Three-loop anomalous dimension of the non-singlet transversity operator in QCD

Nuclear Physics B

Volumn 864, Issue 1, 2012, Pages 113-140

  Velizhanin, V N ^a  

^a PETERSBURG NUCLEAR PHYSICS INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84863833240     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2012.06.010     Document Type: Article

References (75)

1. Gross D.J., Wilczek F. Asymptotically free gauge theories. 1. Phys. Rev. D 1973, 8:3633-3652. doi:10.1103/PhysRevD.8.3633.
2. Georgi H., Politzer H.D. Electroproduction scaling in an asymptotically free theory of strong interactions. Phys. Rev. D 1974, 9:416-420. doi:10.1103/PhysRevD.9.416.
3. Altarelli G., Parisi G. Asymptotic freedom in parton language. Nucl. Phys. B 1977, 126:298. doi:10.1016/0550-3213(77)90384-4.
4. Floratos E.G., Ross D.A., Sachrajda C.T. Higher order effects in asymptotically free gauge theories: The anomalous dimensions of Wilson operators. Nucl. Phys. B 1977, 129:66-88. doi:10.1016/0550-3213(77)90020-7.
5. Gonzalez-Arroyo A., Lopez C., Yndurain F.J. Second order contributions to the structure functions in deep inelastic scattering. 1. Theoretical calculations. Nucl. Phys. B 1979, 153:161-186. doi:10.1016/0550-3213(79)90466-8.
6. Curci G., Furmanski W., Petronzio R. Evolution of parton densities beyond leading order: The nonsinglet case. Nucl. Phys. B 1980, 175:27. doi:10.1016/0550-3213(80)90003-6.
7. Moch S., Vermaseren J.A.M., Vogt A. The three-loop splitting functions in QCD: The non-singlet case. Nucl. Phys. B 2004, 688:101-134. arxiv:hep-ph/0403192.
8. Baikov P.A., Chetyrkin K.G. New four loop results in QCD. Nucl. Phys. B (Proc. Suppl.) 2006, 160:76-79. doi:10.1016/j.nuclphysbps.
9. Velizhanin V.N. Four loop anomalous dimension of the second moment of the non-singlet twist-2 operator in QCD. Nucl. Phys. B 2012, 860:288-294. arxiv:1112.3954.
10. Ralston J.P., Soper D.E. Production of dimuons from high-energy polarized proton proton collisions. Nucl. Phys. B 1979, 152:109. doi:10.1016/0550-3213(79)90082-8.
11. Jaffe R.L., Ji X.-D. Chiral odd parton distributions and polarized Drell-Yan. Phys. Rev. Lett. 1991, 67:552-555. doi:10.1103/PhysRevLett.
12. Jaffe R.L., Ji X.-D. Chiral odd parton distributions and Drell-Yan processes. Nucl. Phys. B 1992, 375:527-560. doi:10.1016/0550-3213(92)90110-W.
13. Cortes J.L., Pire B., Ralston J.P. Measuring the transverse polarization of quarks in the proton. Z. Phys. C 1992, 55:409-416. doi:10.1007/BF01565099.
14. Collins J.C. Fragmentation of transversely polarized quarks probed in transverse momentum distributions. Nucl. Phys. B 1993, 396:161-182. arxiv:hep-ph/9208213.
15. Jaffe R.L., Ji X.-D. Novel quark fragmentation functions and the nucleon?s transversity distribution. Phys. Rev. Lett. 1993, 71:2547-2550. arxiv:hep-ph/9307329.
16. Tangerman R.D., Mulders P.J. Polarized twist-three distributions g(T) and h(L) and the role of intrinsic transverse momentum arxiv:hep-ph/9408305.
17. Boer D., Mulders P.J. Time-reversal odd distribution functions in leptoproduction. Phys. Rev. D 1998, 57:5780-5786. arxiv:hep-ph/9711485.
18. Artru X., Mekhfi M. Transversely polarized parton densities, their evolution and their measurement. Z. Phys. C 1990, 45:669. doi:10.1007/BF01556280.
19. Baldracchini F., Craigie N.S., Roberto V., Socolovsky M. A survey of polarization asymmetries predicted by QCD. Fortschr. Phys. 1981, 30:505-550. doi:10.1002/prop.
20. Shifman M.A., Vysotsky M.I. Form-factors of heavy mesons in QCD. Nucl. Phys. B 1981, 186:475. doi:10.1016/0550-3213(81)90023-7.
21. Bukhvostov A.P., Frolov G.V., Lipatov L.N., Kuraev E.A. Evolution equations for quasi-partonic operators. Nucl. Phys. B 1985, 258:601-646. doi:10.1016/0550-3213(85)90628-5.
22. Blumlein J. On the anomalous dimension of the transversity distribution h1(x,Q2). Eur. Phys. J. C 2001, 20:683-687. arxiv:hep-ph/0104099.
23. Mukherjee A., Chakrabarti D. Quark transversity distribution in perturbative QCD: Light-front Hamiltonian approach. Phys. Lett. B 2001, 506:283-288. arxiv:hep-ph/0102003.
