Low-energy elastic (anti)neutrino−nucleon scattering in covariant baryon chiral perturbation theory

doi:10.1007/s11467-024-1417-4

Front. Phys.

2024, Vol. 19

Issue (6) : 64202 https://doi.org/10.1007/s11467-024-1417-4

Low-energy elastic (anti)neutrino−nucleon scattering in covariant baryon chiral perturbation theory

Jin-Man Chen¹, Ze-Rui Liang¹, De-Liang Yao^1,^2,³(

)

¹. School of Physics and Electronics, Hunan University, Changsha 410082, China
². Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, Hunan University, Changsha 410082, China
³. CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

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Abstract

The low-energy antineutrino- and neutrino−nucleon neutral current elastic scattering is studied within the framework of the relativistic SU(2) baryon chiral perturbation theory up to the order of $O (p 3)$ . We have derived the model-independent hadronic amplitudes and extracted the form factors from them. It is found that differential cross sections $d σ / d Q 2$ for the processes of (anti)neutrino−proton scattering are in good agreement with the existing MiniBooNE data in the $Q 2$ region $[0.13, 0.20]$ GeV², where nuclear effects are expected to be negligible. For $Q 2 ≤ 0.13$ GeV², large deviation is observed, which is mainly owing to the sizeable Pauli blocking effect. Comparisons with the simulation data produced by the NuWro and GENIE Mento Carlo events generators are also discussed. The chiral results obtained in this work can be utilized as inputs in various nuclear models to achieve the goal of precise determination of the strangeness axial vector form factor, in particular when the low-energy MicroBooNE data are available in the near future.

Keywords chiral perturbation theory neutrino−nucleon scattering form factors chiral Lagrangians one-loop amplitude neutral weak current

Corresponding Author(s): De-Liang Yao

Issue Date: 19 June 2024

Cite this article:

Jin-Man Chen,Ze-Rui Liang,De-Liang Yao. Low-energy elastic (anti)neutrino−nucleon scattering in covariant baryon chiral perturbation theory[J]. Front. Phys. , 2024, 19(6): 64202.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-024-1417-4
https://academic.hep.com.cn/fop/EN/Y2024/V19/I6/64202

Fig.1 Kinematics of neutral current elastic neutrino-nucleon scattering under the one-boson exchange approximation.

Physical process	$C 3$	$C 0$

$ν + p → ν + p$	1	1
$ν ¯ + p → ν ¯ + p$	1	1
$ν + n → ν + n$	$− 1$	1
$ν ¯ + n → ν ¯ + n$	$− 1$	1

Tab.1 Isospin factors for physical processes.

Fig.2 Tree-level Feynman diagrams up to and including

O (p 3)

. The solid, dashed and wavy lines represent the nucleon, pions and the

Z

boson, in order. The circled numbers indicate the chiral orders of the vertices.

Fig.3 One-loop Feynman diagrams up to and including

O (p 3)

. The solid, dashed and wavy lines represent the nucleon, pions and the

Z

boson, in order. The circled numbers indicate the chiral orders of the vertices.

	LEC	Value	Source

$L π N (1)$	$g$	$1.13 ± 0.01$	$G A$ [53]
$L π N (2)$	$c 6$	$1.35 ± 0.04$	$κ p$ and $κ n$ [12, 43]
	$c 7$	$− 2.68 ± 0.08$	$κ p$ and $κ n$ [12, 43]
$L π N (3)$	$d 6$	$0.0 ± 1.0$	−
	$d 7$	$− 0.49$	Electromagnetic radii [26]
	$d 16$	$− 0.83 ± 0.03$	$G A$ [53]
	$d 22$	$0.96 ± 0.03$	$G A$ [53]

Tab.2 Values of the LECs involved in neutrino−nucleon NCE scattering. The axial coupling constant

g

is dimensionless. The LECs

c i

and

d j

are in units of GeV⁻¹ and GeV⁻², respectively.

Fig.4 Differential cross section

d σ / d Q 2

ν

−

p

NCE scattering, with the neutrino energy being

E ν = 0.8

GeV. The MiniBooNE data [4, 5] are marked by black dots with error bars. The NuWro data for free nucleon, bound nucleon with and without Pauli blocking effect are represented by orange diamonds, red crosses and green triangles in order. The blue solid line denotes the ChPT result up to

O (p 3)

, while the magenta dashed line stands for the sum of our ChPT prediction and Pauli blocking effect. The error bands are obtained by varying the LECs in their 1−

σ

uncertainties. We use the abbreviation “PBE” for “Pauli blocking effect” in the figure.

Fig.5 Differential cross section

d σ / d Q 2

ν ¯

−

p

NCE scattering, with the anti neutrino energy being

E ν ¯ = 0.65

GeV. Other description is the same as Fig.4.

Fig.6 Differential cross sections

[d σ / d Q 2] ν n → ν n

with

E ν = 0.8

GeV and

[d σ / d Q 2] ν ¯ n → ν ¯ n

with

E ν ¯ = 0.65

GeV. The ChPT and NuWro simulation results are represented by solid lines and blue diamonds, respectively. The red error bands are obtained by varying the LECs in their 1−

σ

uncertainties.

Fig.7 Contour plot of

Q 2

with varying

E ν

and

cos ? θ

Fig.8 Total cross sections at different chiral orders. Our ChPT prediction is expected to be reliable up to

E ν (ν ¯) m a x = 0.28

GeV, indicated by the gray vertical line. For comparison, the simulation data produced by NuWro and GENIE events generators are also shown by red crosses and black diamonds, respectively.

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