Abstract
We calculate P (k ⊥), the probability distribution for an energetic parton that propagates for a distance L through a medium without radiating to pick up transverse momentum k ⊥, for a medium consisting of weakly coupled quark-gluon plasma. We use full or HTL self-energies in appropriate regimes, resumming each in order to find the leading large-L behavior. The jet quenching parameter \( \widehat{q} \) is the second moment of P (k ⊥), and we compare our results to other determinations of this quantity in the literature, although we emphasize the importance of looking at P (k ⊥) in its entirety. We compare our results for P (k ⊥) in weakly coupled quark-gluon plasma to expectations from holographic calculations that assume a plasma that is strongly coupled at all length scales. We find that the shape of P (k ⊥) at modest k ⊥ may not be very different in weakly coupled and strongly coupled plasmas, but we find that P (k ⊥) must be parametrically larger in a weakly coupled plasma than in a strongly coupled plasma — at large enough k ⊥. This means that by looking for rare (but not exponentially rare) large-angle deflections of the jet resulting from a parton produced initially back-to-back with a hard photon, experimentalists can find the weakly coupled short-distance quark and gluon quasiparticles within the strongly coupled liquid quark-gluon plasma produced in heavy ion collisions, much as Rutherford found nuclei within atoms or Friedman, Kendall and Taylor found quarks within nucleons.
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BRAHMS collaboration, I. Arsene et al., Transverse momentum spectra in Au+Au and d+Au collisions at \( \sqrt{s}=200 \) GeV and the pseudorapidity dependence of high p T suppression, Phys. Rev. Lett. 91 (2003) 072305 [nucl-ex/0307003] [INSPIRE].
PHENIX collaboration, S. Adler et al., Absence of suppression in particle production at large transverse momentum in \( \sqrt{{{s_{NN }}}}=200 \) GeV d + Au collisions, Phys. Rev. Lett. 91 (2003) 072303 [nucl-ex/0306021] [INSPIRE].
PHOBOS collaboration, B. Back et al., Centrality dependence of charged hadron transverse momentum spectra in d + Au collisions at \( \sqrt{{{s_{NN }}}}=200 \) GeV, Phys. Rev. Lett. 91 (2003) 072302 [nucl-ex/0306025] [INSPIRE].
STAR collaboration, J. Adams et al., Evidence from d + Au measurements for final state suppression of high p T hadrons in Au+Au collisions at RHIC, Phys. Rev. Lett. 91 (2003) 072304 [nucl-ex/0306024] [INSPIRE].
ATLAS collaboration, Observation of a centrality-dependent dijet asymmetry in lead-lead collisions at \( \sqrt{{{s_{NN }}}}=2.77 \) TeV with the ATLAS detector at the LHC, Phys. Rev. Lett. 105 (2010) 252303 [arXiv:1011.6182] [INSPIRE].
ALICE collaboration, Suppression of charged particle production at large transverse momentum in central PbPb collisions at \( \sqrt{{{s_{NN }}}}=2.76 \) TeV, Phys. Lett. B 696 (2011) 30 [arXiv:1012.1004] [INSPIRE].
CMS collaboration, Observation and studies of jet quenching in PbPb collisions at nucleon-nucleon center-of-mass energy = 2.76 TeV, Phys. Rev. C 84 (2011) 024906 [arXiv:1102.1957] [INSPIRE].
CMS collaboration, Study of high-p T charged particle suppression in PbPb compared to pp collisions at \( \sqrt{{{s_{NN }}}}=2.76 \) TeV, Eur. Phys. J. C 72 (2012) 1945 [arXiv:1202.2554] [INSPIRE].
CMS collaboration, Jet momentum dependence of jet quenching in PbPb collisions at \( \sqrt{{{s_{NN }}}}=2.76 \) TeV, Phys. Lett. B 712 (2012) 176 [arXiv:1202.5022] [INSPIRE].
CMS collaboration, Studies of jet quenching using isolated-photon+jet correlations in PbPb and pp collisions at \( \sqrt{{{s_{NN }}}}=2.76 \) TeV, Phys. Lett. B 718 (2013) 773 [arXiv:1205.0206] [INSPIRE].
