Muon Anomalies and Their Future Investigations Fermilab Muon - PowerPoint PPT Presentation

� 16 The Proton Radius Puzzle ๏ The proton’s charge radius, r p , is defined as the RMS of its charge distribution ๏ Laser spectroscopy of Hydrogen has long been used to measure physical constants such as R ∞ and r p Both methods have generally agreed ‣ R ∞ , the Rydberg constant, is the wavenumber of the lowest energy photon capable of ionizing hydrogen E ( nS ) ≈ − R ∞ n 2 + L 1 S n 3 ๏ The Lamb shift, L 1S , contains dependence on r p ‣ It’s the splitting between L=0 and L=1 orbital angular momentum states ‣ L=0 has penetration to the nucleus, so its energy is raised due to finite nuclear size, more so than the L=1 state ๏ One can extract both terms with two transitions ๏ Additionally, electron proton scattering has been used extensively to measure r p average ‣ Differential cross section ➜ electric (and magnetic) form factor ‣ Typically extrapolate the slope of the electric form factor at low Q 2 , down to Q 2 =0 ( − 1) n (2 n + 1)! < r 2 n > Q 2 n X G E ( Q 2 ) = 1 + n> 0 ◆ 1 / 2 − 6d G E ( Q 2 ) � ✓ √ < r 2 > = � r p ≡ � d Q 2 � Q 2 =0 Jason Bono, jbono@fnal.gov

� 17 The Proton Radius Puzzle CREMA (Charge Radius Experiment With Muonic Atoms) ๏ 2010: Study muonic hydrogen to dramatically increase precision of r p The Bohr radius is reduced by a factor of 200 ‣ The Lamb shift is exaggerated by 𝒫 (10^7) ‣ Finite nuclear size effects in energy transitions are enhanced by a factor of 100! ‣ - ~2% for of the total lamb shift for 2S-2P! ๏ Achieved, in one measurement, 10x better precision than the all of the world’s electron data combined E ( nS ) ≈ − R ∞ n 2 + L 1 S n 3 Jason Bono, jbono@fnal.gov

� 18 The Proton Radius Puzzle CREMA (Charge Radius Experiment With Muonic Atoms) E ( nS ) ≈ − R ∞ n 2 + L 1 S n 3 ๏ 2010: Study muonic hydrogen to dramatically increase precision of r p DOI: 10.1146/annurev-nucl-102212-170627 The Bohr radius is reduced by a factor of 200 ‣ The Lamb shift is exaggerated by 𝒫 (10^7) ‣ Finite nuclear size effects in energy transitions are enhanced by a factor of 100! ~5 σ ‣ - ~2% for of the total lamb shift for 2S-2P! ๏ Achieved, in one measurement, 10x the world average of electron data DOI: 10.1146/annurev-nucl-102212-170627 The experiment “shrunk” the proton radius by ~4% Jason Bono, jbono@fnal.gov

� 19 The Proton Radius Puzzle CREMA (Charge Radius Experiment With Muonic Atoms) E ( nS ) ≈ − R ∞ n 2 + L 1 S n 3 ๏ 2010: Study muonic hydrogen to dramatically increase precision of r p The Bohr radius is reduced by a factor of 200 ‣ The Lamb shift is exaggerated by 𝒫 (10^7) ‣ Finite nuclear size effects in energy transitions are enhanced by a factor of 100! ‣ - ~2% for of the total lamb shift for 2S-2P! 7 σ ๏ Achieved, in one measurement, 10x the world average of electron data DOI: 10.1146/annurev-nucl-102212-170627 Subsequent electron measurements worsened the discrepancy Jason Bono, jbono@fnal.gov

� 20 The Proton Radius Puzzle Possible Explanations ๏ Lepton non universality? Past experiments have compared e-p and 𝝂 -p interactions, with no ‣ discrepancies ๏ Have the majority (or all) of laser spectroscopy and electron scattering experiments have much larger error bars than stated? All relevant results have been triple checked by independent groups! ‣ ๏ Finite proton mass effect for muonic H? This has recently been shown to be small ‣ ๏ Flaws with QCD calculations for atomic H? Results from a few weeks ago may provide a clue Jason Bono, jbono@fnal.gov

� 21 The Proton Radius Puzzle Possible Explanations ๏ Lepton non universality? Past experiments have compared e-p and 𝝂 -p interactions, with no ‣ discrepancies ๏ Have the majority of laser spectroscopy and electron scattering experiments have much larger error bars than stated? All relevant results have been triple checked by independent groups! ‣ ๏ Finite proton mass effect for muonic H? This has been shown to be small ‣ ๏ Flaws with QCD calculations for atomic H? Results from a few weeks ago may provide a clue Jason Bono, jbono@fnal.gov

� 22 The Proton Radius Puzzle ๏ New result using electrons ๏ Most precise spectroscopy measurement to date using atomic hydrogen Agreement with the muonic hydrogen results ‣ Plot of Rydberg constant is nearly identical, hence the double axes Jason Bono, jbono@fnal.gov