24. Hayashigaki A., Kanazawa Y., Koike Y. Next-to-leading order Q2-evolution of the transversity distribution h1(x,Q2). Phys. Rev. D 1997, 56:7350-7360. arxiv:hep-ph/9707208.
25. Kumano S., Miyama M. Two-loop anomalous dimensions for the structure function h1. Phys. Rev. D 1997, 56:2504-2508. arxiv:hep-ph/9706420.
26. Vogelsang W. Next-to-leading order evolution of transversity distributions and Soffer?s inequality. Phys. Rev. D 1998, 57:1886-1894. arxiv:hep-ph/9706511.
27. Gracey J.A. Three loop anomalous dimension of non-singlet quark currents in the RI? scheme. Nucl. Phys. B 2003, 662:247-278. arxiv:hep-ph/0304113.
28. Gracey J.A. Three loop anomalous dimension of the second moment of the transversity operator in the MS-bar and RI? schemes. Nucl. Phys. B 2003, 667:242-260. arxiv:hep-ph/0306163.
29. Gracey J.A. Three loop anomalous dimensions of higher moments of the non-singlet twist-2 Wilson and transversity operators in the MSbar and RI? schemes. JHEP 2006, 0610:040. arxiv:hep-ph/0609231.
30. Gracey J.A. Three loop MS-bar transversity operator anomalous dimensions for fixed moment n?8. Phys. Lett. B 2006, 643:374-378. arxiv:hep-ph/0611071.
31. Blumlein J., Klein S., Todtli B. O(?s2) and O(?s3) heavy flavor contributions to transversity at Q2?m2. Phys. Rev. D 2009, 80:094010. arxiv:0909.1547.
32. Vogt A., Moch S., Vermaseren J.A.M. The three-loop splitting functions in QCD: The singlet case. Nucl. Phys. B 2004, 691:129-181. arxiv:hep-ph/0404111.
33. Vermaseren J.A.M., Vogt A., Moch S. The third-order QCD corrections to deep-inelastic scattering by photon exchange. Nucl. Phys. B 2005, 724:3-182. arxiv:hep-ph/0504242.
34. Moch S., Vermaseren J.A.M., Vogt A. Third-order QCD corrections to the charged-current structure function F3. Nucl. Phys. B 2009, 813:220-258. arxiv:0812.4168.
35. Kotikov A.V., Lipatov L.N., Velizhanin V.N. Anomalous dimensions of Wilson operators in N=4 SYM theory. Phys. Lett. B 2003, 557:114-120. arxiv:hep-ph/0301021.
36. Kotikov A.V., Lipatov L.N., Onishchenko A.I., Velizhanin V.N. Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model. Phys. Lett. B 2004, 595:521-529. arxiv:hep-th/0404092.
37. Kotikov A.V., Lipatov L.N., Rej A., Staudacher M., Velizhanin V.N. Dressing and wrapping. J. Stat. Mech. 2007, 0710:P10003. arxiv:0704.3586.
38. Lukowski T., Rej A., Velizhanin V.N. Five-loop anomalous dimension of twist-two operators. Nucl. Phys. B 2010, 831:105-132. arxiv:0912.1624.
39. Velizhanin V.N. Six-loop anomalous dimension of twist-three operators in N=4 SYM. JHEP 2010, 1011:129. arxiv:1003.4717.
40. Blumlein J., Kauers M., Klein S., Schneider C. Determining the closed forms of the O(a3(s)) anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra. Comput. Phys. Commun. 2009, 180:2143-2165. arxiv:0902.4091.
41. Bagaev A., Bednyakov A., Pikelner A., Velizhanin V. The 16th moment of the three loop anomalous dimension of the non-singlet transversity operator in QCD arxiv:1206.2890.
42. Gorishnii S.G., Larin S.A., Surguladze L.R., Tkachov F.V. MINCER: Program for multiloop calculations in quantum field theory for the schoonschip system. Comput. Phys. Commun. 1989, 55:381-408. doi:10.1016/0010-4655(89)90134-3.
43. Steinhauser M. MATAD: A program package for the computation of massive tadpoles. Comput. Phys. Commun. 2001, 134:335-364. arxiv:hep-ph/0009029.
44. Bierenbaum I., Blumlein J., Klein S. Mellin moments of the O(?s3) heavy flavor contributions to unpolarized deep-inelastic scattering at Q2?m2 and anomalous dimensions. Nucl. Phys. B 2009, 820:417-482. arxiv:0904.3563.
45. Collins J.C. Structure of counterterms in dimensional regularization. Nucl. Phys. B 1974, 80:341. doi:10.1016/0550-3213(74)90521-5.
46. Larin S.A., Vermaseren J.A.M. The three loop QCD Beta function and anomalous dimensions. Phys. Lett. B 1993, 303:334-336. arxiv:hep-ph/9302208.
47. Tarasov O.V., Vladimirov A.A. Two loop renormalization of the Yang-Mills theory in an arbitrary gauge. Sov. J. Nucl. Phys. 1977, 25:585.
