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A resolution of the puzzle of low Vus values from inclusive flavor-breaking sum rule analyses of hadronic τ decay data

  • 1.

    York University, Toronto, ON M3J 1P3, Canada

  • 2.

    CSSM, University of Adelaide, Adelaide, SA 5005, Australia

Funds:  Supported by the Natural Sciences and Engineering Research Council of Canada and the Australian Research Council.
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2016.05.004
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  • Corresponding author: MALTMAN K. (corresponding author), male, born in 1950, PhD/Prof. Research field: theoretical particle physics.
  • Received Date: 27 November 2015
  • Accepted Date: 20 April 2016
  • Rev Recd Date: 20 April 2016
  • Publish Date: 31 May 2016
    Abstract

  • Abstract

    Continuum and lattice methods are used to investigate systematic issues in the sum rule determination of Vus using inclusive hadronic τ decay data. Results for Vus employing assumptions for D>4 OPE contributions used in previous conventional implementations of this approach are shown to display unphysical dependence on the sum rule weight, w, and choice of upper limit, s0, of the relevant experimental spectral integrals. Continuum and lattice results suggest a new implementation of the sum rule approach with not just ｜Vus｜, but also D>4 effective condensates fit to data. Lattice results are also shown to provide a quantitative assessment of truncation uncertainties for the slowly converging D=2 OPE series. The new sum rule implementation yields ｜Vus｜ results free of unphysical s0- and w-dependences and ～0.002 0 higher than that obtained using the conventional implementation. With preliminary new experimental results for the Kπ branching fraction, the resulting ｜Vus｜ is in excellent agreement with that based on Kl3, and compatible within errors with expectations from three-family unitarity.

