Neutrino Physics at a Muon Collider: CKM, PDFs, and more

Manuel Morales-Alvarado XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Neutrino Physics at a Muon Collider: CKM, PDFs, and more In collaboration with D. Marzocca, F. Montagno Bozzone, A. Wulzer [2510.XXYY] INFN, Sezione di Trieste The most important slide 2 1. The high energy, collimated neutrino flux from muon decays at a muon collider (MuC) will enable highly precise forward target deep-inelastic scattering (DIS) measurements. 2. The setup will allow for exceptionally sensitive measurements of quantities like CKM matrix elements, parton distribution functions (PDFs), fragmentation functions (FFs), and others, greatly surpassing current standards. 3. The exploitation of correlations and shape information of different dynamical quantities is crucial for precision measurements. 4. The precision reached will constitute a demanding test of SM physics and potential BSM signatures. 5. This analysis will benefit from parallel MuC studies: additional observables and constraints, experiment design, estimation of systematics, … XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Outline Background Physics from MuC neutrinos Summary 3 XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Outline Background Physics from MuC neutrinos Summary 4 XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado MuC for the Standard Model and beyond Theory Experiment 5 In the context of future collider facilities, the MuC (10 km ring running at the 10 TeV scale) is a revolutionary proposal to explore the Universe at the most fundamental level [2504.21417]. XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado MuC for the Standard Model and beyond 6 The physics program at a MuC is very broad: Precision SM measurements at high energies (Higgs physics, EW, …). 2504.21417 Direct and indirect searches of new physics (EFT, DM, ALPS, …). XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado MuC neutrinos 7 The muon beam offers excellent precision and discovery potential, but there is more … Via muon decay, we have access to collimated, high energy, neutrino beams. The neutrino beam can interact with a forward target via DIS and enable high precision measurements: CKM and parton distribution functions. 9907.033 XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado The CKM matrix 8 It can be regarded as a rotation between quark mass and weak eigenstates The elements of the matrix are fundamental SM parameters. (We will devote our attention to the first 2 rows of the CKM matrix). XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado 9 Why measure it? -It mediates flavour changing transitions in quarks. -Direct source of CP violation in the SM. -Further constrain the Cabibbo angle anomaly: -Constrain new physics from rare meson decays: -Shed light on the inclusive/exclusive tension in b to c transitions. -… The CKM matrix XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado -PDFs are dynamical quantities: -They are crucial elements in deep inelastic scattering (DIS). Parton distribution functions -Some intuition. Consider the proton PDF of the up quarks: <latexit sha1_base64="OH2yuK5RWmKSbkyTrsC3t+MH3OM=">AAACEnicbVDLSsNAFJ3UV62vqEs3g0WoC0sivjZC0Y3LCvYBbQiT6aQdOpmEmUkxhvyFS7f6Ee7ErT/gN/gTTtssbOuByz2ccy/3cryIUaks69soLC2vrK4V10sbm1vbO+buXlOGscCkgUMWiraHJGGUk4aiipF2JAgKPEZa3vB27LdGREga8geVRMQJUJ9Tn2KktOSapu+mcVZ5PIbXMIa6u2bZqloTwEVi56QMctRd86fbC3EcEK4wQ1J2bCtSToqEopiRrNSNJYkQHqI+6WjKUUCkk04+z+CRVnrQD4UuruBE/buRokDKJPD0ZIDUQM57Y/E/rxMr/8pJKY9iRTieHvJjBlUIxzHAHhUEK5ZogrCg+leIB0ggrHRYM1cUHT6d+CThAeKZTseez2KRNE+r9kX1/P6sXLvJcyqCA3AIKsAGl6AG7kAdNAAGI/ACXsGb8Wy8Gx/G53S0YOQ7+2AGxtcvqlSdCw==</latexit> fu(x)=u(x) PDF: the ‘probability’ of finding an up-quark in the proton carrying a fraction x of the momentum of the proton. NNPDF, 2109.02653 16 -PDFs describe the structure of nucleons in terms of elementary constituents. XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado 17 -For our analysis we adopt PDF4LHC21_40, a combined PDF fit of individual methodologies. -It is designed to be a conservative joint representation. -The baseline PDF4LHC21 consists of 900 members/replicas which are compressed for public use to a set of 40 replicas. But enough about proton PDFs… 2203.05506 XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Parton distribution functions 18 Finally, we consider the target to be isoscalar: same number of protons and neutrons. Proton PDFs, Q = 100 GeV Isoscalar target The latter case is just built from linear combinations of the proton PDF. Going back to the observable… Neutrino DIS PDFs XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Neutrino DIS 19 Consider the charged current (CC) diagram: With the kinematics: (Momentum transfer) (Parton momentum fractions) DIS double differential cross section: XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado PDF 20 A representative DIS distribution