Determining $\alpha_s$ from hadronic $\tau$ decay: the pitfalls of truncating the OPE

doi:10.21468/SciPostPhysProc.1.053

Title: Determining $$\alpha_s$$ from hadronic $$\tau$$ decay: the pitfalls of truncating the OPE

Abstract

We discuss sum-rule determinations of \alpha_s $α_{s}$ from non-strange hadronic \tau $τ$ -decay data. We investigate, in particular, the reliability of the assumptions underlying the “truncated OPE strategy,” which specifies a certain treatment of non-perturbative contributions, and which was employed in Refs. . Here, we test this strategy by applying the strategy to the R $R$ -ratio obtained from e^+e^- $e^{+} e^{-}$ data, which extend beyond the \tau $τ$ mass, and demonstrate that the assumptions underlying this strategy are not, in general, valid. We then present a brief overview of new results on the form of duality-violating non-perturbative contributions, which are conspicuously present in the experimentally determined spectral functions. As we show, with the current precision claimed for the extraction of \alpha_s $α_{s}$ , including a representation of duality violations is unavoidable if one wishes to avoid uncontrolled theoretical errors.

Authors:

Boito, Diogo ^[1];

^[2]; Maltman, Kim ^[3];

^[4]

University of Sao Paulo
San Francisco State University
University of Adelaide, York University
Autonomous University of Barcelona

Publication Date:: 2019-02-22

Sponsoring Org.:: USDOE

OSTI Identifier:: 1495814

Grant/Contract Number:: SC0013682

Resource Type:: Published Article

Journal Name:: SciPost Physics Proceedings

Additional Journal Information:: Journal Name: SciPost Physics Proceedings Journal Issue: 1

Publisher:: Stichting SciPost

Country of Publication:: Country unknown/Code not available

Language:: English

Citation Formats


                    Boito, Diogo, Golterman, Maarten, Maltman, Kim, and Peris, Santiago. Determining $\alpha_s$ from hadronic $\tau$ decay: the pitfalls of truncating the OPE.  Country unknown/Code not available: N. p., 2019. 
        Web.  doi:10.21468/SciPostPhysProc.1.053.

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                    Boito, Diogo, Golterman, Maarten, Maltman, Kim, & Peris, Santiago. Determining $\alpha_s$ from hadronic $\tau$ decay: the pitfalls of truncating the OPE.  Country unknown/Code not available.  doi:10.21468/SciPostPhysProc.1.053.

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                    Boito, Diogo, Golterman, Maarten, Maltman, Kim, and Peris, Santiago. Fri .  
        "Determining $\alpha_s$ from hadronic $\tau$ decay: the pitfalls of truncating the OPE".  Country unknown/Code not available.  doi:10.21468/SciPostPhysProc.1.053.

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@article{osti_1495814,

  title        = {Determining $\alpha_s$ from hadronic $\tau$ decay: the pitfalls of truncating the OPE},

  author       = {Boito, Diogo and Golterman, Maarten and Maltman, Kim and Peris, Santiago},

  abstractNote = {We discuss sum-rule determinations of \alpha_s α s from non-strange hadronic \tau τ -decay data. We investigate, in particular, the reliability of the assumptions underlying the “truncated OPE strategy,” which specifies a certain treatment of non-perturbative contributions, and which was employed in Refs. . Here, we test this strategy by applying the strategy to the R R -ratio obtained from e^+e^- e + e − data, which extend beyond the \tau τ mass, and demonstrate that the assumptions underlying this strategy are not, in general, valid. We then present a brief overview of new results on the form of duality-violating non-perturbative contributions, which are conspicuously present in the experimentally determined spectral functions. As we show, with the current precision claimed for the extraction of \alpha_s α s , including a representation of duality violations is unavoidable if one wishes to avoid uncontrolled theoretical errors.},

  doi          = {10.21468/SciPostPhysProc.1.053},

  journal      = {SciPost Physics Proceedings},

  number       = 1,

  volume       = ,

  place        = {Country unknown/Code not available},

  year         = {2019},

  month        = {2}

}

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Title: Determining $$\alpha_s$$ from hadronic $$\tau$$ decay: the pitfalls of truncating the OPE

Abstract

Citation Formats

QCD analysis of the tau hadronic width journal, April 1992

Hyperasymptotics and quark-hadron duality violations in QCD journal, March 2018

Resurgence, operator product expansion, and remarks on renormalons in supersymmetric Yang-Mills theory journal, March 2015

Constraints on the behaviour of the e+e− hadron annihilation cross section in asymptotically free theories and in theories with anomalous dimensions journal, February 1977

Strong coupling from e + e − → hadrons below charm journal, October 2018

Erratum: Decay correlations of heavy leptons in e + + e − → l + + l − journal, February 1976

Finite energy sum rules for the cross section of e+e−-annihilation into hadrons in QCD journal, May 1978

Spectral function sum rules in quantum chromodynamics journal, August 1979

Duality violations and spectral sum rules journal, August 2005

Gaussian sum rules in quantum chromodynamics and local duality journal, January 1985

