[Paper Review] The relative yields of heavy hadrons as function of transverse momentum at LHC experiments

A. Berezhnoy, А. К. Лиходед|arXiv (Cornell University)|Sep 8, 2013

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper investigates the transverse momentum ($p_T$) dependence of relative yields of heavy hadrons—specifically $f_{s}/f_{d}$, $f_{ar{B}_c}/f_B$, and $f_{\Lambda_b}/f_B$—at the LHC, challenging the assumption of constant yields across $p_T$. It argues that fragmentation models fail at low $p_T$, where nonfragmentation mechanisms (e.g., $1/p_T^6$-suppressed contributions) dominate, especially for $B_c$ mesons. The key result is that $f_{s}/f_{d}$ is expected to plateau at high $p_T$, while $f_{\bar{B}_c}/f_B$ decreases rapidly with $p_T$ and shows no plateau, highlighting the need for precise $p_T$-resolved measurements to disentangle production mechanisms.

ABSTRACT

It is shown that the dependence of ratio $f_s/f_d$ could be understood within the fragmentation approach. However, the validity of fragmentation model is questionable at low $p_T$, and contributions of nonfragmentation mechanisms are possible. It is demonstrated, that the precise measurements of $p_T$ dependence of $f_s/f_d$, $f_{Λ_b}/f_{B}$ and analogous values as function of $p_T$ can essentially improve our understanding of heavy hadron production.At large $p_T$ a plateau is expected in $f_s/f_d$ distribution. Contrary, a plateau is not expected in $f_{B_c}/f_{B}$ distribution on $p_T$.

Motivation & Objective

• To understand the $p_T$ dependence of relative yields of beauty and charmed hadrons at LHC, challenging the assumption of constant yields across transverse momentum.
• To assess the validity of the fragmentation model for heavy hadron production at low and medium $p_T$, where nonperturbative and nonfragmentation contributions may dominate.
• To quantify the expected shape of $f_{\bar{B}_c}/f_B$ and $f_s/f_d$ ratios as functions of $p_T$ to guide future LHC measurements.
• To demonstrate that precise $p_T$-resolved measurements of these ratios are essential for accurately estimating rare decay branching ratios, such as $B_s \to \mu^+\mu^-$.

Proposed method

• Uses leading-order perturbative QCD (pQCD) calculations for subprocesses like $gg \to B_c + X$ to estimate $B_c$ production cross sections at various $p_T$ values.
• Applies the FONLL (Fixed-Order plus Next-to-Leading Logarithmic) approach to compute $B$-meson cross sections, using a web-based FONLL calculator for consistency.
• Models the $p_T$ dependence of fragmentation and nonfragmentation contributions: fragmentation scales as $1/p_T^4$, while recombination/nonfragmentation mechanisms scale as $1/p_T^6$.
• Compares contributions from fragmentation-type diagrams ($A_3$) and recombination-type diagrams ($A_1$, $A_2$) in $gg \to B_c + X$ processes, noting their interference and gauge dependence.
• Uses the ratio $f_{H}/f_B = \sigma_H / \sigma_B$ to define relative yields, with $\sigma_H$ derived from pQCD and $\sigma_B$ from FONLL, varying renormalization and factorization scales ($\mu_R$, $\mu_F$) to assess uncertainty.
• Analyzes the $p_T$-dependence of $f_{\bar{B}_c}/f_B$ using multiple scale choices (e.g., $\mu_R = \mu_F = 10$ GeV, $\mu_R = \mu_F = \sqrt{s_{gg}}/4$) to test robustness of predictions.

Experimental results

Research questions

• RQ1 Does the fragmentation model accurately describe the $p_T$ dependence of $f_s/f_d$ across the LHC $p_T$ range?
• RQ2 What is the expected $p_T$ behavior of the $f_{\bar{B}_c}/f_B$ ratio, and does it exhibit a plateau at high $p_T$?
• RQ3 How significant are nonfragmentation contributions (e.g., $1/p_T^6$) to $B_c$ and other heavy hadron production at experimentally accessible $p_T$ values?
• RQ4 Can $p_T$-resolved measurements of $f_s/f_d$, $f_{\Lambda_b}/f_B$, and $f_{\bar{B}_c}/f_B$ distinguish between fragmentation and recombination mechanisms?

Key findings

• The $f_s/f_d$ ratio is expected to exhibit a plateau at high $p_T$, consistent with the dominance of fragmentation mechanisms in this regime.
• The $f_{\bar{B}_c}/f_B$ ratio is predicted to decrease rapidly with increasing $p_T$, with no plateau expected, due to the $1/p_T^6$ suppression of nonfragmentation contributions.
• Nonfragmentation mechanisms (e.g., $gg \to B_c + X$) dominate at low and medium $p_T$ for $B_c$ production, with contributions scaling as $1/p_T^6$, while fragmentation scales as $1/p_T^4$.
• The fragmentation model is questionable at low $p_T$, and precise $p_T$-dependent measurements of relative yields are essential to probe nonfragmentation contributions.
• The $p_T$-dependence of $f_{\bar{B}_c}/f_B$ is qualitatively robust across different scale choices ($\mu_R$, $\mu_F$), though quantitative values are uncertain due to theoretical uncertainties in $B_c$ cross sections.
• The recombination mechanism, though not gauge-invariant alone, contributes significantly at low $p_T$ and behaves like $1/p_T^6$, similar to nonfragmentation contributions.