[go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Effect of magnetic field on jet transport coefficient \(\hat{q}\)

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

We report the estimation of jet transport coefficient \(\hat{q}\) for quark- and gluon-initiated jets using a simple quasiparticle model in the absence and presence of magnetic field. This model introduces a temperature and magnetic field-dependent degeneracy factor of partons, which is tuned by fitting the entropy density of lattice quantum chromodynamics data. At a finite magnetic field, \(\hat{q}\) for quark jets splits into parallel and perpendicular components whose magnetic field dependence comes from two sources: the field-dependent degeneracy factor and the phase-space part guided by the shear viscosity-to-entropy density ratio. Due to the electrically neutral nature of gluons, the estimation of \(\hat{q}\) for gluon jets is affected only by the field-dependent degeneracy factor. In the presence of a finite magnetic field, we find a significant enhancement in \(\hat{q}\) for both quark- and gluon-initiated jets at low temperature, which gradually decreases towards high temperature. We compare the obtained results with the earlier calculations based on the anti-de Sitter/conformal field theory correspondence, and a qualitatively similar trend is observed. The change in \(\hat{q}\) in the presence of magnetic field is, however, quantitatively different for quark- and gluon-initiated jets. This is an interesting observation which can be explored experimentally to verify the effect of magnetic field on \(\hat{q}\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. M Connors, C Nattrass, R Reed and S Salur, Rev. Mod. Phys. 90, 025005 (2018)