� 23 The Proton Radius Puzzle Looking Forward ๏ The Muon Proton Scattering Experiment (MUSE) @ PSI ‣ Compare e - -p with 𝝂 — p, and e + p, with 𝝂 + p scattering ๏ New CREMA measurements ‣ Have/will continue to investigate muonic deuterium and muonic- ionic-helium ๏ PRad @ Jlab ‣ Will collect statistics for scattering at very low scattering Q 2 for reliable extrapolation ๏ Various improvements on atomic energy level splitting measurements The muonic measurements have revealed something, but we don’t know what, yet Jason Bono, jbono@fnal.gov

The Muon’s Anomalous Magnetic Moment

� 25 The Muon’s Anomalous Magnetic Moment The g-factor ๏ A particle’s magnetic moment is coupled to its spin by its gyromagnetic ratio: µ = g e ~ ~ S 2 mc ๏ For a Dirac particle, g = 2 ๏ The anomalous component of the magnetic moment comes in internal structure, and from vacuum fluctuations from everything, known and unknown, that couples, either directly or indirectly, the the system in question a = g − 2 2 Sensitive to a wide range of phenomena Jason Bono, jbono@fnal.gov

� 26 The Muon’s Anomalous Magnetic Moment The g-factor ๏ A particle’s magnetic moment is coupled to its spin by its gyromagnetic ratio: µ = g e ~ ~ S 2 mc ๏ For a Dirac particle, g = 2 ๏ E.g. the magnetic moments of nucleons: g p ⇡ 5 . 6 6 = 2 Internal Structure g n ⇡ � 3 . 8 6 = 0 ๏ E.g. the magnetic moment of the electron Independent measurement of α g exp / 2 = 1 . 00115965218073(28) e QED corrections work! g QED / 2 = 1 . 001159652181643(764) e Phys. Rev. Lett. 100, 120801 (2008) Jason Bono, jbono@fnal.gov

� 27 The Muon’s Anomalous Magnetic Moment The g-factor + Easy to produce and stable measured to 0.28 parts per trillion! ➡ e - Small mass Low sensitivity to new physics ➡ Clean calculations ➡ + Abundant from pion decays + 200 times the mass of the electron ~40,000 times the sensitivity to new physics ➡ µ ± Unstable Utilize the decay ➡ + long lifetime of 2.2 us Sufficient time to interact with external magnetic field ➡ + 17 times the muon mass More sensitivity! ➡ τ - Disproportionally difficult to produce - Short lifetime, ~0.29 ps Jason Bono, jbono@fnal.gov

� 28 The Muon’s Anomalous Magnetic Moment The Muon’s g-factor e ~ ~ µ µ = g µ S 2 m µ c Dirac: g µ = 2 x Jason Bono, jbono@fnal.gov

� 29 The Muon’s Anomalous Magnetic Moment The Muon’s g-factor e ~ µ µ = g µ ~ S 2 m µ c Dirac: g µ = 2 + 1 st order QED: 10 th order QED: g µ = 2 . 002331 g µ = 2 . 0023 Jason Bono, jbono@fnal.gov

� 30 The Muon’s Anomalous Magnetic Moment The Muon’s g-factor e hadrons ~ ~ µ µ = g µ S 2 m µ c Dirac: g µ = 2 + 1 st order QED: 10 th order QED: g µ = 2 . 002331 g µ = 2 . 0023 + Hadronic Corrections: g µ = 2 . 00233184 Jason Bono, jbono@fnal.gov

� 31 The Muon’s Anomalous Magnetic Moment The Muon’s g-factor e ~ ~ µ µ = g µ S 2 m µ c Dirac: g µ = 2 + 1 st order QED: 10 th order QED: g µ = 2 . 002331 g µ = 2 . 0023 + Hadronic Corrections: g µ = 2 . 00233184 + Electroweak Corrections: g µ = 2 . 00233184178 Jason Bono, jbono@fnal.gov

� 32 The Muon’s Anomalous Magnetic Moment The Muon’s g-factor e ~ ~ µ µ = g µ S 2 m µ c Dirac: g µ = 2 + 1 st order QED: 10 th order QED: g µ = 2 . 002331 g µ = 2 . 0023 + Hadronic Corrections: g µ = 2 . 00233184 + Electroweak Corrections: g µ = 2 . 00233184178 Jason Bono, jbono@fnal.gov

� 33 The Muon’s Anomalous Magnetic Moment The Muon’s g-factor e ~ ~ µ µ = g µ S 2 m µ c Dirac: g µ = 2 + 1 st order QED: 10 th order QED: g µ = 2 . 002331 g µ = 2 . 0023 + Hadronic Corrections: g µ = 2 . 00233184 + Electroweak Corrections: g µ = 2 . 00233184178 Jason Bono, jbono@fnal.gov

� 34 The Muon’s Anomalous Magnetic Moment The Muon’s Anomalous Magnetic Moment a µ = g µ − 2 2 Theory (420 ppb) a SM = a QED + a EW + a Hadron = (11 , 659 , 182 . 8 ± 4 . 9) · 10 − 10 µ µ µ µ Hagiwara et al. J. Phys. G38 085003 (2011) Experiment (540 ppb) a EXP = 116 , 592 , 089(63) · 10 − 11 µ 2004: E821 @ BNL 3.3 σ discrepancy a EXP − a SM = (26 . 1 ± 8 . 0) · 10 − 10 µ µ Jason Bono, jbono@fnal.gov

