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Christine Davies University of Glasgow HPQCD Collaboration

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Christine Davies University of Glasgow HPQCD Collaboration Turning the screws on the Standard Model: theory predictions for the anomalous magnetic moment of the muon Christine Davies University of Glasgow Birmingham February 2019 HPQCD collaboration Outline 1) Introduction : what is the anomalous magnetic moment (a µ ) of the muon and how is it determined (so accurately) in experiment? (recap) 2) Theory calculations in the Standard Model: QED/EW perturbation theory 3) Pinning down QCD effects, using experimental data and using Lattice QCD calculations. 4) Conclusions and prospects e, µ, ⌧ have electric charge and spin Interaction with an external em field p0 has a magnetic component: q 0 µ ! ieu(p0)Γ (p, p0)u(p)A (q) − µ µ⌫ µ µ 2 iσ q⌫ 2 Γ (p, p0)=γ F1(q )+ F2(q ) p 2m Electric field interaction (charge consvn): F1(0) = 1 Magnetic field intn, equiv. to scattering from potential : V (x)= µ~ B~ (x) h i · e ~ e µ~ = [F (0) + F (0)] g S~ m 1 2 2 ⌘ 2m Peskin + Schroeder ⇣ ⌘g =2+2F2(0) 1 Introduction The Standard-Model (SM) value of the muon anomaly can be calculated with sub-parts- per-million precision. The comparison between the measured and the SM prediction provides a test of the completeness of the Standard Model. At present, there appears to be a three- to four-standard deviation between these two values, which has motivated extensive theoretical and experimental work on the hadronic contributions to the muon 1 Introduction anomaly. A lepton (` = e, µ, ⌧)hasamagneticmomentwhichisalongitsspin,givenbythe The Standard-Model (SM) value of the muon anomaly can be calculated with sub-parts- relationship per-million precision. The comparison between the measured and the SM prediction Qe g` 2 provides a test of the completeness of the Standard Model. At present,µ~ ` = thereg` appears~s, g` =2(1 + a`),a` = − (1) to be a three- to four-standard deviation between these two values, which has2 motivatedm` 2 Dirac extensive theoretical and experimental work on the hadronic contributions to the muon where Q = 1, e>0andm is the lepton mass. Dirac theory predicts that g 2, anomaly. ± ` | {z } ⌘ A lepton (` = e, µ, ⌧)hasamagneticmomentwhichisalongitsspin,givenbythebut experimentally, it is known to be greater than 2. The small number a,theanomaly, relationship arises from quantum fluctuations, with the largest contribution coming from the mass- Qe independentg single-loop` 2 diagram in Fig. 1(a). With his famous calculation that obtained µ~ ` = g` ~s, g` =2(1 + a`),a` = − (1) 2m` a =(↵/2⇡)=02.00116 , Schwinger [1] started an “industry”, which required Aoyama, Dirac Hayakawa, Kinoshita and··· Nio to calculate more than 12,000 diagrams to evaluate the where Q = 1, e>0andm is the lepton mass. Dirac theory predicts that g 2, ± ` | {z } tenth-order (five loop) contribution⌘ [2]. but experimentally, it is known to be greater than 2. The smallAnomalous number amagnetic,theanomaly, moment g 2 arises from quantum fluctuations, with the largest contribution coming from the mass-ae,µ,⌧ = − = F2(0) independent single-loop diagram in Fig. 1(a). With his famous calculationγ that obtained 2 γ γ a =(↵/2⇡)=0.00116 , Schwinger [1] started an “industry”, which requiredµ Aoyama, X X ··· µ LO contribn is leptonµ masse− independentµ Hayakawa, Kinoshita and Nio to calculate more than 12,000 diagrams to evaluate the Schwinger 1948 µ γ ↵ µ µ Y tenth-order (five loop) contribution [2]. =0.00116 ...+ γ 2⇡ γ e (a) (b) (c) many higher order pieces ….. γ γ γ New physics could appear in loops Figure 1: The FeynmanX graphs for: (a) The lowest-order (Schwinger) contribution to µ µ X 2 µ e− µ new physics m the lepton anomaly ; (b) Theδa vacuum polarization` 1 TeV? contribution, which is one of five µ γ µ µ Y2 ` / m2 γ e+ γ fourth-order, (↵/⇡) , terms; (c) The schematicX contribution of new particles X and Y (a) (b) flavour,CP-conserving(c) Motivates study of µ rather than e that couple to the muon. 8 13 10− 10− chirality flipping ⇡ ⇡ Figure 1: The Feynman graphs for: (a) The lowest-order (Schwinger) contribution to the lepton anomaly ; (b) The vacuum polarizationThe contribution, interaction which shown is one in of Fig. five 1(a) is a chiral-changing, flavor-conserving process, fourth-order, (↵/⇡)2, terms; (c) The schematic contribution of new particles X and Y which gives it a special sensitivity to possible new physics [3, 4]. Of course heavier that couple to the muon. particles can also contribute, as indicated by the diagram in Fig. 1(c). For example, 0 X = W ± and Y = ⌫µ, along with X = µ and Y = Z , are the lowest-order weak The interaction shown in Fig. 