Decay rates of charmonia within a quark-antiquark confining potential

Smruti Patel; P. C. Vinodkumar; Shashank Bhatnagar

doi:10.1088/1674-1137/40/5/053102

Chinese Physics C> 2016, Vol. 40> Issue(5) : 053102 DOI: 10.1088/1674-1137/40/5/053102

Decay rates of charmonia within a quark-antiquark confining potential

1.
Department of Physics, Sardar Patel University, Vallabh Vidyanagar, India
2.
Department of Physics, Addis Ababa University, P. O. Box 101739, Addis Ababa, Ethiopia

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Abstract：
In this work, we investigate the spectroscopy and decay rates of charmonia within the framework of the non-relativistic Schrödinger equation by employing an approximate inter quark-antiquark potential. The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are employed to compute the spectroscopy of the excited S states and a few low-lying P and D waves. The resultant wave functions at zero inter quark separation as well as some finite separations are employed to predict the di-gamma, di-leptonic and di-gluon decay rates of charmonia states using the conventional Van Royen-Weisskopf formula. The di-gamma and di-leptonic decay widths are also computed by incorporating the relativistic corrections of order ν⁴ within the NRQCD formalism. We have observed that the NRQCD predictions with their matrix elements computed at finite radial separation yield results which are found to be in better agreement with experimental values for both di-gamma and di-leptonic decays. The same scenario is seen in the case when di-gamma and di-leptonic decay widths are computed with the Van Royen-Weisskopf formula. It is also observed that the di-gluon decay width with the inclusion of binding energy effects are in better agreement with the experimental data available for 1S-2S and 1P. The di-gluon decay width of 3S and 2P waves waves are also predicted. Thus, the present study of decay rates clearly indicates the importance of binding energy effects.
- potential models ,
- heavy quarkonia ,
- radiative decays ,
- non relativistic quark model

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[52]	Bodwin G T and Petrelli A, Phys. Rev. D, 66:094011(2002)
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[54]	Lakhina O and Swanson E S, Phys. Rev. D, 74:014012(2006)
[55]	Okamoto M et al, Phys. Rev. D, 65:094508(2002)
[56]	M. Shah, A. Parmar, and P. C. Vinodkumar, Phys. Rev. D, 86:034015(2012)
[57]	Daniel Mohler et al, Fermilab Lattice and MILC Collaborations, arXiv:hep-lat/1412.1057v1
[58]	E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T. M.Yan, Phys. Rev. D, 17:3090(1978)
[59]	Stanley F. Radford, and Wayne W. Repko, Phys. Rev. D, 75:074031(2007)
[60]	Buchmuller and Tye, Phys. Rev. D, 24:132(1981)
[61]	Vinodkumar P C, Pandya J N, Bannur V M, and Khadkikar S B, Eur. Phys.J. A, 4:83(1999)
[62]	Gonzalez P, Valcarce A, Garcilazo H, and Vijande J, Phys. Rev. D, 68:034007(2003)
[63]	Bai-Qing Li and Kuang-Ta Chao, Phys. Rev. D, 79:094004(2009)
[64]	Chien-Wen Hwang and Rurng-Sheng Guo, Phy. Rev. D, 82:034021(2010)
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References

