The muon g 2 : a new data-based analysis Alex Keshavarzi with - PowerPoint PPT Presentation

The muon g − 2 : a new data-based analysis Alex Keshavarzi with Daisuke Nomura, Thomas Teubner (KNT18) [arXiv:1802.02995, accepted for publication in Phys. Rev. D (in press)] Muon g − 2 Theory Initiative Workshop, JGU Mainz 20th June 2018

Introduction Hadronic cross section input � ∞ s R ( s ) K ( s ) , where R ( s ) = σ 0 = α 2 had ,γ ( s ) d s a had , LO VP µ 3 π 2 4 πα 2 / 3 s s th 10000 Υ (1s−6s) J/ ψ    Non-perturbative Perturbative ψ (2s) (Experimental data, (pQCD) 1000 isopsin, ChPT...) 100 φ Non R(s) ρ / ω -perturbative/ 10 perturbative (Experimental data, 1 pQCD, Breit-Wigner...) 0.1 1 10 100 √ s [GeV] Must build full hadronic cross section/ R -ratio... Alex Keshavarzi (KNT18) The muon g − 2 : HVP 20th June 2018 1 / 14

Introduction Building the hadronic R -ratio m π ≤ √ s ≤ 2 GeV 2 ≤ √ s ≤ 11 . 2 GeV 11 . 2 ≤ √ s < ∞ GeV Input experimental Can use experimental Calculate R using hadronic cross section inclusive R data* or pQCD ( rhad ) data* pQCD * σ had experiments Combine all available Must use data at data in exclusive quark flavour KLOE hadronic final states thresholds BaBar ( π + π − , K + K − , ... ) Combine all available SND Sum ∼ 35 exclusive R data CMD-(2/3) channels Robust treatment of KEDR Detailed data analysis experimental errors BESIII Robust treatment of Include narrow experimental errors resonances Estimate missing data input (isospin Question: for reliable precision, how are data correlated relations, ChPT...) and how should those correlations be implemented? Alex Keshavarzi (KNT18) The muon g − 2 : HVP 20th June 2018 2 / 14

KNT data combination Data combination: setup ⇒ Re-bin data into clusters → Scan cluster sizes for preferred solution (error, χ 2 , check by sight...) ⇒ Correlated data beginning to dominate full data compilation... → Non-trivial, energy dependent influence on both mean value and error estimate KNT18 prescription Construct full covariance matrices for each channel & entire compilation ⇒ Framework available for inclusion of any and all inter-experimental correlations If experiment does not provide matrices... → Statistics occupy diagonal elements only → Systematics are 100% correlated If experiment does provide matrices... → Use all information provided Use correlations to full capacity Alex Keshavarzi (KNT18) The muon g − 2 : HVP 20th June 2018 3 / 14

KNT data combination Data combination consideration Question: What are the main points of concern when combining experimental data to evaluate a had, VP ? µ ⇒ When combining data... → ...how to best combine large amounts of data from different experiments → ...the correct implementation of correlated uncertainties (statistical and systematic) → ...finding a solution that is free from bias d’Agostini bias [Nucl.Instrum.Meth. A346 (1994) 306-311] � p 2 x 2 p 2 x 1 x 2 � x 1 = 0 . 9 ± δx 1 ⇒ ¯ x ≃ 0 . 98 (systematic bias) 1 C sys = p 2 x 2 x 1 p 2 x 2 x 2 = 1 . 1 ± δx 2 2 Effect worsened with full, (Normalisation uncertainties defined by data) iterative data combination Alex Keshavarzi (KNT18) The muon g − 2 : HVP 20th June 2018 3 / 14

KNT data combination Data combination consideration Question: What are the main points of concern when combining experimental data to evaluate a had, VP ? µ ⇒ When combining data... → ...how to best combine large amounts of data from different experiments → ...the correct implementation of correlated uncertainties (statistical and systematic) → ...finding a solution that is free from bias Fixed matrix method [R. D. Ball et al. [NNPDF Collaboration], JHEP 1005 (2010) 075.] � p 2 ¯ x 2 p 2 ¯ x 2 � x 1 = 0 . 9 ± δx 1 ⇒ ¯ x = 1 . 00 (systematic bias) C sys = p 2 ¯ x 2 p 2 ¯ x 2 x 2 = 1 . 1 ± δx 2 Redefinition repeated at each stage (Normalisation uncertainties defined by estimator) of iterative data combination Alex Keshavarzi (KNT18) The muon g − 2 : HVP 20th June 2018 4 / 14

