Advertisement

Arabian Journal for Science and Engineering

, Volume 44, Issue 1, pp 623–630 | Cite as

Tensor Form Factors for \(B\rightarrow K\) Decays from the Lattice

  • Ahmed Abdo Al-HaydariEmail author
  • Mahyoub Hezam Al Buhairi
Research Article - Physics
  • 6 Downloads

Abstract

A calculation of the tensor form factor (\(f_\mathrm{T}\)) for rare decays of the B-meson to the K-meson is presented. In order to study the heavy quark mass dependence, we also give \(f_\mathrm{T}\) for D-meson decays. For decays of B and D to the K-meson, we calculate the vector form factors (\(f_+\) and \(f_0\)). The lattice results are obtained from a quenched \(40^{3}\times 80\) lattice with an inverse lattice spacing of \(a^{-1}\simeq 4.97\) GeV using the Wilson gauge action and the O(a) improved Wilson action for quarks.

Keywords

Tensor form factor Heavy quark mass Meson decay Quanched lattice Wilson action 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

Many thanks are due in particular to A.Ali Khan, V.M. Braun and to S. Collins, M. Göckeler, M. Panero and A. Schäfer for collaboration at the early stages of this work and many discussions. We would like to thank the HLRB in Munich for use of the Hitachi SR 8000-F1.

