# Variation of Top Quark Mass (mt) with Quantum Chromodynamics (QCD) Scale Parameter a and Down Quark (md)

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#### Variation of Top Quark Mass (mt) with Quantum Chromodynamics (QCD) Scale Parameter a and Down Quark (md)

Dr. Deepak Dubey Deptt. Of Physics

Baba Tikam Singh Kanya Mahavidhyalaya, Khairgarh Firozabad (U.P.) India

Dr. Pradeep Kumar Department of Applied Science,

Mangalmay Institute of Engineering and Technology Greater Noida,(U.P.) India

#### Abstract- Variation of top quark mass mt with QCD scale parameter = 0.1 GeV, =0.15 GeV and =0.3 GeV with down quark md (0.3285, 0.3286.0.3305) GeV. Variation of mt and md was reported. The top quark is a member of the third generation quark doublet in standard model of particle physics. Although the standard model has shown incredible successes with regard to experiments, the top quark remained elusive for quite a long time and these were several predictions on top quark mass around 120 GeV or above. The central value extracted from precision electroweak measurement at LEP suggest that the top quark mass can be taken to be about 174 GeV. The purpose of the present work is to estimate discuss the

parameter =0.1 GeV, S. quark mass ms=.450 Gev and

V P

V P

M 2 M 2 0.45 GeV2.

V P

V P

The model consists of a linear and a colour-coulomb potential along with spin dependent potential obtained from the reduction of Bethe-Salpeter Kernel into Breit interaction. The model has been found to be successful in its application quarkonium spectroscopy [7]. This model is simple. It requires minimum number of parameters and has high correlative powers. We apply this model to the determination of top quark mass on the basis of the following assumptions:

V

V

#### empirical result M 2 MP2 is a constant (0.56 GeV2) for non-

(i)

M 2 M 2 0.45 GeV2

#### self conjugate mesons containing one light and one heavy quark.

1. The top quark mass mt

is very large compared to

Keywords: Mass, QCD scale parameters.

INTRODUCTION

v p

v p

The top quark is a member of the third generation quark doublet model of particle physics. Although the standard model has incredible success with regard to experiments, the top quark remained elusive for quite a long time [1,2] and these were several predictions on top quark mass around 120 GeV or above [3]. The central value extracted from precision electroweak measurement at LEP [4] suggest that the top quark mass [5] can be taken to be about 174 GeV. It is interesting to see whether it is possible to obtain such a high value for the top mass with the QCD based potential. The purpose of the present work is to estimate discuss the top quark mass in quantum chromodynamics (QCD) motivated potential model using the emperical result [6] M 2 M 2 is a constant 0.56 GeV 2 for non-self conjugate mesons containing one light and one heavy quark.

Mass of the basis of the empirical relation

V P

V P

M 2 M 2 0.56, where MV and MP stand for mass of

vector and pseudo-scalar meson, respectively. It is assumed that the mass of top quark should be much greater than that of s quark. This quantum chromodynamic potential (QCD) model consists of a colour coulomb potential and a linear potential with spin-dependent forces obtained from the reduction of the Bethe-Salpeter Kernel into Breit interaction. The confinement potential is assumed to be scalar-vector admixture with dominance of scalar interaction. The top quark mass comes out to be 179.991 GeV for the QCD scale

s-quark mass ms , so that the reduced mass for

T ts meson is approximately equal to ms .

2. The spin dependent correction terms can be neglected in the sum MV MP .

The top quark is the heaviest standard model (SM) particle found so far, with a mass mt

~175 GeV ~ VH / 2 (VH is vacuum expectation of Higgs Field) and with a Yu-Kawa coupling very close to unity. This fact is probably related to a nature of the electroweak symmetry-breaking- mechanism. In the SM the top quark is very heavy but at the same time is assumed to be point like. Because of these and other unusual top quark properties, possible deviations from SM predictions might be first manifest in the top quark sector.

Top quark being produced singly through the electroweak interaction give a unique opportunity to investigate a number of delicate top quark properties.

THEORY

Variation of top quark mass:

It is assumed that start with the expressions for the masses of vector and pseudo-scalar mesons given by [8].

