A Theoretical Study On Jet Substructures In High Energy Nuclear Collisions

Quantum chromodynamics(QCD)is the fundamental theory for describing strong interactions.One important feature of QCD is the asymptotic freedom,which states that at short distance or with large momentum transfer the interactions between quarks and gluons become weaker,the coupling constantαs(μ)is rather small and perturbative calculations are applicable.In recent years,the study of jet productions has become a very active research topic in the field of perturbative QCD.Jet is a collimated spray of energetic hadrons observed in the final-state of high-energy collisions.The Jet production in proton-proton collisions is of great importance,not only for the verification of fundamental properties of the QCD theory,but also for providing a baseline for jet productions in high-energy nuclear-nuclear reactions.In high-energy nuclear collisions,quark-gluon plasma(QGP),a new kind of de-confined QCD matter at very high temperature and density,is expected to be formed.When a parton jet traversing the QGP,it may lose energy due to jet-medium interactions,which effect is called jet quenching.The study of jet productions in high-energy nuclear collisions may shed light on jet quenching mechanism,and also be utilized to exact the properties of the QGP in relativistic heavy-ion collisions.In the thesis,we focus on the theoretical calculations of jet substructures in high-energy proton-proton and nucleus-nucleus collisions.Firstly,we calculate the original form of the semi-inclusive jet functions in different gauges based on Soft Collinear Effective Theory(SCET).SCET is an effective field theory in QCD aiming to control the infrared divergences in quantum chromodynamics(QCD)calculations that involve soft and collinear particles.we have made the calculations both in the Feynman gauge and light-cone gauge and demonstrated that the results agree with each other,which is provided as an concrete example of the gauge invariance.It is noted the calculation process in the light-cone gauge becomes simpler.Our computations give a baseline for the next-to-leading order calculation of the semi-inclusive jet functions.With these results,we derive the analytic expressions for the semi-inclusive quark jet function and the gluon jet function at the next-to-leading order in the cone algorithm,the anti-kT algorithm,the JET(Ⅰ)and the JET(Ⅱ)algorithms in detail.The analytic results obtained by this calculation can well describe the whole process from the initial parton to a jet.Afterward,when discussing different jet algorithms,we mainly take the algorithmic constraints as the starting point,and the determination of the algorithmic constraints is mainly based on the original definition of each algorithm and combined with the jet reconstruction process.We compute the analytical results of the JET(Ⅰ)and algorithms which have not been used in the experiments so far,and compare the results of the four algorithms and find that all results contain divergence terms.Finally,in order to solve the divergence problem,we use the renormalization group equation to obtain the final analytic result by subtracting and removing the singularities from the divergent integral expressions.We find that the form of the final analytical result is exactly the same as the usual time-like DGLAP evolution equation for the standard fragmentation functions,which provides a convenient way to calculate the jet fragmentation function.Secondly,We calculate the jet fragmentation function in the framework of SCET.We construct a specific form of the jet fragmentation function that not only depends on the jet function but is also related to a new function,the fragmenting jet function.We derive the analytic expressions for the semi-inclusive fragmenting jet functions in the cone algorithm,the anti-kT algorithm,the JET(Ⅰ)and the JET(Ⅱ)algorithm.We find that the results not only have UV divergence but also IR divergence.For the UV divergence,we derive the renormalization group equation for the semi-inclusive fragmenting jet function and find that the result satisfies the usual time-like DGLAP evolution equation for fragmentation functions,and for the IR divergence,we match onto standard collinear fragmentation functions,and the all results satisfy the sum rule.This provides a theoretical basis for extending our analytical results to numerical calculations as well as simplifying the computational process.such as the fragmentation functions for single hadron production in proton-proton collisions.Thirdly,in order to provide further insight into the effect of jet medium interaction on the jet substructure observables,we have studied the groomed momentum splitting fraction zg and the groomed jet angular distance between the leading and sub-leading prong θg in nucleus-nucleus collisions after different jet grooming techniques.The calculations are made with the Soft Drop and the dynamical grooming algorithms.We obtain the distributions of zg and θg in heavy-ion collisions at(?)(?)TeV by Monte Carlo simulations combined with existing energy-loss models,and compare them with recent measurements by the ALICE Collaboration.We show that the model can describe the experimental data well within the experimental error bars.Our calculations show that in nucleusnucleus collisions,the distribution of zg does not change significantly after the grooming,while θg has an enhancement in the region of small values and a depression in the region of larger values,showing a clear preference for small-angle splitting.Then we calculate numerically the corresponding zg andθg distributions under the dynamical grooming algorithm.The distribution of zg does not change significantly after grooming.We present the distribution of the observables in different momentum intervals,and show that the distribution of zg is insensitive to the momentum region in both p+p collisions and Pb+Pb collisions.However,the distribution of θg depends on the momentum region:as the momentum increases,there is a clear tendency for smaller angle splitting,and the overall distribution becomes narrowed.At last,we compare the distribution of θg in Pb+Pb collisions with these two grooming methods,and find that the distribution after dynamic grooming tends to be enhanced in the small θg region,and the distribution will be narrower.Finally,we calculate the distribution of differences between three jet axes and studied their respective medium modification effects.We consider the standard jet axis,the Soft Drop groomed axis,and the WTA axis constructed by the WTA recombination scheme.With the numerical calculations,we show that the results of the jet axis differences between the groomed jet axis and the standard axis ΔRSD-ST in proton-proton collisions can fit nicely with preliminary data by ALICE.We also give predictions for the angular difference between the WTA axis and the standard axis ΔRWTA-ST,as well as the angular difference between the WTA axis and the Soft Drop groomed axis ＠RWTA-SD.Then,we study the distributions of ΔRSD-ST,ΔRWTA-ST,and ΔRWTA-SD in heavy ion collisions,and observe thatΔRSD-ST distribution in Pb+Pb is overall shifted toward the region with a large angle as compared to that in proton-proton collisions,as a result of more soft radiation being removed.Since the soft radiation is not sensitive to the determination of the WTA axis,in the medium modification,the standard axis moves closer to the direction of the WTA axis due to energy loss inside the jet,leading to a shift ofΔRWTA-ST distribution towards the small value.The energy loss effect in three choices of the jet axis is also discussed.