CMS collaboration, Measurement of jet fragmentation into charged particles in pp and PbPb collisions at \( \sqrt{{{s_{NN }}}}=2.76 \) TeV, JHEP 10 (2012) 087 [arXiv:1205.5872] [INSPIRE].
ATLAS collaboration, Measurement of the jet radius and transverse momentum dependence of inclusive jet suppression in lead-lead collisions at \( \sqrt{{{s_{NN }}}}=2.76 \) TeV with the ATLAS detector, Phys. Lett. B 719 (2013) 220 [arXiv:1208.1967] [INSPIRE].
R. Granier de Cassagnac, Overview of results on photon and electroweak boson production from the CMS collaboration, talk at Quark Matter 2012 conference, Washington DC U.S.A. August 2012.
G. Roland, Experimental highlights from the CMS collaboration, talk at Quark Matter 2012 conference, Washington DC U.S.A. August 2012.
M. Spousta, ATLAS jets, talk at Quark Matter 2012 conference, Washington DC U.S.A. August 2012.
P. Steinberg, Photons and electroweak probes in ATLAS, talk at Quark Matter 2012 conference, Washington DC U.S.A. August 2012.
G. Veres, Overview of results on jets from the CMS collaboration, talk at Quark Matter 2012 conference, Washington DC U.S.A. August 2012.
B. Wosiek, ATLAS highlights, talk at Quark Matter 2012 conference, Washington DC U.S.A. August 2012.
M. McCumber, A technique for charm and beauty separation via DCA unfolding, talk at Quark Matter 2012 conference, Washington DC U.S.A. August 2012.
T. Sakaguchi, PHENIX highlights, talk at Quark Matter 2012 conference, Washington DC U.S.A. August 2012.
M. Gyulassy and X.-N. Wang, Multiple collisions and induced gluon bremsstrahlung in QCD, Nucl. Phys. B 420 (1994) 583 [nucl-th/9306003] [INSPIRE].
R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Radiative energy loss of high-energy quarks and gluons in a finite volume quark-gluon plasma, Nucl. Phys. B 483 (1997) 291 [hep-ph/9607355] [INSPIRE].
R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Radiative energy loss and p T broadening of high-energy partons in nuclei, Nucl. Phys. B 484 (1997) 265 [hep-ph/9608322] [INSPIRE].
B. Zakharov, Radiative energy loss of high-energy quarks in finite size nuclear matter and quark-gluon plasma, JETP Lett. 65 (1997) 615 [hep-ph/9704255] [INSPIRE].
U.A. Wiedemann, Gluon radiation off hard quarks in a nuclear environment: opacity expansion, Nucl. Phys. B 588 (2000) 303 [hep-ph/0005129] [INSPIRE].
M. Gyulassy, P. Levai and I. Vitev, Non-Abelian energy loss at finite opacity, Phys. Rev. Lett. 85 (2000) 5535 [nucl-th/0005032] [INSPIRE].
M. Gyulassy, P. Levai and I. Vitev, Reaction operator approach to non-Abelian energy loss, Nucl. Phys. B 594 (2001) 371 [nucl-th/0006010] [INSPIRE].
X.-F. Guo and X.-N. Wang, Multiple scattering, parton energy loss and modified fragmentation functions in deeply inelastic eA scattering, Phys. Rev. Lett. 85 (2000) 3591 [hep-ph/0005044] [INSPIRE].
X.-N. Wang and X.-F. Guo, Multiple parton scattering in nuclei: parton energy loss, Nucl. Phys. A 696 (2001) 788 [hep-ph/0102230] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon emission from ultrarelativistic plasmas, JHEP 11 (2001) 057 [hep-ph/0109064] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon emission from quark gluon plasma: complete leading order results, JHEP 12 (2001) 009 [hep-ph/0111107] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon and gluon emission in relativistic plasmas, JHEP 06 (2002) 030 [hep-ph/0204343] [INSPIRE].
