skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: The MSR mass and the $$ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $$ renormalon sum rule

Abstract

Here, we provide a detailed description and analysis of a low-scale short-distance mass scheme, called the MSR mass, that is useful for high-precision top quark mass determinations, but can be applied for any heavy quark Q. In contrast to earlier low-scale short-distance mass schemes, the MSR scheme has a direct connection to the well known MS¯ mass commonly used for high-energy applications, and is determined by heavy quark on-shell self-energy Feynman diagrams. Indeed, the MSR mass scheme can be viewed as the simplest extension of the MS¯mass concept to renormalization scales << mQ. The MSR mass depends on a scale R that can be chosen freely, and its renormalization group evolution has a linear dependence on R, which is known as R-evolution. Using R-evolution for the MSR mass we provide details of the derivation of an analytic expression for the normalization of the $$ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $$ renormalon asymptotic behavior of the pole mass in perturbation theory. This is referred to as the $$ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $$ renormalon sum rule, and can be applied to any perturbative series. The relations of the MSR mass scheme to other low-scale short-distance masses are analyzed as well.

Authors:
 [1];  [2];  [1];  [3]; ORCiD logo [4];  [5];  [6]
  1. Univ. of Vienna, Wien (Austria)
  2. Indian Institute of Science Education and Research Bhopal, Bhopal (India)
  3. Univ. de Salamanca, Salamanca (Spain); Instituto de Fisica Teorica UAM-CSIC, Madrid (Spain)
  4. Univ. of Vienna, Wien (Austria); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  5. Univ. Complutense de Madrid (UCM), Madrid (Spain)
  6. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1501475
Grant/Contract Number:  
SC0011090
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 4; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Heavy Quark Physics; Perturbative QCD; Quark Masses and SM Parameters; Renormalization Regularization and Renormalons

Citation Formats

Hoang, André H., Jain, Ambar, Lepenik, Christopher, Mateu, Vicent, Preisser, Moritz, Scimemi, Ignazio, and Stewart, Iain W. The MSR mass and the $ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $ renormalon sum rule. United States: N. p., 2018. Web. doi:10.1007/jhep04(2018)003.
Hoang, André H., Jain, Ambar, Lepenik, Christopher, Mateu, Vicent, Preisser, Moritz, Scimemi, Ignazio, & Stewart, Iain W. The MSR mass and the $ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $ renormalon sum rule. United States. doi:10.1007/jhep04(2018)003.
Hoang, André H., Jain, Ambar, Lepenik, Christopher, Mateu, Vicent, Preisser, Moritz, Scimemi, Ignazio, and Stewart, Iain W. Tue . "The MSR mass and the $ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $ renormalon sum rule". United States. doi:10.1007/jhep04(2018)003. https://www.osti.gov/servlets/purl/1501475.
@article{osti_1501475,
title = {The MSR mass and the $ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $ renormalon sum rule},
author = {Hoang, André H. and Jain, Ambar and Lepenik, Christopher and Mateu, Vicent and Preisser, Moritz and Scimemi, Ignazio and Stewart, Iain W.},
abstractNote = {Here, we provide a detailed description and analysis of a low-scale short-distance mass scheme, called the MSR mass, that is useful for high-precision top quark mass determinations, but can be applied for any heavy quark Q. In contrast to earlier low-scale short-distance mass schemes, the MSR scheme has a direct connection to the well known MS¯ mass commonly used for high-energy applications, and is determined by heavy quark on-shell self-energy Feynman diagrams. Indeed, the MSR mass scheme can be viewed as the simplest extension of the MS¯mass concept to renormalization scales << mQ. The MSR mass depends on a scale R that can be chosen freely, and its renormalization group evolution has a linear dependence on R, which is known as R-evolution. Using R-evolution for the MSR mass we provide details of the derivation of an analytic expression for the normalization of the $ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $ renormalon asymptotic behavior of the pole mass in perturbation theory. This is referred to as the $ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $ renormalon sum rule, and can be applied to any perturbative series. The relations of the MSR mass scheme to other low-scale short-distance masses are analyzed as well.},
doi = {10.1007/jhep04(2018)003},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2018,
place = {United States},
year = {2018},
month = {4}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 5 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

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


How heavy must quarks BE in order to build coulombic bound states?
journal, May 1980


Power corrections to event shapes with mass-dependent operators
journal, January 2013


The top-antitop threshold at the ILC: NNLL QCD uncertainties
journal, May 2014

  • Hoang, André H.; Stahlhofen, Maximilian
  • Journal of High Energy Physics, Vol. 2014, Issue 5
  • DOI: 10.1007/JHEP05(2014)121

