Simulation studies of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>η</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>φ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>η</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>φ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> correlation functions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:math> collisions with the PYTHIA and HERWIG models

We report studies of charge-independent (CI) and charge-dependent (CD) two-particle differential-number correlation functions, ${\mathrm{R}}_{2}\left(\mathrm{\ensuremath{\Delta}}\ensuremath{\eta},\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}\right)$, and transverse momentum (${\mathit{p}}_{\mathrm{T}}$) correlation functions, ${\mathrm{P}}_{2}\left(\mathrm{\ensuremath{\Delta}}\ensuremath{\eta},\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}\right)$, of charged particles in $\sqrt{\mathit{s}}=2.76\phantom{\rule{0.16em}{0ex}}\mathrm{TeV}$ pp collisions with the PYTHIA and HERWIG models. Model predictions are presented for inclusive charged hadrons (${h}^{\ifmmode\pm\else\textpm\fi{}}$), as well as pions (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$), kaons (${\mathrm{K}}^{\ifmmode\pm\else\textpm\fi{}}$), and (anti-)protons ($\overline{\mathrm{p}}$/p) in the ranges $0.2&lt;{\mathit{p}}_{\mathrm{T}}\ensuremath{\le}2.0\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}/\mathit{c}$, $2.0&lt;{\mathit{p}}_{\mathrm{T}}\ensuremath{\le}5.0\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}/\mathit{c}$, and $5.0&lt;{\mathit{p}}_{\mathrm{T}}\ensuremath{\le}30.0\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}/\mathit{c}$, with full azimuthal coverage in the range $|\ensuremath{\eta}|&lt;1.0$. We compare the model predictions for the strength and shape of the ${\mathrm{R}}_{2}$ and ${\mathrm{P}}_{2}$ correlators as these pertain to recent measurements by the ALICE collaboration. The ${\mathrm{R}}_{2}$ and ${\mathrm{P}}_{2}$ correlation functions estimated with PYTHIA and HERWIG exhibit qualitatively similar near-side and away-side correlation structures but feature important differences. Our analysis indicates that comparative studies of ${\mathrm{R}}_{2}$ and ${\mathrm{P}}_{2}$ correlation functions would provide valuable insight towards the understanding of particle production in pp collisions, and by extension, should also be useful in studies of heavy-ion collisions. Comparison of the $\mathrm{\ensuremath{\Delta}}\ensuremath{\eta}$ dependence of ${\mathrm{R}}_{2}$ and ${\mathrm{P}}_{2}$ could contribute, in particular, to a better understanding and modeling of the angular ordering of particles produced by hadronization in jets, as well as a better description of jet fragmentation functions of identified species at low momentum fraction $(z)$.