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

▶
neutral current weak form factors neutrino scattering
SMART_READER_LITE
LIVE PREVIEW

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

Mar 17, 2023 273 likes •454 views

Neutral Current Weak Form Factors & Neutrino Scattering Raza Sabbir Sufian USQCD All Hands Meeting 2018 Neutrino-Nucleon Neutral Current Elastic Scattering ( q 1 , 1 ) ( q 2 , 2 ) + p + p Z 0 ( q ) + p +

slide-1
SLIDE 1

Neutral Current Weak Form Factors & Neutrino Scattering

Raza Sabbir Sufian

USQCD All Hands’ Meeting 2018

slide-2
SLIDE 2

Neutrino-Nucleon Neutral Current Elastic Scattering

Matrix element in V-A structure of leptonic current

ν + p → ν + p ¯ ν + p → ¯ ν + p,

M = i 2 p 2GF ¯ ν(q2)γµ(1 γ5)ν(q1) | {z }

leptonic current

hN(p2)|Jµ

Z|N(p1)i

| {z }

hadronic current

.

Z0(q) ν(q1, σ1) ν(q2, σ2) N(p1, κ1) N(p2, κ2)

hN(p2)| Jµ

Z |N(p1)i = ¯

u(p2)[F Z

1 (Q2) + F Z 2 (Q2)iσµνqν

2MN + F Z

A (Q2)γµγ5]u(p1)

slide-3
SLIDE 3

(Anti)Neutrino-Nucleon Scattering Differential Cross Section

d dQ2 G2

F

2 Q2 E2

  • A BW CW2;

W 4E=Mp ;

A 1

4fGZ A21FZ 1 2 FZ 2 214FZ 1 FZ 2 g;

B 1

4GZ AFZ 1 FZ 2 ;

C 1 64 GZ

A2 FZ 1 2 FZ 2 2:

Neutral Weak Dirac & Pauli FFs Weak axial FF

slide-4
SLIDE 4

Calculation of F1Z and F2Z

F Z,p

1,2 =

✓1 2 sin2 θW ◆ (F p

1,2(Q2) F n 1,2(Q2)) sin2 θW(F p 1,2 + F n 1,2) F s 1,2

2

Ye, Arrington, Hill, Lee

RSS, Yang, Alexandru, Draper, Liang, Liu

PL B 777 (2018) 8-15 PRL 118, 042001 (2017)

Nucleon EMFF from Model Independent z-expansion

Strange EMFF from Lattice QCD

Physical point 4 lattice spacings 3 volumes

slide-5
SLIDE 5

Inputs for Previous Neutral Weak EMFFs

PRD 95, 014011(2017) RSS, de Teramond, Brodsky, Dosch, Deur

Strange EMFF Nucleon EMFF (total)

PRL 2018 de Teramond, Liu, RSS, Brodsky, Dosch, Deur

slide-6
SLIDE 6

ffiffiffi

Calculation of Neutral Weak EMFFs

PRD 96, 093007 (2017) RSS

Radiative corrections for e-p scattering

GZ,p(n)

E,M (Q2) = 1

4  (1−4 sin2 ✓W )(1+Rp(n)

V

)Gγ,p(n)

E,M (Q2)

−(1+Rn(p)

V

)Gγ,n(p)

E,M (Q2)− Gs E,M(Q2)

slide-7
SLIDE 7

*Use MiniBooNE data (0.27 < Q2 < 0.65 GeV2)

Reason 1: Uncertainty in GsE,M becomes very large and values consistent with zero

Reason 2: Nuclear effect can be large for at low Q2

Determination of Neutral Current Weak Axial FF

C ~ 1

[ ]

slide-8
SLIDE 8

GZA (0) = - 0.751 (56) Mdipole = 0.95(6) GeV

dσ dQ2 From MiniBooNE Experiment

)(F p

1,2

− F n

1,2)}

From Experiment

  • − F s

1,2

From Lattice QCD

Determination of Neutral Current Weak Axial FF

In preparation with Keh-Fei Liu & David Richards

slide-9
SLIDE 9

Impact of Lattice QCD Strange EMFF

Possibility: Since strange quark contribution is small set

=0

(??)

(0))Gs E,M(

Discrepancy !!

