×

Basic features of the pion valence-quark distribution function. (English) Zbl 1317.81253

Summary: The impulse-approximation expression used hitherto to define the pion’s valence-quark distribution function is flawed because it omits contributions from the gluons which bind quarks into the pion. A corrected leading-order expression produces the model-independent result that quarks dressed via the rainbow-ladder truncation, or any practical analogue, carry all the pion’s light-front momentum at a characteristic hadronic scale. Corrections to the leading contribution may be divided into two classes, responsible for shifting dressed-quark momentum into glue and sea-quarks. Working with available empirical information, we use an algebraic model to express the principal impact of both classes of corrections. This enables a realistic comparison with experiment that allows us to highlight the basic features of the pion’s measurable valence-quark distribution, \(q^\pi(x)\); namely, at a characteristic hadronic scale, \(q^\pi(x) \sim(1 - x)^2\) for \(x \gtrsim 0.85\); and the valence-quarks carry approximately two-thirds of the pion’s light-front momentum.

MSC:

81V05 Strong interaction, including quantum chromodynamics
81U35 Inelastic and multichannel quantum scattering
81R40 Symmetry breaking in quantum theory
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Pieper, S. C.; Wiringa, R. B., Annu. Rev. Nucl. Part. Sci., 51, 53-90 (2001)
[2] Machleidt, R.; Entem, D., Phys. Rep., 503, 1-75 (2011)
[3] Maris, P.; Roberts, C. D.; Tandy, P. C., Phys. Lett. B, 420, 267-273 (1998)
[4] Ezawa, Z. F., Nuovo Cimento A, 23, 271-290 (1974)
[5] Farrar, G. R.; Jackson, D. R., Phys. Rev. Lett., 35, 1416 (1975)
[6] Holt, R. J.; Roberts, C. D., Rev. Mod. Phys., 82, 2991-3044 (2010)
[7] Conway, J. S., Phys. Rev. D, 39, 92-122 (1989)
[9] Bjorken, J. D., Phys. Rev., 179, 1547-1553 (1969)
[10] Cloët, I. C.; Roberts, C. D., Prog. Part. Nucl. Phys., 77, 1-69 (2014)
[11] Munczek, H. J., Phys. Rev. D, 52, 4736-4740 (1995)
[12] Bender, A.; Roberts, C. D.; von Smekal, L., Phys. Lett. B, 380, 7-12 (1996)
[13] Chang, L.; Roberts, C. D., Phys. Rev. Lett., 103, 081601 (2009)
[14] Bicudo, P., Phys. Rev. D, 65, 076008 (2002)
[15] Binosi, D.; Theußl, L., Comput. Phys. Commun., 161, 76-86 (2004)
[16] Shigetani, T.; Suzuki, K.; Toki, H., Phys. Lett. B, 308, 383-388 (1993)
[17] Davidson, R. M.; Ruiz Arriola, E., Phys. Lett. B, 348, 163-169 (1995)
[18] Bentz, W.; Hama, T.; Matsuki, T.; Yazaki, K., Nucl. Phys. A, 651, 143-173 (1999)
[19] Dorokhov, A. E.; Tomio, L., Phys. Rev. D, 62, 014016 (2000)
[20] Hecht, M. B.; Roberts, C. D.; Schmidt, S. M., Phys. Rev. C, 63, 025213 (2001)
[21] Nguyen, T.; Bashir, A.; Roberts, C. D.; Tandy, P. C., Phys. Rev. C, 83, 062201(R) (2011)