� 35 The Muon’s Anomalous Magnetic Moment BLN’s E821 was in uncharted territory. Did they see the effects of something new? a µ = g µ − 2 2 Theory a SM = a QED + a EW + a Hadron = (11 , 659 , 182 . 8 ± 4 . 9) · 10 − 10 µ µ µ µ Hagiwara et al. J. Phys. G38 085003 (2011) Experiment a EXP = 116 , 592 , 089(63) · 10 − 11 µ E821 at BNL x 3.3 σ discrepancy a EXP − a SM = (26 . 1 ± 8 . 0) · 10 − 10 µ µ Jason Bono, jbono@fnal.gov

� 36 The Muon’s Anomalous Magnetic Moment Did BLN’s E821 See Beyond the Standard Model? a µ = g µ − 2 2 Theory a SM = a QED + a EW + a Hadron = (11 , 659 , 182 . 8 ± 4 . 9) · 10 − 10 µ µ µ µ Hagiwara et al. J. Phys. G38 085003 (2011) Higher precision needed Experiment a EXP = 116 , 592 , 089(63) · 10 − 11 µ E821 at BNL x 3.3 σ discrepancy a EXP − a SM = (26 . 1 ± 8 . 0) · 10 − 10 µ µ Jason Bono, jbono@fnal.gov

Delivery of BNL’s muon storage ring to Fermilab

A vigorous global theory effort

� 39 The Muon’s Anomalous Magnetic Moment: Fermilab’s g-2 Higher Precision on the Way ๏ A new muon beamline at FNAL will deliver 21x the statistics as in E821 As well as reduced 3x systematic uncertainty from B field uniformity ‣ Overall 4 fold improvement: 540 ppb @ BNL → 140 ppb @ FNAL ‣ ๏ First physics run to begin this month! Should be the highest statistics dataset in a few months ‣ ๏ Theory expected to improved by a factor of 2 on experiments timescale If central values remain the same: ‣ - ~5 σ discrepancy if theory does not improve - ~7-8 σ discrepancy if theory improves as expected Jason Bono, jbono@fnal.gov

� 40 The Muon’s Anomalous Magnetic Moment: Fermilab’s g-2 ~3 GeV, polarized muons kicked into the storage ring, which has a uniform 1.45 T B-field. Anisotropic Pions in the delivery ring, Vertical confinement by electric quadrupoles 8 GeV proton beam positions detected wait out decay e + p μ + π + γ ~ 29.3 Incident on production target, Select “forward going” muons lifetime: 2.2 μ s → 64.4 μ s select pions Jason Bono, jbono@fnal.gov

� 41 The Muon’s Anomalous Magnetic Moment: Fermilab’s g-2 The Extraction of a μ ! c = − q ~ B If then the cyclotron frequency is B · ~ ~ ~ P µ = 0 m � ! s = − g q ~ 2 m − (1 − � ) q ~ B B The spin precession frequency is ~ � m And if g = 2 → ~ ! s = ~ ! c q ~ q ~ ! c = − g − 2 B B So, one may define ~ ! a ≡ ~ ! s − ~ m = − a µ 2 m spin, relative to momentum, precession anomalous magnetic moment � x ~ ~ 1 ! a = − q E However, because of the quadruples, ~ m [ a µ ~ B − ( a µ − � 2 − 1) ] c = 0 But at the “magic momentum” ( γ ~ 29.3), the 2nd term vanishes Jason Bono, jbono@fnal.gov

� 42 The Muon’s Anomalous Magnetic Moment: Fermilab’s g-2 The Extraction of a μ ! c = − q ~ B If then the cyclotron frequency is B · ~ ~ ~ P µ = 0 m � ! s = − g q ~ 2 m − (1 − � ) q ~ B B The spin precession frequency is ~ � m Need to measure this, too. Won’t be covered here! And if g = 2 → ~ ! s = ~ ! c q ~ q ~ ! c = − g − 2 B B So, one may define ~ ! a ≡ ~ ! s − ~ m = − a µ 2 m spin, relative to momentum, precession anomalous magnetic moment � x ~ ~ 1 ! a = − q E However, because of the quadruples, ~ m [ a µ ~ B − ( a µ − � 2 − 1) ] c = 0 But at the “magic momentum” ( γ ~ 29.3), the 2nd term vanishes Jason Bono, jbono@fnal.gov

