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Charming , Beautiful Bottom, and - Plasma in the Large Collider Era

Santosh K. Das1 and Raghunath Sahoo2

The primordial of and , which filled our universe just after few micro-seconds of its creation through Big Bang, is expected to be created in the laboratory by colliding nuclei at relativistic energies. The ongoing nuclear collision programs at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) are two experimental facilities, where matter in the state of Quark-Gluon Plasma (QGP) can be created and characterized. Heavy quarks, mainly charm and bottom quarks, are considered as novel probes to characterize QGP, and hence the QCD matter. Heavy quark diffusion coefficients play a significant role to understand the properties of QCD matter. Experimental measurements of nuclear suppression factor and elliptic flow are able to constrain the heavy quark diffusion coefficients, which is a key ingredient for the phenomenological study and disentangle different energy loss models. We give a general perspective of heavy quark diffusion coefficient in QGP and discuss its potential as a probe to disentangle different hadronization mechanisms, as well as to probe the initial electromagnetic field produced in non-central collisions. Experimental perspective on future measurements are discussed with special emphasis on heavy-flavors as next generation probes.

Key Words: Big Bang, quark gluon plasma, heavy-ion collisions, heavy flavors

The second half of twentieth century was a energy interactions in cosmic rays and tremendous success in physics accelerators. Although the free existence of through the discovery of of these fundamental like quarks and by Murray Gell-Mann and George the force carrier of - the Zweig, the of Particle gluons is not observed because of Physics by Glashow, Salam and Weinberg confinement property of strong interaction, (and many others) through unification of the quest to create a matter with partonic fundamental forces. The endeavours in degrees of freedom has been a frontier of basic science, while looking for the research since decades. For an illustration, fundamental constituents of matter, have Fig. 1 shows the confinement of quarks contributed immensely to the developments inside hadrons and quark matter consisting in particle detection and accelerator of deconfined colored quarks and gluons. technologies, which have given direct and indirect social benefits of colossal nature. Theoretical calculations based on lattice As the present day understanding of QCD (lQCD) predict that hadronic matter constituents of matter, we have 6-quarks, 6- at high temperatures and densities dissolves , their and the force into a deconfined state of quarks and gluons carriers. However, among these, we only - called Quark Gluon Plasma (QGP)1. In encounter the light quarks – up and down, this state, hadrons like and and in normal nuclear matter. , which form the normal matter Other heavy particles are created in high- around us, lose their identity and their

1 Santosh K. Das is at Indian Institute of Technology Goa, India, Email: [email protected] 2 Raghunath Sahoo, FInstP is at Indian Institute of Technology Indore, India, Email: Raghunath.Sahoo@.ch (Corresponding Author)

1 constituents -- quarks and gluons, can move up, down and strange quarks, which are freely in this plasma. The major goals of the taken as light quarks (flavors). Although ongoing nucleus-nucleus collision charm, bottom and top are considered as programmes at Relativistic Heavy Ion heavy-quarks, because of huge mass of top Collider (RHIC) at the Brookhaven National Laboratory, USA and the Large quark and its low production cross section, Hadron Collider (LHC) at CERN, it is not considered for the present Switzerland at Giga and Terra volt discussions. energies are to create and characterize QGP in the laboratory. This state of matter is found to behave like a nearly perfect fluid having a remarkably small value of shear viscosity to entropy density ratio. QGP is believed to be the primordial matter formed at the infancy of our universe just after few micro-seconds of the creation of the universe through Big Bang. This primordial matter of quarks and gluons, because of large concentration of energy and high temperature, expands with time (like an Fig.1: Pictorial representation of expanding fireball) through various confinement of quarks inside hadrons complex processes. These processes (, etc.) and the deconfined include, formation of composite hadrons quark matter called quark-gluon plasma. 25 out of quarks and gluons, called Figure courtesy . hadronization (corresponding to a system temperature, which marks the quark-hadron phase transition: deconfinement transition); chemical freezeout, where the particle abundancies are frozen (inelastic collision stops) and kinetic freeze-out (ceasing of elastic collisions) followed by free streaming of the secondary particles to reach the detectors sitting all around the interaction point of the nuclear collisions in the experimental area. The study of the properties of QGP is a field of high contemporary interest and remarkable progress has been made in the last decades Fig.2: Pictorial representation of three towards the understanding of the properties generations of quarks and their masses. of strongly interacting Quark Gluon Plasma. In this article, we shall focus on Heavy quarks2,3,4, mainly charm and heavy flavour particles as a powerful probe bottom quarks, thanks to their large masses, of this primordial matter and their enriched are considered as novel probes to measurements at the LHC energies in view characterize the properties of QGP phase. of the upgrade programmes. First of all they are created in hard processes which are accessible to A pictorial representation of three perturbative QCD (pQCD) calculations and generations of quarks and their masses are therefore, their initial distribution is theoretically known and could be verified given in Fig. 2 for illustration. The masses by experiments. They are produced in the of charm and bottom quarks are higher than