1/ 3

1 6

The parameters required for this analysis are

2 C obtained from Ref. [8]. These are as follows- ms=0.450, C1= –

1/

1/

M m m

• C Âµ

0

2 Âµ 3

V 1 2 1

6mm 3 s 10 1

(1)

1 2

23.1265, C2= – 2.12419, b=0.95388, a (all in GeV

5

and

units) and QCD scale parameter 0.100 Gev s is calculated using the formula [7].

M m m C Âµ1/ 3 1

6 0 2 C2 Âµ1/ 3

12

P 1 2 1

2mm 3 s 10

s

(2)

1 2

33 2 n

f Ln

Q2 / 2

Hence

Here

Q 4s

and

nf 3

[11]. Equation (7) in

conjuction with equns (8-11) and the parameters given above

M M

2 6 Âµ

0 2 C2 Âµ1/ 3

give the value of m .

(3)

V P 3mm 3

s 10 t

1 2

For a meson containg a very heavy quark like the top, it is a good approximation to neglect the spin dependent term in MV MP , so that

Table-1,

RESULTS AND DISCUSSION

The results of our calculations are presented in

V P 1 2 1

V P 1 2 1

M M 2m m 2 C Âµ1/ 3

The variation of top quark mass with the QCD scale

parameter and m for M 2 M 2 0.4(45) GeV 2 are

V p

V p

2

2

The assumptions above would not effect the result significantly but would simplify the calculations very much. A similar but rather crude approximation was adopted in the work of Frank and O Donnel [9]. With 0 baÂµ obtained from scaling (10) and by multiplying equation (4) by equation (3). It is assumed that obtained an expression for M 2 M 2 which can written in the form

s V p

presented in 1. In the column first of the Table values of mass of s-quarks are presented which vary from 0.440 to 0.460 GeV. In column second, third, fourth calculated values of mass of top quarks are presented with QCD scale parameter

V p

V p

=0.1 GeV, =0.15 GeV and =0.3 GeV respectively. From table we find that the top quark mass is 179.991 GeV for s- quark mass equal to 0.450 GeV in the case of =0.1 GeV, M 2 M 2 0.45 GeV 2 . This value of top quark mass is

2C 64 C ba 2C C Âµ1 64

in experimental agreement [12]. The table shows that the

2 Âµ2 / 3 1 s 1 2 ba M 2 M 2 va0lues 0.15 GeV and 0.3 GeV for are not possible for ms =

15 9 m m 15 m m 9

s V p

0.440 to 0.460 GeV. The Fermi lab experiments suggests that

1 2 1 2

(5)

For a meson containing t and S quarks. The assumptions mt ms gives Âµ ms . Hence for T meson,

the value =0.1 GeV and ms = 0.450 GeV are possible choice. Thus, we fix the parameters like s-quark mass and QCD scale parameter. We find that using the standard value of the parameters like , ms and the experimental value of

equation (5) become

M 2 M 2 , the top quark mass estimated from the potential

m2 m 0

V p

(6)

t t

The solution of which is

model matches well with the recently observed value. The value of the top quark mass comes out to be 179.991 GeV,

where

mt

2 4 2

which tallies with the value of obtained from experimental results [12,13]. Thus we find that it is possib(le7)to obtain the present fermilab prediction on top quark from a QCD based

potential model.

2C2 m 2 / 3 64

ba M 2 M 2

Table-1: Variation of top quark mass mt with QCD scale

15 s

9 s V p

parameter and ms.

(8)

2C2 m 1/ 3 64 s ba C1 m 1/ 3 2C1 C2 m 1

15 s 9 s 15 s

64 s ba M 2 M 2 m

(9)

9 V p s

64 s ba C1 m 2 / 3

(10)

