Pole- versus MS-mass definitions in the electroweak theory

Faisst, M.; Kühn, Johann H.; Veretin, O. L.

doi:10.1016/j.physletb.2004.03.045

Cited by 29 publications

(33 citation statements)

References 18 publications

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“…[17,20] and [18,19,21,22], respectively, and electroweak effects have been considered in Refs. [23][24][25][26][27]. The main task of this Letter is the computation of the four-loop QCD corrections to Z OS m and, consequently, to z m .…”

mentioning

confidence: 99%

Quark Mass Relations to Four-Loop Order in Perturbative QCD

Marquard¹,

Smirnov²,

Smirnov³

et al. 2015

Phys. Rev. Lett.

247

302

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We present results for the relation between a heavy quark mass defined in the on-shell and minimal subtraction (MS) scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the MS quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the MS heavy quark masses. DOI: 10.1103/PhysRevLett.114.142002 PACS numbers: 12.38.Bx, 12.38.Cy, 14.65.Fy, 14.65.Ha The precise knowledge of quark masses plays an important role in many phenomenological applications. This is in particular true for the heavy top, bottom, and charm quarks. For example, the top quark mass enters as a crucial parameter the combined electroweak fits which have been used to obtain indirect information about the Higgs boson mass, and nowadays serve as consistency checks for the standard model, see, e.g., Refs. [1,2]. The uncertainty in the top quark mass is also dominant in the analyses of the stability of the electroweak vacuum [3][4][5]. A prominent example where a precise bottom quark mass is required are B-meson decays which are often proportional to the fifth power of m b . Precise charm and bottom quark masses are important to obtain accurate predictions for the Higgs boson decays into the respective quark flavors. Also in the context of top and bottom Yukawa coupling unification, precise mass values are indispensable since they serve as boundary conditions at low energies. Last but not least, quark masses enter the Lagrange density of the standard model as fundamental parameters. Thus, it is mandatory to obtain precise numerical values by comparing high-order theoretical predictions with precise experimental data.At lowest order in perturbation theory there is no need to fix the renormalization scheme for the quark masses. However, after including quantum corrections it is necessary to apply renormalization conditions which fix the renormalization scheme. A natural scheme for heavy quark masses, i.e., the charm, bottom, and top quark masses, is the on-shell (OS) scheme where one requires that the inverse heavy quark propagator with momentum q has a zero at the position of the on-shell mass, M, i.e., for q 2 ¼ M 2. It is well known that perturbation theory has a bad convergence behavior in case the on-shell quark mass is used as a parameter. Another widely used renormalization scheme is based on minimal subtraction. This means that the mass parameter entering the quark propagator is defined in such a way that just divergent terms (and no finite contributions) are absorbed such that the quark propagator is finite (after wave function renormalization). In this Letter we consider four-loop corrections to the relation between the on-shell and the minimal subtraction (MS) definition of a heavy quark mass that allows for a precise conversion from one renormalization scheme into the other.For the various heavy quarks, different methods re...

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mentioning

confidence: 99%

Quark Mass Relations to Four-Loop Order in Perturbative QCD

Marquard¹,

Smirnov²,

Smirnov³

et al. 2015

Phys. Rev. Lett.

247

302

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“…Also important are two-loop [9,10,11,12,13] An important ingredient for the interpretation of these results in terms of top mass measurements performed at hadron colliders or at a future linear collider is the relation between the pole mass and the MS-mass definitions, the former being useful for the determination of m t at colliders, the latter being employed in actual calculations and in short-distance considerations. To match the present three-loop precision of the ρ parameter, this relation must be know in two-loop approximation [16,17,18,19], and for the four-loop calculation under discussion the corresponding three-loop result [20,21,22] must be employed.For fixed pole mass of the top quark, the three-loop result leads to a shift of about 10 MeV in the mass of the W -boson as discussed in [15,23]. (This applies both to the pure QCD corrections and the mixed QCDelectroweak one.)…”

mentioning

confidence: 99%

Four-Loop QCD Corrections to the ElectroweakρParameter

Chetyrkin

Faisst²,

Kühn³

et al. 2006

Phys. Rev. Lett.