2 early stages of the collisions and witness the element. The heavy quarks drag, and entire space-time evolution of QGP phase momentum diffusion coefficients are and can act as an effective probe of the related through the fluctuation-dissipation created matter. The spectra of the heavy theorem (FDT), Dp=M γ T. Here T is the quarks are too hard to come to equilibrium temperature of the thermal bath and M is with the QGP phase during the expansion. the HQ mass. The spatial diffusion Therefore, the heavy quark momentum coefficient, Ds, can be calculated from the spectra carry the information of their diffusion coefficients in momentum space 2 interaction with the plasma constituents in the static limit (p → 0): Ds=T /Dp. The during the expansion and hence, the plasma major aim of all the theoretical studies are properties. Heavy quarks (HQ), as colored to extract the heavy quark spatial diffusion objects, interact strongly with the plasma coefficients (Ds), which quantify the constituents and their momentum spectra interaction of heavy quarks with the are strongly modified. This is expressed by medium, that is directly related to the 5,6 the nuclear suppression factor , RAA(pT), thermalization time and can be evaluated the ratio of the measured heavy quarks using lattice QCD. The Ds, Ds=T/M* γ (in momentum spectra (yields) in nucleus- the limit of momentum, p → 0), is directly nucleus to proton-proton collisions, related to the heavy quark drag coefficient rescaled by the number of binary collisions. γ. Drag coefficient appearing in Ds is If there were no interactions with the QGP expected to scale with the mass, hence, (as well as no cold nuclear matter effects provides a measure of the QCD interaction like shadowing) one would indeed find RAA ideally independent of the mass of the = 1. Another observable is the elliptic quark. One can estimate the heavy quark 7,8 -1 flow , v2(pT ) = < cos(2Φ) >. It is a thermalization time, τth= γ (p→0) by: measure of the anisotropy in the angular 2 distribution of the produced heavy τth=M/2πT (2 π TDs) as a response to the initial anisotropy in coordinate space in non-central nucleus- A simultaneous description of both RAA(pT) nucleus collisions, transferred by the bulk and v2(pT) is a top challenge to all the to the heavy quarks. theoretical models and is known as “heavy quark puzzle”. Several theoretical efforts have been made to study RAA and v2 of the heavy quarks Before the first experimental results, it was measured in experiments within the Fokker expected that HQ interaction with the QGP Planck (FP) approach and the relativistic medium could be characterized by means of Boltzmann approach. Heavy quarks drag perturbative QCD, which led to the (γ) and momentum diffusion coefficients expectations of a smaller modification of (Dp) are the key inputs, to solve the FP their spectra and a small v2. However, the equation to study the momentum evolution first observations of non-photonic electrons of heavy quarks in QGP medium to coming from heavy decays compute its RAA and v2, which contain the measured at the highest RHIC energy have microscopic details mentioning how the shown a surprisingly large modification of heavy quarks interact with the hot QGP their spectra and a quite large v2, indicating medium. Heavy quark drag coefficient is quite strong interactions between HQ and responsible for the heavy quark energy loss the QGP medium. This is substantially and diffusion coefficient is responsible for beyond the expectations from perturbative its momentum broadening. The drag and QCD interactions. These observations diffusion coefficients of the heavy quarks triggered several studies in which non- can be computed starting from the heavy perturbative effects have been quark - light quark scattering matrix incorporated. In the recent past, a

