Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules

Hüseyin Dağ

doi:10.38088/jise.1011406

Research Article

Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules

Year 2022, , 94 - 107, 08.06.2022

Hüseyin Dağ

https://doi.org/10.38088/jise.1011406

Abstract

In this work, we investigated the mixing between strange axial vector mesons K1(1270) and K1(1400) by using QCD Sum Rules approach. Since these states couple to the same interpolating currents, we defined them in terms of orbital angular momentum eigen states K1A and K1B. By using the axial vector and tensor interpolating currents which are almost purely coupling to K1A and K1B, and then employing the orthogonality of the physical states, we obtained an analytical expression for the K1 mixing angle. We performed a Monte Carlo based numerical analysis to estimate the value of the mixing angle.

Keywords

QCD Sum Rules, K1 Mixing, Non-Perturbative QCD, Strange Meson

Thanks

H. Dağ thanks to A. Özpineci, G. Erkol and V. Zamiralov for fruitful discussions and their contributions at the very early stages of this work.

References

[1] Oerter, R. (2006). The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics Penguin Group. p. 2. ISBN 978-0-13-236678-6.
[2] Yang, C. N. and Mills, R. (1954). "Conservation of Isotopic Spin and Isotopic Gauge Invariance". Physical Review. 96 (1).
[3] Glashow, S.L. (1961). "Partial-symmetries of weak interactions". Nuclear Physics 22 (4), 579–588.
[4] Weinberg, S. (1967). "A Model of Leptons". Physical Review Letters 19 (21), 1264–1266.
[5] Salam, A. (1968). Svartholm, N. (ed.). Elementary Particle Physics: Relativistic Groups and Analyticity. Eighth Nobel Symposium. Stockholm: Almquvist and Wiksell. p. 367.
[6] Englert, F. and Brout, R. (1964). "Broken Symmetry and the Mass of Gauge Vector Mesons". Physical Review Letters. 13 (9), 321–323.
[7] Higgs, P.W. (1964). "Broken Symmetries and the Masses of Gauge Bosons". Physical Review Letters. 13 (16), 508–509.
[8] CMS collaboration (2012). "Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC". Physics Letters B 716 (1), 30–61. arXiv:1207.7235.
[9] ATLAS collaboration (2012). "Observation of a New Particle in the Search for the Standard Model Higgs Boson with the ATLAS Detector at the LHC". Physics Letters B 716 (1), 1–29. arXiv:1207.7214.
[10] Aaij, R. et al., LHCb Collaboration (2021). "Test of lepton universality in beauty-quark decays", LHCb-PAPER-2021-004, CERN-EP-2021-042 e-Print: arXiv:2103.11769 [hep-ex].
[11] Aaij, R. et al., LHCb Collaboration , (2014). "Differential branching fractions and isospin asymmetries of B → K(∗)µ +µ − decays", JHEP 06 , 133, arXiv:1403.8044[hep-ex].
[12] Aaij, R. et al., LHCb Collaboration, (2015). "Angular analysis and differential branching fraction of the decay B0 s → φµ+µ −", JHEP 09 (2015) 179, [1506.08777].
[13] Hiller, G. and Kruger, F. (2004). "More model-independent analysis of b → s processes", Phys. Rev. D69, 074020, arXiv:0310219[hep-ex].
[14] Bobeth, C., Hiller, G. and Piranishvili, G. (2007). "Angular distributions of B¯ → K ¯ll decays", JHEP 07, 040, arXiv:0709.4174[hep-ex].
[15] Bordone, M., Isidori, G. and Pattori, A. (2016). "On the Standard Model predictions for RK and RK∗", Eur. Phys. J. C76 440.
[16] Zyla, P.A. et al. (Particle Data Group). (2020). "The Review of Particle Physics", Prog. Theor. Exp. Phys. 2020, 083C01.
[17] Suzuki, M. (1993), "Strange axial-vector mesons", Phys. Rev. D 47, 1252.
[18] Dağ, H. (2010). "Investigating the Semileptonic B to K1(120,1400) Decays in QCD Sum Rules", PhD Thesis, Middle East Technical University, Ankara, Turkey, 83p.
[19] Dağ, H. et al. (2011). "The Semileptonic B to K1(1270,1400) Decays in QCD Sum Rules", J. Phys. G38, 015002.
[20] Carnegie, R.K. et al. (1977). "Q1(1290) and Q2 (1400) decay rates and their SU(3) implications", Physics Letters B Volume 68, Issue 3, Pages 287-291.
[21] Blundell, H.G. et al. (1996), "Properties of the Strange Axial Mesons in the Relativized Quark Model", Phys. Rev. D 53, 3712-3722.