Perturbative pole mass in QCD
journal, July 1998


High-precision quark masses and QCD coupling from n f = 4 lattice QCD
journal, March 2015


Top Quark Mass Calibration for Monte Carlo Event Generators
journal, November 2016


Non-Abelian Dipole Radiation and the Heavy Quark Expansion
journal, April 1998


Top mass determination in leptonic final states with J/ψ
journal, March 2000


Heavy quark effective theory beyond perturbation theory: renormalons, the pole mass and the residual mass term
journal, September 1994


Moments of heavy quark current correlators at four-loop order in perturbative QCD
journal, September 2008


N Jettiness: An Inclusive Event Shape to Veto Jets
journal, August 2010


Double fermionic contributions to the heavy-quark vacuum polarization
journal, July 2008


Total hadronic cross section in e + e annihilation at the four-loop level of perturbative QCD
journal, February 1991


Quark-antiquark potential in QCD
journal, October 1977


Jets from massive unstable particles: Top-mass determination
journal, April 2008


Strong IR cancellation in heavy quarkonium and precise top mass determination
journal, November 2015

  • Kiyo, Y.; Mishima, G.; Sumino, Y.
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)084

Total Top-Quark Pair-Production Cross Section at Hadron Colliders Through O ( α S 4 )
journal, June 2013


The pole mass in perturbative QCD
journal, June 1981


Top quark mass measurements at and above threshold at CLIC
journal, August 2013


QCD and resonance physics. theoretical foundations
journal, February 1979


Next-to-Next-to-Next-to-Leading Order QCD Prediction for the Top Antitop S -Wave Pair Production Cross Section Near Threshold in e + e Annihilation
journal, November 2015


Renormalons
journal, August 1999


A quark mass definition adequate for threshold problems
journal, August 1998


Estimate of 4-loop pole-<mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mover accent="true"><mml:mrow><mml:mi mathvariant="normal">MS</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:math> mass relation from static QCD potential
journal, January 2014


On the ultimate uncertainty of the top quark pole mass
journal, December 2017


Charm- and bottom-quark masses from perturbative QCD
journal, October 2006


1 S and MS ¯ bottom quark masses from Υ sum rules
journal, December 1999


"Optical" sum rule for form factors of heavy mesons
journal, October 1992


Light quark mass effects in the on-shell renormalization constants
journal, October 2007


Third-order Coulomb corrections to the S-wave Green function, energy levels and wave functions at the origin
journal, May 2005


Higher moments of heavy quark correlators in the low energy limit at
journal, July 2008


Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD
journal, August 2006


R evolution: Improving perturbative QCD
journal, July 2010


B Decay and the ϒ Mass
journal, January 1999


The static potential in quantum chromodynamics
journal, August 1977


Two loop soft function for secondary massive quarks
journal, January 2014


Fit to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules in a renormalon based approach
journal, September 2005


Measurement of the top quark mass using proton-proton data at ( s ) = 7 and 8 TeV
journal, April 2016


The gell-mann-low function of QCD in the three-loop approximation
journal, June 1980


Charm mass determination from QCD charmonium sum rules at order $ \alpha_s^3 $
journal, September 2013

  • Dehnadi, Bahman; Hoang, Andre H.; Mateu, Vicent
  • Journal of High Energy Physics, Vol. 2013, Issue 9
  • DOI: 10.1007/JHEP09(2013)103

The three-loop splitting functions in QCD: the non-singlet case
journal, June 2004


The three-loop relation between the and the pole quark masses
journal, June 2000


QCD and resonance physics. applications
journal, February 1979


Renormalization of the Wilson loops beyond the leading order
journal, January 1987


Four-Loop Tadpoles: Applications in QCD
journal, October 2006


Determination of the top quark mass from leptonic observables
journal, September 2014

  • Frixione, Stefano; Mitov, Alexander
  • Journal of High Energy Physics, Vol. 2014, Issue 9
  • DOI: 10.1007/JHEP09(2014)012

Pole mass of the heavy quark: Perturbation theory and beyond
journal, August 1994


Bottom and charm mass determinations from global fits to Q Q ¯ $$ Q\overline{Q} $$ bound states at N3LO
journal, January 2018


Full formula for heavy quarkonium energy levels at next-to-next-to-next-to-leading order
journal, December 2014


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


The four-loop β-function in quantum chromodynamics
journal, May 1997


The second physical moment of the heavy quark vector correlator at <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi mathvariant="script">O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>α</mml:mi><mml:mi>s</mml:mi><mml:mn>3</mml:mn></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math>
journal, October 2008