� 43 The Muon’s Anomalous Magnetic Moment: Fermilab’s g-2 The Extraction of a μ ! c = − q ~ B If then the cyclotron frequency is B · ~ ~ ~ P µ = 0 m � ! s = − g q ~ 2 m − (1 − � ) q ~ B B The spin precession frequency is ~ � m Need to measure this, too. Won’t be covered here! And if g = 2 → ~ ! s = ~ ! c q ~ q ~ ! c = − g − 2 B B So, one may define ~ ! a ≡ ~ ! s − ~ m = − a µ 2 m spin, relative to momentum, precession anomalous magnetic moment � x ~ ~ 1 ! a = − q E However, because of the quadruples, ~ m [ a µ ~ B − ( a µ − � 2 − 1) ] c A non-zero electric dipole moment would also affect the spin = 0 But at the “magic momentum” ( γ ~ 29.3), the 2nd term vanishes precession, but we’re not going in to that! Jason Bono, jbono@fnal.gov

� 44 The Muon’s Anomalous Magnetic Moment: Fermilab’s g-2 The Extraction of 𝟃 a ๏ 𝟃 a is the difference between the ensemble averaged muon spin precession and cyclotron frequencies ๏ In the CM frame, muon spin direction is correlated with positron angle ๏ In the lab frame (as well as the CM frame), the positron energy is correlated with it’s angle relative to the muon spin Jason Bono, jbono@fnal.gov

� 45 The Muon’s Anomalous Magnetic Moment: Fermilab’s g-2 The Extraction of 𝟃 a ๏ 𝟃 a is the difference between the ensemble averaged muon spin precession and cyclotron frequencies ๏ In the CM frame, muon spin direction is correlated with positron angle ๏ In the lab frame (as well as the CM frame), the positron energy is correlated with it’s angle relative to the muon spin Maximal energy when positron momentum and muon spin are parallel ‣ E e, lab = γ ( E e, CM + β P e, CM cos θ CM ) ≈ γ E e, CM (1 + cos θ CM ) Jason Bono, jbono@fnal.gov

� 46 The Muon’s Anomalous Magnetic Moment: Fermilab’s g-2 The Extraction of 𝟃 a ๏ 𝟃 a is the difference between the ensemble averaged muon spin precession and cyclotron frequencies ๏ In the CM frame, muon spin direction is correlated with positron angle ๏ In the lab frame (as well as the CM frame), the positron energy is correlated with it’s angle relative to the muon spin Maximal energy when positron momentum and muon spin are parallel ‣ E e, lab = γ ( E e, CM + β P e, CM cos θ CM ) ≈ γ E e, CM (1 + cos θ CM ) S µ · ˆ ˆ P µ = 1 S µ · ˆ ˆ P µ = − 1 Jason Bono, jbono@fnal.gov

� 47 The Muon’s Anomalous Magnetic Moment: Fermilab’s g-2 The Extraction of 𝟃 a ๏ 𝟃 a is the difference between the ensemble averaged muon spin precession and cyclotron frequencies ๏ In the CM frame, muon spin direction is correlated with positron angle ๏ In the lab frame (as well as the CM frame), the positron energy is correlated with it’s angle relative to the muon spin Maximal energy when positron momentum and muon spin are parallel ‣ E e, lab = γ ( E e, CM + β P e, CM cos θ CM ) ≈ γ E e, CM (1 + cos θ CM ) ๏ Also note that the electron angular distribution peaks for parallel alignment: � ˆ d n S µ · ˆ � d Ω = 1 + a ( E ) S µ · ˆ ˆ P e P µ = 1 S µ · ˆ ˆ P µ = − 1 Jason Bono, jbono@fnal.gov

� 48 The Muon’s Anomalous Magnetic Moment: Fermilab’s g-2 The Extraction of 𝟃 a The “wiggle plot” Choose a cutoff energy, and and fit for 𝟃 a ! ๏ 𝟃 a is the difference between the ensemble averaged muon spin precession and cyclotron frequencies ๏ In the CM frame, muon spin direction is correlated with positron angle ๏ In the lab frame (as well as the CM frame), the positron energy is correlated with it’s angle relative to the muon spin 𝟃 p is measured as a proxy for B One could just plot number of event with equal weighting, as above. Maximal energy when positron momentum and muon spin are parallel ‣ Or, one could weight the probability according to energy. Many possibilities! E e, lab = γ ( E e, CM + β P e, CM cos θ CM ) ≈ γ E e, CM (1 + cos θ CM ) ๏ Also note that the electron angular distribution peaks for parallel These form the basis for any extraction technique that will be used alignment: � ˆ d n S µ · ˆ � d Ω = 1 + a ( E ) S µ · ˆ ˆ P e P µ = 1 S µ · ˆ ˆ P µ = − 1 Jason Bono, jbono@fnal.gov

� 49 The Muon’s Anomalous Magnetic Moment: Fermilab’s g-2 Current: 3.3 σ Projected: ~7 σ Stay tuned in the coming months for preliminary results! Jason Bono, jbono@fnal.gov

Hints of Lepton Flavor Non-Universality in B decays

� 51 Hints of Lepton Flavor Non-Universality in B decays Semi-Leptonic B-Meson Decays ๏ Lepton Universality: e , 𝜈 , and 𝝊 differ only by their masses Identical coupling constants ‣ ๏ In semi-leptonic decays of B mesons, both e and 𝜈 can be treated as massless [1] ‣ Therefore expect identical rates and kinematics of the decay for either lepton in the final state ๏ The mass of the 𝝊 must be accounted for [1] m 𝝊 ~ 1777 MeV ~ 17 x m 𝜈 ‣ hadronic effects ‣ ๏ These decays are well understood in the SM, and so can be used to probe for new phenomena B ( ¯ B → Dl − ¯ ν l ) [1] Z. Phys. C - Particles and Fields 46, 93-109 (1990) Jason Bono, jbono@fnal.gov

