Abstract
Strangeness was discovered roughly seventy years ago, lodged in a particle now known as the kaon, K. Kindred to the pion, \(\pi \); both states are massless in the absence of Higgs-boson couplings. Kaons and pions are Nature’s most fundamental Nambu–Goldstone modes. Their properties are largely determined by the mechanisms responsible for emergent mass in the standard model, but modulations applied by the Higgs are crucial to Universe evolution. Despite their importance, little is known empirically about K and \(\pi \) structure. This study delivers the first parameter-free predictions for all K distribution functions (DFs) and comparisons with the analogous \(\pi \) distributions, i.e. the one-dimensional maps that reveal how the light-front momentum of these states is shared amongst the gluons and quarks from which they are formed. The results should stimulate improved analyses of existing data and motivate new experiments sensitive to all K and \(\pi \) DFs.
Similar content being viewed by others
Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data generated during this study are represented in this published article.]
References
G.D. Rochester, C.C. Butler, Evidence for the existence of new unstable elementary particles. Nature 160, 855–857 (1947)
Y. Nambu, Quasiparticles and gauge invariance in the theory of superconductivity. Phys. Rev. 117, 648–663 (1960)
J. Goldstone, Field theories with superconductor solutions. Nuovo Cim. 19, 154–164 (1961)
T. Horn, C.D. Roberts, The pion: an enigma within the standard model. J. Phys. G. 43, 073001 (2016)
A.C. Aguilar et al., Pion and kaon structure at the electron-ion collider. Eur. Phys. J. A 55, 190 (2019)
C. D. Roberts, S. M. Schmidt, Reflections upon the Emergence of Hadronic Mass – arXiv:2006.08782 [hep-ph], Eur. Phys. J. ST (in press)
J. Christenson, J. Cronin, V. Fitch, R. Turlay, Evidence for the \(2\pi \) Decay of the \(K_2^0\) Meson. Phys. Rev. Lett. 13, 138–140 (1964)
S.-S. Xu, L. Chang, C.D. Roberts, H.-S. Zong, Pion and kaon valence-quark parton quasidistributions. Phys. Rev. D 97, 094014 (2018)
Z.-F. Cui, J.-L. Zhang, D. Binosi, F. de Soto, C. Mezrag, J. Papavassiliou, C.D. Roberts, J. Rodríguez-Quintero, J. Segovia, S. Zafeiropoulos, Effective charge from lattice QCD. Chin. Phys. C 44, 083102 (2020)
N. Nakanishi, A General survey of the theory of the Bethe–Salpeter equation. Prog. Theor. Phys. Suppl. 43, 1–81 (1969)
L. Chang, I.C. Cloet, J.J. Cobos-Martinez, C.D. Roberts, S.M. Schmidt, P.C. Tandy, Imaging dynamical chiral symmetry breaking: pion wave function on the light front. Phys. Rev. Lett. 110, 132001 (2013)
C.D. Roberts, Three lectures on hadron physics. J. Phys. Conf. Ser. 706, 022003 (2016)
G.P. Lepage, S.J. Brodsky, Exclusive processes in quantum chromodynamics: evolution equations for hadronic wave functions and the form-factors of mesons. Phys. Lett. B 87, 359–365 (1979)
A.V. Efremov, A.V. Radyushkin, Factorization and asymptotical behavior of pion form- factor in QCD. Phys. Lett. B 94, 245–250 (1980)
M. Ding et al., Drawing insights from pion parton distributions. Chin. Phys. C. (Lett.) 44, 031002 (2020a)
M. Ding et al., Symmetry, symmetry breaking, and pion parton distributions. Phys. Rev. D 101, 054014 (2020)
