Orthopositronium lifetime at O (α) and O (α3 lnα) in closed form

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 80, Issue 5, 2009, Pages

  Kniehl, B A ^a   Kotikov, A V ^a,b   Veretin, O L ^a  

^a UNIVERSITY OF HAMBURG   (Germany)

^b JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY PRECISION; CLOSED FORM; IRRATIONAL NUMBERS; ORTHO-POSITRONIUM LIFETIME; OTHER APPLICATIONS; POLYLOGARITHMS; RADIATIVE CORRECTIONS; TRANSFORMATION FORMULA;

EID: 70449087454     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.052501     Document Type: Article

References (87)

1. M. Deutsch, Phys. Rev. 82, 455 (1951). 10.1103/PhysRev.82.455
2. W. E. Caswell and G. P. Lepage, Phys. Lett. B 167, 437 (1986). 10.1016/0370-2693(86)91297-9
3. M. Deutsch, Phys. Rev. 83, 866 (1951). 10.1103/PhysRev.83.866
4. A. Ore and J. L. Powell, Phys. Rev. 75, 1696 (1949). 10.1103/PhysRev.75. 1696
5. R. H. Beers and V. W. Hughes, Bull. Am. Phys. Soc. 13, 633 (1968).
6. W. E. Caswell, G. P. Lepage, and J. R. Sapirstein, Phys. Rev. Lett. 38, 488 (1977). 10.1103/PhysRevLett.38.488
7. I. Harris and L. M. Brown, Phys. Rev. 105, 1656 (1957). 10.1103/PhysRev.105.1656
8. C. I. Westbrook, D. W. Gidley, R. S. Conti, and A. Rich, Phys. Rev. Lett. 58, 1328 (1987) 10.1103/PhysRevLett.58.1328
9. C. I. Westbrook, D. W. Gidley, R. S. Conti, and A. Rich, Phys. Rev. Lett. 58, 2153 (E) (1987) 10.1103/PhysRevLett.58.2153.6
10. C. I. Westbrook, D. W. Gidley, R. S. Conti, and A. Rich, Phys. Rev. A 40, 5489 (1989). 10.1103/PhysRevA.40.5489
11. R. S. Vallery, P. W. Zitzewitz, and D. W. Gidley, Phys. Rev. Lett. 90, 203402 (2003). 10.1103/PhysRevLett.90.203402
12. O. Jinnouchi, S. Asai, and T. Kobayashi, Phys. Lett. B 572, 117 (2003). 10.1016/j.physletb.2003.08.018
13. W. E. Caswell and G. P. Lepage, Phys. Rev. A 20, 36 (1979). 10.1103/PhysRevA.20.36
14. I. B. Khriplovich and A. S. Yelkhovsky, Phys. Lett. B 246, 520 (1990). 10.1016/0370-2693(90)90641-I
15. S. G. Karshenboim, Sov. Phys. JETP 76, 541 (1993)
16. S. G. Karshenboim, [Zh. Eksp. Teor. Fiz. 103, 1105 (1993)].
17. M. A. Stroscio and J. M. Holt, Phys. Rev. A 10, 749 (1974) 10.1103/PhysRevA.10.749
18. M. A. Stroscio, Phys. Rep. 22, 215 (1975) 10.1016/0370-1573(75)90029-0
19. G. S. Adkins, Ann. Phys. (N.Y.) 146, 78 (1983) 10.1016/0003-4916(83) 90053-2
20. G. S. Adkins, A. A. Salahuddin, and K. E. Schalm, Phys. Rev. A 45, 7774 (1992) 10.1103/PhysRevA.45.7774
21. G. S. Adkins, Phys. Rev. Lett. 76, 4903 (1996). 10.1103/PhysRevLett.76. 4903
22. G. S. Adkins, R. N. Fell, and J. R. Sapirstein Phys. Rev. Lett. 84, 5086 (2000) 10.1103/PhysRevLett.84.5086
23. G. S. Adkins, R. N. Fell, and J. R. Sapirstein Phys. Rev. A 63, 032511 (2001). 10.1103/PhysRevA.63.032511
24. G. S. Adkins, Phys. Rev. A 72, 032501 (2005). 10.1103/PhysRevA.72.032501
25. B. A. Kniehl and A. A. Penin, Phys. Rev. Lett. 85, 1210 (2000) 10.1103/PhysRevLett.85.1210
26. B. A. Kniehl and A. A. Penin, Phys. Rev. Lett. 85, 3065 (E) (2000) 10.1103/PhysRevLett.85.3065