    Abstract

    Continuum and lattice methods are used to investigate systematic issues in the sum rule determination of Vus using inclusive hadronic τ decay data. Results for Vus employing assumptions for D>4 OPE contributions used in previous conventional implementations of this approach are shown to display unphysical dependence on the sum rule weight, w, and choice of upper limit, s0, of the relevant experimental spectral integrals. Continuum and lattice results suggest a new implementation of the sum rule approach with not just ｜Vus｜, but also D>4 effective condensates fit to data. Lattice results are also shown to provide a quantitative assessment of truncation uncertainties for the slowly converging D=2 OPE series. The new sum rule implementation yields ｜Vus｜ results free of unphysical s0- and w-dependences and ～0.002 0 higher than that obtained using the conventional implementation. With preliminary new experimental results for the Kπ branching fraction, the resulting ｜Vus｜ is in excellent agreement with that based on Kl3, and compatible within errors with expectations from three-family unitarity.
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    • References(40)
  • [1]
    GAMIZ E, PRADES J, JAMIN M, et al. Determination of ms and |Vus| from hadronic τ decays[J]. JHEP, 2003(1): 060.
    [2]
    GAMIZ E, JAMIN M, PICH A, et al. Vus and ms from hadronic τ decays[J]. Phys Rev Lett, 2005, 94: 011803.
    [3]
    GAMIZ E, JAMIN M, PICH A, et al. Theoretical progress on the Vus determination from tau decays[J]. Proceedings of Science, 2007: PoS(KAON)008.
    [4]
    TSAI Y S. Decay correlations of heavy leptons in e++e-→l++l-[J]. Phys Rev D, 1971, 4: 2821-2837(Erratum: Phys Rev D, 1976, 13: 771).
    [5]
    MALTMAN K. Problems with extracting ms from flavor breaking in hadronic τ decays[J]. Phys Rev D, 1998, 58: 093015.
    [6]
    MALTMAN K, KAMBOR J. Longitudinal contributions to hadronic τ decay[J]. Phys Rev D, 2001, 64: 093014.
    [7]
    JAMIN M, OLLER J A, PICH A. S-wave Kπ scattering in chiral perturbation theory with resonances[J]. Nucl Phys B, 2000, 587: 331-362.
    [8]
    JAMIN M, OLLER J A, PICH A. Strangeness-changing scalar form factors[J]. Nucl Phys B, 2002, 622: 279-308.
    [9]
    JAMIN M, OLLER J A, PICH A. Scalar Kπ form factor and light quark masses[J]. Phys Rev D, 2006, 74: 074009.
    [10]
    MALTMAN K, KAMBOR J. Decay constants, light quark masses, and quark mass bounds from light quark pseudoscalar sum rules[J]. Phys Rev D, 2002, 65: 074013.
    [11]
    HARDY J C, TOWNER I S. Parametrization of the statistical rate function for select superallowed transitions[J]. Phys Rev C, 2015, 91: 015501.
    [12]
    LUSIANI A. Determination of |Vus| from the tau lepton branching fractions[DB/OL]. arXiv: 1411.4526 [hep-ex].
    [13]
    PASSEMAR E. Determinations of |Vus| from hadronic tau decays: A theory perspective[C]// the 8th International Workshop on the CKM Unitarity Triangle (CKM 2014), Vienna, Austria, September 8-12, 2014.
    [14]
    MALTMAN K, WOLFE C E. Joint extraction of ms and Vus from hadronic τ decays[J]. Phys Lett B, 2007, 650: 27-32.
    [15]
    MALTMAN K, WOLFE C E, BANERJEE S, et al. Status of the hadronic τ determination of Vus[J]. Int J Mod Phys A, 2008, 23: 3191-3195.
    [16]
    MALTMAN K, WOLFE C E, BANERJEE S, et al. Status of the hadronic τ decay determination of |Vus|[J]. Nucl Phys Proc Suppl, 2009, 189: 175-180.
    [17]
    MALTMAN K. A critical look at Vus determinations from hadronic τ decay data[J]. Nucl Phys Proc Suppl, 2011, 218: 146-151.
    [18]
    BOITO D, GOLTERMAN M, JAMIN M, et al. Updated determination of αs from τ decays[J]. Phys Rev D, 2012, 85: 093015.
    [19]
    BOITO D, GOLTERMAN M, MALTMAN K, et al. Strong coupling from the revised ALEPH data for hadronic τ decays[J]. Phys Rev D, 2015, 91: 034003.
    [20]
    CHETYRKIN K G, KWIATKOWSKI A. Mass corrections to the tau decay rate[J]. Z Phys C, 1993, 59: 525-531
    [21]
    BAIKOV PA, CHETYRKIN K G, KHN J H. Strange-quark mass from tau-lepton decays with Oα3s accuracy[J]. Phys Rev Lett, 2005, 95: 012003.
    [22]
    HUDSPITH R J, LEWIS R, MALTMAN K, et al. Determining the QCD coupling from lattice vacuum polarization[DB/OL]. arXiv:1510.04890 [hep-lat].
    [23]
    AOKI S, AOKI Y, BERNARD C, et al. Review of lattice results concerning low-energy particle physics[J]. Eur Phys J C, 2014, 74: 2890.
    [24]
