gluon scattering - personal.kent.edumstrick6/qcdseminar/spring14/nopoush.pdfhow useful are my...
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GLUON SCATTERING
By: Mohammad Nopoush
Advisor: Dr. Strickland
KSU QCD Seminar, spring 2014
April 14, 2014
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MOTIVATION
¢ Shear and bulk viscosity are transport coefficients that determine how fast the system goes to the equilibrium.*
¢ All information about dissipative terms are in Collisional Kernel:
¢ Sending an energetic parton jet through QGP, one obtains the main dissipative mechanisms are to be collisional (22) and radiative (23) ones.**
* J-W. Chen, J. Deng, H. Dong, Q. Wang, Phys. Rev. C 87, 024910 (2013)
** S. K. Das and J. Alam, Phys. Rev. D 82, 051502(R) (2010)
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Kinetic equilibration Chemical equilibration
HOW USEFUL ARE MY TECHNIQUES?
¢ 22 Gluon Scattering
¢ 23 Gluon Scattering (325 distinct diagrams)*
where is the number of colors.
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*F. A. Berendes et al., Phys. Lett. B 103, 124(1981)
FEYNMAN RULES
¢ External lines
¢ Propagators
¢ Vertices
q Ghosts: § Mathematical creatures that make the theory consistent
§ Breaking symmetry among system paths picking up the physical one
§ Odd particles: violating statistical rules.
§ In feynman diagrams they replace the gluon loops.
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gg ! gg amplitude
¢ Let’s get started with M1: For each momentum k we appoint a polarization vector
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SCATTERING AMPLITUDES A
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DEFINITIONS (SPIN & MOMENTUM)
¢ Gauge invariance Transverse polarization for massless gauge bosons (like gluon)
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z
xY
GELL-MANN MATRICES
¢ Gell-Mann Matrices: Infinitesimal generators of the special unitary group SU(3)
¢ In Adjoint Representation:
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SIMPLIFICATIONS FOR RR RR
¢ Lorentz Gauge Condition
where s, t u are Mandelstam variables.
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OTHER POLARIZATIONS
¢ 16 possible polarization states for 22 scattering. ¢ 6 allowed ones by conservation of angular momentum
¢ By parity conservation of QCD
¢ Crossing Symmetry makes it even easier!
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22 SCATTERING CROSS SECTION
¢ Dividing to incoming particles’ colors and spins: ( )
(17.78) of Peskin
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gg ! ggg Amplitude
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CUT DIAGRAMS
¢ Imaginary part of scattering amplitude arises when virtual particles are sent on shell.
¢ Relating imaginary part to discontinuity and using Cutkosky rules.
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GEOMETRICALLY DISTINCT DIAGRAMS A
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SUMMARY OF FIVE-GLUON CUT DIAGRAMS* A
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Term Symmetries No. of terms
1 1 8 15
2 2 4 30
3 2 8 15
4 2 2 60
5 2 2 60
6 2 2 60
7 2 4 30
8 1 12 10
9 2 4 30
10 2 8 15
=325 * T. Gottschalk, D. Sivers, Phys. Rev D, 21, 102 (1980).
CALCULATION OF CUT DIAGRAMS*
I. Construct the expression for each diagram using Feynman Rules
II. Remove the factor for each cut propagator
III. Multiply the result by -1 (using T matrix instead of S)
IV. For a given diagram calculate the one with gluons loops replaced with ghost one.
V. Multiply each ghost diagram by
VI. Add them up.
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* T. Gottschalk, D. Sivers, Phys. Rev D, 21, 102.
CONCLUSIONS AND FUTURE STUDIES
¢ Categorization of the higher order diagrams seems quite essential because of shear number of diagrams involved.
¢ Cut-diagram method is a very helpful technique.
¢ Making the computer programs that are able to produce and calculate diagrams seems necessary and timesaving.
¢ Having calculated the inelastic gluon scattering, one can see if anisotropic Hydro. is sensitive to the process of this kind.
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REFRENCES
¢ M. Peskin and D. Schroeder, An introduction to quantum field theory Addison-Wesley, 1995.
¢ J-W. Chen, J. Deng, H. Dong, Q. Wang, Phys. Rev. C 87, 024910 (2013)
¢ S. K. Das and J. Alam, Phys. Rev. D 82, 051502(R) (2010)
¢ F. A. Berendes et al., Phys. Lett. B 103, 124 (1981).
¢ T. Gottschalk, D. Sivers, Phys. Rev D, 21, 102 (1980).
¢ D. Griffiths, Introduction to elementary particles, Wiley-VCH Verlag GmbH & Co. KGaA (2004).
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