48. Vladimirov A.A. Method for computing renormalization group functions in dimensional renormalization scheme. Theor. Math. Phys. 1980, 43:417. doi:10.1007/BF01018394.
49. O.V. Tarasov, A.A. Vladimirov, Three loop calculations in nonabelian gauge theories, preprint JINR-E2-80-483.
50. Vermaseren J.A.M. New features of FORM arxiv:math-ph/0010025.
51. Velizhanin V.N. Three-loop renormalization of the N=1, N=2, N=4 supersymmetric Yang-Mills theories. Nucl. Phys. B 2009, 818:95-100. arxiv:0809.2509.
52. Tentyukov M., Fleischer J. A Feynman diagram analyser DIANA. Comput. Phys. Commun. 2000, 132:124-141. arxiv:hep-ph/9904258.
53. Nogueira P. Automatic Feynman graph generation. J. Comput. Phys. 1993, 105:279-289. doi:10.1006/jcph.
54. van Ritbergen T., Schellekens A.N., Vermaseren J.A.M. Group theory factors for Feynman diagrams. Int. J. Mod. Phys. A 1999, 14:41-96. arxiv:hep-ph/9802376.
55. Gonzalez-Arroyo A., Lopez C. Second order contributions to the structure functions in deep inelastic scattering. 3. The singlet case. Nucl. Phys. B 1980, 166:429. doi:10.1016/0550-3213(80)90207-2.
56. Vermaseren J.A.M. Harmonic sums, Mellin transforms and integrals. Int. J. Mod. Phys. A 1999, 14:2037-2076. arxiv:hep-ph/9806280.
57. Blumlein J., Kurth S. Harmonic sums and Mellin transforms up to two loop order. Phys. Rev. D 1999, 60:014018. arxiv:hep-ph/9810241.
58. Lipatov L.N. Reggeization of the vector meson and the vacuum singularity in nonabelian gauge theories. Sov. J. Nucl. Phys. 1976, 23:338-345.
59. Kuraev E.A., Lipatov L.N., Fadin V.S. The Pomeranchuk singularity in nonabelian gauge theories. Sov. Phys. JETP 1977, 45:199-204.
60. Balitsky I.I., Lipatov L.N. The Pomeranchuk singularity in quantum chromodynamics. Sov. J. Nucl. Phys. 1978, 28:822-829.
61. Kotikov A.V., Lipatov L.N. DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory. Nucl. Phys. B 2003, 661:19-61. arxiv:hep-ph/0208220.
62. Fadin V.S., Lipatov L.N. BFKL pomeron in the next-to-leading approximation. Phys. Lett. B 1998, 429:127-134. arxiv:hep-ph/9802290.
63. Gribov V.N., Lipatov L.N. Deep inelastic ep scattering in perturbation theory. Sov. J. Nucl. Phys. 1972, 15:438-450.
64. Gribov V.N., Lipatov L.N. e+e? pair annihilation and deep inelastic ep scattering in perturbation theory. Sov. J. Nucl. Phys. 1972, 15:675-684.
65. Dokshitzer Y.L. Calculation of the structure functions for deep inelastic scattering and e+e? annihilation by perturbation theory in quantum chromodynamics. Sov. Phys. JETP 1977, 46:641-653.
66. Ablinger J., Blumlein J., Klein S., Schneider C., Wissbrock F. The O(?s3) massive operator matrix elements of O(nf) for the structure function F2(x,Q2) and transversity. Nucl. Phys. B 2011, 844:26-54. arxiv:1008.3347.
67. Dokshitzer Y.L., Marchesini G., Salam G.P. Revisiting parton evolution and the large-x limit. Phys. Lett. B 2006, 634:504-507. arxiv:hep-ph/0511302.
68. Dokshitzer Y.L., Marchesini G. N=4 SUSY Yang-Mills: Three loops made simple(r). Phys. Lett. B 2007, 646:189-201. arxiv:hep-th/0612248.
69. Beccaria M., Forini V. Four loop reciprocity of twist two operators in N=4 SYM. JHEP 2009, 0903:111. arxiv:0901.1256.
70. Lenstra A.K., Lenstra H.W., Lovasz L. Factoring polynomials with rational coefficients. Math. Ann. 1982, 261:515-534. doi:10.1007/BF01457454.
71. Goncharov A.B. Multiple polylogarithms, cyclotomy and modular complexes. Math. Res. Lett. 1998, 5:497-516.
72. Borwein J.M., Bradley D.M., Broadhurst D.J., Lisonek P. Special values of multiple polylogarithms. Trans. Amer. Math. Soc. 2001, 353:907-941. arxiv:math/9910045.
73. Remiddi E., Vermaseren J.A.M. Harmonic polylogarithms. Int. J. Mod. Phys. A 2000, 15:725-754. arxiv:hep-ph/9905237.
74. Maitre D. HPL, a Mathematica implementation of the harmonic polylogarithms. Comput. Phys. Commun. 2006, 174:222-240. arxiv:hep-ph/0507152.
75. Maitre D. Extension of HPL to complex arguments. Comput. Phys. Commun. 2012, 183:846. arxiv:hep-ph/0703052.