    Article  ADS  Google Scholar 

  2. I Y Aref’eva, Teor. Mat. Fiz. 184, 398 (2015)

    Article  Google Scholar 

  3. R Chatterjee and D K Srivastava, Nucl. Phys. A 830, 503C (2009)

    Article  ADS  Google Scholar 

  4. M Gyulassy and M Plumer, Phys. Lett. B 243, 432 (1990)

    Article  ADS  Google Scholar 

  5. X N Wang and M Gyulassy, Phys. Rev. Lett. 68, 1480 (1992)

    Article  ADS  Google Scholar 

  6. A Majumder and M Van Leeuwen, Prog. Part. Nucl. Phys. 66, 41 (2011)

    Article  ADS  Google Scholar 

  7. JET: K M Burke et al, Phys. Rev. C 90, 014909 (2014)

  8. NA49: A Laszlo, Indian J. Phys. 85, 787 (2011)

  9. PHENIX: A Adare et al, Phys. Rev. C 82, 011902 (2010)

  10. CMS: S Chatrchyan et al, Eur. Phys. J. C 72, 1945 (2012)

  11. ATLAS: M Aaboud et al, Phys. Lett. B 790, 108 (2019)

  12. ATLAS: G Aad et al, Phys. Rev. C 107, 054908 (2023)

  13. ALICE: B Abelev et al, JHEP 03, 013 (2014)

  14. R Baier, Y L Dokshitzer, A H Mueller, S Peigne and D Schiff, Nucl. Phys. B 484, 265 (1997)

    Article  ADS  Google Scholar 

  15. B G Zakharov, JETP Lett. 65, 615 (1997)

    Article  ADS  Google Scholar 

  16. X Feal, C A Salgado and R A Vazquez, Phys. Lett. B 816, 136251 (2021)

    Article  Google Scholar 

  17. X F Chen, C Greiner, E Wang, X N Wang and Z Xu, Phys. Rev. C 81, 064908 (2010)

    Article  ADS  Google Scholar 

  18. X F Chen, T Hirano, E Wang, X N Wang and H Zhang, Phys. Rev. C 84, 034902 (2011)

    Article  ADS  Google Scholar 

  19. G Y Qin, J Ruppert, C Gale, S Jeon, G D Moore and M G Mustafa, Phys. Rev. Lett. 100, 072301 (2008)

    Article  ADS  Google Scholar 

  20. B Schenke, C Gale and S Jeon, Phys. Rev. C 80, 054913 (2009)

    Article  ADS  Google Scholar 

  21. Z Q Liu, H Zhang, B W Zhang and E Wang, Eur. Phys. J. C 76, 20 (2016)

    Article  ADS  Google Scholar 

  22. C Andrés, N Armesto, M Luzum, C A Salgado and P Zurita, Eur. Phys. J. C 76, 475 (2016)

    Article  ADS  Google Scholar 

  23. M Xie, S Y Wei, G Y Qin and H Z Zhang, Eur. Phys. J. C 79, 589 (2019)

    Article  ADS  Google Scholar 

  24. M Xie, X N Wang and H Z Zhang, Phys. Rev. C 103, 034911 (2021)

    Article  ADS  Google Scholar 

  25. Q F Han, M Xie and H Z Zhang, Eur. Phys. J. Plus 137, 1056 (2022)

    Article  Google Scholar 

  26. M Gyulassy, P Levai and I Vitev, Nucl. Phys. B 594, 371 (2001)

    Article  ADS  Google Scholar 

  27. I Vitev and M Gyulassy, Phys. Rev. Lett. 89, 252301 (2002)

    Article  ADS  Google Scholar 

  28. A Buzzatti and M Gyulassy, Phys. Rev. Lett. 108, 022301 (2012)

    Article  ADS  Google Scholar 

  29. A Majumder, Phys. Rev. D 85, 014023 (2012)

    Article  ADS  Google Scholar 

  30. X f Guo and X N Wang, Phys. Rev. Lett. 85, 3591 (2000). https://inspirehep.net/literature/546886

  31. X N Wang and X f Guo, Nucl. Phys. A 696, 788 (2001). https://inspirehep.net/literature/553250

    Article  ADS  Google Scholar 

  32. K C Zapp, F Krauss and U A Wiedemann, JHEP 03, 080 (2013)

    Article  ADS  Google Scholar 

  33. K C Zapp, Eur. Phys. J. C 74, 2762 (2014)

    Article  ADS  Google Scholar 

  34. J G Milhano and K Zapp, Eur. Phys. J. C 82, 1010 (2022)

    Article  ADS  Google Scholar 

  35. ALICE: S Acharya et al, Phys. Rev. C 101, 034911 (2020)

  36. PHENIX: A Adare et al, Phys. Rev. Lett. 101, 232301 (2008)

  37. PHENIX: A Adare et al, Phys. Rev. C 87, 034911 (2013)

  38. ALICE: B Abelev et al, Phys. Lett. B 720, 52 (2013)

  39. CMS: S Chatrchyan et al, Eur. Phys. J. C 72, 1945 (2012)

  40. STAR: B I Abelev et al, Phys. Rev. C 82, 034909 (2010)

  41. STAR: L Adamczyk et al, Phys. Lett. B 760, 689–696 (2016)

  42. ATLAS: G Aad et al. JHEP 09, 050 (2015)

  43. ALICE: K Aamodt et al, Phys. Rev. Lett. 108, 092301 (2012)

  44. CMS: R Conway, Nucl. Phys. A 904–905, 451c (2013)

  45. ALICE: J Adam et al, Phys. Lett. B 763, 238 (2016)

  46. CMS: V Khachatryan et al, JHEP 04, 039 (2017)

  47. ALICE: S Acharya et al, JHEP 11, 013 (2018)

  48. M Xie, W Ke, H Zhang and X N Wang, arXiv:2208.14419 [hep-ph] (2022)

  49. K Tuchin, Adv. High Energy Phys. 2013, 490495 (2013)

    Article  MathSciNet  Google Scholar 

  50. S Satapathy, S Paul, A Anand, R Kumar and S Ghosh, J. Phys. G 47, 045201 (2020)

    Article  ADS  Google Scholar 

  51. S Borsanyi, Z Fodor, C Hoelbling, S D Katz, S Krieg and K K Szabo, Phys. Lett. B 730, 99 (2014)

    Article  ADS  Google Scholar 

  52. HotQCD: A Bazavov et al, Phys. Rev. D 90, 094503 (2014)

  53. G S Bali, F Bruckmann, G Endrodi, Z Fodor, S D Katz and A Schäfer, Phys. Rev. D 86, 071502 (2012)

    Article  ADS  Google Scholar 

  54. G S Bali, F Bruckmann, G Endrödi, S D Katz and A Schäfer, JHEP 08, 177 (2014)

    Article  ADS  Google Scholar 

  55. X Li, W J Fu and Y X Liu, Phys. Rev. D 99, 074029 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  56. A N Tawfik, A M Diab and M T Hussein, J. Phys. G 45, 055008 (2018)

