Run Group E Jeopardy Update

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Run Group E Jeopardy Update Run Group E Jeopardy Update W. Armstrong,1 M. Arratia,2 W.K. Brooks, A. El Alaoui, H. Hakobyan, J. L´opez, T. Mineeva,3 R. Dupr´e,4 L. El Fassi,5 G. Gilfoyle,6 K. Hicks,7 M. Holtrop,8 K. Joo,9 G. Niculescu, I. Niculescu,10 O. Soto,11 and M. Wood12 1Argonne National Laboratory, Lemont IL, USA 2University of California, Riverside CA, USA, and Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA 3Universidad T´ecnica Federico Santa Mar´ıa, Valpara´ıso, Chile 4Universit´eParis-Saclay, CNRS, IJCLab, 91405, Orsay, France 5Mississippi State University, Mississippi State MS, USA 6University of Richmond, Richmond VA, USA 7Ohio University, Athens OH, USA 8University of New Hampshire, Durham NH, USA 9University of Connecticut, Storrs CT, USA 10James Madison University, VA, USA 11INFN Frascati, Frascati, Italy 12Canisius College, Buffalo NY, USA (Dated: June 2020) Run Group E consists of Jefferson Lab experiment matics. This time is at the femtometer scale, and thus it E12-06-117 "Quark Propagation and Hadron Formation" can only be directly measured by the interaction within which was originally approved in 2006 and later given nuclei, which have dimensions of that same scale. We will the scientific rating of "A−" by PAC 36 in 2010[15]. also extract the interaction cross sections of a variety of The experiment will make use of nuclear targets to gain mesons and baryons and study the kinematic dependen- substantial new insights into the propagation of QCD cies needed to describe their formation mechanisms. color through strongly interacting systems. There are two essential thrusts of these studies. First, we seek to characterize the fundamental QCD subprocesses of color A. Advances in Theory and Phenomenology propagation and hadron formation in quark fragmenta- tion, extrapolating from observations with nuclear tar- Recently, members of our team completed an extrac- gets to the more general cases of proton targets or the tion of the color lifetime for light quarks from HERMES early universe[2]. Second, we seek to greatly expand our published data[4]. The method employed by Brooks and knowledge about the color structure of nuclei from these L´opez (BL) was to fit two observables simultaneously in a studies by using the struck quark as a colored probe of geometrical framework with realistic nuclear density dis- the medium. By studying the strength of the interac- tributions. The framework is not a dynamical model, but tion between the colored quark and the nuclear medium rather it makes a geometrical association between stages using the transport coefficientq ^, we gain quantitative of the hadronization process and experimental observ- understanding of the color structure of bound nucleons ables, with the outcome strongly constrained by the fixed via color charge form factors[7]. An extraction of theq ^ nuclear density distributions of the three heavier nuclei. transport coefficient was recently performed by members The first observable, transverse momentum broadening of our collaboration[4]. The same analysis will be car- 2 of charged pions ∆pT , was associated in the framework ried out on the data from our 12 GeV experiment, and with partonic multiple scattering over a period of time will measure the multivariate dependence ofq ^, promising corresponding to the color lifetime. The second observ- an enormous advance in our understanding of the color π able, the hadronic multiplicity ratio RM , was associated structure of nuclei. with interaction of formed hadrons within the nuclear medium. An excellent fit of the data was obtained for all three of the heavier nuclei (neon, krypton, and xenon) in I. PHYSICS GOALS AND NEW this simple physical picture with two fit parameters: the DEVELOPMENTS color lifetime, and the strength of the transverse quark- medium interaction. The published pion-nucleon cross The first physics aim of the experiment is to ex- sections were used for the baseline version of the model. plore fundamental characteristics of color propagation The fit to the data is shown in Fig.1. and hadron formation. These processes are unique to In the BL study the color lifetime was shown to depend QCD because of the non-Abelian nature of the strong on the standard SIDIS zh observable, zh = Eh/ν, with interaction that confines quarks into hadrons. With the exactly the magnitudes and functional dependence pre- data from this experiment we will extract the color life- dicted by the Lund String Model (LSM). A plot of these time of quasi-free quarks during the brief time that they results is shown in Fig.2, and in this figure it can be seen are liberated following a hard interaction in DIS kine- that the values found for the color lifetime range from 2 zh = 0.32 zh = 0.53 zh = 0.75 zh = 0.94 ) 2 0.02 (GeV i . 