[22] Maris, P.; Tandy, P. C., Phys. Rev. C, 62, 055204 (2000)
[23] Brodsky, S. J.; Hwang, D. S.; Schmidt, I., Phys. Lett. B, 530, 99-107 (2002)
[24] Nambu, Y.; Jona-Lasinio, G., Phys. Rev., 122, 345-358 (1961)
[25] Roberts, H. L.L.; Roberts, C. D.; Bashir, A.; Gutiérrez-Guerrero, L. X.; Tandy, P. C., Phys. Rev. C, 82, 065202 (2010)
[26] Chang, L., Phys. Rev. Lett., 110, 132001 (2013)
[27] Lepage, G. P.; Brodsky, S. J., Phys. Lett. B, 87, 359-365 (1979)
[28] Efremov, A. V.; Radyushkin, A. V., Phys. Lett. B, 94, 245-250 (1980)
[29] Lepage, G. P.; Brodsky, S. J., Phys. Rev. D, 22, 2157-2198 (1980)
[30] Mezrag, C., 2014, in progress; see also
[31] Roberts, C. D., Nucl. Phys. A, 605, 475-495 (1996)
[32] Beringer, J., Phys. Rev. D, 86, 010001 (2012)
[33] Qin, S.-X.; Chang, L.; Liu, Y.-X.; Roberts, C. D.; Wilson, D. J., Phys. Rev. C, 84, 042202(R) (2011)
[34] Dokshitzer, Y. L., Sov. Phys. JETP, 46, 641-653 (1977)
[35] Gribov, V. N.; Lipatov, L. N., Sov. J. Nucl. Phys., 15, 438-450 (1972)
[36] Lipatov, L. N., Sov. J. Nucl. Phys., 20, 94-102 (1975)
[37] Altarelli, G.; Parisi, G., Nucl. Phys. B, 126, 298 (1977)
[38] Chang, L.; Roberts, C. D.; Wilson, D. J., (PoS QCD-TNT-II (2012)), 039
[39] Alkofer, R.; Bender, A.; Roberts, C. D., Int. J. Mod. Phys. A, 10, 3319-3342 (1995)
[40] Maris, P.; Roberts, C. D., Phys. Rev. C, 58, 3659-3665 (1998)
[41] Chang, L.; Cloët, I. C.; Roberts, C. D.; Schmidt, S. M.; Tandy, P. C., Phys. Rev. Lett., 111, 141802 (2013)
[42] Gasser, J.; Leutwyler, H., Ann. Phys., 158, 142 (1984)
[43] Gluck, M.; Reya, E.; Schienbein, I., Eur. Phys. J. C, 10, 313-317 (1999)
[44] Gluck, M.; Reya, E.; Stratmann, M.; Vogelsang, W., Phys. Rev. D, 53, 4775-4786 (1996)
[45] Brommel, D., (PoS, vol. LAT2007 (2007)), 140
[46] Best, C., Phys. Rev. D, 56, 2743-2754 (1997)
[47] Detmold, W.; Melnitchouk, W.; Thomas, A. W., Phys. Rev. D, 68, 034025 (2003)
[48] Aicher, M.; Schäfer, A.; Vogelsang, W., Phys. Rev. Lett., 105, 252003 (2010)
[49] Wijesooriya, K.; Reimer, P. E.; Holt, R. J., Phys. Rev. C, 72, 065203 (2005)
[50] Sutton, P. J.; Martin, A. D.; Roberts, R. G.; Stirling, W. J., Phys. Rev. D, 45, 2349-2359 (1992)
[51] Chang, L.; Roberts, C. D.; Schmidt, S. M., Phys. Lett. B, 727, 255-259 (2013)
[52] Holtmann, H.; Levman, G.; Nikolaev, N. N.; Szczurek, A.; Speth, J., Phys. Lett. B, 338, 363-368 (1994)
[53] Londergan, J. T.; Liu, G. Q.; Rodionov, E. N.; Thomas, A. W., Phys. Lett. B, 361, 110-114 (1995)
[54] Londergan, J. T.; Liu, G. Q.; Thomas, A. W., Phys. Lett. B, 380, 393-398 (1996)
[55] Holt, R. J.; Reimer, P. E., AIP Conf. Proc., 588, 234-239 (2001)
[56] Petrov, V. A.; Ryutin, R. A.; Sobol, A. E.; Murray, M. J., Eur. Phys. J. C, 72, 1886 (2012)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.