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Theoretical Tools

  • Matthew John KirkEmail author
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

In this chapter we explore some of the concepts, tools and methods which will be used in the rest of the thesis. The idea of effective field theories (EFTs) is one of the most powerful in physics, and we will explain them in Sect. 2.1, along with a specific example of an EFT in Sect. 2.3. Another omnipresent tool is the Heavy Quark Expansion, which we see in Sect. 2.2.

References

  1. 1.
    Buchmuller W, Wyler D (1986) Effective lagrangian analysis of new interactions and flavor conservation. Nucl Phys B 268:621–653.  https://doi.org/10.1016/0550-3213(86)90262-2ADSCrossRefGoogle Scholar
  2. 2.
    Grzadkowski B, Iskrzynski M, Misiak M, Rosiek J (2010) Dimension-six terms in the standard model lagrangian. JHEP 10:085.  https://doi.org/10.1007/JHEP10(2010)085, arXiv:1008.4884
  3. 3.
    Khoze VA, Shifman MA (1983) HEAVY QUARKS. Sov Phys Usp 26:387.  https://doi.org/10.1070/PU1983v026n05ABEH004398ADSCrossRefGoogle Scholar
  4. 4.
    Shifman MA, Voloshin MB (1985) Preasymptotic effects in inclusive weak decays of charmed particles. Sov J Nucl Phys 41:120Google Scholar
  5. 5.
    Bigi IIY, Uraltsev NG (1992) Gluonic enhancements in non-spectator beauty decays: an Inclusive mirage though an exclusive possibility. Phys Lett B 280:271–280.  https://doi.org/10.1016/0370-2693(92)90066-DADSCrossRefGoogle Scholar
  6. 6.
    Bigi IIY, Uraltsev NG, Vainshtein AI (1992) Nonperturbative corrections to inclusive beauty and charm decays: QCD versus phenomenological models. Phys Lett B 293:430–436.  https://doi.org/10.1016/0370-2693(92)90908-M,  https://doi.org/10.1016/0370-2693(92)91287-J, arXiv:hep-ph/9207214
  7. 7.
    Blok B, Shifman MA (1993) The Rule of discarding 1/N(c) in inclusive weak decays. 1. Nucl Phys B399: 441–458.  https://doi.org/10.1016/0550-3213(93)90504-I, arXiv:hep-ph/9207236ADSCrossRefGoogle Scholar
  8. 8.
    Blok B, Shifman MA (1993) The Rule of discarding 1/N(c) in inclusive weak decays. 2. Nucl Phys B399:459–476. https://doi.org/10.1016/0550-3213(93)90505-J, arXiv:hep-ph/9209289ADSCrossRefGoogle Scholar
  9. 9.
    Chay J, Georgi H, Grinstein B (1990) Lepton energy distributions in heavy meson decays from QCD. Phys Lett B 247:399–405.  https://doi.org/10.1016/0370-2693(90)90916-TADSCrossRefGoogle Scholar
  10. 10.
    Luke ME (1990) Effects of subleading operators in the heavy quark effective theory. Phys Lett B 252:447–455.  https://doi.org/10.1016/0370-2693(90)90568-QADSCrossRefGoogle Scholar
  11. 11.
    Lenz A (2015) Lifetimes and heavy quark expansion. Int J Mod Phys A 30:1543005.  https://doi.org/10.1142/S0217751X15430058, arXiv:1405.3601ADSCrossRefGoogle Scholar
  12. 12.
    HFLAV collaboration, Amhis Y et al (2017) Averages of b-hadron, c-hadron, and \(\tau \)-lepton properties as of summer 2016. Eur Phys J C77:895,  https://doi.org/10.1140/epjc/s10052-017-5058-4, arXiv:1612.07233
  13. 13.
    HFLAV collaboration. https://hflav.web.cern.ch
  14. 14.
    HFLAV collaboration (2018) B lifetime and oscillation parameters, PDG. http://www.slac.stanford.edu/xorg/hflav/osc/PDG_2018/
  15. 15.
    Eichten E, Feinberg F (1981) Spin dependent forces in QCD. Phys Rev D 23:2724.  https://doi.org/10.1103/PhysRevD.23.2724ADSCrossRefGoogle Scholar
  16. 16.
    Caswell WE, Lepage GP (1986) Effective lagrangians for bound state problems in QED, QCD, and other field theories. Phys Lett 167B:437–442.  https://doi.org/10.1016/0370-2693(86)91297-9ADSCrossRefGoogle Scholar
  17. 17.
    Politzer HD, Wise MB (1988) Leading logarithms of heavy quark masses in processes with light and heavy quarks. Phys Lett B206:681–684,  https://doi.org/10.1016/0370-2693(88)90718-6ADSCrossRefGoogle Scholar
  18. 18.