3 simultaneous study of both the observables, experimental data, along with the results 9 RAA(pT) and v2(pT), received significant from lattice QCD . Here, Tc is the critical 10 attention , as it has the potential to temperature for a deconfinement transition. constrain the temperature dependence of heavy quark transport coefficient in QGP In Fig.3, we show the variation of HQ D , a and disentangle different energy loss s standard quantification of the space models. Recent studies based on diffusion coefficient is done in terms of a temperature and momentum dependence of dimensionless quantity, obtained within transport coefficients and Bayesian model different models in comparison with the to data analysis also obtained similar lQCD results. Being a mass independent conclusions from different viewpoints11,12. quantity it can provide a general measure of

the QCD interaction. Another fundamental Interestingly, the origin of the v2 is quite aspect is that it is a quantity that can be different for the heavy quarks than the bulk calculated in lQCD being directly related matter. The bulk develops its v2 from the with the spectral function. This highlights combined effect of the initial coordinate heavy quarks as a probe of QGP, have the space anisotropy created in non-central potential to link the phenomenology collisions and the interaction among the constrained from the experimental data to quarks and gluons which constitute the lattice QCD for studying the transport bulk. However, heavy quarks develop a properties of the hot QCD matter. Energy substantial part of the v2 due to their loss experienced by energetic partons leads interactions with the bulk medium and a to a suppression of final hadrons with high part from the light partons as a consequence 13 momentum known as jet quenching. At of hadronization . A coupled study of light high momenta, one can extract the heavy and heavy particle flow harmonics in heavy quark jet quenching parameter, the average ion collisions on event-by-event basic is transverse momentum broadening squared another interesting topic. Experimental per unit length, which contains information measurements in this direction will offer regarding jet-medium interactions. further new insights on heavy quark - bulk in-medium interaction and the temperature Once the temperature of the system goes dependence of the heavy quark transport below the quark-hadron transition coefficients. temperature heavy quarks convert to hadrons, through a process called hadronization. Hadronization dynamics plays an important role in determining the final momentum spectra and therefore, the RAA and v2 in both the light and heavy quark sectors. In particular, for heavy quarks it is generally expected that a coalescence mechanism13 is in action especially in the low and intermediate momentum. Heavy to heavy meson ratios, (Λc/D and Λb/B), are considered fundamental for the understanding of in-medium hadronization14,15. Furthermore, the heavy baryon to meson ratio can serve as a tool to Fig.3: Spatial diffusion coefficient as a disentangle different hadronization function of scaled-temperature obtained mechanisms14,16. within different models to describe

4 It has been also recently recognized that phase, the phase produced before the extremely strong magnetic fields are formation of QGP. The effect of the pre- created in non-central heavy-ion collisions equilibrium phase might be more at high energies. The estimated values of significant for low-energy heavy-ion the initial field strengths (1019 Gauss) are collisions: for example, in the case of several orders of magnitude higher than the Au+Au collisions at RHIC energy, values predicted at the surface of simulation analysis shows that equilibration magnetars. This is the highest ever is achieved approximately within 1 fm/c, produced magnetic field on the earth while the lifetime of the QGP phase turns created by human being. But the magnetic out to be about 5 fm/c. Hence the lifetime fields rapidly decrease as two charges of the out-of-equilibrium phase is recede from each other, still remain much approximately 20% of the total lifetime of stronger than the critical field during the the QGP. Currently heavy quarks are also lifetime of the QGP. Since the heavy quarks used as a tool to probe the Glasma20 , strong are produced at the gluon field produced in the early stages of early stages of heavy-ion collisions, their high-energy heavy-ion collisions. dynamics will be affected by such a strong magnetic field17 and they will be able to On the experimental front, there have been retain these effects till their detection as D several measurements on heavy-flavor mesons in experiments. HQ directed flow spectra, nuclear modification factor, elliptic v , is identified as a novel observable to 1 and directed flow in proton-proton and probe the initial electromagnetic field produced in high energy heavy-ion heavy-ion collisions. However, going to collisions. The sign of the directed flow for lower transverse momentum and dealing a charged particle will be opposite to its anti-particle mainly due to the response of opposite charges to electromagnetic field. The recent LHC measurement18, along with 19 the RHIC findings , on the D-meson v1, give the indications of the strong electromagnetic field produced in high energy heavy-ion collisions. It can be mentioned that the magnitude of the heavy quark directed flow at LHC energy is about 1000 times larger than that of light quarks. This is mainly because HQs are produced in Fig.4: Layout of the planned ALICE ITS3 the early stages of the collisions, hence, Inner Barrel to be installed during Long witness the peak of the electromagnetic Shutdown-3 (LS3) at the LHC. The figure field. Furthermore, the HQs, due to their shows the two half-barrels mounted around large relaxation time in contrast to light the beam pipe21. quarks, are capable of retaining the memory of the initial non-equilibrium dynamics with signal-to-background ratio has been a more effectively and hence, lending challenge so far, because of technological stronger signal of the early electromagnetic limitations. Contrary, the future is more fields. exciting, because ALICE, which is a As mentioned before, heavy quarks are dedicated experiment for studying QGP, produced in the very early stages of heavy- has entered into detector upgrades with Gas ion collisions due to their large masses. Electron Multiplier-based Time Projection Hence, it can probe the pre-equilibrium Chamber to deal with high-multiplicity and