would look like: Neutrino DIS XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Neutrino DIS 21 We have both (muon and antielectron) neutrino contributions… … and also the neutral current contributions. + XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado 22 An additional consideration: the neutrino beam is not monochromatic, we need to account for the energy distribution of the neutrinos. The cross section acquires an extra kinematic dependence due to the variable neutrino energy: Neutrino DIS XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado <latexit sha1_base64="R5EcSDl1lZxoCZsU2uJQCDKEtVE=">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</latexit> d2 dxdy !d3 dEdxdy Neutrino DIS 23 The (CC) muon neutrino distribution is given by And analogous for electron antineutrino (change spectrum and parton channels). spectrum parton kin. CKM CKMPDF PDF However, to reconstruct the outgoing parton we need to be able to account for fragmentation functions. The aim is to estimate uncertainties coming from the tagging of the final state… XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Fragmentation functions 24 Some intuition: fragmentation functions are the final state analog of PDFs. 1706.09857 : the ‘probability’ that a parton of type q hadronises into a hadron of type H carrying a fraction z of its momentum at an energy scale Q2. XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Fragmentation functions 25 XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado -FFs are used to model the reconstruction of the outgoing parton. -With them we can estimate uncertainties coming from the tagging of the final state -We have access to FFs for -D* mesons (c-tagging) -B-hadrons (b-tagging) - Defining z-windows for integration allows us to model tagging efficiencies 1706.09857 2210.06078 CKM determination 32 Constraints on CKM elements (profiled over the nuisance and other elements): XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Stability in the PDF basis 33 -We used PDF4LHC21_40. -Do more flexible PDF parametrisations yield the same result? -We assess the stability of the results by carrying out the analysis with Hessian sets of different dimensions: 20, 40, 60, 80, 100, and ask: -The Hessian sets are produced via mc2hessian conversion from the PDF4LHC21 baseline fit (900 MC replicas). XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado PDF posteriors 34 Our DIS setup allows us to constrain also the PDFs. A substantial improvement in precision is achieved across the board, even for the gluon: XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Additional scenarios 35 MuC @ 3 TeV bounds: XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Type of target: CKM determination 36 To be further explored: -Additional sources of theory uncertainties (higher order contributions, mass effects, …) -Reconstruction of neutrino flux, event kinematics and tagging/fragmentation…. -Nuclear corrections in parton densities, isospin symmetry breaking effects… -… The analysis we have presented goes forward in parallel with other aspects of the MuC physics programme. XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Outline Background Physics from MuC neutrinos Summary 37 XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado The most important slide 38 1. The high energy, collimated neutrino flux from muon decays at a MuC will enable highly precise forward target deepinelastic scattering (DIS) measurements. 2. The setup will allow for exceptionally sensitive measurements of quantities like CKM matrix elements, parton distribution functions, and fragmentation functions, among others, surpassing current standards. 3. The exploitation of correlations and shape information of different quantities is crucial for precision measurements. 4. The precision reached will constitute a demanding test of SM physics and potential BSM signatures. 5. This analysis will benefit from parallel MuC studies: additional observables and constraints, experiment design, estimation of systematics, … XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Thank you for your attention! XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Backup XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado Protons and partons -The most powerful collider we have at the moment is the LHC, at which we collide protons. -Proton are not elementary particles. They are QCD bound states of elementary particles called partons (quarks, gluons, …). -The parton model postulates that interactions between hadrons (protons, in particular) are interactions of point-like parton convolved with functions that parametrise the structure of the hadron: parton distribution functions (PDFs). q q q g g g Proton 41 XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado MuC @ 3 TeV results 48 Precision: Stability in PDF members: XXI Workshop on Neutrino Telescopes, Padova 2025 | Manuel Morales-Alvarado