Benchmark MC and Theoretical Calculations of $\nu_\mu$ Reactions

    Warning

• You are not required to do all benchmark calculations listed below, but please try to do as many as possible. Any number of the calculations and any portion of the calculations are acceptable. For example, showing the quasi-elastic contibution alone is acceptable for the benchmark calculation 1, if you are not set up to calculate the entire inclusive cross section.
• Use the parameter values specified below, and do not use your favorite values even if you would consider yours to be better. The objective of the benchmark calculations is a calibration of the instruments, your MC codes and theoretical methods, and the use of the common parameter values is thus vital.

   Guidelines

• Make the binning size as small as possible.
• Draw straight plots (neither semi-log, nor log plots, unless specified).
• Use the neutrino-nucleon cross section as specified below.

1. ${}^{16}{\rm O}(\nu_\mu,\mu^-)$ Inclusive.

(Relevant to Panel Discussions 1 and 2)

Main:

(Three figures)
$(d^2\sigma)/(4\pi d(\cos\theta_\mu)d E_\mu)$ at $\theta_\mu = 30{}^o$ for $E_\nu =$ 0.5, 1.0, and 5.0 GeV as a function of $E_\nu - E_\mu$ from 0 to 500 MeV, also showing a curve for the quasi-elastic contribution in each figure.
(Please draw semi-log plots for 5.0 GeV.)

Suppl.:

a.

(Three figures)
$(d\sigma)/(d E_\mu)$ for $E_\nu =$ 0.5, 1.0, and 5.0 GeV as a function of $E_\mu$ from 0 to 1.0 GeV, also showing a curve for the quasi-elastic contribution in each figure.

b.

(Three figures)
$(d\sigma)/(4\pi d\cos\theta_\mu)$ for $E_\nu =$ 1.0 and 2.0 GeV as a function of $\cos\theta_\mu$ from 1 to -1, also showing a curve for the quasi-elastic contribution in each figure.

2. ${}^{16}{\rm O}(\nu_\mu,\mu^-p)$ Semi-inclusive

(Relevant to Panel Discussion 1 and 2)

a.

(Two figures)
$(d\sigma)/(d^3p_p)$ (with $\vec{k}_\mu$ integrated) at $\theta_p =$ 60${}^o$ for $E_\nu =$ 1.0 and 2.0 GeV as a function of $\vert\vec{p}_p\vert$ from 0 to 500 MeV/c, also showing a curve for the quasi-elastic contribution in each figure.

b.

(Two figures)
$(d\sigma)/(d^3p_p)$ (with $\vec{k}_\mu$ integrated) at $\vert\vec{p}_p\vert=$ 500 MeV for $E_\nu =$ 1.0 and 2.0 GeV as a function of $\theta_p$from 0 to 90${}^o$, also showing a curve for the quasi-elastic contribution in each figure.

3. ${}^{16}$O and/or ${}^{56}$Fe Pion production

(Relevant to Panel Discussion 3)
(The number of the figures indicated below is for each of ${}^{16}$O and ${}^{56}$Fe)

Main:

a.

[Two figures = 1 fig. (for nucleus) + 1 fig. (for neutron)]
Pion multiplicity
as a function of $E_\nu$ from 0.5 GeV to 5.0 GeV for $\nu_\mu$ -nucleus and -neutron reactions.

b.

[Two figures = 1 fig. (for nucleus) + 1 fig. (for neutron)]
Average pion energy (per pion)
as a function of $E_\nu$ from 0.5 GeV to 5.0 GeV for $\nu_\mu$ -nucleus and -neutron reactions.

Suppl.:

a.

[Eight figures
= 2 figs. (for nucleus and neutron)
$\times$ 2 figs. (for the directiuon and magnitude)
$\times$ 2 figs. (30 MeV/c and 50 MeV/c cut-off)]
Hadron emission momentm vector (direction and magnitude)
as a function of $E_\nu$ from 0.5 GeV to 5.0 GeV for $\nu_\mu$ -nucleus and -neutron reactions. [The vector is defined to be the weighted average of all emitted hadron (nucleons and mesons) momenta above the 30 MeV/c and 50 MeV/c cut-offs.]

b.

(Twelve numbers)
The above main a. and b. and the supplemental a. at 10 GeV/c.

$\nu$ - Nucleon Cross Section Parameters

$$G_F \cos \theta_c = 1.14 \times 10^{-5} \,{\rm GeV}^{-2}$$

$$M_V^2 = 0.71 \, {\rm GeV}^2$$

$$g_A = -1.26$$

$$M_A = 1.03 \, {\rm GeV}.$$

$$1 + \mu_p -\mu_n = 4.71 \, ({\rm nuclear \,\,magneton})$$

Also set

$$F_p(q) = 0. \nonumber$$

The neutrino-neutron cross section ${d\sigma}/dt$ is given by, e.g., C. H. Llewellyn Smith, Physics Report 3 no. 5 (1972) pp300-, Subsection 3.3 -A & B.

back to MAIN Last modified: Wed Oct 17 14:40:00 JST 2001