2 T 0 00 p h Model ∆ 0.02 Data − 0.8 Ne M R Kr Xe 0.6 Model Data 3 4 5 3 4 5 3 4 5 3 4 5 A1/3 A1/3 A1/3 A1/3 FIG. 1. Fits of the two-parameter BL model to HERMES published data. The fit is performed for two observables simultane- ously in a given bin in zh. 2 fm/c at high zh to 8 fm/c at lower zh. The curves in year 2000, Guo and Qiu determined that transverse mo- the fit correspond to two LSM analytical expressions for mentum broading is related to the quark-gluon correlator the color lifetime. The curve labeled LSM corresponds Tqg(xB; 0; 0) between energetic quarks and soft gluons[9]. to the color lifetime for the struck quark, and the other Using leading order pQCD, they determined the relation- curve takes into account the full string evolution. If the ship between pT broadening and Tqg(xB; 0; 0) to be: LSM string tension is left as a fit parameter, when fitted to the color lifetimes from the BL study of the HERMES 2 2 P 2 data, we find string tension values that are compatible 4π α z eqTqg(xB; 0; 0)Dh=q(zh) ∆ k2 = s h q (1) with 1 GeV/fm, the well-known magnitude of this quan- hT P 2 h i Nc q eqfq=A(xB)Dh=q(zh) tity. This result is a strong validation of the geometrical framework that was used for this analysis. where khT is the transverse momentum of the parton that fragments into the observed hadron h, and f and D are the usual parton distribution functions and frag- 2 LSM, χ /dof = 1.1 mentation functions. In 2016, Kang, Wang, Wang and κ = 1.04 0.06 (GeV/fm) ± Zing (KWWZ) reproduced this result from the year 2000 15 Bialas et. al, χ2/dof = 0.35 and extended it to next-to-leading-order (NLO) using the κ = 0.86 0.05 (GeV/fm) higher-twist collinear factorization framework[11]. They ± Fit result evaluated at NLO the transverse-momentum-weighted differential cross section d k2 σD =dx dydz at twist 4, (fm) B h 10 h hT i c considering contributions from quark-gluon and gluon- L gluon double scatterings, as well as interferences be- tween single and triple scatterings. They found that 5 2 D d khT σ =dxBdydzh can be factorized as a convolution ofh twist-4i nuclear parton correlation functions, the usual Q2 = 2.4 GeV2, ν = 12.4 GeV twist-2 fragmentation function, and hard parts which are h i h i finite and free of divergences. 0.0 0.2 0.4 0.6 0.8 1.0 Last year, Ru, Kang, Wang, Xing and Zhang (RK- z WXZ) [19] used the insights from the above efforts to perform a global fit to a variety of types of data, in- FIG. 2. A secondary fit of the results from the HERMES cluding the HERMES pT broadening, to constrain theq ^ fit to LSM analytical expressions for the color lifetime. The transport coefficient discussed earlier. The analysis took curve labelled "LSM" is for the struck quark, while the other into account the world data on transverse momentum curve is from Bialas and Gyulassy[3]. broadening in semi-inclusive electron-nucleus deep inelas- tic scattering, Drell-Yan dilepton and heavy quarkonium There have been substantial theory advances that are production in proton-nucleus collisions, as well as the directly relevant to this experiment since PAC 36 in 2010. nuclear modification of the structure functions in deep We list only a few here, due to space constraints. In the inelastic scattering, comprising a total of 215 data points 3 and K−. According to this work, quark energy loss plays a more minor role in describing the HERMES multiplic- ity ratios. The paper goes on to explore the implications for the LHC and the EIC. In a foundational theoretical effort, in 2013 Qin and Majumder derived a differential equation for the time evolution of the momentum distribution of a hard parton traveling through the nuclear medium[18]. This equa- tion describes in-medium evolution of hard jets which experience longitudinal drag and diffusion in addition to the transverse broadening caused by multiple scatterings from the medium. While the relative importance of lon- gitudinal drag vs. longitudinal diffusion may not yet be clear, collisional energy loss cannot simply be neglected in a theoretically correct description. This is not only true for the suppression of single inclusive hadrons, but also for jet shower evolution, energy loss distribution within 2 and outside the jet cone, as well as energy and momen- FIG. 3. Dependence ofq ^ on xBj and Q found by the RKWXZ theory collaboration tum deposition into the medium by the jet shower.
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