    Politzer HD, Wise MB (1988) Effective field theory approach to processes involving both light and heavy fields. Phys Lett B 208:504–507.  https://doi.org/10.1016/0370-2693(88)90656-9ADSCrossRefGoogle Scholar
  19. 19.
    Eichten E, Hill BR (1990) An effective field theory for the calculation of matrix elements involving heavy quarks. Phys Lett B 234:511–516.  https://doi.org/10.1016/0370-2693(90)92049-OADSCrossRefGoogle Scholar
  20. 20.
    Eichten E, Hill BR (1990) Static effective field theory: 1/m corrections. Phys Lett B 243:427–431.  https://doi.org/10.1016/0370-2693(90)91408-4ADSCrossRefGoogle Scholar
  21. 21.
    Grinstein B (1990) The static quark effective theory. Nucl Phys B 339:253–268.  https://doi.org/10.1016/0550-3213(90)90349-IADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Georgi H (1990) An effective field theory for heavy quarks at low-energies. Phys Lett B 240:447–450.  https://doi.org/10.1016/0370-2693(90)91128-XADSCrossRefGoogle Scholar
  23. 23.
    Falk AF, Georgi H, Grinstein B, Wise MB (1990) Heavy meson form-factors from QCD. Nucl Phys B 343:1–13.  https://doi.org/10.1016/0550-3213(90)90591-ZADSCrossRefGoogle Scholar
  24. 24.
    Falk AF, Grinstein B, Luke ME (1991) Leading mass corrections to the heavy quark effective theory. Nucl Phys B 357:185–207.  https://doi.org/10.1016/0550-3213(91)90464-9ADSCrossRefGoogle Scholar
  25. 25.
    Georgi H (1991) Heavy quark effective field theory. In: Theoretical advanced study institute in elementary particle physics (TASI 91): perspectives in the standard model boulder, Colorado, June 2–28, pp. 0589–630. http://www.people.fas.harvard.edu/~hgeorgi/tasi.pdf
  26. 26.
    Neubert M (1994) Heavy quark symmetry. Phys Rept 245:259–396.  https://doi.org/10.1016/0370-1573(94)90091-4, arXiv:hep-ph/9306320ADSCrossRefGoogle Scholar
  27. 27.
    Buras AJ (1998) Weak Hamiltonian, CP violation and rare decays. In: Probing the standard model of particle interactions. Proceedings, summer School in theoretical physics, NATO advanced study Institute, 68th session, Les Houches, France, July 28–September 5, 1997. Pt. 1, 2, pp. 281–539, arXiv:hep-ph/9806471
  28. 28.
    Nachtmann O (1990) Elementary particle physics: concepts and phenomenaCrossRefGoogle Scholar
  29. 29.
    Bóna M (2001) Analysis of two-body charmless decays for branching ratio and CP-violating asymmetry measurements with the BaBar experiment, PhD thesis, Universita’ di Torino, 2001. http://inspirehep.net/record/923685/files/cer-002642923.pdf
  30. 30.
    Gabbiani F, Gabrielli E, Masiero A, Silvestrini L (1996) A Complete analysis of FCNC and CP constraints in general SUSY extensions of the standard model. Nucl Phys B 477:321–352.  https://doi.org/10.1016/0550-3213(96)00390-2, arXiv:hep-ph/9604387ADSCrossRefGoogle Scholar
  31. 31.
    Aoki S et al (2017) Review of lattice results concerning low-energy particle physics. Eur Phys J C 77:112.  https://doi.org/10.1140/epjc/s10052-016-4509-7, arXiv:1607.00299
  32. 32.
    FLAG collaboration. http://flag.unibe.ch/MainPage
  33. 33.
    Srednicki M (2004) Quantum field theory. Part 2. Spin one half, arXiv:hep-th/0409036
  34. 34.
    Inami T, Lim CS (1981) Effects of superheavy quarks and leptons in low-energy weak processes \(K_L \rightarrow \mu \bar{\mu }\), \(K^+ \rightarrow \pi ^+ \nu \bar{\nu }\) and \(K^0 \longleftrightarrow \bar{K}^0\). Prog Theor Phys 65:297.  https://doi.org/10.1143/PTP.65.297ADSCrossRefGoogle Scholar
  35. 35.
    Artuso M, Borissov G, Lenz A (2016) CP violation in the \(B_s^0\) system. Rev Mod Phys 88:045002.  https://doi.org/10.1103/RevModPhys.88.045002, arXiv:1511.09466
  36. 36.
    Buras AJ, Jamin M, Weisz PH (1990) Leading and next-to-leading QCD corrections to \(\epsilon \) parameter and \(B^0 - \bar{B}^0\) mixing in the presence of a heavy top quark. Nucl Phys B 347:491–536.  https://doi.org/10.1016/0550-3213(90)90373-LADSCrossRefGoogle Scholar