[22] L. Burakovsky and T. Goldman, "Constraint on axial-vector meson mixing angle from the nonrelativistic constituent quark model", Phys. Rev. D 56, R1368(R)
[23] Asner, D., et al. (2000). "Resonance structure of τ-→K-π+π-ντ decays", Phys. Rev. D, 62(7).
[24] Cheng, H-Y. (2003), "Hadronic Charmed Meson Decays Involving Axial Vector Mesons", Phys. Rev. D 67 (2003) 094007.
[25] Roca, L. et al. (2004). "Decay of axial-vector mesons into VP and Pγ", Phys. Rev. D 70, 094006, arXiv:0306188[hep-ph].
[26] Li, D-M. and Li, Z. (2006). "Strange axial-vector mesons mixing angle", Eur. Phys. J. A 28, 369-373, arXiv: 0606297[hep-ph].
[27] Hatanaka, H. and Yang, K-C. (2008). "B→K1γ Decays in the Light-Cone QCD Sum Rules", Phys. Rev. D77, 094023, 2008; Erratum-ibid.D78:059902,2008, arXiv:0804.3198v4 [hep-ph].
[28] Cheng, H-Y. (2012). "Revisiting Axial-Vector Meson Mixing", Phys. Lett. B 707, 116-120, e-Print: 1110.2249 [hep-ph].
[29] Divotgey, F. et al. (2014). "Phenomenology of axial-vector and pseudovector mesons: decays and mixing in the kaonic sector", Eur. Phys. J. A 49, 135, arXiv:1306.1193.
[30] Liu, X. et al. (2014). "Penguin-dominated B→ϕK1(1270) and ϕK1(1400) decays in the perturbative QCD approach", Phys. Rev. D 90, 094019, arXiv:1404.2089v2 [hep-ph].
[31] Zhang, Z-Q. et al. (2018). "Study of the K1(1270)−K1(1400) mixing in the decays B→J/ΨK1(1270),J/ΨK1(1400)", Eur. Phys. J. C 78, 219, arXiv:1705.00524 [hep-ph].
[32] Bashiry, V. and Azizi, K. (2010). "Forward-backward asymmetry, branching ratio and rate difference between electron and muon channels of B → K 1(K*)ℓ+ℓ− transition in supersymmetric models", JHEP 1001, 033, arXiv:0903.1505 [hep-ph].
[33] Ahmed, I. et al. (2008). "Exclusive B→K1ℓ+ℓ- decay in model with single universal extra dimension", Eur. Phys. J. C 54, 591-599, arXiv:0802.0740 [hep-ph].
[34] Ahmed, A. et al. (2011). K1(1270 )−K1(1400 ) mixing and the fourth generation standard model effects in B→K1l+l− decays, Phys. Rev. D 84, 033010, arXiv:1105.3887 [hep-ph].
[35] Li, Y. et al. (2011). "B→K1ℓ+ℓ− decays in a family non-universal Z′ model", EPJC 71, 1775, arXiv:1107.0630 [hep-ph].
[36] Ahmed, N. et al. (2015). "Analysis of forward–backward and lepton polarization asymmetries in B → K1ℓ+ℓ− decays in the two-Higgs-doublet model", PTEP 2015, 1, 113B06, arXiv:1509.08113 [hep-ph].
[37] Munir, F. et al. (2016). "Polarized forward-backward asymmetries of lepton pair in B→K1ℓ+ℓ− decay in the presence of New physics", PTEP 2016 1, 013B02, arXiv:1511.07075 [hep-ph].
[38] Huang, Z-R. et al. (2019). "Testing Leptoquark and Z′ Models via B→K1(1270,1400)μ+μ− Decays", Phys. Rev. D 100, 055038, arXiv:1812.03491 [hep-ph].
[39] Bhatta, A. and Mohanta, R. (2020). "Implications of new physics in B→K1μ+μ− decay processes", arXiv:2011.05820 [hep-ph].
[40] Sugiyama, J. et al. (2007). "Mixings of 4-quark components in light non-singlet scalar mesons in QCD sum rules", Phys. Rev. D76, 114010, arXiv:0707.2533 [hep-ph].
[41] Aliev, T. et al. (2011). "Mixing Angle of Hadrons in QCD: A New View", Phys. Rev. D 83, 016008, arXiv:1007.0814 [hep-ph].
[42] Belyaev, V.M. and Ioffe, .L. (1982). "Determination of Baryon and Baryonic Resonance Masses from QCD Sum Rules". 1. Nonstrange Baryons, Sov. Phys. JETP 56, 493-50.
[43] Shifman, M.A. et al. (1979). "QCD and Resonance Physics. Theoretical Foundations", Nucl. Phys. B 147 (1979) 385-447.
[44] Colangelo, P. and Khodjamirian, A., (1995). "QCD Sum Rules, a Modern Perspective", printed in ”At the Frontier of Particle Physics: Handbook of QCD” ed. by M. Shifman (World Scientific, Singapore, 2001), V. 3.
[45] Türkan, A. and Dağ. H. (2019).” Exploratory study of X_{c1} (4140) and like states in QCD sum rules”, Nucl. Phys. A 985, 38-65.
[46] Mutuk, H. (2021). "Monte-Carlo based QCD sum rules analysis of X0(2900) and X1(2900)", J. Phys. G 48 , 5, 055007, e-Print: 2009.02492 [hep-ph].
[47] Barlow, R. J. (2002). “Systematic Errors: Facts and Fictions” in Proc. Durham conference on Advanced Statistical Techniques in Particle Physics, M. R. Whalley and L. Lyons (Eds). IPPP/02/39. 2002.

