μ → e conversion on light nuclei

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