    Article  ADS  Google Scholar 

  57. A N Tawfik, A M Diab, N Ezzelarab and A G Shalaby, Adv. High Energy Phys. 2016, 1381479 (2016)

    Google Scholar 

  58. R L S Farias, V S Timoteo, S S Avancini, M B Pinto and G Krein, Eur. Phys. J. A 53, 101 (2017)

    Article  ADS  Google Scholar 

  59. A Majumder, B Muller and X N Wang, Phys. Rev. Lett. 99, 192301 (2007)

    Article  ADS  Google Scholar 

  60. J Casalderrey-Solana and X N Wang, Phys. Rev. C 77, 024902 (2008)

    Article  ADS  Google Scholar 

  61. J Xu, J Liao and M Gyulassy, Chin. Phys. Lett. 32, 092501 (2015)

    Article  ADS  Google Scholar 

  62. J Xu, J Liao and M Gyulassy, JHEP 02, 169 (2016)

    Article  ADS  Google Scholar 

  63. E Shuryak, Rev. Mod. Phys. 89, 035001 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  64. A Ayala, I Dominguez, J Jalilian-Marian and M E Tejeda-Yeomans, Phys. Rev. C 94, 024913 (2016)

    Article  ADS  Google Scholar 

  65. A N Mishra, D Sahu and R Sahoo, MDPI Phys. 4, 315 (2022)

    Article  Google Scholar 

  66. S Li, K A Mamo and H U Yee, Phys. Rev. D 94, 085016 (2016)

    Article  ADS  Google Scholar 

  67. H Liu, K Rajagopal and U A Wiedemann, Phys. Rev. Lett. 97, 182301 (2006)

    Article  ADS  Google Scholar 

  68. J Dey, S Satapathy, A Mishra, S Paul and S Ghosh, Int. J. Mod. Phys. E 30, 2150044 (2021)

    Article  ADS  Google Scholar 

  69. HERMES: A Airapetian et al, Nucl. Phys. B 780, 1 (2007)

  70. W T Deng and X N Wang, Phys. Rev. C 81, 024902 (2010)

    Article  ADS  Google Scholar 

  71. X L Shang, A Li, Z Q Miao, G F Burgio and H J Schulze, Phys. Rev. C 101, 065801 (2020)

    Article  ADS  Google Scholar 

  72. E Lifshitz and P L P, Physical kinetics (Elsevier, 1981)

  73. X G Huang, M Huang, D H Rischke and A Sedrakian, Phys. Rev. D 81, 045015 (2010)

    Article  ADS  Google Scholar 

  74. X G Huang, A Sedrakian and D H Rischke, Ann. Phys. 326, 3075 (2011)

    Article  ADS  Google Scholar 

  75. K Tuchin, J. Phys. G 39, 025010 (2012)

    Article  ADS  Google Scholar 

  76. S Li and H U Yee, Phys. Rev. D 97, 056024 (2018)

    Article  ADS  Google Scholar 

  77. P Mohanty, A Dash and V Roy, Eur. Phys. J. A 55, 35 (2019)

    Article  ADS  Google Scholar 

  78. S Ghosh, B Chatterjee, P Mohanty, A Mukharjee and H Mishra, Phys. Rev. D 100, 034024 (2019)

    Article  ADS  Google Scholar 

  79. S i Nam and C W Kao, Phys. Rev. D 87, 114003 (2013)

    Article  ADS  Google Scholar 

  80. A Dash et al, Phys. Rev. D 102, 016016 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  81. A Das, H Mishra and R K Mohapatra, Phys. Rev. D 100, 114004 (2019)