9 s

 S.No. ms (GeV) mt =0.1 GeV =0.15 GeV =0.3 GeV 1 0.440 194.502 84.601 49.506 2 0.441 192.785 84.329 49.453 3 0.442 191.313 84.092 49.400 4 0.443 189.876 83.885 49.339 5 0.444 188.246 83.683 49.285 6 0.445 186.847 83. 478 49.231 7 0.446 185.471 83.246 49.177 8 0.447 183.921 83.043 49.118 9 0.448 182.590 82.842 49.065 10 0.449 181.280 82.642 49.010 11 0.450 179.991 82.411 48.950 12 0.451 178.721 82.213 48.897 13 0.452 177.470 82.016 48.843 14 0.453 176.238 81.820 48.790 15 0.454 175.025 81.625 48.737 16 0.455 173.829 81.431 48.684 17 0.456 172.641 81.238 48.631 18 0.457 172.556 81.047 48.578 19 0.458 170.326 80.856 48.525 20 0.459 169.199 80.663 48.473 21 0.460 168.078 80.489 48.420
 S.No. ms (GeV) mt =0.1 GeV =0.15 GeV =0.3 GeV 1 0.440 194.502 84.601 49.506 2 0.441 192.785 84.329 49.453 3 0.442 191.313 84.092 49.400 4 0.443 189.876 83.885 49.339 5 0.444 188.246 83.683 49.285 6 0.445 186.847 83. 478 49.231 7 0.446 185.471 83.246 49.177 8 0.447 183.921 83.043 49.118 9 0.448 182.590 82.842 49.065 10 0.449 181.280 82.642 49.010 11 0.450 179.991 82.411 48.950 12 0.451 178.721 82.213 48.897 13 0.452 177.470 82.016 48.843 14 0.453 176.238 81.820 48.790 15 0.454 175.025 81.625 48.737 16 0.455 173.829 81.431 48.684 17 0.456 172.641 81.238 48.631 18 0.457 172.556 81.047 48.578 19 0.458 170.326 80.856 48.525 20 0.459 169.199 80.663 48.473 21 0.460 168.078 80.489 48.420

GeV.

CONCLUSION

The quark mass are ms = 0.450 GeV, mt = 179.991

REFERENCES

1. For a recent review see Kane, G.L., Top quark physics (University of Michigan, USA), Report No. UM-TH-91-32

(1991) Unpublished.

(1991) Unpublished.

2. Roy, D.P., Top quark search-an overview, Proc 2nd Workshop on High energy Physics Phenomenology (WHEPP-I1), Calcutta, January 1991 (World Scientific Singapore) Preprint TIFR/TH/ 91-30.

3. Berends, F.A., Tausk, J.B. and Giele W.T., Top search in multijet signals, Preprint FERMI LAB-Pub-92/196-T; Chakrabarty, S. and Deoghuria, S. J. Fiz Mal., 8 (1987) 104.

4. Hollik, K., Status _of the electro weak standard model presented at the XVI International Symposium on Lepton Photon Interactions, Cornell University, Aug. 10-15, (1993) Ithaca, NY.

5. Eichten Estia and Lane Kenneth, Multiscale techni color and top production, FERMI LAB-Pub-94/007-T.

6. Martin, A. Proc. Conf. on High Energy Physics ed Petiau P and Porneuf, M. (1992) P 92 (J. Phys. Call, 43 (1982), C3 43).

7. Deoghuria, S. and Chakrabarty, S.J. Phys. G. Nucl. Part. Phys., 15(1989), 1213.

8. Chakrabary, S. Indian J. Phys. 68A (1994), 95.

9. Frank, M. and ODonnell, P.J. Phys. Lett. 15913 (1985), 174.

10. Quigg, C. and Rosner, J.L. Phys. Rep. 56C (1979) 167.

11. Igi, K. and Ono, S., Phys. Rev. 32D (1985) 232.

12. CDF Collaboration : Abe, F. et. al., FERMI LAB-Pub-Conf. 93/212-E (1993) : Chikamatsu T, search for 'the Top Quark in the Dilepton channel at CDF, in Proc. 9th Topical workshop in pp colider Physics, Tsukuba (1993) ed by Kondo K.

13. CDF collaboration : Strowink M., Proc. Internatinal Euro-Physics Conference on High Energy Physics Marseille (1993), eds Carr. J. and Perrottet M., Fatyoa, M., Search for the Top Quark in Single Lepton Plus Jets channel t CDF in Proc. 9th Topical Wprkshop in ppcollider Physics. Tsukuba (1993) ed by Kondo K.

14. 14 L.K. Thompson and S.S. Tandon, Inorg. Chem. 18 (1996) 125.