    MCNEILE C, BAZAVOV A, DAVIES C T H, et al. Direct determination of the strange and light quark condensates from full lattice QCD[J]. Phys Rev D, 2013, 87: 034503.
    [25]
    GASSER J, LEUTWYLER H. Chiral perturbation theory: Expansions in the mass of the strange quark[J]. Nucl Phys B, 1985, 250: 465-516.
    [26]
    AOKI Y, ARTHUR R, BLUM T, et al (RBC and UKQCD Collaborations). Continuum limit physics from 2+1 flavor domain wall QCD[J]. Phys Rev D, 2011, 83: 074508.
    [27]
    DAVIER M, HOECKER A, MALAESCU B, et al. Update of the ALEPH non-strange spectral functions from hadronic  decays[J]. Eur Phys J C, 2014, 74: 2803.
    [28]
    AUBERT B, BONA M, BOUTIGNY D, et al (BaBar Collaboration). Measurement of the τ-→K-π0ντ branching fraction[J]. Phys Rev D, 2007, 76:051104(R).
    [29]
    EPIFANOV D, ADACHI I, AIHARA H, et al (Belle Collaboration). Study of τ-→KSπ-ντ decay at Belle[J]. Phys Lett, B, 2007, 654: 65-73.
    [30]
    NUGENT I M (on behalf of the BaBar Collaboration). Invariant mass spectra of τ-→h-h-h+ντ decays[J]. Nucl Phys Proc Suppl, 2014, 253-255: 38-41.
    [31]
    RYU S (for the Belle Collaboration). Measurement of the branching fractions and mass spectra for τ lepton decays including KS0 at Belle[J]. Nucl Phys Proc Suppl, 2014, 253-255: 33-37.
    [32]
    BARATE R, DECAMP D, GHEZ P, et al (ALEPH Collaboration). Study of τ decays involving kaons, spectral functions and determination of the strange quark mass[J]. Eur Phys J C, 1999, 11: 599-648.
    [33]
    ADAMETZ A. Measurement of τ decays into charged hadron accompanied by neutral π mesons and determination of the CKM matrix element Vus[D]. Heidelberg, Germany: University of Heidelberg.
    [34]
    MALTMAN K, YAVIN T. αs(M2Z) from hadronic τ decays [J]. Phys Rev D, 2008, 78: 094020.
    [35]
    ANTONELLI M, CIRIGLIANO V, LUSIANI A, et al. Predicting the tau strange branching ratios and implications for Vus[J]. JHEP, 2013, 1310: 070.
    [36]
    MOULSON M. Experimental determination of Vus from kaon decays[J]. arXiv:1411.5252 [hep-ex].
    [37]
    BOYLE P A, CHRIST N H, FLYNN J M, et al (the RBC/UKQCD Collaboration). The kaon semileptonic form factor in Nf=2+1 domain wall lattice QCD with physical light quark masses[J]. JHEP, 2015, 1506:164.
    [38]
    PRIMER T, TOUSSAINT D, EL-KHADRA A, et al (FNAL and MILC Collaborations). Kaon and D meson semileptonic form factors from lattice QCD[J].Proceedings of Science, 2014: PoS(LATTICE2014)374.
    [39]
    BLUM T, BOYLE PA, CHRIST N H, et al (RBC/UKQCD Collaboration). Domain wall QCD with physical quark masses[J]. arXiv: 1411.7017 [hep-lat].
    [40]
    BAZAVOV A, BERNARD C, KOMIJANI J, et al (FNAL and MILC Collaborations). Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks[J] Phys Rev D, 2014, 90: 074509.
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    [1]
    GAMIZ E, PRADES J, JAMIN M, et al. Determination of ms and |Vus| from hadronic τ decays[J]. JHEP, 2003(1): 060.
    [2]
    GAMIZ E, JAMIN M, PICH A, et al. Vus and ms from hadronic τ decays[J]. Phys Rev Lett, 2005, 94: 011803.
    [3]
    GAMIZ E, JAMIN M, PICH A, et al. Theoretical progress on the Vus determination from tau decays[J]. Proceedings of Science, 2007: PoS(KAON)008.
    [4]
    TSAI Y S. Decay correlations of heavy leptons in e++e-→l++l-[J]. Phys Rev D, 1971, 4: 2821-2837(Erratum: Phys Rev D, 1976, 13: 771).
    [5]
    MALTMAN K. Problems with extracting ms from flavor breaking in hadronic τ decays[J]. Phys Rev D, 1998, 58: 093015.
    [6]
    MALTMAN K, KAMBOR J. Longitudinal contributions to hadronic τ decay[J]. Phys Rev D, 2001, 64: 093014.
    [7]
    JAMIN M, OLLER J A, PICH A. S-wave Kπ scattering in chiral perturbation theory with resonances[J]. Nucl Phys B, 2000, 587: 331-362.
    [8]
    JAMIN M, OLLER J A, PICH A. Strangeness-changing scalar form factors[J]. Nucl Phys B, 2002, 622: 279-308.
    [9]
    JAMIN M, OLLER J A, PICH A. Scalar Kπ form factor and light quark masses[J]. Phys Rev D, 2006, 74: 074009.
    [10]
    MALTMAN K, KAMBOR J. Decay constants, light quark masses, and quark mass bounds from light quark pseudoscalar sum rules[J]. Phys Rev D, 2002, 65: 074013.
    [11]
    HARDY J C, TOWNER I S. Parametrization of the statistical rate function for select superallowed transitions[J]. Phys Rev C, 2015, 91: 015501.
    [12]
    LUSIANI A. Determination of |Vus| from the tau lepton branching fractions[DB/OL]. arXiv: 1411.4526 [hep-ex].
    [13]
