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                            2009
Light front Hamiltonian and its application in QCD
	Jun Li
		Recommended Citation
tmp.1335711608.pdf.Wn_4x
                        
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Graduate Theses and Dissertations
Iowa State University Capstones, Theses and

Dissertations

2009

Light front Hamiltonian and its application in
QCD
Jun Li
Iowa State University

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Li, Jun, "Light front Hamiltonian and its application in QCD" (2009). Graduate Theses and Dissertations. 11067.
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Page 2

Light front Hamiltonian and its application in QCD

by

Jun Li

A dissertation submitted to the graduate faculty

in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

Major: Nuclear Physics

Program of Study Committee:
James Vary, Major Professor

Alexander Roitershtein
Marzia Rosati
Kirill Tuchin

Kerry Whisnant

Iowa State University

Ames, Iowa

2009

Copyright c° Jun Li, 2009. All rights reserved.

Page 49

36

−RGBBB̄ + RBGGḠ + GRBBB̄ −GBRRR̄−BRGGḠ + BGRRR̄)

= 0:015734(−RG(RR̄ + GḠ + BB̄)B + RB(RR̄ + GḠ + BB̄)G−BR(RR̄ + GḠ + BB̄)G

+BG(RR̄ + GḠ + BB̄)R−GB(RR̄ + GḠ + BB̄)R + GR(RR̄ + GḠ + BB̄)B)

+0:229990(−RGB + RBG−BRG + BGR−GBR + GRB)(RR̄ + GḠ + BB̄): (3.17)

Using the same method, we can get a very similar structure for the second singlet state.

From these two states, we note that we can construct two color singlet states which then

simulate an interesting intrinsic structure. The first one appears as the color product space of

the baryon and the meson

(−RGB + RBG−BRG + BGR−GBR + GRB)(RR̄ + GḠ + BB̄): (3.18)

The second one appears as an intrinsic state of these 5 partons that does not separate into

the asymptotic state of a meson and a baryon

(−RG(RR̄ + GḠ + BB̄)B + RB(RR̄ + GḠ + BB̄)G−BR(RR̄ + GḠ + BB̄)G

+BG(RR̄ + GḠ + BB̄)R−GB(RR̄ + GḠ + BB̄)R + GR(RR̄ + GḠ + BB̄)B): (3.19)

The above construction was carried out in order to illustrate the challenges of discerning

substructures within complicated multi-parton color space states. We have found no general

method that is guaranteed to reveal substructures of multi-parton color space states.

Next, we consider the case with three quarks and three antiquarks.

Using the operator F 2, we have the conclusion that there exists six color singlet states

which have the required zero eigenvalues.

And we have only one color singlet state with completely symmetric wavefunction which

is given by

1√
10

(RRRR̄R̄R̄ + GGGḠḠḠ + BBBB̄B̄B̄)

+
1√
90

(RRGR̄R̄Ḡ + c:s:p)

+
1√
90

(RRBR̄R̄B̄ + c:s:p)

+
1√
90

(GGRḠḠR̄ + c:s:p)

Page 50

37

+
1√
90

(BBRB̄B̄R̄ + c:s:p)

+
1√
90

(GGBḠḠB̄ + c:s:p)

+
1√
90

(BBGB̄B̄Ḡ + c:s:p)

+
1√
360

(RGBR̄ḠB̄ + c:s:p); (3.20)

where c.s.p represents the complete symmetric partners.

The other five color singlet states are either antisymmetic or possess mixed symmetry.

3.1.5 Summary of multiparton hadrons

In this section, we give a summary of multiparton hadrons. Some of the results we obtained

are displayed in Fig. 3.1. In Fig. 3.1, the upper curves are counts of all color configurations

with zero color projection after we employ the operator constraints provided by T3 and Y .

The lower curves are counts of global color singlet states resulting from diagonalization for the

specified number of quarks and gluons.

Page 97

84

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