S. Jeon and G.D. Moore, Energy loss of leading partons in a thermal QCD medium, Phys. Rev. C 71 (2005) 034901 [hep-ph/0309332] [INSPIRE].
S. Turbide, C. Gale, S. Jeon and G.D. Moore, Energy loss of leading hadrons and direct photon production in evolving quark-gluon plasma, Phys. Rev. C 72 (2005) 014906 [hep-ph/0502248] [INSPIRE].
C.A. Salgado and U.A. Wiedemann, Calculating quenching weights, Phys. Rev. D 68 (2003) 014008 [hep-ph/0302184] [INSPIRE].
A. Majumder and B. Müller, Higher twist jet broadening and classical propagation, Phys. Rev. C 77 (2008) 054903 [arXiv:0705.1147] [INSPIRE].
R. Baier, D. Schiff and B. Zakharov, Energy loss in perturbative QCD, Ann. Rev. Nucl. Part. Sci. 50 (2000) 37 [hep-ph/0002198] [INSPIRE].
A. Kovner and U.A. Wiedemann, Gluon radiation and parton energy loss, hep-ph/0304151 [INSPIRE].
M. Gyulassy, I. Vitev, X.-N. Wang and B.-W. Zhang, Jet quenching and radiative energy loss in dense nuclear matter, nucl-th/0302077 [INSPIRE].
P. Jacobs and X.-N. Wang, Matter in extremis: ultrarelativistic nuclear collisions at RHIC, Prog. Part. Nucl. Phys. 54 (2005) 443 [hep-ph/0405125] [INSPIRE].
J. Casalderrey-Solana and C.A. Salgado, Introductory lectures on jet quenching in heavy ion collisions, Acta Phys. Polon. B 38 (2007) 3731 [arXiv:0712.3443] [INSPIRE].
A. Accardi, F. Arleo, W. Brooks, D. D’Enterria and V. Muccifora, Parton propagation and fragmentation in QCD matter, Riv. Nuovo Cim. 32 (2010) 439 [arXiv:0907.3534] [INSPIRE].
U.A. Wiedemann, Jet quenching in heavy ion collisions, arXiv:0908.2306 [INSPIRE].
A. Majumder and M. Van Leeuwen, The theory and phenomenology of perturbative QCD based jet quenching, Prog. Part. Nucl. Phys. A 66 (2011) 41 [arXiv:1002.2206] [INSPIRE].
C.W. Bauer, S. Fleming and M.E. Luke, Summing Sudakov logarithms in B → X/sγ in effective field theory, Phys. Rev. D 63 (2000) 014006 [hep-ph/0005275] [INSPIRE].
C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An effective field theory for collinear and soft gluons: heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].
C.W. Bauer and I.W. Stewart, Invariant operators in collinear effective theory, Phys. Lett. B 516 (2001) 134 [hep-ph/0107001] [INSPIRE].
C.W. Bauer, D. Pirjol and I.W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65 (2002) 054022 [hep-ph/0109045] [INSPIRE].
A. Idilbi and A. Majumder, Extending soft-collinear-effective-theory to describe hard jets in dense QCD media, Phys. Rev. D 80 (2009) 054022 [arXiv:0808.1087] [INSPIRE].
F. D’Eramo, H. Liu and K. Rajagopal, Transverse momentum broadening and the jet quenching parameter, redux, Phys. Rev. D 84 (2011) 065015 [arXiv:1006.1367] [INSPIRE].
G. Ovanesyan and I. Vitev, An effective theory for jet propagation in dense QCD matter: jet broadening and medium-induced bremsstrahlung, JHEP 06 (2011) 080 [arXiv:1103.1074] [INSPIRE].
G. Ovanesyan and I. Vitev, Medium-induced parton splitting kernels from soft collinear effective theory with Glauber gluons, Phys. Lett. B 706 (2012) 371 [arXiv:1109.5619] [INSPIRE].
Z.-T. Liang, X.-N. Wang and J. Zhou, The transverse-momentum-dependent parton distribution function and jet transport in medium, Phys. Rev. D 77 (2008) 125010 [arXiv:0801.0434] [INSPIRE].