Unraveling duality violations in hadronic tau decays journal, May 2008

Update of the ALEPH non-strange spectral functions from hadronic $$\tau $$ τ decays journal, March 2014

Smearing method in the quark model journal, April 1976

QCD predictions for the decay of the τ lepton journal, April 1988

Illustrative example of how quark-hadron duality might work journal, March 1998

Highly excited mesons, linear Regge trajectories, and the pattern of the chiral symmetry realization journal, February 2008

Decay Correlations of Heavy Leptons in e + + e − → l + + l − journal, November 1971

Testing QCD with τ decays journal, September 1992

Muon g − 2 and α ( M Z 2 ) : A new data-based analysis journal, June 2018

The use of finite energy sum rules for the description of the hadronic properties of QCD journal, December 1983

Strong coupling from hadronic τ decays: A critical appraisal journal, February 2017

Possible duality violations in τ decay and their impact on the determination of α s journal, March 2009

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects journal, August 2012

Determination of the QCD coupling from ALEPH τ decay data journal, August 2016

Measurement of the strong coupling constant $\alpha_{\rm s}$ and the vector and axial-vector spectral functions in hadronic tau decays journal, March 1999

Determination of the quark-gluon coupling constant journal, February 1977

Strong coupling from the revised ALEPH data for hadronic τ decays journal, February 2015

Updated determination of α s from τ decays journal, May 2012

Systematics of radial and angular-momentum Regge trajectories of light nonstrange q q ¯ -states journal, May 2012

The case for duality violations in the analysis of hadronic τ decays journal, September 2016

New determination of α s from hadronic τ decays journal, December 2011

What can asymptotic freedom say about e+e− → hadrons? journal, June 1977

Constraints on hadronic spectral functions from continuous families of finite energy sum rules journal, November 1998

α s ( M Z 2 ) from hadronic τ decays journal, November 2008

QCD analysis of the tau hadronic width
journal, April 1992

Hyperasymptotics and quark-hadron duality violations in QCD
journal, March 2018

Resurgence, operator product expansion, and remarks on renormalons in supersymmetric Yang-Mills theory
journal, March 2015

Constraints on the behaviour of the e+e− hadron annihilation cross section in asymptotically free theories and in theories with anomalous dimensions
journal, February 1977

Strong coupling from $e^{+} e^{-} \to hadrons$ below charm
journal, October 2018

Erratum: Decay correlations of heavy leptons in $e^{+} + e^{-} \to l^{+} + l^{-}$
journal, February 1976

Finite energy sum rules for the cross section of e+e−-annihilation into hadrons in QCD
journal, May 1978

Spectral function sum rules in quantum chromodynamics
journal, August 1979

Duality violations and spectral sum rules
journal, August 2005

Gaussian sum rules in quantum chromodynamics and local duality
journal, January 1985

Unraveling duality violations in hadronic tau decays
journal, May 2008

Update of the ALEPH non-strange spectral functions from hadronic $$\tau $$ τ decays
journal, March 2014

Smearing method in the quark model
journal, April 1976

QCD predictions for the decay of the τ lepton
journal, April 1988

Illustrative example of how quark-hadron duality might work
journal, March 1998

Highly excited mesons, linear Regge trajectories, and the pattern of the chiral symmetry realization
journal, February 2008

Decay Correlations of Heavy Leptons in $e^{+} + e^{-} \to l^{+} + l^{-}$
journal, November 1971

Testing QCD with τ decays
journal, September 1992

Muon $g - 2$ and $α (M_{Z}^{2})$ : A new data-based analysis
journal, June 2018

The use of finite energy sum rules for the description of the hadronic properties of QCD
journal, December 1983

Strong coupling from hadronic $τ$ decays: A critical appraisal
journal, February 2017

Possible duality violations in $τ$ decay and their impact on the determination of $α_{s}$
journal, March 2009

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
journal, August 2012

Determination of the QCD coupling from ALEPH $τ$ decay data
journal, August 2016

Measurement of the strong coupling constant $\alpha_{\rm s}$ and the vector and axial-vector spectral functions in hadronic tau decays
journal, March 1999

Determination of the quark-gluon coupling constant
journal, February 1977

Strong coupling from the revised ALEPH data for hadronic $τ$ decays
journal, February 2015

Updated determination of $α_{s}$ from $τ$ decays
journal, May 2012

Systematics of radial and angular-momentum Regge trajectories of light nonstrange $q \bar{q}$ -states
journal, May 2012

The case for duality violations in the analysis of hadronic τ decays
journal, September 2016

New determination of $α_{s}$ from hadronic $τ$ decays
journal, December 2011

What can asymptotic freedom say about e+e− → hadrons?
journal, June 1977

Constraints on hadronic spectral functions from continuous families of finite energy sum rules
journal, November 1998

$α_{s} (M_{Z}^{2})$ from hadronic $τ$ decays
journal, November 2008