Year 2022, , 94 - 107, 08.06.2022

Hüseyin Dağ

https://doi.org/10.38088/jise.1011406

Abstract

References

[1] Oerter, R. (2006). The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics Penguin Group. p. 2. ISBN 978-0-13-236678-6.
[2] Yang, C. N. and Mills, R. (1954). "Conservation of Isotopic Spin and Isotopic Gauge Invariance". Physical Review. 96 (1).
[3] Glashow, S.L. (1961). "Partial-symmetries of weak interactions". Nuclear Physics 22 (4), 579–588.
[4] Weinberg, S. (1967). "A Model of Leptons". Physical Review Letters 19 (21), 1264–1266.
[5] Salam, A. (1968). Svartholm, N. (ed.). Elementary Particle Physics: Relativistic Groups and Analyticity. Eighth Nobel Symposium. Stockholm: Almquvist and Wiksell. p. 367.
[6] Englert, F. and Brout, R. (1964). "Broken Symmetry and the Mass of Gauge Vector Mesons". Physical Review Letters. 13 (9), 321–323.
[7] Higgs, P.W. (1964). "Broken Symmetries and the Masses of Gauge Bosons". Physical Review Letters. 13 (16), 508–509.
[8] CMS collaboration (2012). "Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC". Physics Letters B 716 (1), 30–61. arXiv:1207.7235.
[9] ATLAS collaboration (2012). "Observation of a New Particle in the Search for the Standard Model Higgs Boson with the ATLAS Detector at the LHC". Physics Letters B 716 (1), 1–29. arXiv:1207.7214.
[10] Aaij, R. et al., LHCb Collaboration (2021). "Test of lepton universality in beauty-quark decays", LHCb-PAPER-2021-004, CERN-EP-2021-042 e-Print: arXiv:2103.11769 [hep-ex].
[11] Aaij, R. et al., LHCb Collaboration , (2014). "Differential branching fractions and isospin asymmetries of B → K(∗)µ +µ − decays", JHEP 06 , 133, arXiv:1403.8044[hep-ex].
[12] Aaij, R. et al., LHCb Collaboration, (2015). "Angular analysis and differential branching fraction of the decay B0 s → φµ+µ −", JHEP 09 (2015) 179, [1506.08777].
[13] Hiller, G. and Kruger, F. (2004). "More model-independent analysis of b → s processes", Phys. Rev. D69, 074020, arXiv:0310219[hep-ex].
[14] Bobeth, C., Hiller, G. and Piranishvili, G. (2007). "Angular distributions of B¯ → K ¯ll decays", JHEP 07, 040, arXiv:0709.4174[hep-ex].
[15] Bordone, M., Isidori, G. and Pattori, A. (2016). "On the Standard Model predictions for RK and RK∗", Eur. Phys. J. C76 440.
[16] Zyla, P.A. et al. (Particle Data Group). (2020). "The Review of Particle Physics", Prog. Theor. Exp. Phys. 2020, 083C01.
[17] Suzuki, M. (1993), "Strange axial-vector mesons", Phys. Rev. D 47, 1252.
[18] Dağ, H. (2010). "Investigating the Semileptonic B to K1(120,1400) Decays in QCD Sum Rules", PhD Thesis, Middle East Technical University, Ankara, Turkey, 83p.
[19] Dağ, H. et al. (2011). "The Semileptonic B to K1(1270,1400) Decays in QCD Sum Rules", J. Phys. G38, 015002.
[20] Carnegie, R.K. et al. (1977). "Q1(1290) and Q2 (1400) decay rates and their SU(3) implications", Physics Letters B Volume 68, Issue 3, Pages 287-291.
[21] Blundell, H.G. et al. (1996), "Properties of the Strange Axial Mesons in the Relativized Quark Model", Phys. Rev. D 53, 3712-3722.
[22] L. Burakovsky and T. Goldman, "Constraint on axial-vector meson mixing angle from the nonrelativistic constituent quark model", Phys. Rev. D 56, R1368(R)
[23] Asner, D., et al. (2000). "Resonance structure of τ-→K-π+π-ντ decays", Phys. Rev. D, 62(7).
[24] Cheng, H-Y. (2003), "Hadronic Charmed Meson Decays Involving Axial Vector Mesons", Phys. Rev. D 67 (2003) 094007.
[25] Roca, L. et al. (2004). "Decay of axial-vector mesons into VP and Pγ", Phys. Rev. D 70, 094006, arXiv:0306188[hep-ph].
