Neutral Current Weak Form Factors & Neutrino Scattering Raza - PowerPoint PPT Presentation

Neutral Current Weak Form Factors & Neutrino Scattering Raza Sabbir Sufian USQCD All Hands’ Meeting 2018

Neutrino-Nucleon Neutral Current Elastic Scattering ν ( q 1 , σ 1 ) ν ( q 2 , σ 2 ) ν + p ν + p → Z 0 ( q ) ν + p ¯ ν + p, ¯ → N ( p 1 , κ 1 ) N ( p 2 , κ 2 ) Matrix element in V-A structure of leptonic current i h N ( p 2 ) | J µ p M = 2 G F ¯ ν ( q 2 ) γ µ (1 � γ 5 ) ν ( q 1 ) Z | N ( p 1 ) i . 2 | {z } | {z } leptonic current hadronic current 2 ( Q 2 ) i σ µ ν q ν h N ( p 2 ) | J µ u ( p 2 )[ F Z 1 ( Q 2 ) + F Z + F Z A ( Q 2 ) γ µ γ 5 ] u ( p 1 ) Z | N ( p 1 ) i = ¯ 2 M N

(Anti)Neutrino-Nucleon Scattering Differential Cross Section dQ 2 � G 2 Q 2 d � F � A � BW � CW 2 � ; E 2 2 � � W � 4 � E � =M p � � � ; 1 � 2 � � � F Z 4 f � G Z A � 2 � 1 � � ���� F Z 2 � 2 �� 1 � � �� 4 � F Z 1 F Z A � 1 2 g ; C � 1 4 G Z A � F Z 1 � F Z B � � 1 A � 2 � � F Z 1 � 2 � � � F Z 2 � ; 64 � �� G Z 2 � 2 � : Neutral Weak Dirac & Pauli Weak axial FF FFs

Calculation of F 1Z and F 2Z 1 , 2 ) � F s ✓ 1 ◆ 2 � sin 2 θ W 1 , 2 ( Q 2 )) � sin 2 θ W ( F p 1 , 2 F Z,p ( F p 1 , 2 ( Q 2 ) � F n 1 , 2 + F n 1 , 2 = 2 Nucleon EMFF from Strange EMFF from Model Independent Lattice QCD z-expansion PRL 118, 042001 (2017) RSS, Yang, Alexandru, Draper, Liang, Liu PL B 777 (2018) 8-15 Ye, Arrington, Hill, Lee Physical point 4 lattice spacings 3 volumes

Inputs for Previous Neutral Weak EMFFs Nucleon EMFF (total) Strange EMFF PRD 95, 014011(2017) RSS, de Teramond, Brodsky, Dosch, Deur PRL 2018 de Teramond, Liu, RSS, Brodsky, Dosch, Deur

Calculation of Neutral Weak EMFFs E,M ( Q 2 ) = 1  Radiative corrections (1 − 4 sin 2 ✓ W )(1+ R p ( n ) G Z,p ( n ) ) G γ ,p ( n ) E,M ( Q 2 ) V 4 for e-p scattering � − (1+ R n ( p ) ) G γ ,n ( p ) E,M ( Q 2 ) − G s E,M ( Q 2 ) V ffiffiffi PRD 96, 093007 (2017) RSS

Determination of Neutral Current Weak Axial FF *Use MiniBooNE data (0.27 < Q 2 < 0.65 GeV 2 ) Reason 1: Uncertainty in G sE,M becomes very large and values consistent with zero Reason 2: Nuclear effect can be large for at low Q 2 C ~ 1 [ ]

Determination of Neutral Current Weak Axial FF d σ dQ 2 From MiniBooNE Experiment 1 , 2 ) } )( F p From Experiment 1 , 2 � − F n From Lattice QCD − F s 1 , 2 G ZA (0) = - 0.751 (56) M dipole = 0.95(6) GeV In preparation with Keh-Fei Liu & David Richards

Impact of Lattice QCD Strange EMFF Possibility: Since strange quark contribution is small set =0 (0) ) G s (??) E,M ( Discrepancy !! X =0 (0) ) G s E,M ( X

Reconstruction of Differential Cross Sections Nuclear effects Pauli blocking & nuclear shadowing at Q 2 < 0.15 GeV 2 BNL E734 data was NOT used in the analysis