=0

(0))Gs E,M(

X

X

slide-10
SLIDE 10

Reconstruction of Differential Cross Sections

BNL E734 data was NOT used in the analysis Nuclear effects Pauli blocking & nuclear shadowing at Q2 < 0.15 GeV2

slide-11
SLIDE 11

GZ

A 1 2GCC A Gs A;

= - 0.23(11)

Estimate of GsA(0)

Gs

A(0)

This Calculation

GZ

A(0) = −0.751(56)

GCC

A (0) = 1.2723(23)

Other Calculations

MiniBooNE, PRD 82 (2010) Gs

A(0) = 0.08(26)

BNL E734, PRC 48 (1993)

0.1 0.2 0.3 0.4 0.5 mπ (GeV) −0.18 −0.16 −0.14 −0.12 −0.10 −0.08 −0.06 −0.04 −0.02 0.00 gs

A

QCDSF Engelhardt ETMC CSSM and QCDSF/UKQCD LHPC χQCD Phenomenology (JAM15) Phenomenology (JAM17) Phenomenology (NNPDFpol1.1)

From Jeremy Green’s Talk

Gs

A(0) = - 0.21(10)

slide-12
SLIDE 12

Precise estimate of NC weak axial form factor GZA

Summary

Strange quark contribution cannot be ignored

Reconstruction of (anti)neutrino- nucleon diff. cross sections with correct prediction of GZA and lattice input of GsE,M

Lattice QCD calculation of GsA in the continuum and infinite volume limit with controlled systematic uncertainties required

slide-13
SLIDE 13

An Example: LQCD Constraint on Models

Many models of meson-baryon fluctuations to study s(x)-s(x) asymmetry

In Preparation

slide-14
SLIDE 14

EPJ Web Conf. 66 (2014) 06018

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

  • 1
  • 0.5

0.5

  • 1
  • 0.5

0.5

s A

G

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

  • 0.2

0.2 0.4

  • 0.2

0.2 0.4

s M

G

)

2

(GeV

2

Q 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

  • 0.2

0.2

  • 0.2

0.2

s E

G

Pate, et al

TABLE II. Two solutions for the strange form factors at Q2 0:5 GeV2 produced from the E734 and HAPPEX data. Solution 1 Solution 2 Gs

E

0:02 0:09 0:37 0:04 Gs

M

0:00 0:21 0:87 0:11 Gs

A

0:09 0:05 0:28 0:10

[13] S.F. Pate, Phys. Rev. Lett. 92, 082002 (2004), [14] D. Armstrong, R. McKeown, Ann.Rev.Nucl.P

Q2 = 0.5 GeV2

slide-15
SLIDE 15

Weak Axial FF form e-p scattering

Ap

PV = − GF Q2

4 √ 2πα 1 [(Gp

E)2 + τ(Gp M)2]

× {((Gp

E)2 + τ(Gp M)2)(1 − 4 sin2 θW )(1 + Rp V )

− (Gp

EGn E + τGp MGn M)(1 + Rn V )

− (Gp

EGs E + τGp MGs M)(1 + R(0) V )

− ′(1 − 4sin2θW )Gp

MGe A} ,

(2 with τ = Q2 4M 2

p

, =

  • 1 + 2(1 + τ)tan2 θ

2 −1 , ′ =

  • τ(1 + τ)(1 − 2) ,

RT =1

A

RT =0

A

R(0)

A

  • ne-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)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

  • 2.5
  • 2
  • 1.5
  • 1
  • 0.5

0.5

Ge,(T =1)

A

Q2 (Ge V/ c

2)

G0 A4 Zhu et al. SAMPLE

slide-16
SLIDE 16

Particle Lifetime (ns) Decay mode Branching ratio (%) π+ 26.03 µ+ + νµ 99.9877 e+ + νe 0.0123 K+ 12.385 µ+ + νµ 63.44 π0 + e+ + νe 4.98 π0 + µ+ + νµ 3.32 K0

L

51.6 π− + e+ + νe 20.333 π+ + e− + νe 20.197 π− + µ+ + νµ 13.551 π+ + µ− + νµ 13.469 µ+ 2197.03 e+ + νe + νµ 100.0

νµ + n → µ− + p , ¯ νµ + p → µ+ + n , νe + n → e− + p , ¯ νe + p → e+ + n .

slide-17
SLIDE 17

9