Manifestly soft gauge invariant formulation of vNRQCD

Rothstein, Ira Z.; Shrivastava, Prashant; Stewart, Iain W.

doi:10.1016/j.nuclphysb.2018.12.027

Title: Manifestly soft gauge invariant formulation of vNRQCD

Abstract

Homogeneous power counting in Non-Relativistic QCD (NRQCD) implies the simultaneous existence of both soft and ultrasoft gluons. In the velocity renormalization group (vNRQCD) formalism we show that operators involving soft fields interacting with heavy potential quarks can be put in a manifestly gauge invariant form by utilizing gluon and quark building blocks which contain Wilson lines, and are analogous to those used in the soft collinear effective theory. This leads to several simplifications, in particular significantly reducing the size of the operator basis, which stream-lines matching and anomalous dimension calculations at subleading order in the velocity expansion. Also, soft ghosts no longer couple via potential like interactions to the heavy quark fields, and hence do not appear until two loops. Furthermore the the color structures that appear at each order in αs in the static potential are only those which should arise according to non-Abelian exponentiation. We also discuss how zero-bin subtractions clarify the role of iε terms in the heavy quark propagator poles carrying soft momenta. Even though the choice of the direction of the soft Wilson lines in our building blocks does not matter, there is still a limited set of consistent choices, and the predicted form ofmore »« less

Authors:

Rothstein, Ira Z.; Shrivastava, Prashant;

Publication Date:: Fri Feb 01 00:00:00 EST 2019

Research Org.:: Univ. of Arizona, Tucson, AZ (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Carnegie Mellon Univ., Pittsburgh, PA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); Simons Foundation

OSTI Identifier:: 1489422

Alternate Identifier(s):: OSTI ID: 1609537; OSTI ID: 1755494

Grant/Contract Number:: FG02-04ER41338; FG02-06ER41449; SC0011090; 327942; SC0010118

Resource Type:: Published Article

Journal Name:: Nuclear Physics. B

Additional Journal Information:: Journal Name: Nuclear Physics. B Journal Volume: 939 Journal Issue: C; Journal ID: ISSN 0550-3213

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; physics; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Rothstein, Ira Z., Shrivastava, Prashant, and Stewart, Iain W. Manifestly soft gauge invariant formulation of vNRQCD.  Netherlands: N. p., 2019. 
Web.  doi:10.1016/j.nuclphysb.2018.12.027.

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                    Rothstein, Ira Z., Shrivastava, Prashant, & Stewart, Iain W. Manifestly soft gauge invariant formulation of vNRQCD.  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2018.12.027

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                    Rothstein, Ira Z., Shrivastava, Prashant, and Stewart, Iain W. Fri .  
"Manifestly soft gauge invariant formulation of vNRQCD".  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2018.12.027.

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@article{osti_1489422,

  title        = {Manifestly soft gauge invariant formulation of vNRQCD},

  author       = {Rothstein, Ira Z. and Shrivastava, Prashant and Stewart, Iain W.},

  abstractNote = {Homogeneous power counting in Non-Relativistic QCD (NRQCD) implies the simultaneous existence of both soft and ultrasoft gluons. In the velocity renormalization group (vNRQCD) formalism we show that operators involving soft fields interacting with heavy potential quarks can be put in a manifestly gauge invariant form by utilizing gluon and quark building blocks which contain Wilson lines, and are analogous to those used in the soft collinear effective theory. This leads to several simplifications, in particular significantly reducing the size of the operator basis, which stream-lines matching and anomalous dimension calculations at subleading order in the velocity expansion. Also, soft ghosts no longer couple via potential like interactions to the heavy quark fields, and hence do not appear until two loops. Furthermore the the color structures that appear at each order in αs in the static potential are only those which should arise according to non-Abelian exponentiation. We also discuss how zero-bin subtractions clarify the role of iε terms in the heavy quark propagator poles carrying soft momenta. Even though the choice of the direction of the soft Wilson lines in our building blocks does not matter, there is still a limited set of consistent choices, and the predicted form of the eikonal poles does influence results at two-loops and beyond.},

  doi          = {10.1016/j.nuclphysb.2018.12.027},

  journal      = {Nuclear Physics. B},

  number       = C,

  volume       = 939,

  place        = {Netherlands},

  year         = {Fri Feb 01 00:00:00 EST 2019},

  month        = {Fri Feb 01 00:00:00 EST 2019}

}

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Title: Manifestly soft gauge invariant formulation of vNRQCD

Abstract

Citation Formats

Static Quark-Antiquark Potential in QCD to Three Loops journal, January 1997

Exponentiation of eikonal cross sections in nonabelian gauge theories journal, December 1983

Effective field theory of gravity for extended objects journal, May 2006

Heavy quark effective theory and nonrelativistic QCD Lagrangian to order α s / m 3 journal, July 1997