Estimate of G sA (0) This Calculation Other Calculations G Z A � G s A � 1 2 �� G CC MiniBooNE, PRD 82 (2010) G s A � ; A (0) = 0 . 08(26) A (0) = - 0.21(10 ) G s BNL E734, PRC 48 (1993) G Z A (0) = − 0 . 751(56) 0 . 00 − 0 . 02 G CC A (0) = 1 . 2723(23) − 0 . 04 − 0 . 06 − 0 . 08 QCDSF A Engelhardt g s − 0 . 10 ETMC G s = - 0.23(11) A (0) CSSM and QCDSF/UKQCD − 0 . 12 LHPC χ QCD − 0 . 14 Phenomenology (JAM15) Phenomenology (JAM17) − 0 . 16 Phenomenology (NNPDFpol1.1) − 0 . 18 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 m π (GeV) From Jeremy Green’s Talk

Summary Precise estimate of NC weak axial form factor G ZA Strange quark contribution cannot be ignored Reconstruction of (anti)neutrino- nucleon diff. cross sections with correct prediction of G ZA and lattice input of G sE,M Lattice QCD calculation of G sA in the continuum and infinite volume limit with controlled systematic uncertainties required

An Example: LQCD Constraint on Models Many models of meson-baryon fluctuations to study s(x)-s(x) asymmetry In Preparation

Pate, et al EPJ Web Conf. 66 (2014) 06018 [13] S.F. Pate, Phys. Rev. Lett. 92 , 082002 (2004), 0 0.2 0.4 0.6 0.8 1 0.5 0.5 [14] D. Armstrong, R. McKeown, Ann.Rev.Nucl.P Two solutions for the strange form factors at Q 2 � 0 0 TABLE II. 0 : 5 GeV 2 produced from the E734 and HAPPEX data. -0.5 -0.5 s G -1 -1 A Solution 1 Solution 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 G s 0 : 02 � 0 : 09 0 : 37 � 0 : 04 0.4 0.4 E G s 0 : 00 � 0 : 21 � 0 : 87 � 0 : 11 0.2 0.2 M G s � 0 : 09 � 0 : 05 0 : 28 � 0 : 10 0 0 A s G -0.2 -0.2 M 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.2 0.2 Q 2 = 0.5 GeV 2 0 0 s G -0.2 -0.2 E 0 0.2 0.4 0.6 0.8 1 2 2 Q (GeV )

Weak Axial FF form e-p scattering PV = − G F Q 2 1 A p √ E ) 2 + τ ( G p [ � ( G p M ) 2 ] 4 2 πα 0.5 E ) 2 + τ ( G p M ) 2 )(1 − 4 sin 2 θ W )(1 + R p G e,(T =1) × { ( � ( G p V ) 0 A − ( � G p E + τ G p E G n M G n M )(1 + R n V ) -0.5 M )(1 + R (0) − ( � G p E + τ G p E G s M G s V ) -1 − � ′ (1 − 4sin 2 θ W ) G p M G e A } , (2 SAMPLE -1.5 G0 A4 with -2 Zhu et al. -2.5 � − 1 τ = Q 2 � 1 + 2(1 + τ )tan 2 θ � = , , 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 4 M 2 2 Q 2 (Ge 2 ) V/ c p � ′ = � τ (1 + τ )(1 − � 2 ) , R (0) R T =1 R T =0 A A A one-quark − 0 . 172 − 0 . 253 − 0 . 551 many-quark − 0 . 086(0 . 34) 0.014(0.19) N/A total − 0 . 258(0 . 34) − 0 . 239(0 . 20) − 0 . 55(0 . 55)

ν µ + n → µ − + p ν µ + p → µ + + n , ¯ , ν e + n → e − + p ν e + p → e + + n . ¯ , Particle Lifetime (ns) Decay mode Branching ratio (%) µ + + ν µ π + 26.03 99.9877 e + + ν e 0.0123 µ + + ν µ K + 12.385 63.44 π 0 + e + + ν e 4.98 π 0 + µ + + ν µ 3.32 π − + e + + ν e K 0 51.6 20.333 L π + + e − + ν e 20.197 π − + µ + + ν µ 13.551 π + + µ − + ν µ 13.469 e + + ν e + ν µ µ + 2197.03 100.0

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