� 52 Hints of Lepton Flavor Non-Universality in B decays Semi-Leptonic B-Meson Decays ๏ SM predictions for the semi-leptonic B branching ratios: Small suppression for 𝝊 in the final state ‣ D ∗ = B ( ¯ ν e ) = B ( ¯ B → D ∗ τ − ¯ ν τ ) B → D ∗ τ − ¯ ν τ ) R SM ν µ ) = 0 . 252 ± 0 . 003 B ( ¯ B ( ¯ B → D ∗ e − ¯ B → D ∗ µ − ¯ = B ( ¯ ν e ) = B ( ¯ B → D τ − ¯ ν τ ) B → D τ − ¯ ν τ ) R SM ν µ ) = 0 . 300 ± 0 . 008 B ( ¯ B ( ¯ D B → De − ¯ B → Dµ − ¯ Jason Bono, jbono@fnal.gov

� 53 Hints of Lepton Flavor Non-Universality in B decays Semi-Leptonic B-Meson Decays ๏ SM predictions for the semi-leptonic B branching ratios: Small suppression for 𝝊 in the final state ‣ D ∗ = B ( ¯ ν e ) = B ( ¯ B → D ∗ τ − ¯ ν τ ) B → D ∗ τ − ¯ ν τ ) R SM ν µ ) = 0 . 252 ± 0 . 003 B ( ¯ B ( ¯ B → D ∗ e − ¯ B → D ∗ µ − ¯ = B ( ¯ ν e ) = B ( ¯ B → D τ − ¯ ν τ ) B → D τ − ¯ ν τ ) R SM ν µ ) = 0 . 300 ± 0 . 008 B ( ¯ B ( ¯ D B → De − ¯ B → Dµ − ¯ ๏ These ratios have been measured in pp and e + e - production BaBar & Belle: ~10 GeV lepton collider data collected from 1999 to ~2010 ‣ LHCb: 7-8 TeV hadron collider data collected from 2008 to 2012 ‣ Jason Bono, jbono@fnal.gov

� 54 Hints of Lepton Flavor Non-Universality in B decays B-Meson Measurements ๏ All analyses fit to m 2miss , E 𝓂 , and q 2 The invariant mass squared of all undetected particles, lepton energy in the B rest frame, and ‣ invariant mass squared of the 𝓂𝜉 system ๏ BaBar and Belle require B tag , D (*) and 𝓂 in the final state Hadronic B tagging algorithm ‣ Semileptonic B tagging algorithm ‣ ๏ Similarly for LHCb Jason Bono, jbono@fnal.gov

� 55 Hints of Lepton Flavor Non-Universality in B decays B-Meson Measurements ๏ All analyses fit to m 2miss , E 𝓂 , and q 2 The invariant mass squared of all undetected particles, lepton energy in the B rest frame, and ‣ invariant mass squared of the 𝓂𝜉 system ๏ BaBar and Belle require B tag , D (*) and 𝓂 in the final state HT: Hadronic B tagging algorithm ‣ ST: Semileptonic B tagging algorithm ‣ ๏ Similarly for LHCb SM doi:10.1038/nature22346 Jason Bono, jbono@fnal.gov

� 56 Hints of Lepton Flavor Non-Universality in B decays B-Meson Measurements doi:10.1038/nature22346 Accounting for correlations, the combined discrepancies from R D and R D* gives ~4 σ Jason Bono, jbono@fnal.gov

� 57 Hints of Lepton Flavor Non-Universality in B decays B-Meson Measurements ๏ Similarly, can test lepton universality with a kaon in the final state = B ( ¯ B → K + µ − ¯ ν µ ) R SM ν e ) ≈ 1 B ( ¯ K B → K + e − ¯ ๏ These ratios have been measured in pp and e + e - production BaBar, Belle & CDF had large error bars, results consistent with the SM ‣ LHCb produced a better measurement: Phys. Rev. Lett. 113, 151601 (2014) ‣ Jason Bono, jbono@fnal.gov

� 58 Hints of Lepton Flavor Non-Universality in B decays B-Meson Measurements ๏ Similarly, can test lepton universality with a kaon in the final state = B ( ¯ B → K + µ − ¯ ν µ ) R SM ν e ) ≈ 1 B ( ¯ K B → K + e − ¯ R LHCb = 0 . 745 ± 0 . 090 0 . 074 ± 0 . 036 K A 2.6 σ departure from unity Jason Bono, jbono@fnal.gov