Three-Loop Static Potential
journal, March 2010


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


Order α s 4 QCD Corrections to Z and τ Decays
journal, July 2008


Variable-flavor-number scheme for final state jets in thrust
journal, December 2014


Analytic three-loop static potential
journal, September 2016


Quark Mass Relations to Four-Loop Order in Perturbative QCD
journal, April 2015


Estimations of order αs3 and αs4 corrections to mass-dependent observables
journal, June 1997


Aspects of Heavy-Quark Theory
journal, December 1997


Higher-order corrections to in quantum chromodynamics
journal, August 1979


Bottom and charm mass determinations with a convergence test
journal, August 2015

  • Dehnadi, Bahman; Hoang, André H.; Mateu, Vicent
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)155

Peculiar features of the relations between pole and running heavy quark masses and estimates of the O(α s 4 ) contributions
journal, November 2010


Two-loop jet function and jet mass for top quarks
journal, May 2008


A discussion on leading renormalon in the pole mass
journal, August 2017


MS ¯ -on-shell quark mass relation up to four loops in QCD and a general SU ( N ) gauge group
journal, October 2016

  • Marquard, Peter; Smirnov, Alexander V.; Smirnov, Vladimir A.
  • Physical Review D, Vol. 94, Issue 7
  • DOI: 10.1103/PhysRevD.94.074025

On the flavour dependence of the $O(\alpha_{s}^{4})$ correction to the relation between running and pole heavy quark masses
journal, August 2016


Low-energy moments of heavy quark current correlators at four loops
journal, January 2010


Bottom-quark mass from finite energy QCD sum rules
journal, February 2012


Precision thrust cumulant moments at N 3 LL
journal, November 2012


Measurement of masses in the $\mathrm{t}\overline{\mathrm{t}}$ system by kinematic endpoints in pp collisions at $\sqrt{s}=7\ \mathrm{TeV}$
journal, July 2013


B decays in the upsilon expansion
journal, March 1999


The bottom-quark mass from non-relativistic sum rules at NNNLO
journal, February 2015


The four-loop QCD β-function and anomalous dimensions
journal, March 2005


More on ambiguities in the pole mass
journal, January 1995


Three-loop polarization function and O(αs2) corrections to the production of heavy quarks
journal, December 1996


Heavy quark vacuum polarisation to three loops
journal, March 1996


C -parameter distribution at N 3 LL including power corrections
journal, May 2015


Perturbative expansion of the energy of static sources at large orders in four-dimensional SU(3) gauge theory
journal, May 2013


Precise determination of α s from the C -parameter distribution
journal, May 2015


NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron
journal, May 2016

  • Czakon, Michal; Fiedler, Paul; Heymes, David
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)034

Renormalons beyond one loop
journal, July 1997


Three-loop relation of quark $$\overline {MS} $$ and pole masses
journal, December 1990

  • Gray, N.; Broadhurst, D. J.; Grafe, W.
  • Zeitschrift für Physik C Particles and Fields, Vol. 48, Issue 4
  • DOI: 10.1007/BF01614703

Top Mass Measurements from Jets and the Tevatron Top-Quark Mass
journal, December 2008


Thrust at N 3 LL with power corrections and a precision global fit for α s ( m Z )
journal, April 2011


The three-loop QCD β-function and anomalous dimensions
journal, April 1993


Charm quark mass with calibrated uncertainty
journal, February 2017


Heavy quarkonium spectrum at and bottom/top quark mass determination
journal, July 2002


On the light massive flavor dependence of the large order asymptotic behavior and the ambiguity of the pole mass
journal, September 2017

  • Hoang, André H.; Lepenik, Christopher; Preisser, Moritz
  • Journal of High Energy Physics, Vol. 2017, Issue 9
  • DOI: 10.1007/JHEP09(2017)099

Infrared Renormalization-Group Flow for Heavy-Quark Masses
journal, October 2008


Designing gapped soft functions for jet production
journal, March 2008


Renormalization group improved bottom mass from $ \varUpsilon $ sum rules at NNLL order
journal, October 2012

  • Hoang, André H.; Ruiz-Femenía, Pedro; Stahlhofen, Maximilian
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)188

QCD sum rule determination of the charm-quark mass
journal, April 2011


The relation between the and the on-shell quark mass at order αs3
journal, May 2000


Short-Distance Mass of a Heavy Quark at Order α s 3
journal, November 1999


Static limit of quantum chromodynamics
journal, April 1978


A new observable to measure the top-quark mass at hadron colliders
journal, May 2013


QCD phenomenology of static sources and gluonic excitations at short distances
journal, May 2004


Naive nonabelianization and resummation of fermion bubble chains
journal, April 1995