Self Cite

108

147

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The four-loop QCD corrections to the electroweak ρ parameter arising from top and bottom quark loops are computed. Specifically we evaluate the missing "non-singlet" piece. Using algebraic methods the amplitude is reduced to a set of around 50 new master integrals which are calculated with various analytical and numerical methods. Inclusion of the newly completed term halves the final value of the four-loop correction for the minimally renormalized top-quark mass. The predictions for the shift of the weak mixing angle and the W-boson mass is thus stabilized.PACS numbers: 14.65. Ha, 14.70.Fm, 12.38.Bx Electroweak precision measurements and calculations provide stringent and decisive tests of the quantum fluctuations predicted from quantum field theory. As a most notable example, the indirect determination of the top quark mass, m t , mainly through its contribution to the ρ parameter [1], coincides remarkably well with the mass measurement performed by the CDF and D0 experiments at the TEVATRON [2]. Along the same line, the bounds on the mass of the Higgs-boson depend critically on the knowledge of m t and the control of the top-mass dependent effects on precision observables.A large group of dominant radiative corrections can be absorbed in the shift of the ρ parameter from its lowest order value ρ Born = 1. The result for the one-loop approximationhence quadratic in m t , was first evaluated in [3] and used to establish a limit on the mass splitting within one fermion doublet. In order to make full use of the present experimental precision, this one-loop calculation has been improved by two-loop [4,5,6] and even threeloop QCD corrections [7,8]. Also important are two-loop [9,10,11,12,13] An important ingredient for the interpretation of these results in terms of top mass measurements performed at hadron colliders or at a future linear collider is the relation between the pole mass and the MS-mass definitions, the former being useful for the determination of m t at colliders, the latter being employed in actual calculations and in short-distance considerations. To match the present three-loop precision of the ρ parameter, this relation must be know in two-loop approximation [16,17,18,19], and for the four-loop calculation under discussion the corresponding three-loop result [20,21,22] must be employed.For fixed pole mass of the top quark, the three-loop result leads to a shift of about 10 MeV in the mass of the W -boson as discussed in [15,23]. (This applies both to the pure QCD corrections and the mixed QCDelectroweak one.) Conversely, the corresponding shift of the top quark pole mass amounts to 1.5 GeV. (Similar considerations apply to the effective weak mixing angle and other precision observables.) These values are comparable to the experimental precision anticipated for topand W -mass measurements at the International Linear Collider [24]. In addition, there exists a disagreement (on the level of 3σ) between the values of the so-called onshell week mixing angle, sin 2 θ W , as measured by NuTeV collabo...

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“…The leading part of the O(G µ M 2 t α s ) contribution to r 11 was confirmed in Ref. [36] after including the tadpole contribution in the result of Ref. [17].…”

Section: Running Masses In the Smmentioning

confidence: 64%

On the difference between the pole and the MS¯ masses of the top quark at the electroweak scale

2013

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We argue that for a Higgs boson mass M H ∼ 125 GeV, as suggested by recent Higgs searches at the LHC, the inclusion of electroweak radiative corrections in the relationship between the pole and MS masses of the top quark reduces the difference to about 1 GeV. This is relevant for the scheme dependence of electroweak observables, such as the ρ parameter, as well as for the extraction of the top quark mass from experimental data. In fact, the value currently extracted by reconstructing the invariant mass of the top quark decay products is expected to be close to the pole mass, while the analysis of the total cross section of top quark pair production yields a clean determination of the MS mass.

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Pole- versus MS-mass definitions in the electroweak theory

Cited by 29 publications

References 18 publications

Quark Mass Relations to Four-Loop Order in Perturbative QCD

Quark Mass Relations to Four-Loop Order in Perturbative QCD

Four-Loop QCD Corrections to the ElectroweakρParameter

On the difference between the pole and the MS¯ masses of the top quark at the electroweak scale

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