5 high-luminosity, the Inner Tracking System (ITS) with lower material budget to enhance the signal-to-background ratio and detection efficiency at lower transverse momenta. As the lifetimes of heavy-flavors are very less, their the decay lengths (l = c�, c is the speed of light in vacuum and � is the lifetime of the particle in its local rest frame) are small and hence, they decay very close to the interaction vertex by creating a secondary vertex. This necessitates tracking devices nearer to the interaction point with less material budget + - + to reduce the detection background. To Fig.5: Λ c → pK p in central Pb–Pb collisions at √s = 5.5 TeV (L =10 nb-1): have a better grasp, for instance, the NN int signal-to-background ratio (S/B) as a innermost silicon tracker of the CMS 21 function of pT (transverse momentum) . experiment at the LHC, is at 33 mm ITS3 shows a significant enhancement of + distance from the interaction point and the S/B for Λ c (the lightest ) ALICE ITS is 39 mm from the interaction over ITS2 of ALICE. point. Because of the high mass, all the heavy-flavors decay before reaching the To overcome these problems, the LHC detectors and their detection is based on the upgrade plans with next level of reconstruction, where one technology, are highly encouraging. encounters high background from the ALICE – the dedicated experiment at the combinatorics (daughters from other LHC to study the primordial matter – QGP sources and material interactions). This has planned for the installation of ITS3 (the rd makes the experimental studies of heavy- 3 generation Inner Tracking System) in flavors a highly complex endeavour. LHC Long Shutdown-3 (LS3). This will have a novel vertex detector consisting of three curved wafer-scale ultra-thin silicon monolithic pixel sensors arranged in perfectly cylindrical layers, which is shown in Fig.4. This will feature with an unprecedented low material budget of 0.05% X03 per layer, with the innermost ITS layer positioned at only 18 mm radial distance from the interaction point21,22. This upgrade will overcome the present limitations in terms of proper identification

of secondary vertices, efficiency at low-pT

3 X0 is called radiation length and is the mean path Bremsstrahlung radiation– depends on atomic length (in gm.cm-2) required to reduce the energy of number and atomic mass of the material). an electron by the factor 1/e (energy loss through

6 and dealing with signal-to-background ratio to a greater extent. To have a quantitative Acknowledgements understanding, Fig. 5 shows an expected We would like to thank Prof. Y. P. Viyogi, order of magnitude better signal-to- VECC, Kolkata, Prof. Tapan K. Nayak, + background ratio in the detection of Λ c, as NISER Bhubaneswar & CERN, Geneva compared to the ITS2 (the ITS which is and Dr. Andrea Dainese, INFN Padova, being installed during the present ongoing Italy for careful reading and useful Long Shutdown-2 (LS2)). This will help comments on this work. with higher efficiency of detection of heavy-flavor particles, opening up a new References domain of QCD studies. In view of LHC 1. Jacak B. V. and Muller B., The plan for dedicated high-multiplicity pp exploration of hot nuclear matter. Science, runs, the future directions of research and 2012, 337, 310. 2. Rapp R. et al., Extraction of Heavy- the search for QGP droplets in high- Flavor Transport Coefficients in QCD multiplicity pp collisions stay exciting with Matter. Nucl. Phys. A, 2018, 979, 21. HQ as potential probes. 3. Dong . and Greco V., Heavy quark production and properties of Quark Gluon Beyond the energy reach of the present Plasma. Prog. Part. Nucl. Phys., 2019, 104, Large Hadron Collider, the planned Future 97. 4. Cao S. et al., Toward the determination Circular Collider (FCC) at CERN is of heavy-quark transport coefficients in expected to collide proton on proton at a quark-gluon plasma. Phys. Rev. C, 2019, center-of-mass energy of 100 TeV and 99, 054907. heavy-ion collisions at 39 TeV with a 5. Abeleb B. I. et al. (STAR Cllaboration), circumference of 100 km, as compared to Transverse Momentum and Centrality 27 km of the LHC23. This new energy and Dependence of High-pT Nonphotonic luminosity frontier would facilitate to study Electron Suppression in Au+Au Collisions at √s = 200 GeV. Phys. Rev. Lett., 2007, the signals of early universe in proton- NN 98, 192301. proton and heavy-ion collisions with a 6. Adler S. S. et al. (PHENIX variety of new observations with special Collaboration), Nuclear Modification of emphasis on heavy-flavors. Electron Spectra and Implications for Heavy Quark Energy Loss in Au + Au This article gives a theoretical and Collisions at √sNN = 200 GeV. Phys. Rev. experimental status of the characterization Lett. 2006, 96, 032301. 7. Adare A. et al. (PHENIX Collaboration), of the primordial matter – Quark-Gluon Energy Loss and Flow of Heavy Quarks in Plasma using heavy-flavors as potential Au + Au Collisions at √sNN = 200 GeV. probe. The future research in this direction Phys. Rev. Lett., 2007, 98, 172301. with improved technologies and 8. Abelev B. B. et al. (ALICE energy/luminosity would facilitate in Collaboration), Azimuthal anisotropy of D resolving many theoretical issues and -meson production in Pb-Pb collisions at √s = 2.76 TeV. Phys. Rev. C, 2014, 90, having a better understanding of the QCD NN 034904. matter formed in high-energy collisions. 9. Scardina F., Das S. K., Minissale V, Readers not familiar with the subject of Plumari S. and Greco V., Estimating the quark-gluon plasma, are advised to go diffusion coefficient and through Ref.24. thermalization time from spectra