    PASSEMAR E. Determinations of |Vus| from hadronic tau decays: A theory perspective[C]// the 8th International Workshop on the CKM Unitarity Triangle (CKM 2014), Vienna, Austria, September 8-12, 2014.
    [14]
    MALTMAN K, WOLFE C E. Joint extraction of ms and Vus from hadronic τ decays[J]. Phys Lett B, 2007, 650: 27-32.
    [15]
    MALTMAN K, WOLFE C E, BANERJEE S, et al. Status of the hadronic τ determination of Vus[J]. Int J Mod Phys A, 2008, 23: 3191-3195.
    [16]
    MALTMAN K, WOLFE C E, BANERJEE S, et al. Status of the hadronic τ decay determination of |Vus|[J]. Nucl Phys Proc Suppl, 2009, 189: 175-180.
    [17]
    MALTMAN K. A critical look at Vus determinations from hadronic τ decay data[J]. Nucl Phys Proc Suppl, 2011, 218: 146-151.
    [18]
    BOITO D, GOLTERMAN M, JAMIN M, et al. Updated determination of αs from τ decays[J]. Phys Rev D, 2012, 85: 093015.
    [19]
    BOITO D, GOLTERMAN M, MALTMAN K, et al. Strong coupling from the revised ALEPH data for hadronic τ decays[J]. Phys Rev D, 2015, 91: 034003.
    [20]
    CHETYRKIN K G, KWIATKOWSKI A. Mass corrections to the tau decay rate[J]. Z Phys C, 1993, 59: 525-531
    [21]
    BAIKOV PA, CHETYRKIN K G, KHN J H. Strange-quark mass from tau-lepton decays with Oα3s accuracy[J]. Phys Rev Lett, 2005, 95: 012003.
    [22]
    HUDSPITH R J, LEWIS R, MALTMAN K, et al. Determining the QCD coupling from lattice vacuum polarization[DB/OL]. arXiv:1510.04890 [hep-lat].
    [23]
    AOKI S, AOKI Y, BERNARD C, et al. Review of lattice results concerning low-energy particle physics[J]. Eur Phys J C, 2014, 74: 2890.
    [24]
    MCNEILE C, BAZAVOV A, DAVIES C T H, et al. Direct determination of the strange and light quark condensates from full lattice QCD[J]. Phys Rev D, 2013, 87: 034503.
    [25]
    GASSER J, LEUTWYLER H. Chiral perturbation theory: Expansions in the mass of the strange quark[J]. Nucl Phys B, 1985, 250: 465-516.
    [26]
    AOKI Y, ARTHUR R, BLUM T, et al (RBC and UKQCD Collaborations). Continuum limit physics from 2+1 flavor domain wall QCD[J]. Phys Rev D, 2011, 83: 074508.
    [27]
    DAVIER M, HOECKER A, MALAESCU B, et al. Update of the ALEPH non-strange spectral functions from hadronic  decays[J]. Eur Phys J C, 2014, 74: 2803.
    [28]
    AUBERT B, BONA M, BOUTIGNY D, et al (BaBar Collaboration). Measurement of the τ-→K-π0ντ branching fraction[J]. Phys Rev D, 2007, 76:051104(R).
    [29]
    EPIFANOV D, ADACHI I, AIHARA H, et al (Belle Collaboration). Study of τ-→KSπ-ντ decay at Belle[J]. Phys Lett, B, 2007, 654: 65-73.
    [30]
    NUGENT I M (on behalf of the BaBar Collaboration). Invariant mass spectra of τ-→h-h-h+ντ decays[J]. Nucl Phys Proc Suppl, 2014, 253-255: 38-41.
    [31]
    RYU S (for the Belle Collaboration). Measurement of the branching fractions and mass spectra for τ lepton decays including KS0 at Belle[J]. Nucl Phys Proc Suppl, 2014, 253-255: 33-37.
    [32]
    BARATE R, DECAMP D, GHEZ P, et al (ALEPH Collaboration). Study of τ decays involving kaons, spectral functions and determination of the strange quark mass[J]. Eur Phys J C, 1999, 11: 599-648.
    [33]
    ADAMETZ A. Measurement of τ decays into charged hadron accompanied by neutral π mesons and determination of the CKM matrix element Vus[D]. Heidelberg, Germany: University of Heidelberg.
    [34]
    MALTMAN K, YAVIN T. αs(M2Z) from hadronic τ decays [J]. Phys Rev D, 2008, 78: 094020.
    [35]
    ANTONELLI M, CIRIGLIANO V, LUSIANI A, et al. Predicting the tau strange branching ratios and implications for Vus[J]. JHEP, 2013, 1310: 070.
    [36]
    MOULSON M. Experimental determination of Vus from kaon decays[J]. arXiv:1411.5252 [hep-ex].
    [37]
    BOYLE P A, CHRIST N H, FLYNN J M, et al (the RBC/UKQCD Collaboration). The kaon semileptonic form factor in Nf=2+1 domain wall lattice QCD with physical light quark masses[J]. JHEP, 2015, 1506:164.
    [38]
    PRIMER T, TOUSSAINT D, EL-KHADRA A, et al (FNAL and MILC Collaborations). Kaon and D meson semileptonic form factors from lattice QCD[J].Proceedings of Science, 2014: PoS(LATTICE2014)374.
    [39]
    BLUM T, BOYLE PA, CHRIST N H, et al (RBC/UKQCD Collaboration). Domain wall QCD with physical quark masses[J]. arXiv: 1411.7017 [hep-lat].
    [40]
    BAZAVOV A, BERNARD C, KOMIJANI J, et al (FNAL and MILC Collaborations). Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks[J] Phys Rev D, 2014, 90: 074509.
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