KNT data combination Linear χ 2 minimisation [KNT18: arXiv:1802.02995, PRD (in press)] ⇒ Clusters are defined to have linear cross section → Fix covariance matrix with linear interpolants at each iteration (extrapolate at boundary) N tot N tot χ 2 = � � R ( m ) C − 1 � R ( n ) − R i i ( m ) , j ( n ) �� − R j � � � i m j n i =1 j =1 ⇒ Through correlations and linearisation, result is the minimised solution of all available uncertainty information → ... through a method that has been shown to avoid d’Agostini bias 1400 Local √ ( χ 2 min /d.o.f.) ⇒ The flexibly of the fit to vary due to the 3 Global √ ( χ 2 min /d.o.f.) = 1.30 1200 σ 0 (e + e − → π + π − ) energy dependent, correlated uncertainties 1000 σ 0 (e + e − → π + π − ) [nb] 2.5 min /d.o.f.) benefits the combination 800 2 600 √ ( χ 2 → ... and any data tensions are 1.5 400 reflected in a local and global 200 1 χ 2 0 min / d . o . f . error inflation 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 √ s [GeV] Alex Keshavarzi (KNT18) The muon g − 2 : HVP 20th June 2018 5 / 14

Results Results from individual channels π + π − channel [KNT18: arXiv:1802.02995, PRD (in press)] ⇒ π + π − accounts for over 70% of a had , LO VP µ → Combines 30 measurements totalling 999 data points 1400 1400 BESIII (15) BESIII (15) 1300 1200 KLOE combination KLOE combination CMD-2 (06) CMD-2 (06) 1200 σ 0 (e + e - → π + π - ) [nb] 1000 σ 0 (e + e - → π + π - ) [nb] SND (04) SND (04) 1100 CMD-2 (03) CMD-2 (03) 800 Fit of all π + π - data Fit of all π + π - data 1000 BaBar (09) BaBar (09) 600 900 400 800 200 700 0 600 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 √ s [GeV] √ s [GeV] ⇒ Correlated & experimentally corrected σ 0 ππ ( γ ) data now entirely dominant [0 . 305 ≤ √ s ≤ 1 . 937 GeV ] = 502 . 97 ± 1 . 14 stat ± 1 . 59 sys ± 0 . 06 vp ± 0 . 14 fsr a π + π − µ = 502 . 97 ± 1 . 97 tot HLMNT11: 505 . 77 ± 3 . 09 ⇒ 15% local χ 2 min / d . o . f . error inflation due to tensions in clustered data Alex Keshavarzi (KNT18) The muon g − 2 : HVP 20th June 2018 6 / 14

Results Results from individual channels π + π − channel [KNT18: arXiv:1802.02995, PRD (in press)] ⇒ Tension exists between BaBar data and all other data in the dominant ρ region. → Agreement between other radiative return measurements and direct scan data largely compensates this. 0.4 π + π - (0.6 ≤  √ s ≤ 0.9 GeV) = (369.41 ± 1.32) x 10 -10 BESIII (15) a µ 1400 χ 2 KLOE combination min /d.o.f. = 1.30 CMD-2 (06) Fit of all π + π − data: 369.41 ± 1.32 0.3 SND (04) 1200 CMD-2 (03) σ 0 (e + e - → π + π - ) [nb] Fit of all π + π - data 1000 Direct scan only: 370.77 ± 2.61 0.2 BaBar (09) Fit Fit )/ σ 0 σ 0 (e + e - → π + π - ) 800 - σ 0 KLOE combination: 366.88 ± 2.15 0.1 ( σ 0 600 BaBar (09): 376.71 ± 2.72 0 400 BESIII (15): 368.15 ± 4.22 200 -0.1 0 0.6 0.65 0.7 0.75 0.8 0.85 0.9 360 365 370 375 380 385 390 395 π + π − √ s [GeV] √ s ≤ 0.9 GeV) x 10 10 a µ (0.6 ≤  Compared to a π + π − = 502 . 97 ± 1 . 97 : ⇒ a π + π − ( BaBar data only ) = 513 . 2 ± 3 . 8 . µ µ Simple weighted average of all data ⇒ a π + π − ( Weighted average ) = 509 . 1 ± 2 . 9 . µ (i.e. - no correlations in determination of mean value) BaBar data dominate when no correlations are taken into account for the mean value Highlights importance of fully incorporating all available correlated uncertainties Alex Keshavarzi (KNT18) The muon g − 2 : HVP 20th June 2018 7 / 14