7 at energies available at the BNL Relativistic 17. Das S. K., Plumari S., Chatterjee S., Heavy Ion Collider and the CERN Large Alam J, Scardina F. and Greco V, Directed Hadron Collider. Phys. Rev. C 2017, 96, Flow of Charm Quarks as a Witness of the 044905. Initial Strong Magnetic Field in Ultra- 10. Das S. K., Scardina F., Plumari S. and Relativistic Heavy Ion Collisions. Phys. Greco V., Toward a solution to the RAA and Lett. B, 2017, 768, 260. v2 puzzle for heavy quarks. Phys. Lett. B, 18. Acharya S. et al. (ALICE 2015, 747, 260. Collaboration), Probing the effects of 11. Cao S, Luo T., Qin G. Y. and Wang X. strong electromagnetic fields with charge- N., Linearized Boltzmann transport model dependent directed flow in Pb-Pb collisions for jet propagation in the quark-gluon at the LHC. Phys. Rev. Lett., 2020, plasma: Heavy quark evolution. Phys. Rev. 125, 022301. C, 2016, 94, 014909. 19. Adam J. et al. (STAR Collaboration), 12. Xu Y., Bernhard J. E., Bass S. A., First Observation of the Directed Flow of 0 0 Nahrgang M. and Cao S., Data-driven D and ¯D in Au+Au Collisions at √sNN = analysis for the temperature and 200 GeV. Phys. Rev. Lett., 2019, 123, momentum dependence of the heavy-quark 162301. diffusion coefficient in relativistic heavy- 20. Ruggieri M. and Das S. K, Cathode tube ion collisions. Phys. Rev. C, 2018, 97, effect: Heavy quarks probing the glasma in 014907. p-Pb collisions. Phys. Rev. D, 2018, 98, 13. Greco V., Ko C. M. and Rapp R., Quark 094024. coalescence for charmed mesons in 21. Expression of Interest for an ALICE ultrarelativistic heavy ion collisions. Phys. ITS Upgrade in LS3 (ALICE-PUBLIC- Lett. B, 2004, 595, 202. 2018-013). 14. Plumari S., Minissale V., Das S. K., http://cds.cern.ch/record/2644611 Coci G. and Greco V., Charmed Hadrons 22. Aichelin J. et al., Future physics from Coalescence plus Fragmentation in opportunities for high-density QCD at the relativistic nucleus-nucleus collisions at LHC with heavy-ion and proton beams. RHIC and LHC. Eur. Phys. J. C, 2018, 78, arXiv:1812.06772. 348. 23. https://fcc-cdr.web.cern.ch/ 15. He M. and Rapp R., Hadronization and 24. Sahoo, R. and Nayak, T.K., Early Charm-Hadron Ratios in Heavy-Ion universe signals in proton collisions at the Collisions. Phys. Rev. Lett., 2020, 124, Large Hadron Collider (Under review in 042301. Current Science) 16. Adam J. et al. (STAR Collaboration), 25. Inagaki, T., Hiroshima University, First measurement of Λc baryon production Japan in Au+Au collisions at √sNN = 200 GeV. Phys. Rev. Lett., 2020, 124, 172301.

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