1(a) is a chiral-changing,contributions. flavor-conserving In the Standard-Model, process, aµ gets measureable contributions from QED, the which gives it a special sensitivity to possible newstrong physics interaction, [3, 4]. and Of course from the heavier electroweak interaction, particles can also contribute, as indicated by the diagram in Fig. 1(c). For example, 0 SM QED Had Weak X = W ± and Y = ⌫µ, along with X = µ and Y = Z , are the lowest-ordera weak= a + a + a . (2) contributions. In the Standard-Model, aµ gets measureable contributions from QED, the strong interaction, and from the electroweak interaction,In this document we present the latest evaluations of the SM value of aµ, and then dis- cuss expected improvements that will become available over the next five to seven years. SM QED Had Weak a = a + a The+ a uncertainty. in this evaluation(2) is dominated by the contribution of virtual hadrons in loops. A worldwide e↵ort is under way to improve on these hadronic contributions. In this document we present the latest evaluations of the SM value of a , and then dis- By the time that theµ Fermilab muon (g 2) experiment, E989, reports a result later cuss expected improvements that will become available over the next five to seven years. − The uncertainty in this evaluation is dominatedin by this the contribution decade, the of uncertainty virtual hadrons should be significantly reduced. We emphasize that the in loops. A worldwide e↵ort is under way to improveexistence on these of E821 hadronic at Brookhaven contributions. motivated significant work over the past thirty years By the time that the Fermilab muon (g 2) experiment, E989, reports a result later in this decade, the uncertainty should be− significantly reduced. We emphasize that the 2 existence of E821 at Brookhaven motivated significant work over the past thirty years 2 CURRENT STATUS SM 10 Keshavarzi aµ = 11659182.0(3.6) 10− et al, ⇥ 1802.02995 tantalising 3.7σ discrepancy! details to follow … higher accuracy small-scale experiments possible (Penning trap) but discrepancies will be tiny … very hard since decays in 0.3picoseconds …. 2 + + + δa =5 10− (LEP) e e− e e−⌧ ⌧ − ⌧ ⇥ ! New determination of α (2018) : Mueller et al (h/MCs) Now SM expt SM 14 ∆a a a = 87(36) 10− e ⌘ Twoe − ge-2 anomalies− ⇥ 2.4σ ‘tension’ and opposite sign to discrepancy for µ potentially adds excitement to the story! Davoudiasl+Marciano, 1806.10252 Aoyama, Kinoshita and Nio, 1712.06060 for QED calc. http://resonaances.blogspot.co Davoudiasl & Marciano, m/2018/06/alpha-and-g-minus- arXiv:1806.10252 two.html Accurate experimental results + theory calculations needed Muon g-2: spin 0 Ion traps unsuitable:both helicity -1 in rest frame p ⇡+ ⌫ + µ+ ⇡ ! ! µCyclotron radius =so 2 m,get impossible polarised to load, requireµ beam relativistic pulse speeds (lifetime = 2 us). B field perpendicular to ring, µ spin precesses B measure frequency difference !S !C − Lepton Dipole Moments Adam West, PIC 2015 Qe m 2 β~ E~ ~! ~! = a B~ + a ⇥ + .. S − C − m µ µ − p c " ✓ ◆ ! # Q = 1,µ± ± from directly gives a need uniform µ possible stable B, measure electric field term vanishes to sub-ppm with EDM at ‘magic momentum’ NMR probes β~ B~ calibrated using gp p =3.094 GeV/c / ⇥ measure spin direction from e produced in weak decay µ+ e+ + ⌫ + ⌫ ! e µ direction of highest energy e correlated with µ spin so N e oscillates at ! ! S − C NS62CH10-Roberts ARI 17 September 2012 11:40 a SM Theory (9.4 ppm) CERN μ+ (10 ppm) CERN μ– (13 ppm) E821(97) μ+ (5 ppm) E821(98) μ+ (1.3 ppm) E821(99) μ+ (0.7 ppm) E821(00) μ+ (0.7 ppm) E821(01) μ– World average 116 590 000 116 591 000 116 592 000 116 593 000 116 594 000 116 595 000 −11 aμ (× 10 ) b Fermilab Status of experiment goal Muon g-2 E989 α 4 Brookhaven 2004 ⎛ ⎞ + hadrionic + weak + ? 2013: E821 ring moved ⎝ πE821⎠ - 0.7ppm α 3 CERN III 1979 ⎛ ⎞ + hadrionic to Fermilab ⎝ π ⎠ α 3 CERN II 1968 ⎛ ⎞ ⎝ π ⎠ Experiment α 2 CERN I 1962 ⎛ ⎞ ⎝ π ⎠ α Nevis 1960 2π 10 100 1E7 1,000 10,000 100,000 1,000,000 −11 σαμ (× 10 ) Figure 2 (a) Measurements of aµ.(b)Theuncertaintyonaµ and the physics reach as the uncertainty decreased. by Glasgow University on 03/24/14. For personal use only. Abbreviation: SM, Standard Model. Involvement from that a (m/p)2,sotheEfielddidnotcontributetoGermany,ω .3 ByItaly, measuring UK the frequency ω ,and becomes µ = a a ω the magnetic field B⃗ calibrated to the Larmor frequency of the free proton p , one can determine Annu. Rev. Nucl. Part. Sci. 2012.62:237-264. Downloaded from www.annualreviews.org E989 aµ from the relationship ωa /ωp aµ R , 3. = λ ωa /ωp = λ + − + − R where λ µµ /µp 3.183 345 137 (85) is the muon-to-proton magnetic moment ratio (27).
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