[1]	G. Bonvicini et al(CLEO Collaboration), Phys. Rev. D, 81:031104(2010)
[2]	K. M. Ecklund et al(CLEO Collaboration), Phys. Rev. D, 78:091501(2008)
[3]	B. Auger et al(BABAR Collaboration), Phys. Rev. Lett., 103:161801(2009)
[4]	N Brambilla et al, 2011 Eur. Phys. J. C, 71:1534
[5]	K. Nakamura(Particle Data Group), 2010 J. Phys. G:Nucl. Part. Phys., 37:075021
[6]	K. A. Olive et al(Particle Data Group), Chinese Physics C, 38:(9) 090001(2014)
[7]	M. R. Ahmady and R. R. Mendel, Phys. Rev. D, 51:141(1995)
[8]	D. Ebert, R. N. Faustov, and V. O. Galkin, Mod. Phys. Lett. A, 18:601(2003)
[9]	C. W. Hwang and Z. T. Wei, J. Phys. G, 34:687(2007)
[10]	H. W. Huang, J. H. Liu, J. Tang, and K. T. Chao, Phys. Rev. D, 56:368(1997)
[11]	C. S. Kim, T. Lee, and G. L. Wang, Phys. Lett. B, 606:323(2005)
[12]	J. P. Lansberg and T. N. Pham, Phys. Rev. D, 74:034001(2006); 75:017501(2007)
[13]	J. J. Dudek and R. G. Edwards, Phys. Rev. Lett., 97:172001(2006)
[14]	W. Buchmuller, S.H.H. Tye, Phys. Rev. D, 24:132(1981)
[15]	A. Martin, Phys. Lett. B, 93:338(1980)
[16]	C. Quigg and J.L. Rosner, Phys. Lett. B, 71:153(1977)
[17]	A. K. Rai, J.N. Pandya, and P. C. Vinodkumar, J. Phys. G:Nucl. Part. Phys., 31:1453(2005)
[18]	S. S. Gershtein, V.V. Kiselev, A.K. Likhoded, and A. V. Tkabladze, Phys. Rev. D, 51:3613(1995)
[19]	H. Khan and P. Hoodbhoy, Phys. Rev. D, 53:2534(1996)
[20]	G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev. D, 51:1125(1995); 55:5853(1997)(E)
[21]	G. T. Bodwin, D. Kang, and J. Lee, Phys. Rev. D, 74:014014(2006)
[22]	G. T. Bodwin, H.S. Chang, D. Kang, J. Lee, and Chaehyun Yu, Phys. Rev. D, 77:094017(2008)
[23]	N.N. Singh et al, Phys. Rev. D, 38:1454(1988); S. Chakrabarty et al, Prog. Part. Nucl. Phys., 22:143180(1989)
[24]	A. Mittal et al, Phys. Rev. Lett., 57:290(1986); K. K. Gupta et al, Phys. Rev. D, 42:1604(1990); A. Sharma et al, Phys. Rev. D, 50:454(1994)
[25]	S.Bhatnagar, and S-Y.Li, J. Phys. G, 32:949(2006)
[26]	S. Bhatnagar, J. Mahecha, and Y. Mengesha, Phys. Rev D, 90:014034(2014)
[27]	R. Alkofer, P. Watson, and H. Weigel, Phys. Rev. D, 65:094026(2002)
[28]	R. Alkofer and L. W. Smekel, Phys. Rep., 353:281(2001)
[29]	G. Cvetic, C. S. Kim, G.-Li Wang, and W. Namgung, Phys. Lett. B, 596:84(2004)
[30]	A. N. Mitra and B. M. Sodermark, Nucl. Phys. A, 695:328(2001)
[31]	T. Barnes, S. Godfrey, and E.S. Swanson, Phys. Rev. D, 72:054026(2005)
[32]	Olga Lakhina and Eric S. Swanson, Phys. Rev D, 74:014012(2006), arXiv:hep-ph/0603164
[33]	M.B. Voloshin, Prog. Part. Nucl. Phys., 61:455(2008), arXiv:0711.4556[hep-ph]
[34]	E. Eichten, S. Godfrey, and H. Mahlke, J.L. Rosner, Rev. Mod. Phys., 80:1161(2008)
[35]	W. Lucha and F. Shoberl, Int. J. Mod. Phys. C, 10:(1999), arXiv:hep-ph/9811453
[36]	L. Landau, Phys. Abstracts A, 52:125(1949)
[37]	C. N. Yang, Phys. Rev., 77:242(1950)
[38]	Kwong Waikwok et al, Phys. Rev. D, 37:3210(1988)
[39]	Arpit Parmar, Bhavin Patel, and P. C. Vinodkumar, Nuclear Physics A, 848:299-316(2010)
[40]	Patel Bhavin, et al, J. Phys. G:Nucl. Part. Phys., 36:035003(2009)