Invariant operators in collinear effective theory journal, September 2001

The static potential in QCD to two loops journal, February 1999

Bound states and power counting in effective field theories journal, April 1997

Introduction to noncovariant gauges journal, October 1987

Static QCD Potential at Three-Loop Order journal, March 2010

Infrared behavior of the static potential in perturbative QCD journal, October 1999

Effective-field theories for heavy quarkonium journal, December 2005

The zero-bin and mode factorization in quantum field theory journal, October 2007

An effective field theory for collinear and soft gluons: Heavy to light decays journal, May 2001

Renormalization group improvement of the nonrelativistic QCD Lagrangian and heavy quarkonium spectrum journal, March 2002

Renormalization group analysis of the QCD quark potential to order v 2 journal, June 2000

Renormalization group scaling in nonrelativistic QCD journal, March 2000

The renormalization group for correlated scales: one-stage versus two-stage running journal, August 2000

The renormalization group improvement of the QCD static potentials journal, December 2000

Running Coulomb potential and Lamb shift in QCD journal, June 2001

Potential NRQCD: an effective theory for heavy quarkonium journal, January 2000

Logarithms of α in QED Bound States from the Renormalization Group journal, September 2000

Ultrasoft renormalization in nonrelativistic QCD journal, June 2003

Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium journal, February 1995

Three-loop anomalous dimension of the heavy quark pair production current in nonrelativistic QCD journal, February 2004

Effective lagrangians for bound state problems in QED, QCD, and other field theories journal, February 1986

Effective field theory and matching in nonrelativistic gauge theories journal, January 1998

Next-to-leading ultrasoft running of the heavy quarkonium potentials and spectrum: Spin-independent case journal, July 2011

Asymptotic expansion of Feynman integrals near threshold journal, June 1998

Running of the heavy quark production current and 1 / | k | potential in QCD journal, January 2001

Non-abelian eikonal exponentiation journal, November 1984

Effective field theory for ultrasoft momenta in NRQCD and NRQED journal, May 1998

Two-loop ultrasoft running of the O ( v 2 ) QCD quark potentials journal, March 2007

Threshold expansion and dimensionally regularized NRQCD journal, October 1998

Next-to-leading-log renormalization-group running in heavy-quarkonium creation and annihilation journal, September 2002

Static limit of quantum chromodynamics journal, April 1978

QCD heavy-quark potential to order v 2 : One loop matching conditions journal, September 2000

Soft-collinear factorization in effective field theory journal, February 2002

Renormalization group scaling of the 1 / m 2 HQET Lagrangian journal, January 1998

Static Quark-Antiquark Potential in QCD to Three Loops
journal, January 1997

Exponentiation of eikonal cross sections in nonabelian gauge theories
journal, December 1983

Effective field theory of gravity for extended objects
journal, May 2006

Heavy quark effective theory and nonrelativistic QCD Lagrangian to order $α_{s} {/ m}^{3}$
journal, July 1997

Invariant operators in collinear effective theory
journal, September 2001

The static potential in QCD to two loops
journal, February 1999

Bound states and power counting in effective field theories
journal, April 1997

Introduction to noncovariant gauges
journal, October 1987

Static QCD Potential at Three-Loop Order
journal, March 2010

Infrared behavior of the static potential in perturbative QCD
journal, October 1999

Effective-field theories for heavy quarkonium
journal, December 2005

The zero-bin and mode factorization in quantum field theory
journal, October 2007

An effective field theory for collinear and soft gluons: Heavy to light decays
journal, May 2001

Renormalization group improvement of the nonrelativistic QCD Lagrangian and heavy quarkonium spectrum
journal, March 2002

Renormalization group analysis of the QCD quark potential to order $v^{2}$
journal, June 2000

Renormalization group scaling in nonrelativistic QCD
journal, March 2000

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journal, August 2000

The renormalization group improvement of the QCD static potentials
journal, December 2000

Running Coulomb potential and Lamb shift in QCD
journal, June 2001

Potential NRQCD: an effective theory for heavy quarkonium
journal, January 2000

Logarithms of $α$ in QED Bound States from the Renormalization Group
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Ultrasoft renormalization in nonrelativistic QCD
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Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium
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Three-loop anomalous dimension of the heavy quark pair production current in nonrelativistic QCD
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Effective field theory and matching in nonrelativistic gauge theories
journal, January 1998

Next-to-leading ultrasoft running of the heavy quarkonium potentials and spectrum: Spin-independent case
journal, July 2011

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Effective field theory for ultrasoft momenta in NRQCD and NRQED
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Two-loop ultrasoft running of the $O (v^{2})$ QCD quark potentials
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Threshold expansion and dimensionally regularized NRQCD
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Next-to-leading-log renormalization-group running in heavy-quarkonium creation and annihilation
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