27. R. J. Hill and G. P. Lepage, Phys. Rev. D 62, 111301 (R) (2000) 10.1103/PhysRevD.62.111301
28. K. Melnikov and A. Yelkhovsky, Phys. Rev. D 62, 116003 (2000). 10.1103/PhysRevD.62.116003
29. G. S. Adkins, R. N. Fell, and J. R. Sapirstein, Ann. Phys. (N.Y.) 295, 136 (2002) 10.1006/aphy.2001.6219
30. D. Sillou, Int. J. Mod. Phys. A 19, 3919 (2004). 10.1142/ S0217751X04020178
31. A. Rubbia, Int. J. Mod. Phys. A 19, 3961 (2004) 10.1142/S0217751X0402021X
32. S. N. Gninenko, N. V. Krasnikov, V. A. Matveev, and A. Rubbia, Phys. Part. Nucl. 37, 321 (2006) 10.1134/S1063779606030038
33. S. N. Gninenko, N. V. Krasnikov, and V. A. Matveev, Phys. Rev. D 78, 097701 (2008). 10.1103/PhysRevD.78.097701
34. K. Akama, Lect. Notes Phys. 176, 267 (1983) 10.1007/3-540-11994-9-41
35. V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B 125, 136 (1983) 10.1016/0370-2693(83)91253-4
36. M. Visser, Phys. Lett. B 159, 22 (1985) 10.1016/0370-2693(85)90112-1
37. I. Antoniadis, Phys. Lett. B 246, 377 (1990) 10.1016/0370-2693(90)90617-F
38. N. V. Krasnikov, Phys. Lett. B 273, 246 (1991). 10.1016/0370-2693(91) 91678-O
39. N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Lett. B 429, 263 (1998) 10.1016/S0370-2693(98)00466-3
40. I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Lett. B 436, 257 (1998) 10.1016/S0370-2693(98)00860-0
41. L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999) 10.1103/PhysRevLett.83.3370
42. L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999). 10.1103/PhysRevLett.83.4690
43. V. A. Rubakov, Phys. Usp. 44, 871 (2001) 10.1070/PU2001v044n09ABEH001000
44. V. A. Rubakov, [Usp. Fiz. Nauk 171, 913 (2001)]. 10.3367/UFNr.0171. 200109a.0913
45. S. L. Dubovsky, V. A. Rubakov, and P. G. Tinyakov, Phys. Rev. D 62, 105011 (2000). 10.1103/PhysRevD.62.105011
46. I. Oda, Phys. Lett. B 496, 113 (2000). 10.1016/S0370-2693(00)01284-3
47. S. L. Dubovsky, V. A. Rubakov, and P. G. Tinyakov, J. High Energy Physics 08 (2000), 041 10.1088/1126-6708/2000/08/041
48. S. L. Dubovsky and V. A. Rubakov, in Proceedings of the XXXVIIth Rencontres de Moriond: 2002 Electroweak Interactions and Unified Theories, edited by, J. Trĝn Thanh Vĝn, (Thê Giói, Vietnam, 2003), p. 367.
49. S. N. Gninenko, N. V. Krasnikov, and A. Rubbia, Phys. Rev. D 67, 075012 (2003). 10.1103/PhysRevD.67.075012
50. A. Badertscher, P. Crivelli, W. Fetscher, U. Gendotti, S. N. Gninenko, V. Postoev, A. Rubbia, V. Samoylenko, and D. Sillou, Phys. Rev. D 75, 032004 (2007). 10.1103/PhysRevD.75.032004
51. M. A. Stroscio, Phys. Rev. Lett. 48, 571 (1982) 10.1103/PhysRevLett.48. 571
52. G. S. Adkins, Phys. Rev. A 27, 530 (1983). 10.1103/PhysRevA.27.530
53. B. A. Kniehl, A. V. Kotikov, and O. L. Veretin, Phys. Rev. Lett. 101, 193401 (2008). 10.1103/PhysRevLett.101.193401
54. L. Lewin, Polylogarithms and Associated Functions (Elsevier, New York, 1981).
55. B. A. Kniehl and A. V. Kotikov, Phys. Lett. B 638, 531 (2006). 10.1016/j.physletb.2006.04.057
56. A. Devoto and D. W. Duke, Riv. Nuovo Cim. 7, 1 (1984). 10.1007/BF02724330