� 59 Hints of Lepton Flavor Non-Universality in B decays B-Meson Measurements ๏ SM discrepancies in R D(*) from three independent experiments Adds up to 4 σ departure ‣ ๏ SM discrepancy in R K from LHCb 2.6 σ departure ‣ ๏ Could be seeing the effects of a new interaction that breaks lepton flavor universality A new vector boson, W’ - , with different couplings for different quarks and leptons? ‣ A scalar, i.e. charged Higgs, H - ? ‣ Leptoquarks? ‣ ๏ No conclusion yet ‣ Underestimated experimental uncertainties? SM predictions lacking some ordinary ingredient? ‣ ‣ Awaiting Belle II and the LHCb upgrade Jason Bono, jbono@fnal.gov

Searches for Charged Lepton Flavor Violation

� 61 Searches for Charged Lepton Flavor Violation Charged Lepton Flavor Violation ๏ The recent anomalies in the lepton sector certainly add to the excitement of looking for Charged Lepton Flavor Violation (CLFV) ๏ But these searches have always been interesting! Recall the role that the early muon experiments had in piecing together the SM ‣ Jason Bono, jbono@fnal.gov

� 62 Searches for Charged Lepton Flavor Violation Flavor Violation in the SM ๏ The quarks commit Flavor Violation They mix via the W ‣ Jason Bono, jbono@fnal.gov

� 63 Searches for Charged Lepton Flavor Violation Flavor Violation in the SM ๏ The quarks commit Flavor Violation They mix via the W ‣ ๏ The neutrinos can change into their partners (and vice versa) 𝞷 µ µ - - 𝞷 e W - e - Jason Bono, jbono@fnal.gov

� 64 Searches for Charged Lepton Flavor Violation Flavor Violation in the SM ๏ The quarks commit Flavor Violation They mix via the W ‣ ๏ The neutrinos can change into their partners (and vice versa) ๏ And the neutrinos also mix! Jason Bono, jbono@fnal.gov

� 65 Searches for Charged Lepton Flavor Violation Flavor Violation in the SM ๏ The quarks commit Flavor Violation They mix via the W ‣ ๏ The neutrinos can change into their partners (and vice versa) ๏ And the neutrinos also mix! What’s going on with the charged leptons? Jason Bono, jbono@fnal.gov

� 66 Searches for Charged Lepton Flavor Violation CLFV in the Standard Model ๏ All CLFV processes are dynamically suppressed in the SM ‣ it’s impossible to proceed through SM interactions without violating deeper conservation laws But neutrino mixing implies an encouraging fact… Jason Bono, jbono@fnal.gov

� 67 Searches for Charged Lepton Flavor Violation CLVF Must Occur ๏ Neutrino oscillations require CLFV on some level 2 ∆ m 2 � � B ( µ → e γ ) = 3 α e.g. X 10 − 54 � il � U ∗ µi U ei � � M 2 32 π � � W i =2 , 3 ๏ But that level is tiny, because all SM CLFV processes involve loops with W and 𝞷 q q 𝞭 W W 🔵 e 𝛏 𝝂 𝛏 e 𝝂 Charged lepton flavor is not an exact symmetry in our universe, so there’s no formal reason for new phenomena to feature it. Furthermore, if CLFV is observed, it’s physics beyond the standard model, unequivocally Jason Bono, jbono@fnal.gov

� 68 Searches for Charged Lepton Flavor Violation CLFV Searches Jason Bono, jbono@fnal.gov

� 69 Searches for Charged Lepton Flavor Violation CLFV Searches Next generation experiments will bring us a ~1-4 orders of magnitude increase in sensitivity Jason Bono, jbono@fnal.gov

� 70 Searches for Charged Lepton Flavor Violation CLFV Searches Muons, with their relative ease of production, long lifetime, large mass, and simple decay, offer the best combination of access to new physics and experimental sensitivity Jason Bono, jbono@fnal.gov

� 71 Text Many Muon Searches Planned µ → e γ The oldest search 𝝂 - e conversion. Extremely sensitive searches to come! µN → eN µ → eee Excellent complimentary to above Lepton number violation can also be searched for µ − N → e + N ( Z − 2) by the 𝝂 - e conversion experiments! µ − e − → e − e − Likely won’t be searched for until CLFV is observed Limits come from 𝝂→ eee µ + e − → µ − e + Muonium-antimuonium conversion. Best limit is from the 90s. Nothing new planned yet! (to my knowledge) Jason Bono, jbono@fnal.gov

� 72 Searches for Charged Lepton Flavor Violation A Long History of CLFV Searches With Muons ๏ Despite nearly eight decades of searching, it’s never been observed Why continue to search? Thanks to Nina Hazen, NYC Jason Bono, jbono@fnal.gov

� 73 Searches for Charged Lepton Flavor Violation A 10 to 10000 Fold Leap In Sensitivity ๏ Leading New Physics models predict CLFV rates to be within reach ๏ The next generation of rare muon decay searches, with their revolutionary sensitivity, will ultimately help guide future experimental and theoretical developments in HEP Hidden structure is often lurking at better “resolution” a 10K increase in pixels Jason Bono, jbono@fnal.gov