    Article  ADS  Google Scholar 

  82. G S Denicol et al, Phys. Rev. D 98, 076009 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  83. Z Chen, C Greiner, A Huang and Z Xu, Phys. Rev. D 101, 056020 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  84. J Dey, S Satapathy, P Murmu and S Ghosh, Pramana – J. Phys. 95, 125 (2021)

    Article  ADS  Google Scholar 

  85. J Xu, A Buzzatti and M Gyulassy, JHEP 08, 063 (2014)

    Article  ADS  Google Scholar 

  86. Y Hidaka and R D Pisarski, Phys. Rev. D 78, 071501 (2008)

    Article  ADS  Google Scholar 

  87. Y Hidaka and R D Pisarski, Phys. Rev. D 81, 076002 (2010)

    Article  ADS  Google Scholar 

  88. A Dumitru, Y Guo, Y Hidaka, C P K Altes and R D Pisarski, Phys. Rev. D 83, 034022 (2011)

    Article  ADS  Google Scholar 

  89. S Lin, R D Pisarski and V V Skokov, Phys. Lett. B 730, 236 (2014)

    Article  ADS  Google Scholar 

  90. J Liao and E Shuryak, Phys. Rev. C 75, 054907 (2007)

    Article  ADS  Google Scholar 

  91. J Liao and E Shuryak, Phys. Rev. Lett. 101, 162302 (2008)

    Article  ADS  Google Scholar 

  92. J Liao and E Shuryak, Phys. Rev. Lett. 109, 152001 (2012)

    Article  ADS  Google Scholar 

  93. I Grishmanovskii, T Song, O Soloveva, C Greiner and E Bratkovskaya, Phys. Rev. C 106, 014903 (2022)

    Article  ADS  Google Scholar 

  94. STAR: arXiv:2304.03430 [nucl-ex] (2023)

  95. ALICE: S Acharya et al, Phys. Rev. Lett. 125, 022301 (2020)

  96. S K Das, S Plumari, S Chatterjee, J Alam, F Scardina and V Greco, Phys. Lett. B 768, 260 (2017)

    Article  ADS  Google Scholar 

  97. ATLAS and CMS: R Longo, EPJ Web Conf. 276, 05003 (2023)

  98. J M Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  99. S S Gubser, I R Klebanov and A M Polyakov, Phys. Lett. B 428, 105 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  100. O Aharony, S S Gubser, J M Maldacena, H Ooguri and Y Oz, Phys. Rep. 323, 183 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  101. Z q Zhang and K Ma, Eur. Phys. J. C 78, 532 (2018). https://inspirehep.net/literature/1080600

    Article  ADS  Google Scholar 

  102. K A Mamo, JHEP 05, 121 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  103. R Rougemont, Phys. Rev. D 102, 034009 (2020)

    Article  ADS  Google Scholar 

  104. K J Eskola, H Honkanen, C A Salgado and U A Wiedemann, Nucl. Phys. A 747, 511 (2005)

    Article  ADS  Google Scholar 

  105. A Dainese, C Loizides and G Paic, Eur. Phys. J. C 38, 461 (2005)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the following members of TPRC-IITBH who previously worked on quasiparticle picture [50, 68]: Sarthak Satapathy, Jayanta Dey, Anki Anand, Ranjesh Kumar, Ankita Mishra and Prasant Murmu. D Banerjee acknowledges the Inspire Fellowship research grant (DST/INSPIRE Fellowship/2018/IF180285). A Modak and P Das acknowledge the Institutional Fellowship research grant of Bose Institute. Significant part of computation for this work was carried out using the computing server facility at CAPSS, Bose Institute, Kolkata.

Author information

Authors and Affiliations

  1. Department of Physics, Bose Institute, EN 80, Sector-V, Salt Lake, Kolkata, 700 091, India

    Debjani Banerjee, Prottoy Das, Abhi Modak & Sidharth K Prasad

  2. Department of Physical Sciences, Indian Institute of Science Education and Research, Mohanpur, Kolkata, 741 246, India

    Souvik Paul

  3. Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400 005, India

    Ankita Budhraja

  4. IIT Bhilai, Durg, Chhattisgarh, 491001, India

    Sabyasachi Ghosh

Authors
  1. Debjani Banerjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Prottoy Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Souvik Paul
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Abhi Modak
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ankita Budhraja
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Sabyasachi Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Sidharth K Prasad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Debjani Banerjee.