57. J. Fleischer, A. V. Kotikov, and O. L. Veretin, Phys. Lett. B 417, 163 (1998) 10.1016/S0370-2693(97)01195-7
58. J. Fleischer, M. Yu. Kalmykov, and A. V. Kotikov, Phys. Lett. B 462, 169 (1999) 10.1016/S0370-2693(99)00892-8
59. A. Kotikov, J. H. Kühn, and O. Veretin, Nucl. Phys. B 788, 47 (2008). 10.1016/j.nuclphysb.2007.07.018
60. J. Fleischer, A. V. Kotikov, and O. L. Veretin, Nucl. Phys. B 547, 343 (1999). 10.1016/S0550-3213(99)00078-4
61. M. Yu. Kalmykov and O. Veretin, Phys. Lett. B 483, 315 (2000). 10.1016/S0370-2693(00)00574-8
62. A. I. Davydychev and M. Yu. Kalmykov, Nucl. Phys. B 699, 3 (2004). 10.1016/j.nuclphysb.2004.08.020
63. B. A. Kniehl, A. V. Kotikov, and O. L. Veretin, Nucl. Phys. B (Proc. Suppl.) 183, 14 (2008). 10.1016/j.nuclphysbps.2008.09.075
64. D. J. Broadhurst, e-print arXiv:hep-th/9604128
65. D. J. Broadhurst, Eur. Phys. J. C 8, 311 (1999). 10.1007/s100529900935
66. L. Avdeev, J. Fleischer, S. Mikhailov, and O. Tarasov, Phys. Lett. B 336, 560 (1994) 10.1016/0370-2693(94)90573-8
67. L. Avdeev, J. Fleischer, S. Mikhailov, and O. Tarasov, Phys. Lett. B 349, 597 (E) (1995) 10.1016/0370-2693(95)00269-Q
68. J. Fleischer and O. V. Tarasov, Nucl. Phys. B (Proc. Suppl.) 37, 115 (1994) 10.1016/0920-5632(94)90666-1
69. K. G. Chetyrkin, J. H. Kühn, and M. Steinhauser, Phys. Lett. B 351, 331 (1995). 10.1016/0370-2693(95)00380-4
70. S. Laporta and E. Remiddi, Phys. Lett. B 379, 283 (1996). 10.1016/0370-2693(96)00439-X
71. D. J. Broadhurst and A. V. Kotikov, Phys. Lett. B 441, 345 (1998). 10.1016/S0370-2693(98)01146-0
72. B. A. Kniehl and A. V. Kotikov, Phys. Lett. B 642, 68 (2006). 10.1016/j.physletb.2006.09.008
73. B. A. Kniehl, A. V. Kotikov, A. I. Onishchenko, and O. L. Veretin, Phys. Rev. Lett. 97, 042001 (2006). 10.1103/PhysRevLett.97.042001
74. H. R. P. Ferguson and D. H. Bailey, RNR Technical Report No. RNR-91-032 (unpublished)
75. H. R. P. Ferguson, D. H. Bailey, and S. Arno, NASA Technical Report No. NAS-96-005 (unpublished).
76. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1980).
77. D. I. Kazakov and A. V. Kotikov, Nucl. Phys. B 307, 721 (1988) 10.1016/0550-3213(88)90106-X
78. D. I. Kazakov and A. V. Kotikov, Nucl. Phys. B 345, 299 (E) (1990)
79. D. I. Kazakov and A. V. Kotikov, Theor. Math. Phys. 73, 1264 (1988) 10.1007/BF01041909
80. D. I. Kazakov and A. V. Kotikov, [Teor. Mat. Fiz. 73, 348 (1987)]
81. A. V. Kotikov, Theor. Math. Phys. 78, 134 (1989) 10.1007/BF01018678
82. A. V. Kotikov, [Teor. Mat. Fiz. 78, 187 (1989)].
83. M. Yu. Kalmykov and B. A. Kniehl, Nucl. Phys. B 809, 365 (2009). 10.1016/j.nuclphysb.2008.08.022
84. Equation corrects a misprint in Eq. (15) of Ref., which is, however, inconsequential because the difference between these expressions cancels due to the x1 x3 symmetry.
85. The subscript of the universal contribution G3 is to indicate that all its parts carry weight three.
86. Some examples were already considered in Ref..
87. We may use Eq. as definition of the "sums" Sm with half-integer arguments.