Study of Open Charm Mesons Productions in Proton-Lead Collisions at LHCb

Quantum chromodynamics (QCD) is a basic theory to describe the strong interaction between quarks and gluons. In relativistic heavy ion collisions, quarks and gluons originally bound in neutrons and protons are deconfined to form a strong coupling QCD matter: quark gluon plasma (QGP). The heavy flavor hadrons produced in the collision are excellent probes for the state of QGP: the production suppression of high transverse momentum heavy flavor hadrons is helpful to quantitatively understand the QGP and the transport properties of heavy flavor quarks in QGP; The ratio of strange charm hadron to non-strange charm hadron is also helpful to understand the production mechanism of heavy flavor hadrons and the strangeness enhancement in QGP during hadronization. However, cold nuclear matter (CNM) effects can also affect the production of final heavy flavor hadrons in heavy ion collisions, such as the modification of nuclear parton distribution functions (nPDFs). It is generally believed that the proton-lead ($p$Pb) collision is an ideal platform for studying the effects of cold nuclear matter because the space-time scale is too small to create QGP. CNM effects such as nPDFs can be constrained quantitatively by measuring the final heavy flavor hadron production. In addition, in 2017, ALICE experiment observed for the first time the production enhancement of light strange hadrons in high multiplicity proton-proton collisions, which means that there is an enhancement mechanism for $s$ quark in small systems with high multiplicity. Looking for the enhancement of strange charm hadron yield in high multiplicity $p$Pb collisions is also of great scientific significance for understanding the mechanism of strangeness enhancement and charm hadron production in this small system. In 2016, the LHCb detector collected $p$Pb collision data with an integrated luminosity of about $30.75\invnb $and $\sqrt{s_{\mathrm{NN}}}=8.16$TeV. Using these data, this thesis measured the double differential cross sections of the forward prompt $D^+_s$ and $D^+$ in $p$Pb collision, covering the forward rapidity region of $1.5 < y < 4.0$ and the backward rapidity region of $-5.0 < y < -2.5 $, and the transverse momentum range of $1 < \pt < 13 $GeV/$c $. Based on these results, the nuclear modification factor and the forward-backward ratio are calculated, and the influence of CNM effect on the open charm meson cross section is studied. In addition, this thesis also measured $D^+_s/D^+$ cross section ratio, and the variation of this ratio with multiplicity in different transverse momentum and rapidity intervals is studied. The measurements of the nuclear modification factor and the forward-backward ratio show that there is an obvious CNM effect in $p$Pb collision at 8.16TeV. Compared with the $pp$ collision, the differential cross sections of $D^+_s$ and $D^+$ are significantly depressed in the forward rapidity interval, which is in good agreement with the theoretical calculations of nPDF and CGC, suggesting that there is a nuclear shadowing effect in the small momentum fraction $x$. The suppression effect in the backward section is not obvious, suggesting that there may be a nuclear anti-shadowing effect in the middle momentum fraction $x$. However, in the backward high transverse momentum region, there are differences between the nuclear modification factor and the forward-backward ratio and the nPDF theoretical calculation, which indicates that there may be unknown nuclear matter effects in the backward region of $p$Pb collision. It is also found for the first time that $D^+_s/D^+$ cross-section ratio increases significantly with the increase of multiplicity, and the increasing trend in the backward low transverse momentum (12.6$\sigma$) is more significant than that in the high transverse momentum (4.9$\sigma$). This finding indicates that there is also a significant strangeness enhancement in charm quark hadronization in high multiplicity $p$Pb collisions, and there is an urgent need for theory to explain this enhancement mechanism.