� 74 Searches for Charged Lepton Flavor Violation A 10 to 10000 Fold Leap In Sensitivity ๏ Leading New Physics models predict CLFV rates to be within reach ๏ The next generation of rare muon decay searches, with their revolutionary sensitivity, will ultimately help guide future experimental and theoretical developments in HE Hidden structure is often lurking at better “resolution” And if it isn’t, that’s also interesting! Jason Bono, jbono@fnal.gov

� 75 Searches for Charged Lepton Flavor Violation A History of Searches for CLFV Muon Decays R.H. Bernstein, P.S. Cooper, Phys. Rep. 532 (2013) 27 Limit @ 90% CL) µ ≠ e* ( log scale CLFV Rates 𝞷 µ ≠ 𝞷 e Leading BSM Predictions Upgrades Year Breaking Through the Plateau… And Beyond the SM? Jason Bono, jbono@fnal.gov

� 76 Searches for Charged Lepton Flavor Violation The Future of Muon CLFV Searches R.H. Bernstein, P.S. Cooper, Phys. Rep. 532 (2013) 27 Limit @ 90% CL) µ ≠ e* Mu3e @PSI MEG II @ PSI ( log scale CLFV Rates 𝞷 µ ≠ 𝞷 e Leading BSM Predictions Mu2e @ FNAL Year COMET @ KEK Breaking Through the Plateau… And Beyond the SM? Jason Bono, jbono@fnal.gov

� 77 Searches for Charged Lepton Flavor Violation Effective CLFV Lagrangian: de Gouvea, A., and P. Vogel (2013) Magnetic moment type operator Supersymmetry Heavy neutrinos Two Higgs doublets Contact term operator New heavy bosons / Compositeness Leptoquarks anomalous coupling Jason Bono, jbono@fnal.gov

� 78 Searches for Charged Lepton Flavor Violation Effective CLFV Lagrangian: de Gouvea, A., and P. Vogel (2013) A. de Gouvêa, P. Vogel, arXiv:1303.4097 I Mu2e I e 2 u M Λ (TeV) κ >> 1 κ << 1 MEG II κ Loop Contact dominated dominated Jason Bono, jbono@fnal.gov

� 79 Searches for Charged Lepton Flavor Violation Observables and a Handful of New Physics Models Vanishingly small effects Moderate, but visible effects Large effects Altmannshofer, Buras, et al , Nucl.Phys.B830:17-94, 2010 Jason Bono, jbono@fnal.gov

� 80 Searches for Charged Lepton Flavor Violation Check out the theory reviews: Y. Kuno, Y. Okada, 2001 A. de Gouvêa, P. Vogel, 2013 M. Raidal et al. , 2008 Jason Bono, jbono@fnal.gov

� 81 Searches for Charged Lepton Flavor Violation ๏ Precision searches and measurements needn’t be theoretically motivated Recall the discovery of the muon! ‣ Or, Pauli to Stern: “Don’t you know the Dirac theory? It is obvious that g p =2.” ‣ Jason Bono, jbono@fnal.gov

� 82 Searches for Charged Lepton Flavor Violation ๏ Precision searches and measurements needn’t be theoretically motivated Recall the discovery of the muon! ‣ Or, Pauli to Stern: “Don’t you know the Dirac theory? It is obvious that g p =2.” ‣ F A I L Luckily for Stern, he didn’t listen Jason Bono, jbono@fnal.gov

� 83 Searches for Charged Lepton Flavor Violation Complementarity ๏ If BSM physics is seen in CLFV searches or elsewhere, the complementarity between measurements will be crucial for discerning its nature R. Bernstein Jason Bono, jbono@fnal.gov

� 84 Searches for Charged Lepton Flavor Violation Conversion Experiments With Various Nuclei ๏ Can begin to distinguish models by changing target material Cirigliano, V., R. Kitano, Y. Okada, and P. Tuzon (2009), Phys. Rev. D 80, 013002, arXiv:0904.0957 [hep-ph] R μ e (Normalized to Al) Z Jason Bono, jbono@fnal.gov

� 85 Searches for Charged Lepton Flavor Violation Results in the years to come! mu2e g-2 Jason Bono, jbono@fnal.gov

Muons and The Great Pyramid of Giza

Muons and The Great Pyramid of Giza published two weeks ago: “We have been very surprised to discover something so big—a big anomaly” Not quite the type of anomaly that we’ve been talking about, but that’s ok!

� 88 Muons and the Great Pyramid of Giza The Great Pyramid of Giza ๏ The oldest of the six “pyramids of Giza” ‣ Built more than 4.5 millennia ago, as a Mausoleum for the fourth dynasty Egyptian Pharaoh Khufu ๏ The oldest and only standing of the Seven Wonders of the Ancient World ๏ Was the world’s tallest man-made structure for nearly four millennia (135x230 m) ‣ The finishing of the pyramid marked the end of an “period of experimentation” ‣ Subsequently, conventions of visual art became fixed, and architecture simplified ๏ Has a comparatively complex internal architecture ‣ But the most complete account of construction is from Herodotus, two millennia later! Jason Bono, jbono@fnal.gov