Appendix A

Appendix A

In terms of the Fermi–Dirac (FD) distribution function of quarks and the Bose–Einstein (BE) distribution function of gluons, the energy density (\(\epsilon \)) of the QGP system can be expressed as

$$\begin{aligned} \epsilon _{\textrm{QGP}} ={}&\frac{g_{g}}{(2\pi )^{3}} \int _{0}^{\infty } \frac{\omega _{g}}{\textrm{e}^{\beta \omega _{g}} - 1} {\textrm{d}^{3}\vec {k}}\nonumber \\&+ \frac{g_{Q} }{(2\pi )^{3}}\int _{0}^{\infty } \frac{\omega _{Q}}{\textrm{e}^{\beta \omega _{Q}} + 1} {\textrm{d}^{3}\vec {k}}. \end{aligned}$$
(A.1)

Here \(\omega _{g}\) and \(\omega _{Q}\) are energies and can be expressed as \(\omega _{g,Q} = \sqrt{\vec k^2+m_{g,Q}^2}\) and \(\beta = 1/T\). Here \(m_{g}\) and \(m_{Q}\) are masses of quarks and gluons. However, for massless QGP, \(m_{g,Q} = 0\). Therefore, for massless QGP, \(\omega _{g,Q} = \vec k_{g,Q}\). If one converts the volume integral to line integral, \(\int _{0}^{\infty } {\textrm{d}^{3}\vec {k}} \rightarrow 4\pi \int _{0}^{\infty }\vec {k}^{2} {\textrm{d}\vec {k}}\).

Equation (A.1) can be expressed as

$$\begin{aligned} \epsilon _{\textrm{QGP}} ={}&\frac{g_{g}}{(2\pi )^{3}} \int _{0}^{\infty } \frac{{\vec {k}_{g}}}{\textrm{e}^{\beta \vec {k_{g}}} - 1} {4\pi {\vec {k}_{g}}^{2} \textrm{d}{\vec {k}_{g}}}\nonumber \\&+ \frac{g_{Q}}{(2\pi )^{3}} \int _{0}^{\infty } \frac{{{\vec {k}_{Q}}}}{\textrm{e}^{\beta {\vec {k}}_{{Q}}} + 1} {4\pi {{\vec {k}}_{Q}}^{2} \textrm{d}{\vec {k}}_{{Q}}}\nonumber \\ ={}&\frac{g_{g}}{2\pi ^{2}} \int _{0}^{\infty } \frac{{\vec {k}_{g}^{3}}}{\textrm{e}^{\vec {k}_{{g}}/T} - 1} {\textrm{d}{\vec {k}}_{{g}}}\nonumber \\&+ \frac{g_{Q}}{2\pi ^{2}} \int _{0}^{\infty } \frac{{\vec {k}_{Q}^{3}}}{\textrm{e}^{\vec {k}_{{Q}}/T} + 1} {\textrm{d}\vec {k_{Q}}} \hspace{0.5cm} [\beta = 1/T]\nonumber \\ ={}&\frac{g_{g}T^{4}}{2\pi ^{2}} \int _{0}^{\infty } \frac{x^{3}}{\textrm{e}^{x} - 1} {\textrm{d}x}\nonumber \\&+ \frac{g_{Q}T^{4}}{2\pi ^{2}} \int _{0}^{\infty } \frac{y^{3}}{\textrm{e}^{y} + 1} {\textrm{d}y} \nonumber \\&\hspace{0.5cm} {[}\vec {k_{g}}/T = x, \vec {k_{Q}}/T = y]\nonumber \\ ={}&\frac{g_{g}T^{4}}{2\pi ^{2}} \int _{0}^{\infty } \frac{x^{3}}{\textrm{e}^{x} (1 - \textrm{e}^{-x})} {\textrm{d}x}\nonumber \\&+ \frac{g_{Q}T^{4}}{2\pi ^{2}} \int _{0}^{\infty } \frac{y^{3}}{\textrm{e}^{y} (1 + \textrm{e}^{-y})} {\textrm{d}y}\nonumber \\ ={}&\frac{g_{g}T^{4}}{2\pi ^{2}} \int _{0}^{\infty } x^{3}\textrm{e}^{-x} (1 - \textrm{e}^{-x})^{-1} {\textrm{d}x}\nonumber \\&+ \frac{g_{Q}T^{4}}{2\pi ^{2}} \int _{0}^{\infty } y^{3}\textrm{e}^{-y} (1 + \textrm{e}^{-y})^{-1} {\textrm{d}y}\nonumber \\ ={}&\frac{g_{g}T^{4}}{2\pi ^{2}} \int _{0}^{\infty } x^{3}\textrm{e}^{-x} \left[ \sum _{n = 0}^{\infty } \textrm{e}^{-nx} \right] {\textrm{d}x}\nonumber \\&+ \frac{g_{Q}T^{4}}{2\pi ^{2}} \int _{0}^{\infty } y^{3}\textrm{e}^{-y} \left[ \sum _{n = 0}^{\infty } (-1)^{n}\textrm{e}^{-ny} \right] {\textrm{d}y}\nonumber \\ ={}&\frac{g_{g}T^{4}}{2\pi ^{2}} \sum _{n = 0}^{\infty } \int _{0}^{\infty } x^{3}\textrm{e}^{-(1+n)x} {\textrm{d}x}\nonumber \\&+ \frac{g_{Q}T^{4}}{2\pi ^{2}} \sum _{n = 0}^{\infty } (-1)^{n} \int _{0}^{\infty } y^{3}\textrm{e}^{-(1+n)y} {\textrm{d}y}. \end{aligned}$$
(A.2)