S.J. Brodsky, G.P. Lepage, Exclusive processes in quantum chromodynamics. Adv. Ser. Direct. High Energy Phys. 5, 93–240 (1989)
Y. L. Dokshitzer, Calculation of the structure functions for deep inelastic scattering and e+ e- annihilation by perturbation theory in quantum chromodynamics. (in russian), Sov. Phys. JETP 46 (1977) 641–653
V. Gribov, L. Lipatov, Deep inelastic e p scattering in perturbation theory. Sov. J. Nucl. Phys. 15, 438–450 (1972)
L.N. Lipatov, The parton model and perturbation theory. Sov. J. Nucl. Phys. 20, 94–102 (1975)
G. Altarelli, G. Parisi, Asymptotic freedom in parton language. Nucl. Phys. B 126, 298 (1977)
A.C. Aguilar, D. Binosi, J. Papavassiliou, The gluon mass generation mechanism: a concise primer. Front. Phys. China 11, 111203 (2016)
F. Gao, S.-X. Qin, C.D. Roberts, J. Rodríguez-Quintero, Locating the Gribov horizon. Phys. Rev. D 97, 034010 (2018)
J.C. Taylor, Ward identities and charge renormalization of the Yang–Mills field. Nucl. Phys. B 33, 436–444 (1971)
A.A. Slavnov, Ward Identities in Gauge theories. Theor. Math. Phys. 10, 99–107 (1972)
C. Becchi, A. Rouet, R. Stora, Renormalization of Gauge theories. Ann. Phys. 98, 287–321 (1976)
I. V. Tyutin, Gauge invariance in field theory and statistical physics in operator formalism. arXiv:0812.0580 [hep-th]
D. Binosi, C. Mezrag, J. Papavassiliou, C.D. Roberts, J. Rodríguez-Quintero, Process-independent strong running coupling. Phys. Rev. D 96, 054026 (2017)
A. Deur, S.J. Brodsky, G.F. de Teramond, The QCD running coupling. Prog. Part. Nucl. Phys. 90, 1–74 (2016a)
D. Binosi, L. Chang, J. Papavassiliou, C.D. Roberts, Bridging a gap between continuum-QCD and ab initio predictions of hadron observables. Phys. Lett. B 742, 183–188 (2015)
A. Deur, S.J. Brodsky, G.F. de Teramond, On the interface between perturbative and nonperturbative QCD. Phys. Lett. B 757, 275–281 (2016b)
R.K. Ellis, W.J. Stirling, B.R. Webber, QCD and collider physics (Cambridge University Press, Cambridge, 2011)
S.J. Brodsky, G.F. de Teramond, Hadronic spectra and light-front wavefunctions in holographic QCD. Phys. Rev. Lett. 96, 201601 (2006)
C.-W. Hwang, Meson distribution amplitudes in holographic models. Phys. Rev. D 86, 014005 (2012)
J.-H. Zhang, J.-W. Chen, X. Ji, L. Jin, H.-W. Lin, Pion distribution amplitude from lattice QCD. Phys. Rev. D 95, 094514 (2017)
C. Shi, L. Chang, C.D. Roberts, S.M. Schmidt, P.C. Tandy, H.-S. Zong, Flavour symmetry breaking in the kaon parton distribution amplitude. Phys. Lett. B 738, 512–518 (2014)
J. Segovia, L. Chang, I.C. Cloet, C.D. Roberts, S.M. Schmidt et al., Distribution amplitudes of light-quark mesons from lattice QCD. Phys. Lett. B 731, 13–18 (2014)
F. Gao, L. Chang, Y.-X. Liu, C.D. Roberts, P.C. Tandy, Exposing strangeness: projections for kaon electromagnetic form factors. Phys. Rev. D 96, 034024 (2017)
P. A. Zyla, et al., Review of particle properties, Prog. Theor. Exp. Phys. 083C01
A. Höll, A. Krassnigg, C.D. Roberts, Pseudoscalar meson radial excitations. Phys. Rev. C 70, 042203(R) (2004)
A. Krassnigg, P. Maris, Pseudoscalar and vector mesons as \(q {\bar{q}}\) bound states. J. Phys. Conf. Ser. 9, 153–160 (2005)
M.S. Bhagwat, A. Krassnigg, P. Maris, C.D. Roberts, Mind the gap. Eur. Phys. J. A 31, 630–637 (2007)
