some theory tools for neutrino interactions with nucleons RICHARD - PowerPoint PPT Presentation

some theory tools for neutrino interactions with nucleons RICHARD HILL UKentucky and Fermilab WWONNI Fermilab 6 November, 2017 thanks to many collaborators and colleagues, including: J.Arrington, M. Betancourt, R. Gran, P. Kammel, A. Kronfeld, G.Lee, W. Marciano, K. McFarland, A. Meyer, G. Paz, J. Simone, A. Sirlin thanks Andreas and Pilar! 1

Overview - topic 0: why - topic 1: amplitude analysis and z expansion - topic 2: muon capture and nucleon axial radius - topic 3: radiative corrections and SCET 2

topic 0. why 3

topic 0. why why bother with neutrino interactions? Isn’t this too hard/ too different/ somebody else’s problem? 4

topic 0. why why bother with neutrino interactions? Isn’t this too hard/ too different/ somebody else’s problem? HEP “The good news is that it’s not my problem” 4

long baseline neutrino oscillation experiment is simple in conception : 2 2 CC spectrum at 1300 km, m = 2.4e-03 eV ν ∆ µ 31 1000 1000 0.2 CC spectrum ν µ 0.18 2 sin 2 = 0.0, =n/a θ δ cp 13 2 sin 2 = 0.1, =- /2 800 800 θ δ π 0.16 cp 13 CC evts/GeV/10kt/MW.yr 2 sin 2 = 0.1, =0 θ δ Appearance Probability cp 13 0.14 LBNE, 1307.7335 2 sin 2 = 0.1, =+ /2 θ δ π cp 13 600 600 0.12 0.1 400 400 0.08 0.06 µ ν 200 200 0.04 0.02 0 0 0 10 20 30 1 10 E (GeV) ν 5

long baseline neutrino oscillation experiment is simple in conception : 2 2 CC spectrum at 1300 km, m = 2.4e-03 eV ν ∆ µ 31 1000 1000 0.2 CC spectrum ν µ 0.18 2 sin 2 = 0.0, =n/a θ δ cp 13 2 sin 2 = 0.1, =- /2 800 800 θ δ π 0.16 cp 13 CC evts/GeV/10kt/MW.yr 2 sin 2 = 0.1, =0 θ δ Appearance Probability cp 13 0.14 LBNE, 1307.7335 2 sin 2 = 0.1, =+ /2 θ δ π cp 13 600 600 0.12 0.1 400 400 0.08 0.06 µ ν 200 200 0.04 Measure fraction 0.02 of ν e appearing 0 0 0 10 20 30 1 10 E (GeV) in ν μ beam ν 5

long baseline neutrino oscillation experiment is simple in conception : 2 2 CC spectrum at 1300 km, m = 2.4e-03 eV ν ∆ µ 31 1000 1000 0.2 CC spectrum ν µ 0.18 2 sin 2 = 0.0, =n/a θ δ cp 13 2 sin 2 = 0.1, =- /2 800 800 θ δ π 0.16 cp 13 CC evts/GeV/10kt/MW.yr 2 sin 2 = 0.1, =0 θ δ Appearance Probability cp 13 0.14 LBNE, 1307.7335 2 sin 2 = 0.1, =+ /2 θ δ π cp 13 600 600 0.12 0.1 400 400 0.08 0.06 Do it as a function µ ν 200 200 0.04 Measure fraction of energy 0.02 of ν e appearing 0 0 0 10 20 30 1 10 E (GeV) in ν μ beam ν 5

long baseline neutrino oscillation experiment is difficult in practice : simple picture is complicated by - ν e versus ν μ cross section differences need theory for σ ν e / σ νμ , at ~% precision of measurement and also - intrinsic ν e component of beam - degeneracy of uncertainty in detector response and neutrino interaction cross sections - imperfect energy reconstruction aided by near detector but - beam divergence and oscillation (near flux ≠ far flux) need theory for σ νμ , at a precision depending on the experimental capabilities 6

current paradigm: constrain neutrino interactions by - determining nucleon level amplitudes - parameterizing/measuring/calculating nuclear modifications folk paradigms: “perfect theory” constrain neutrino interactions by - starting at the quark level - computing nuclear response “perfect expt.” constrain neutrino interactions by - starting directly at the nuclear level - parameterizing and measuring every cross section 7

in any paradigm: near detector has access to primarily ν μ neutrinos ν e appearance signal is directly impacted by ν μ / ν e cross section differences - kinematics - 2nd class currents (G parity violation) - radiative corrections (QED and EW) - signal definition having talked the talk, do some walking: - ν μ / ν e in the time reversal process ( μ p → ν n) - nucleon input uncertainty (e-p, ν d → ν n) - radiative corrections at GeV (e-p) nuclear corrections: see talks of W. Van Order, S. Pastore, A. Ankowski, N. Jachowicz, A. Lovato. experiment: S. Bolognesi; lots of references: NUSTEC white paper 1706.03621 8

Notes: beyond neutrino oscillations related applications relying on quantitative nucleon structure: - fundamental constants (probable 7 sigma shift in Rydberg) - sigma terms and WIMP-DM direct detection - g A and BBN - … QED is “easy”. But QED + nucleon structure is “hard” entering a precision realm where percent level corrections to nucleon structure need to be calculated, not just estimated 9

topic 1. amplitude analysis and z expansion first, e-p elastic scattering second, ν -n CC scattering 10

topic 1. amplitude analysis and z expansion first, e-p elastic scattering second, ν -n CC scattering 11