  37. 37.
    Ellis JR, Gaillard MK, Nanopoulos DV, Rudaz S (1977) The phenomenology of the next left-handed quarks. Nucl Phys B 131:285.  https://doi.org/10.1016/0550-3213(77)90374-1ADSCrossRefGoogle Scholar
  38. 38.
    Hagelin JS (1981) Mass mixing and CP violation in the \(B^0-\bar{B}^0\) system. Nucl Phys B 193:123–149.  https://doi.org/10.1016/0550-3213(81)90521-6ADSCrossRefGoogle Scholar
  39. 39.
    Franco E, Lusignoli M, Pugliese A (1982) Strong interaction corrections to CP violation in B0 anti-b0 mixing. Nucl Phys B 194:403.  https://doi.org/10.1016/0550-3213(82)90018-9ADSCrossRefGoogle Scholar
  40. 40.
    Chau L-L (1983) Quark mixing in weak interactions. Phys Rept 95:1–94.  https://doi.org/10.1016/0370-1573(83)90043-1ADSCrossRefGoogle Scholar
  41. 41.
    Buras AJ, Slominski W, Steger H (1984) \(B^0\)-\(\bar{B}^0\) mixing, C violation and the B-meson decay. Nucl Phys B 245:369–398.  https://doi.org/10.1016/0550-3213(84)90437-1ADSCrossRefGoogle Scholar
  42. 42.
    Khoze VA, Shifman MA, Uraltsev NG, Voloshin MB (1987) On inclusive hadronic widths of beautiful particles. Sov J Nucl Phys 46:112Google Scholar
  43. 43.
    Beneke M, Buchalla G, Greub C, Lenz A, Nierste U (1999) Next-to-leading order QCD corrections to the lifetime difference of \(B_s\) mesons. Phys Lett B 459:631–640.  https://doi.org/10.1016/S0370-2693(99)00684-X, arXiv:hep-ph/9808385ADSCrossRefGoogle Scholar
  44. 44.
    Ciuchini M, Franco E, Lubicz V, Mescia F, Tarantino C (2003) Lifetime differences and CP violation parameters of neutral B mesons at the next-to-leading order in QCD. JHEP 08:031.  https://doi.org/10.1088/1126-6708/2003/08/031, arXiv:hep-ph/0308029CrossRefGoogle Scholar
  45. 45.
    Beneke M, Buchalla G, Lenz A, Nierste U (2003) CP asymmetry in flavor specific B decays beyond leading logarithms. Phys Lett B 576:173–183.  https://doi.org/10.1016/j.physletb.2003.09.089, arXiv:hep-ph/0307344ADSCrossRefGoogle Scholar
  46. 46.
    Beneke M, Buchalla G, Dunietz I (1996) Width difference in the \(B_s-\bar{B_s}\) system. Phys Rev D 54:4419–4431.  https://doi.org/10.1103/PhysRevD.54.4419,  https://doi.org/10.1103/PhysRevD.83.119902, arXiv:hep-ph/9605259
  47. 47.
    Dighe AS, Hurth T, Kim CS, Yoshikawa T (2002) Measurement of the lifetime difference of \(B_d\) mesons: possible and worthwhile? Nucl Phys B 624:377–404.  https://doi.org/10.1016/S0550-3213(01)00655-1, arXiv:hep-ph/0109088ADSCrossRefGoogle Scholar
  48. 48.
    Badin A, Gabbiani F, Petrov AA (2007) Lifetime difference in \(B_s\) mixing: Standard model and beyond. Phys Lett B 653:230–240.  https://doi.org/10.1016/j.physletb.2007.07.049, arXiv:0707.0294ADSCrossRefGoogle Scholar
  49. 49.
    Becirevic D, Gimenez V, Martinelli G, Papinutto M, Reyes J (2002) \(B\)-parameters of the complete set of matrix elements of \(\Delta B = 2\) operators from the lattice. JHEP 04:025.  https://doi.org/10.1088/1126-6708/2002/04/025, arXiv:hep-lat/0110091CrossRefGoogle Scholar
  50. 50.
    Bouchard CM, Freeland ED, Bernard C, El-Khadra AX, Gamiz E, Kronfeld AS et al (2011) Neutral B mixing from 2+1 flavor lattice-QCD: the standard model and beyond, PoS LATTICE2011 274,  https://doi.org/10.22323/1.139.0274, arXiv:1112.5642
  51. 51.
    ETM collaboration, Carrasco N et al (2014) B-physics from \(N_f\) = 2 tmQCD: the standard model and beyond. JHEP 03:016.  https://doi.org/10.1007/JHEP03(2014)016, arXiv:1308.1851
  52. 52.
    Dowdall RJ, Davies CTH, Horgan RR, Lepage GP, Monahan CJ, Shigemitsu J (2014) B-meson mixing from full lattice QCD with physical u, d, s and c quarks, arXiv:1411.6989

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di FisicaLa Sapienza, University of RomeRomeItaly

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