M. Gell-Mann, A schematic model of Baryons and Mesons. Phys. Lett. 8, 214–215 (1964)
G. Zweig, An SU(3) model for strong interaction symmetry and its breaking. Parts 1 and 2 (CERN Reports No. 8182/TH. 401 and No. 8419/TH. 412)
J. Badier et al., Measurement of the \(K^- / \pi ^-\) structure function ratio using the Drell–Yan process. Phys. Lett. B 93, 354 (1980)
S. Drell, T.-M. Yan, Massive lepton pair production in Hadron–Hadron collisions at high-energies, Phys. Rev. Lett. 25 (1970) 316–320, [Erratum: Phys. Rev. Lett. 25, 902 (1970)]
H.-W. Lin, J.-W. Chen, Z. Fan, J.-H. Zhang, R. Zhang, the valence-quark distribution of the kaon from lattice QCD – arXiv:2003.14128 [hep-lat]
Z.F. Ezawa, Wide-angle scattering in softened field theory. Nuovo Cim. A 23, 271–290 (1974)
G.R. Farrar, D.R. Jackson, Pion and nucleon structure functions near x=1. Phys. Rev. Lett. 35, 1416 (1975)
E.L. Berger, S.J. Brodsky, Quark structure functions of mesons and the Drell–Yan process. Phys. Rev. Lett. 42, 940–944 (1979)
F. Yuan, Generalized parton distributions at \(x \rightarrow 1\). Phys. Rev. D 69, 051501 (2004)
R.J. Holt, C.D. Roberts, Distribution functions of the nucleon and pion in the valence region. Rev. Mod. Phys. 82, 2991–3044 (2010)
D. Adikaram, et al. Measurement of tagged deep inelastic scattering (TDIS), approved Jefferson Lab experiment E12-15-006
J. Annand, et al. Measurement of kaon structure function through tagged deep inelastic scattering (TDIS), approved Jefferson Lab experiment C12-15-006A
O. Denisov, et al. Letter of intent (Draft 2.0): a new QCD facility at the M2 beam line of the CERN SPS – arXiv:1808.00848 [hep-ex]
L.D. Landau, I. Pomeranchuk, Limits of applicability of the theory of bremsstrahlung electrons and pair production at high-energies. Dokl. Akad. Nauk Ser. Fiz. 92, 535–536 (1953)
A.B. Migdal, Bremsstrahlung and pair production in condensed media at high-energies. Phys. Rev. 103, 1811–1820 (1956)
L. Chang, C. Mezrag, H. Moutarde, C.D. Roberts, J. Rodríguez-Quintero, P.C. Tandy, Basic features of the pion valence-quark distribution function. Phys. Lett. B 737, 23–29 (2014)
X. Chen, F.-K. Guo, C.D. Roberts, R. Wang, Selected science opportunities for the EicC. Few Body Syst. 61(4), 43 (2020)
Acknowledgements
We are grateful for constructive comments from V. Andrieux, P. Barry, W.-C. Chang, C. Chen, O. Denisov, J. Friedrich, W. Melnitchouk, C. Mezrag, W.-D. Novak, S. Platchkov, M. Quaresma and C. Quintans; and for the hospitality and support of RWTH Aachen University, III. Physikalisches Institut B, Aachen - Germany. Work supported by: National Natural Science Foundation of China (Grant No. 11805097), Jiangsu Provincial Natural Science Foundation of China (Grant No. BK20180323). Jiangsu Province Hundred Talents Plan for Professionals; Alexander von Humboldt Foundation; and Spanish Ministry of Science and Innovation (MICINN), Grant No. PID2019-107844GB-C22.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by David Blaschke
Rights and permissions
About this article
Cite this article
Cui, ZF., Ding, M., Gao, F. et al. Higgs modulation of emergent mass as revealed in kaon and pion parton distributions . Eur. Phys. J. A 57, 5 (2021). https://doi.org/10.1140/epja/s10050-020-00318-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epja/s10050-020-00318-2