12 (up to radiative corrections) p 4 m 2 G M = F 1 + F 2 G E = F 1 + q 2 F 2 q 2 =0 � dq 2 G E ( q 2 ) 2 m p E ≡ 6 d � r 2 h J µ i = γ µ F 1 + σ µ ν q ν F 2 � i � radius as slope of form factor ρ ( r ) for the relativistic, QM, case, define 6 h r 2 i q 2 + . . . = 1 � 1 Z � 2( q · r ) 2 + . . .  e − ρ ( r ) 1 + i q · r � 1 = d 3 r Z e − d 3 r e i q · r ρ ( r ) F ( q 2 ) = pointlike ◆ ✓ d σ d Ω = d Ω | F ( q 2 ) | 2 d σ recall scattering from extended classical charge distribution:

Radius extraction requires data over a Q 2 range where a simple Taylor expansion of the form factor is invalid data of Bernauer et al. (A1 collaboration), PRL 105, 242001 (2010) radius error [sensitivity studies based on bounded z expansion fit] [fm] maximum Q 2 [GeV 2 ] 13

Radius extraction requires data over a Q 2 range where a simple Taylor expansion of the form factor is invalid data of Bernauer et al. (A1 collaboration), PRL 105, 242001 (2010) radius error [sensitivity studies based on bounded z expansion fit] [fm] size of r E anomaly (hydrogen) maximum Q 2 [GeV 2 ] 13

Radius extraction requires data over a Q 2 range where a simple Taylor expansion of the form factor is invalid data of Bernauer et al. (A1 collaboration), PRL 105, 242001 (2010) radius error [sensitivity studies based on bounded z expansion fit] [fm] Cut used for radius extraction size of r E anomaly (hydrogen) maximum Q 2 [GeV 2 ] 13

Radius extraction requires data over a Q 2 range where a simple Taylor expansion of the form factor is invalid data of Bernauer et al. (A1 collaboration), PRL 105, 242001 (2010) radius error [sensitivity studies based on bounded z expansion fit] [fm] Cut used for radius extraction size of r E anomaly (hydrogen) convergence radius for maximum Q 2 [GeV 2 ] simple Taylor expansion 13

That’s ok: underlying QCD tells us that Taylor expansion of form factor in appropriate variable is convergent q 2 z particle thresholds t cut experimental kinematic region t cut − q 2 − √ t cut − t 0 p z ( q 2 , t cut , t 0 ) = , t cut − q 2 + √ t cut − t 0 p X a k [ z ( q 2 )] k F ( q 2 ) = k coefficients in rapidly convergent expansion encode nonperturbative QCD 14

Reanalysis of scattering data reveals strong influence of shape assumptions 2 S − 2 P 1 2 2 S − 2 P 1 2 2 S − 2 P 3 2 2 S − 4 S 1 2 2 S − 4 D 5 2 2 S − 4 P 1 2 2 S − 4 P 3 2 2 S − 6 S 1 2 2 S − 6 D 5 2 2 S − 8 S 1 2 2 S − 8 D 3 2 2 S − 8 D 5 2 2 S − 12 D 3 2 2 S − 12 D 5 2 1 S − 3 S 1 2 Mainz data muonic H other world data electron combination proton radius[fm] Errors larger, but discrepancy remains 15

Reanalysis of scattering data reveals strong influence of shape assumptions 2 S − 2 P 1 2 2 S − 2 P 1 2 2 S − 2 P 3 2 2 S − 4 S 1 2 2 S − 4 D 5 2 2 S − 4 P 1 2 2 S − 4 P 3 2 2 S − 6 S 1 2 2 S − 6 D 5 2 2 S − 8 S 1 2 2 S − 8 D 3 2 2 S − 8 D 5 2 2 S − 12 D 3 2 2 S − 12 D 5 2 1 S − 3 S 1 2 Mainz data muonic H other world data Lee, Arrington, Hill electron combination (2015) reanalysis of Mainz data reanalysis of other world data proton radius[fm] Errors larger, but discrepancy remains 15

2 S − 2 P 1 / 2 CREMA µ H 2010 → 2 S − 2 P 1 / 2 2 S − 2 P 3 / 2 2 S − 4 S 1 / 2 2 S − 4 D 5 / 2 2 S − 4 P 1 / 2 2 S − 4 P 3 / 2 2 S − 6 S 1 / 2 2 S − 6 D 5 / 2 2 S − 8 S 1 / 2 2 S − 8 D 3 / 2 2 S − 8 D 5 / 2 2 S − 12 D 3 / 2 2 S − 12 D 5 / 2 1 S − 3 S 1 / 2 e-p Mainz e-p world CODATA 2010 electron comb. CREMA µ H 2014 → e-p Mainz ( z exp.) e-p world ( z exp.) CODATA 2014 electron comb. µ D + iso. update: Beyer et al. (Science, 2017) H 2S-4P (sensitivity) low- Q 2 e-p (sensitivity) µ -p (sensitivity) 0.8 0.9 1 1.1 r p E (fm) 16

topic 1. amplitude analysis and z expansion first, e-p elastic scattering second, ν -n CC scattering 17

Start with the basic process ν μ μ - σ ( ν n → µp ) = | · · · F A ( q 2 ) · · · | 2 n p poorly known axial-vector form factor A common ansatz for F A has been employed for the last ~40 years: ◆ � 2 1 − q 2 ✓ F dipole ( q 2 ) = F A (0) A m 2 A Inconsistent with QCD. Typically quoted uncertainties are (too) small (e.g. compared to proton charge form factor!) � 1 dF A ⌘ 1 6 r 2 � r A = 0 . 674(9) fm � A F A (0) dq 2 � q 2 =0 18