[Paper Review] Full of charm neutrino DIS

Roberto Fiore, V. R. Zoller|ArXiv.org|May 14, 2008

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper investigates charm-strange quark pair contributions in small-x neutrino deep inelastic scattering (DIS) using the color dipole framework and Double Leading Log Approximation (DLLA). It predicts a rapid rise of the longitudinal structure function $F_L^{cs}$ at small $x$ due to perturbative QCD logarithmic resummation, with significant enhancement in the CCFR/NuTeV kinematic range, while light quark $F_L^{ud}$ remains suppressed by Adler's theorem.

ABSTRACT

The color dipole analysis of small-$(x, Q^2)$ neutrino DIS induced by the charmed-strange ($cs$) current reveals ordering of dipole sizes $m_c^{-2}

Motivation & Objective

• To understand the dominance of charm-strange (cs) current contributions in small-x neutrino DIS at high energies.
• To quantify weak current non-conservation effects in charged current neutrino scattering via light-cone wave functions in the color dipole basis.
• To predict the behavior of the longitudinal structure function $F_L$ in the CCFR/NuTeV experiment using perturbative QCD resummation techniques.
• To assess the role of open charm/strangeness excitation in structure functions at small $x$ and low $Q^2$.
• To evaluate the impact of $cs$ dipole configurations on $F_2$ and $F_L$ in nuclear targets ($\nu Fe$, $\nu Pb$) using BFKL evolution.

Proposed method

• Uses the color dipole (CD) basis in high-energy QCD to describe $W^+$-boson states as superpositions of Fock states, including $|c\bar{s}\rangle$ and $|u\bar{d}\rangle$.
• Applies the Double Leading Log Approximation (DLLA) to resum $\alpha_S \log(1/x)$ logarithms, leading to enhanced $F_L^{cs}$ at small $x$.
• Models the dipole cross section $\sigma(x,r)$ via the perturbative BFKL equation with $\sigma_{pt}(r) \propto r^2 \alpha_S(r^{-2}) L(r^{-2})$, where $L(k^2) \propto \log(\alpha_S(\mu_G^2)/\alpha_S(k^2))$.
• Computes structure functions via $F_\lambda(x,Q^2) = \frac{Q^2}{4\pi^2 \alpha_W} \int dz d^2\mathbf{r} |\Psi_\lambda(z,\mathbf{r})|^2 \sigma(x,r)$, with $|\Psi_\lambda|^2$ derived from light-cone wave functions.
• Treats the $c\bar{s}$ dipole wave function as a sum of $S$-wave and $P$-wave components, with $P$-wave dominance at $Q^2 \ll m_c^2$ due to current non-conservation.
• Evaluates $F_L^{cs}$ using the Bessel function $I_2(2\sqrt{\xi})$ with $\xi = \eta L(m_c^2 + Q^2)$, where $\eta = C_A \log(x_0/x)$, to capture DLLA resummation effects.

Experimental results

Research questions

• RQ1 How do $cs$ dipole configurations contribute to the longitudinal structure function $F_L$ in small-x neutrino DIS?
• RQ2 What is the role of weak current non-conservation in generating $P$-wave $c\bar{s}$ components at low $Q^2$?
• RQ3 Why does $F_L^{cs}$ rise faster than $F_L^{ud}$ at small $x$, and how is this enhanced by perturbative QCD logarithmic resummation?
• RQ4 To what extent do $cs$ excitations dominate $F_2$ and $F_L$ in the $x \lesssim 0.01$ region of the CCFR/NuTeV experiment?
• RQ5 How do the light-cone wave functions of $W^+$-boson states affect the structure function predictions in the color dipole framework?

Key findings

• The $cs$ component of the longitudinal structure function, $F_L^{cs}$, rises rapidly toward small $x$ due to DLLA resummation of $\alpha_S \log(1/x)$ terms, with $F_L^{cs} \sim \frac{N_c C_F}{4} \frac{m_c^2}{m_c^2 + Q^2} \frac{L(m_c^2 + Q^2)}{\eta^{-1}} I_2(2\sqrt{\xi})$.
• At $Q^2 \ll m_c^2$, the $P$-wave component dominates, leading to $|\Psi_L|^2 \propto \frac{m_c^2}{Q^2} \varepsilon^2 K_1^2(\varepsilon r)$, which enhances $F_L^{cs}$ compared to the $S$-wave at low $Q^2$.
• The $S$-wave component dominates at $Q^2 \gg m_c^2$, with $|\Psi_L|^2 \propto Q^2 z^2(1-z)^2 K_0^2(\varepsilon r)$, but contributes less to $F_L^{cs}$ at low $Q^2$.
• The perturbative $F_L^{cs}$ at $Q^2 \ll m_c^2$ scales as $F_L^{cs} \sim \frac{N_c C_F}{4} \frac{m_c^2}{m_c^2 + Q^2} \frac{1}{2!} L^2(m_c^2 + Q^2)$, indicating strong logarithmic enhancement.
• The $ud$ component $F_L^{ud}$ is suppressed by Adler’s theorem, with $F_L^{ud}(x,0) \propto (1/x)^{\Delta_{\text{soft}}}$, $\Delta_{\text{soft}} \approx 0.08$, preventing similar enhancement.
• In the $x \lesssim 0.001$ and $Q^2 \lesssim m_c^2$ region, $F_2$ is dominated by $cs$ contributions, with reasonable agreement between predictions and CCFR/NuTeV data, though $F_2$ may be underestimated in the $x \gtrsim 0.01$ region due to overestimated $u\bar{d}$ short-distance contributions.