� 89 Muons and The Great Pyramid of Giza The Technique: Cosmic Ray Muon Tomography ๏ 10K cosmic muons per square meter per minute, at sea level ‣ About 1% of pass though the Great Pyramid Weeks or months of data collection ‣ ๏ Get muon flux and momentum angular distribution: Three independent muon detection methods: ‣ - Nuclear emulsion films, argon based detectors, scintillating hodoscopes ๏ Obtain angular mass distribution from absorption and deflection Radial component requires multiple detection locations ‣ ๏ Because it’s passive, it’s gaining use in a variety of applications Volcanos -> imaging interior -> predict eruptions ‣ Fukushima -> image the reactor core mass distribution -> safe dismantling ‣ Non proliferation -> no artificial radiation dose on humans, nuclear warheads, or ‣ other sensitive materials -> easy to enforce -> slow the spread of nuclear weapons ‣ And, of course, pyramids - Use in Giza dates back to the 1960s ( Science 167 (3919), 832–839) Jason Bono, jbono@fnal.gov

� 90 Muons and The Great Pyramid of Giza T o m b o f P h a r a o h K h a f r a , K h u f u ' s s o n eh… How’s the muon tomography going? Muon Tomography in Giza dates back to the 1960s, but with null results Jason Bono, jbono@fnal.gov

� 91 Muons and The Great Pyramid of Giza Nagoya University KEK Detector Location Nuclear emulsion films (1st) & Scintillating Hodoscopes (2nd) CEA Argon based detectors (3rd) Jason Bono, jbono@fnal.gov

� 92 Muons and The Great Pyramid of Giza KEK Scintillating hodoscopes in the Queen’s chamber Nagoya University CEA Nuclear emulsion films in the Argon based detectors Queen’s chamber outside the pyramid ๏ 8 m 2 of double sided 70 𝝂 m film ๏ ๏ 4 scintillating layers in 2 4, 50x50 cm micro-pattern gas orthogonal sets detectors ๏ 3D tracks: ~1 𝝂 m & 1.8 mrad ๏ ๏ ๏ 120, 1 cm 2 bars in a layer require coincidence in 3 out of 4 2 sets, 10 m separated horizontally for stereo imaging of detected structures ๏ ๏ 2 units separated Gets solid angles of tracks vertically by 1m ‣ No mention of track resolution in paper ๏ ‣ No stereo imaging of structures trade off between angular acceptance and angular resolution Jason Bono, jbono@fnal.gov

� 93 Muons and The Great Pyramid of Giza KEK Scintillating hodoscopes in the Queen’s chamber Nagoya University CEA Nuclear emulsion films in the Argon based detectors Queen’s chamber outside the pyramid Subtract Monte Carlo simulations, using the pyramid’s known internal structure (~1 cm resolution), from data collected since 2015 Jason Bono, jbono@fnal.gov

� 94 Muons and The Great Pyramid of Giza KEK Scintillating hodoscopes in the Queen’s chamber Nagoya University CEA Nuclear emulsion films in the Argon based detectors Queen’s chamber outside the pyramid Found an excess coming from above the grand gallery ~8 m high × 30 m long × 1-2 m wide Jason Bono, jbono@fnal.gov

� 95 Muons and The Great Pyramid of Giza KEK Scintillating hodoscopes in the Queen’s chamber Nagoya University CEA Nuclear emulsion films in the Argon based detectors Queen’s chamber outside the pyramid Found an excess coming from above the grand gallery ~8 m high × 30 m long × 1-2 m wide Saw a similar excess Jason Bono, jbono@fnal.gov

� 96 Muons and The Great Pyramid of Giza KEK Scintillating hodoscopes in the Queen’s chamber Nagoya University CEA Nuclear emulsion films in the Argon based detectors Queen’s chamber outside the pyramid Found an excess coming from above the grand gallery ~8 m high × 30 m long × 1-2 m wide Saw a similar excess Jason Bono, jbono@fnal.gov

� 97 Muons and The Great Pyramid of Giza KEK Scintillating hodoscopes in the Queen’s chamber Nagoya University CEA Nuclear emulsion films in the Argon based detectors Queen’s chamber outside the pyramid Found an excess coming from above Saw the same excess, projected the grand gallery onto a different plane Saw a similar excess Jason Bono, jbono@fnal.gov

� 98 Muons and The Great Pyramid of Giza KEK Scintillating hodoscopes in the Queen’s chamber Nagoya University CEA Nuclear emulsion films in the Argon based detectors Queen’s chamber outside the pyramid Found an excess coming from above Saw the same excess, projected the grand gallery onto a different plane Saw a similar excess Jason Bono, jbono@fnal.gov

� 99 Muons and The Great Pyramid of Giza KEK Scintillating hodoscopes in the Queen’s chamber Nagoya University CEA Nuclear emulsion films in the Argon based detectors Queen’s chamber outside the pyramid Together, a 10 σ signal for a previously unknown “void" ~8 m high × 30 m long × 1-2 m wide Found an excess coming from above Saw a similar excess, projected the grand gallery onto a different plane Saw a similar excess Jason Bono, jbono@fnal.gov

� 100 Muons and The Great Pyramid of Giza This month’s discovery Last year’s discovery Jason Bono, jbono@fnal.gov