If one considers \((1+n)x = a\) and \((1+n)y = b\), then eq. (A.2) can be represented as

$$\begin{aligned} \epsilon _{\textrm{QGP}} ={}&\frac{g_{g}T^{4}}{2\pi ^{2}} \sum _{n = 0}^{\infty } \frac{1}{(n+1)^{4}} \int _{0}^{\infty } a^{3}\textrm{e}^{-a} {\textrm{d}a}\nonumber \\&+ \frac{g_{Q}T^{4}}{2\pi ^{2}} \sum _{n = 0}^{\infty } (-1)^{n} \frac{1}{(n+1)^{4}} \int _{0}^{\infty } b^{3}\textrm{e}^{-b} {\textrm{d}b.} \end{aligned}$$
(A.3)

Simplification of \(\int _{0}^{\infty } t^{3}\textrm{e}^{-t} {\textrm{d}t} = \Gamma (4) = 6\) and expanding binomially one can get

$$\begin{aligned} \sum _{n = 0}^{\infty } \frac{1}{(n+1)^{4}} = \xi (4) = \frac{\pi ^{4}}{90} \end{aligned}$$
(A.4)

and

$$\begin{aligned} \sum _{n = 0}^{\infty } (-1)^{n} \frac{1}{(n+1)^{4}} = \frac{7}{8} \xi (4) =\frac{7}{8} \frac{\pi ^{4}}{90}. \end{aligned}$$
(A.5)
$$\begin{aligned} \epsilon _{\textrm{QGP}}&= \frac{g_{g}T^{4}}{2\pi ^{2}} \frac{6\pi ^{4}}{90}+ \frac{g_{Q}T^{4}}{2\pi ^{2}}\frac{7}{8} \frac{6\pi ^{4}}{90}\nonumber \\&= \Bigg [g_g+g_{Q}\Bigg (\frac{7}{8}\Bigg )\Bigg ]\frac{3\pi ^2}{90}T^4\approx 15.6~T^4. \end{aligned}$$
(A.6)

Pressure (P) of the QGP system follows similar prescription as the energy density (\(\epsilon \)).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Banerjee, D., Das, P., Paul, S. et al. Effect of magnetic field on jet transport coefficient \(\hat{q}\). Pramana - J Phys 97, 206 (2023). https://doi.org/10.1007/s12043-023-02683-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-023-02683-1

Keywords

PACS

Search

Navigation