References

  1. 1.
    Khodjamirian, A.: Form factors and long-distance effects in \(B\rightarrow V(P)\ell ^{+}\ell ^{-}\) and \(B\rightarrow V\gamma \). In: CKM unitarity triangle. In: Proceedings, 6th International Workshop, CKM 2010, Warwick, UK, September 6-10, 2010 (2011)Google Scholar
  2. 2.
    Kamenik, J.F.: Theory of semileptonic charm decays. In: 3rd International Workshop on Charm Physics (Charm 2009) Leimen, Germany, May 20-22 (2009)Google Scholar
  3. 3.
    Ali Khan, A.: Decay constants of charm and beauty pseudoscalar heavy light mesons on fine lattices. Phys. Lett. B 652(2), 150–157 (2007)CrossRefGoogle Scholar
  4. 4.
    Al-Haydari, A.: Semileptonic form factors d \(\rightarrow \pi \), k and b \(\rightarrow \pi \), k from a fine lattice. Eur. Phys. J. A 43(1), 107 (2010)CrossRefGoogle Scholar
  5. 5.
    Isgur, N.; Wise, M.B.: Relationship between form factors in semileptonic \(\bar{B}\) and \(D\) decays and exclusive rare \(\bar{B}\)-meson decays. Phys. Rev. D 42, 2388–2391 (1990)CrossRefGoogle Scholar
  6. 6.
    Faessler, A.; Gutsche, T.; Ivanov, M.A.; Korner, J.G.; Lyubovitskij, V.E.: The exclusive rare decays \(B\rightarrow \) K(K*) \(\bar{\ell }\ell \) and \(B_c \rightarrow \) D(D*) \(\bar{\ell }\ell \) in a relativistic quark model. Eur. Phys. J. Direct 4(1), 18 (2002)Google Scholar
  7. 7.
    Khodjamirian, A.; Mannel, T.; Pivovarov, A.A.; Wang, Y.M.: Charm-loop effect in \(B\rightarrow K^{({\ast })}\ell ^{+}\ell ^{-}\) and \(B\rightarrow K^{{\ast }}\gamma \). JHEP 09, 089 (2010)CrossRefzbMATHGoogle Scholar
  8. 8.
    Becirevic, D.; Gimenez, V.; Lubicz, V.; Martinelli, G.; Papinutto, M.; Reyes, J.: Renormalization constants of quark operators for the nonperturbatively improved Wilson action. JHEP 08, 022 (2004)CrossRefGoogle Scholar
  9. 9.
    Sint, S.; Weisz, P.: Further one loop results in O(a) improved lattice QCD. Nucl. Phys. Proc. Suppl. 63, 856–858 (1998). [,856(1997)]CrossRefGoogle Scholar
  10. 10.
    Becirevic, Damir; Lubicz, V.; Mescia, F.: An estimate of the \(\text{ B }\rightarrow \text{ K }^{*}\gamma \) decay form factor. Nucl. Phys. B 769(1), 31–43 (2007)CrossRefGoogle Scholar
  11. 11.
    Lepage, G.P.; Mackenzie, P.B.: Viability of lattice perturbation theory. Phys. Rev. D 48, 2250–2264 (1993)CrossRefGoogle Scholar
  12. 12.
    Choe, S.; et al.: Quenched charmonium near the continuum limit. Nucl. Phys. Proc. Suppl. 106, 361–363 (2002)CrossRefGoogle Scholar
  13. 13.
    Göckeler, M.; Horsley, R.; Irving, A.C.; Pleiter, D.; Rakow, P.E.L.; Schierholz, G.; Stüben, H.: Determination of the lambda parameter from full lattice QCD. Phys. Rev. D 73, 014513 (2006)CrossRefGoogle Scholar
  14. 14.
    Göckeler, M.; Horsley, R.; Nakamura, Y.; Perlt, H.; Pleiter, D.; Rakow, P.E.L.; Schäfer, A.; Schierholz, G.; Schiller, A.; Stüben, H.; Zanotti, J.M.: Perturbative and nonperturbative renormalization in lattice QCD. Phys. Rev. D 82, 114511 (2010)CrossRefGoogle Scholar
  15. 15.
    Bhattacharya, T.; Gupta, R.; Lee, W.; Sharpe, S.R.: Scaling behavior of discretization errors in renormalization and improvement constants. Phys. Rev. D 73, 114507 (2006)CrossRefGoogle Scholar
  16. 16.
    Becirevic, Damir; Kaidalov, A.B.: Comment on the heavy light form factors. Phys. Lett. B 478(4), 417–423 (2000)CrossRefGoogle Scholar
  17. 17.
    Abada, A.; Becirevic, D.; Boucaud, P.; Leroy, J.; Lubicz, V.; Mescia, F.: Heavy light semileptonic decays of pseudoscalar mesons from lattice QCD. Nucl. Phys. B 619(1), 565–587 (2001)CrossRefGoogle Scholar
  18. 18.
    Hill, R.J.: Heavy-to-light meson form factors at large recoil. Phys. Rev. D 73, 014012 (2006)CrossRefGoogle Scholar
  19. 19.
    Dowdall, R.J.; Davies, C.T.H.; Horgan, R.R.; Monahan, C.J.; Shigemitsu, J.: B-Meson decay constants from improved lattice nonrelativistic QCD with physical u, d, s, and c quarks. Phys. Rev. Lett. 110(22), 222003 (2013)CrossRefGoogle Scholar
  20. 20.
    Dowdall, R.J.; Davies, C.T.H.; Lepage, G.P.; McNeile, C.: Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks. Phys. Rev. D 88, 074504 (2013)CrossRefGoogle Scholar
  21. 21.
    Aubin, C.; Bernard, C.: Heavy-light semileptonic decays in staggered chiral perturbation theory. Phys. Rev. D 76, 014002 (2007)CrossRefGoogle Scholar
  22. 22.
    Arndt, D.; Lin, C.-J.D.: Heavy meson chiral perturbation theory in finite volume. Phys. Rev. D 70, 014503 (2004)CrossRefGoogle Scholar
  23. 23.
    Becirevic, D.; Kosnik, N.; Mescia, F.; Schneider, E.: Complementarity of the constraints on new physics from \(B_s \rightarrow \mu ^{+}\mu ^{-}\) and from \(B\rightarrow Kl^{+}l^{-}\) decays. Phys. Rev. D 86, 034034 (2012)CrossRefGoogle Scholar
  24. 24.
    Bouchard, C.; Lepage, G.P.; Monahan, C.; Na, H.; Shigemitsu, J.: Rare decay \(B\rightarrow K\ell ^{+}\ell ^{-}\) form factors from lattice QCD. Phys. Rev. D88(5), 054509 (2013). [Erratum: Phys. Rev.D88,no.7,079901(2013)]Google Scholar
  25. 25.
    Abada, A.; Becirevic, D.; Boucaud, P.; Leroy, J.P.; Lubicz, V.; Martinelli, G.; Mescia, F.: Decays of heavy mesons. Nucl. Phys. Proc. Suppl. 83, 268–270 (2000)CrossRefGoogle Scholar
  26. 26.
    Ball, P.; Zwicky, R.: New results on \(b\rightarrow \pi, k,\eta \) decay form factors from light-cone sum rules. Phys. Rev. D 71, 014015 (2005)CrossRefGoogle Scholar
  27. 27.
    Melikhov, D.; Stech, B.: Weak form factors for heavy meson decays: an update. Phys. Rev. D 62, 014006 (2000)CrossRefGoogle Scholar
  28. 28.
    Liu, Z.; Meinel, S.; Hart, A.; Horgan, R.R.; Muller, E.H.; Wingate, M.: A Lattice calculation of \(B- >K^{({\ast })}\) form factors. In: CKM Unitarity Triangle. Proceedings, 6th International Workshop, CKM 2010, Warwick, UK, September 6-10, 2010 (2011)Google Scholar
  29. 29.
    Liu, Y.; et al.: Heavy-meson semileptonic decays for the standard model and beyond. PoS, vol. LATTICE2013, p. 386 (2014)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • Ahmed Abdo Al-Haydari
    • 1
    Email author
  • Mahyoub Hezam Al Buhairi
    • 1
  1. 1.Department of Physics, Faculty of Applied SciencesUniversity of TaizTaizYemen

Personalised recommendations