[26] Li, D-M. and Li, Z. (2006). "Strange axial-vector mesons mixing angle", Eur. Phys. J. A 28, 369-373, arXiv: 0606297[hep-ph].
[27] Hatanaka, H. and Yang, K-C. (2008). "B→K1γ Decays in the Light-Cone QCD Sum Rules", Phys. Rev. D77, 094023, 2008; Erratum-ibid.D78:059902,2008, arXiv:0804.3198v4 [hep-ph].
[28] Cheng, H-Y. (2012). "Revisiting Axial-Vector Meson Mixing", Phys. Lett. B 707, 116-120, e-Print: 1110.2249 [hep-ph].
[29] Divotgey, F. et al. (2014). "Phenomenology of axial-vector and pseudovector mesons: decays and mixing in the kaonic sector", Eur. Phys. J. A 49, 135, arXiv:1306.1193.
[30] Liu, X. et al. (2014). "Penguin-dominated B→ϕK1(1270) and ϕK1(1400) decays in the perturbative QCD approach", Phys. Rev. D 90, 094019, arXiv:1404.2089v2 [hep-ph].
[31] Zhang, Z-Q. et al. (2018). "Study of the K1(1270)−K1(1400) mixing in the decays B→J/ΨK1(1270),J/ΨK1(1400)", Eur. Phys. J. C 78, 219, arXiv:1705.00524 [hep-ph].
[32] Bashiry, V. and Azizi, K. (2010). "Forward-backward asymmetry, branching ratio and rate difference between electron and muon channels of B → K 1(K*)ℓ+ℓ− transition in supersymmetric models", JHEP 1001, 033, arXiv:0903.1505 [hep-ph].
[33] Ahmed, I. et al. (2008). "Exclusive B→K1ℓ+ℓ- decay in model with single universal extra dimension", Eur. Phys. J. C 54, 591-599, arXiv:0802.0740 [hep-ph].
[34] Ahmed, A. et al. (2011). K1(1270 )−K1(1400 ) mixing and the fourth generation standard model effects in B→K1l+l− decays, Phys. Rev. D 84, 033010, arXiv:1105.3887 [hep-ph].
[35] Li, Y. et al. (2011). "B→K1ℓ+ℓ− decays in a family non-universal Z′ model", EPJC 71, 1775, arXiv:1107.0630 [hep-ph].
[36] Ahmed, N. et al. (2015). "Analysis of forward–backward and lepton polarization asymmetries in B → K1ℓ+ℓ− decays in the two-Higgs-doublet model", PTEP 2015, 1, 113B06, arXiv:1509.08113 [hep-ph].
[37] Munir, F. et al. (2016). "Polarized forward-backward asymmetries of lepton pair in B→K1ℓ+ℓ− decay in the presence of New physics", PTEP 2016 1, 013B02, arXiv:1511.07075 [hep-ph].
[38] Huang, Z-R. et al. (2019). "Testing Leptoquark and Z′ Models via B→K1(1270,1400)μ+μ− Decays", Phys. Rev. D 100, 055038, arXiv:1812.03491 [hep-ph].
[39] Bhatta, A. and Mohanta, R. (2020). "Implications of new physics in B→K1μ+μ− decay processes", arXiv:2011.05820 [hep-ph].
[40] Sugiyama, J. et al. (2007). "Mixings of 4-quark components in light non-singlet scalar mesons in QCD sum rules", Phys. Rev. D76, 114010, arXiv:0707.2533 [hep-ph].
[41] Aliev, T. et al. (2011). "Mixing Angle of Hadrons in QCD: A New View", Phys. Rev. D 83, 016008, arXiv:1007.0814 [hep-ph].
[42] Belyaev, V.M. and Ioffe, .L. (1982). "Determination of Baryon and Baryonic Resonance Masses from QCD Sum Rules". 1. Nonstrange Baryons, Sov. Phys. JETP 56, 493-50.
[43] Shifman, M.A. et al. (1979). "QCD and Resonance Physics. Theoretical Foundations", Nucl. Phys. B 147 (1979) 385-447.
[44] Colangelo, P. and Khodjamirian, A., (1995). "QCD Sum Rules, a Modern Perspective", printed in ”At the Frontier of Particle Physics: Handbook of QCD” ed. by M. Shifman (World Scientific, Singapore, 2001), V. 3.
[45] Türkan, A. and Dağ. H. (2019).” Exploratory study of X_{c1} (4140) and like states in QCD sum rules”, Nucl. Phys. A 985, 38-65.
[46] Mutuk, H. (2021). "Monte-Carlo based QCD sum rules analysis of X0(2900) and X1(2900)", J. Phys. G 48 , 5, 055007, e-Print: 2009.02492 [hep-ph].
[47] Barlow, R. J. (2002). “Systematic Errors: Facts and Fictions” in Proc. Durham conference on Advanced Statistical Techniques in Particle Physics, M. R. Whalley and L. Lyons (Eds). IPPP/02/39. 2002.