R. Baier, A. Kovner and U.A. Wiedemann, Saturation and parton level Cronin effect: enhancement versus suppression of gluon production in p-A and A-A collisions, Phys. Rev. D 68 (2003) 054009 [hep-ph/0305265] [INSPIRE].
J.L. Albacete, N. Armesto, A. Kovner, C.A. Salgado and U.A. Wiedemann, Energy dependence of the Cronin effect from nonlinear QCD evolution, Phys. Rev. Lett. 92 (2004) 082001 [hep-ph/0307179] [INSPIRE].
D. Kharzeev, Y.V. Kovchegov and K. Tuchin, Cronin effect and high p T suppression in p-A collisions, Phys. Rev. D 68 (2003) 094013 [hep-ph/0307037] [INSPIRE].
M. Benzke, N. Brambilla, M.A. Escobedo and A. Vairo, Gauge invariant definition of the jet quenching parameter, JHEP 02 (2013) 129 [arXiv:1208.4253] [INSPIRE].
H. Liu, K. Rajagopal and U.A. Wiedemann, Calculating the jet quenching parameter from AdS/CFT, Phys. Rev. Lett. 97 (2006) 182301 [hep-ph/0605178] [INSPIRE].
A.D. Linde, Infrared problem in thermodynamics of the Yang-Mills gas, Phys. Lett. B 96 (1980) 289 [INSPIRE].
O. Kalashnikov and V. Klimov, Infrared behavior of Green functions in Yang-Mills theory at finite temperatures, Sov. J. Nucl. Phys. 33 (1981) 443 [Yad. Fiz. 33 (1980) 848] [INSPIRE].
E. Braaten and R.D. Pisarski, Resummation and gauge invariance of the gluon damping rate in hot QCD, Phys. Rev. Lett. 64 (1990) 1338 [INSPIRE].
J. Frenkel and J. Taylor, High temperature limit of thermal QCD, Nucl. Phys. B 334 (1990) 199 [INSPIRE].
E. Braaten and R.D. Pisarski, Soft amplitudes in hot gauge theories: a general analysis, Nucl. Phys. B 337 (1990) 569 [INSPIRE].
E. Braaten and R.D. Pisarski, Deducing hard thermal loops from Ward identities, Nucl. Phys. B 339 (1990) 310 [INSPIRE].
E. Braaten and R.D. Pisarski, Simple effective Lagrangian for hard thermal loops, Phys. Rev. D 45 (1992) 1827 [INSPIRE].
P.B. Arnold and C. Dogan, QCD splitting/joining functions at finite temperature in the deep LPM regime, Phys. Rev. D 78 (2008) 065008 [arXiv:0804.3359] [INSPIRE].
P.B. Arnold and W. Xiao, High-energy jet quenching in weakly-coupled quark-gluon plasmas, Phys. Rev. D 78 (2008) 125008 [arXiv:0810.1026] [INSPIRE].
S. Caron-Huot, O(g) plasma effects in jet quenching, Phys. Rev. D 79 (2009) 065039 [arXiv:0811.1603] [INSPIRE].
A. Majumder, B. Müller and S. Mrowczynski, Momentum broadening of a fast parton in a perturbative quark-gluon plasma, Phys. Rev. D 80 (2009) 125020 [arXiv:0903.3683] [INSPIRE].
M. Le Bellac, Thermal field theory, Cambridge monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (1996).
K. Kajantie and J.I. Kapusta, Behavior of gluons at high temperature, Annals Phys. 160 (1985) 477 [INSPIRE].
R. Kobes, G. Kunstatter and K. Mak, Linear response of the hot QCD plasma from the gluon propagator, Z. Phys. C 45 (1989) 129 [INSPIRE].
H.A. Weldon, Structure of the gluon propagator at finite temperature, Annals Phys. 271 (1999) 141 [hep-ph/9701279] [INSPIRE].
F.T. Brandt and J. Frenkel, Generalized forward scattering amplitudes in QCD at high temperature, Phys. Rev. D 56 (1997) 2453 [hep-th/9703165] [INSPIRE].
