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

Yıl 2022, Cilt 6, Sayı 1, 94 - 107, 08.06.2022
https://doi.org/10.38088/jise.1011406

Öz

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.

Kaynakça

  • [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.

Yıl 2022, Cilt 6, Sayı 1, 94 - 107, 08.06.2022
https://doi.org/10.38088/jise.1011406

Öz

Kaynakça

  • [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.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik, Temel Bilimler
Yayınlanma Tarihi june 2022
Bölüm Research Articles
Yazarlar

Hüseyin DAĞ> (Sorumlu Yazar)
BURSA TECHNICAL UNIVERSITY
0000-0001-9301-007X
Türkiye

Teşekkür 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.
Erken Görünüm Tarihi 22 Şubat 2022
Yayımlanma Tarihi 8 Haziran 2022
Yayınlandığı Sayı Yıl 2022, Cilt 6, Sayı 1

Kaynak Göster

Bibtex @araştırma makalesi { jise1011406, journal = {Journal of Innovative Science and Engineering}, eissn = {2602-4217}, address = {ursa Technical University, Mimar Sinan Campus, Mimar Sinan Mah. Mimar Sinan Blv. Eflak Cad. No:177 16310 Yıldırım, Bursa / Turkey}, publisher = {Bursa Teknik Üniversitesi}, year = {2022}, volume = {6}, number = {1}, pages = {94 - 107}, doi = {10.38088/jise.1011406}, title = {Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules}, key = {cite}, author = {Dağ, Hüseyin} }
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 . DOI: 10.38088/jise.1011406
MLA Dağ, H. "Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules" . Journal of Innovative Science and Engineering 6 (2022 ): 94-107 <http://jise.btu.edu.tr/tr/pub/issue/68623/1011406>
Chicago Dağ, H. "Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules". Journal of Innovative Science and Engineering 6 (2022 ): 94-107
RIS TY - JOUR T1 - Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules AU - HüseyinDağ Y1 - 2022 PY - 2022 N1 - doi: 10.38088/jise.1011406 DO - 10.38088/jise.1011406 T2 - Journal of Innovative Science and Engineering JF - Journal JO - JOR SP - 94 EP - 107 VL - 6 IS - 1 SN - -2602-4217 M3 - doi: 10.38088/jise.1011406 UR - https://doi.org/10.38088/jise.1011406 Y2 - 2022 ER -
EndNote %0 Journal of Innovative Science and Engineering Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules %A Hüseyin Dağ %T Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules %D 2022 %J Journal of Innovative Science and Engineering %P -2602-4217 %V 6 %N 1 %R doi: 10.38088/jise.1011406 %U 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 (Haziran 2022): 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. 2022; 6(1): 94-107.
Vancouver Dağ H. Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules. Journal of Innovative Science and Engineering. 2022; 6(1): 94-107.
IEEE H. Dağ , "Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules", Journal of Innovative Science and Engineering, c. 6, sayı. 1, ss. 94-107, Haz. 2022, doi:10.38088/jise.1011406


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