There are 47 citations in total.

Details

Primary Language	English
Subjects	Engineering
Journal Section	Research Articles
Authors	Hüseyin Dağ 0000-0001-9301-007X
Publication Date	June 8, 2022
Published in Issue	Year 2022

Cite

APA	Dağ, H. (2022). Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules. Journal of Innovative Science and Engineering, 6(1), 94-107. https://doi.org/10.38088/jise.1011406
AMA	Dağ H. Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules. JISE. June 2022;6(1):94-107. doi:10.38088/jise.1011406
Chicago	Dağ, Hüseyin. “Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules”. Journal of Innovative Science and Engineering 6, no. 1 (June 2022): 94-107. https://doi.org/10.38088/jise.1011406.
EndNote	Dağ H (June 1, 2022) Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules. Journal of Innovative Science and Engineering 6 1 94–107.
IEEE	H. Dağ, “Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules”, JISE, vol. 6, no. 1, pp. 94–107, 2022, doi: 10.38088/jise.1011406.
ISNAD	Dağ, Hüseyin. “Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules”. Journal of Innovative Science and Engineering 6/1 (June 2022), 94-107. https://doi.org/10.38088/jise.1011406.
JAMA	Dağ H. Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules. JISE. 2022;6:94–107.
MLA	Dağ, Hüseyin. “Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules”. Journal of Innovative Science and Engineering, vol. 6, no. 1, 2022, pp. 94-107, doi:10.38088/jise.1011406.
Vancouver	Dağ H. Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules. JISE. 2022;6(1):94-107.

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