O. Kalashnikov and V. Klimov, Polarization tensor in QCD for finite temperature and density, Sov. J. Nucl. Phys. 31 (1980) 699 [Yad. Fiz. 31 (1980) 1357] [INSPIRE].
O. Kalashnikov, Magnetic mass in hot scalar electrodynamics, Kratk. Soobshch. Fiz. (1996) Nos. 7–8 52 [hep-ph/9602308] [INSPIRE].
H.A. Weldon, Covariant calculations at finite temperature: the relativistic plasma, Phys. Rev. D 26 (1982) 1394 [INSPIRE].
V. Klimov, Collective excitations in a hot quark gluon plasma, Sov. Phys. JETP 55 (1982) 199 [Zh. Eksp. Teor. Fiz. 82 (1982) 336] [INSPIRE].
M. Laine, A non-perturbative contribution to jet quenching, Eur. Phys. J. C 72 (2012) 2233 [arXiv:1208.5707] [INSPIRE].
P. Aurenche, F. Gelis and H. Zaraket, A simple sum rule for the thermal gluon spectral function and applications, JHEP 05 (2002) 043 [hep-ph/0204146] [INSPIRE].
U.A. Wiedemann and M. Gyulassy, Transverse momentum dependence of the Landau-Pomeranchuk-Migdal effect, Nucl. Phys. B 560 (1999) 345 [hep-ph/9906257] [INSPIRE].
M. Gyulassy, P. Levai and I. Vitev, Reaction operator approach to multiple elastic scatterings, Phys. Rev. D 66 (2002) 014005 [nucl-th/0201078] [INSPIRE].
P.B. Arnold, Simple formula for high-energy gluon bremsstrahlung in a finite, expanding medium, Phys. Rev. D 79 (2009) 065025 [arXiv:0808.2767] [INSPIRE].
A. Peshier, QCD running coupling and collisional jet quenching, J. Phys. G 35 (2008) 044028 [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
S.-J. Rey, S. Theisen and J.-T. Yee, Wilson-Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity, Nucl. Phys. B 527 (1998) 171 [hep-th/9803135] [INSPIRE].
A. Brandhuber, N. Itzhaki, J. Sonnenschein and S. Yankielowicz, Wilson loops in the large-N limit at finite temperature, Phys. Lett. B 434 (1998) 36 [hep-th/9803137] [INSPIRE].
J. Sonnenschein, What does the string/gauge correspondence teach us about Wilson loops?, hep-th/0003032 [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/string duality, hot QCD and heavy ion collisions, arXiv:1101.0618 [INSPIRE].
M.H. Thoma, New developments and applications of thermal field theory, hep-ph/0010164 [INSPIRE].
Z. Ligeti, I.W. Stewart and F.J. Tackmann, Treating the b quark distribution function with reliable uncertainties, Phys. Rev. D 78 (2008) 114014 [arXiv:0807.1926] [INSPIRE].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, The quark beam function at NNLL, JHEP 09 (2010) 005 [arXiv:1002.2213] [INSPIRE].
G. Molière, Theorie der Streuung schneller geladener Teilchen II. Mehrfach- und Vielfachstreuung (in German), Z. Naturforsch. 3a (1948) 78.
H. Bethe, Moliere’s theory of multiple scattering, Phys. Rev. 89 (1953) 1256 [INSPIRE].
B.G. Zakharov, Applicability of the eikonal approximation for calculation of the probability of passage of ultrarelativistic positronium through matter, Sov. J. Nucl. Phys. 46 (1987) 92.
N.N. Nikolaev and B. Zakharov, Color transparency and scaling properties of nuclear shadowing in deep inelastic scattering, Z. Phys. C 49 (1991) 607 [INSPIRE].
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D’Eramo, F., Lekaveckas, M., Liu, H. et al. Momentum broadening in weakly coupled quark-gluon plasma (with a view to finding the quasiparticles within liquid quark-gluon plasma). J. High Energ. Phys. 2013, 31 (2013). https://doi.org/10.1007/JHEP05(2013)031
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DOI: https://doi.org/10.1007/JHEP05(2013)031