Transverse momentum broadening of a jet in quark-gluon plasma: an open quantum system EFT
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Springer
Received: May 3, 2020 Accepted: September 1, 2020 Published: October 5, 2020
Varun Vaidya and Xiaojun Yao Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.
E-mail: [email protected], [email protected] Abstract: We utilize the technology of open quantum systems in conjunction with the recently developed effective field theory for forward scattering to address the question of massless jet propagation through a weakly-coupled quark-gluon plasma in thermal equilibrium. We discuss various possible hierarchies of scales that may appear in this problem, by comparing thermal scales of the plasma with relevant scales in the effective field theory. Starting from the Lindblad equation, we derive and solve a master equation for the transverse momentum distribution of a massless quark jet, at leading orders both in the strong coupling and in the power counting of the effective field theory. Markovian approximation is justified in the weak coupling limit. Using the solution to the master equation, we study the transverse momentum broadening of a jet as a function of the plasma temperature and the time of propagation. We discuss the physical origin of infrared sensitivity that arises in the solution and a way to handle it in the effective field theory formulation. We suspect that the final measurement constraint can only cut-off leading infrared singularities and the solution to the Markovian master equation resums a logarithmic series. This work is a stepping stone towards understanding jet quenching and jet substructure observables on both light and heavy quark jets as probes of the quark-gluon plasma. Keywords: Heavy Ion Phenomenology ArXiv ePrint: 2004.11403
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)024
JHEP10(2020)024
Transverse momentum broadening of a jet in quark-gluon plasma: an open quantum system EFT
Contents 1
2 Relevant hierarchy of scales 2.1 Dominance of forward scattering regime 2.2 Jets in quark-gluon plasma
4 4 4
3 Soft-collinear effective theory (SCET) and forward scattering 3.1 Review of soft-collinear effective theory 3.2 Glauber mode for forward scattering
6 6 8
4 Lindblad equation for open quantum system 4.1 Unitary evolution part 4.1.1 Subsystem transition 4.1.2 Final expression 4.2 Non-unitary (dissipative) evolution part
11 13 14 15 17
5 Transverse momentum broadening 5.1 Markovian approximation 5.2 Solution to master equation 5.3 IR safety 5.4 Numerical results 5.5 Comparison with previous work
19 20 21 23 25 27
6 Conclusions
28
A Wightman functions in thermal bath
29
B Rate and kernel B.1 Rate B.2 Kernel
33 33 34
C Proof for cancellation of leading IR singularities
35
1
Introduction
Jets are sprays of collimated particles produced in high energy collisions of hadrons and/or electrons. Their formation starts with a highly virtual parton generated from an initial hard scattering, followed by subsequent parton cascade and fragmentation. Jet production can be studied via perturba
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