[41]	Rai A K, Patel B, and Vinodkumar P C, Phys. Rev. C, 78:055202(2008)
[42]	Han-Wen Huang and Kuang-Ta Chao, Phys. Rev. D, 54:6850(1996); Han-Wen Huang and Kuang-Ta Chao, Phys. Rev. D, 56:182(1996)
[43]	R. Barbieri, R. Gatto, and R. Kogerler, Phys. Lett. B, 60:183(1976)
[44]	A. Petrelli, M. Cacciari, M. Greco, F. Maltoni, and M.L. Mangano, Nucl. Phys. B, 514:245(1998)
[45]	Wang G L, Phys. Lett. B, 653; 206(2007)
[46]	J. P. Lansberg, and T. N. Pham, Phys. Rev. D, 79:094016(2009), arXiv:0903.1562[hep-ph]
[47]	R. Barbieri, M. Caffo, R. Gatto, and E. Remiddi, Nucl. Phys. B, 192:61(1981)
[48]	M. Mangano and A. Petrelli, Phys. Lett. B, 352:445(1995)
[49]	Bhavin Patel et al, J. Phy. G.:Nucl. Part. Phys., 35:065001(2008)
[50]	P C Vinodkumar and Bhavin Patel, Chinese Phys. C, 34:1411(2010)
[51]	Appelquist T and Politzer H D, Phys. Rev. Lett., 34:43(1975)
[52]	Bodwin G T and Petrelli A, Phys. Rev. D, 66:094011(2002)
[53]	Bali G S, Schiling K, and Wachter A, Phys. Rev. D, 56:2566
[54]	Lakhina O and Swanson E S, Phys. Rev. D, 74:014012(2006)
[55]	Okamoto M et al, Phys. Rev. D, 65:094508(2002)
[56]	M. Shah, A. Parmar, and P. C. Vinodkumar, Phys. Rev. D, 86:034015(2012)
[57]	Daniel Mohler et al, Fermilab Lattice and MILC Collaborations, arXiv:hep-lat/1412.1057v1
[58]	E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T. M.Yan, Phys. Rev. D, 17:3090(1978)
[59]	Stanley F. Radford, and Wayne W. Repko, Phys. Rev. D, 75:074031(2007)
[60]	Buchmuller and Tye, Phys. Rev. D, 24:132(1981)
[61]	Vinodkumar P C, Pandya J N, Bannur V M, and Khadkikar S B, Eur. Phys.J. A, 4:83(1999)
[62]	Gonzalez P, Valcarce A, Garcilazo H, and Vijande J, Phys. Rev. D, 68:034007(2003)
[63]	Bai-Qing Li and Kuang-Ta Chao, Phys. Rev. D, 79:094004(2009)
[64]	Chien-Wen Hwang and Rurng-Sheng Guo, Phy. Rev. D, 82:034021(2010)
[65]	S N Gupta et al, Phy. Rev. D, 54:2075(1996)
[66]	H. W. Crater, C. Y. Wong, and P. VanAlstine, Phys. Rev. D, 74:054028(2006)
[67]	James T L et al, arXiv:hep-ph/0901.3917
[68]	M. G. Olsson, A. D. Martin, and A.W. Peacock, Phys. Rev. D. 31:81(1985)
[69]	Huang H W et al, Phys. Rev. D. 54:2123(1996)

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Smruti Patel, P. C. Vinodkumar and Shashank Bhatnagar. Decay rates of charmonia within a quark-antiquark confining potential[J]. Chinese Physics C, 2016, 40(5): 053102. doi: 10.1088/1674-1137/40/5/053102

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Received: 2015-08-13
Revised: 2015-11-12

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Supported by Major Research Project NO. F. 40-457/2011(SR), UGC, India

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沈阳化工大学材料科学与工程学院沈阳 110142

Decay rates of charmonia within a quark-antiquark confining potential

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Decay rates of charmonia within a quark-antiquark confining potential

Corresponding author: Smruti Patel,

Corresponding author: P. C. Vinodkumar,

Corresponding author: Shashank Bhatnagar,

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