Multiloop contributions to the on-shell-$$ \overline{{\mathrm{MS}}}$$ heavy quark mass relation in QCD and the asymptotic structure of the corresponding series: the updated consideration

AbstractThe asymptotic structure of the QCD perturbative relation between the on-shell and $$\overline{{\mathrm{MS}}}$$ MS ¯ heavy quark masses is studied. We estimate the five and six-loop contributions to this relation by three different techniques. First, the effective charges motivated approach in two variants is used. Second, the results following from the large-$$\beta _0$$ β 0 approximation are analyzed. Finally, the consequences of applying the asymptotic renormalon-based formula are investigated. We show that all approaches lead to corrections which are qualitatively consistent in order of magnitude. Their sign-alternating character in powers of the number of massless quarks is demonstrated. We emphasize that there is no contradiction in the behavior of the fine structure of the renormalon-based estimates with other approaches if one use the detailed information about the normalization factor included in the renormalon asymptotic formula. The obtained five- and six-loop estimates indicate that in the case of the b-quark the asymptotic character of the studied relation manifests itself above the fourth order of PT, whereas for the t-quark it starts to reveal itself after the seventh order. This allows to conclude that like the running masses, the pole masses of the b and especially t-quark in principle may be used in the phenomenologically-oriented studies.

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On the relation between pole and running heavy quark masses beyond the four-loop approximation

EPJ Web of Conferences ◽

10.1051/epjconf/201819104005 ◽

2018 ◽

Vol 191 ◽

pp. 04005 ◽

Cited By ~ 1

Author(s):

A. L. Kataev ◽

V. S. Molokoedov

Keyword(s):

Heavy Quark ◽

Perturbative Qcd ◽

Mass Relation ◽

Coupling Constant ◽

Quark Masses ◽

Asymptotic Nature ◽

Asymptotic Expressions ◽

Loop Approximation ◽

Euclidean Region ◽

Direct Calculations

The effective charges motivated method is applied to the relation between pole and M̅S̅-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running quark masses. The non-calculated five- and six-loop perturbative QCD coefficients are estimated. This approach predicts for these terms the sign-alternating expansion in powers of number of lighter flavors nl, while the analyzed recently infrared renormalon asymptotic expressions do not reproduce the same behavior. We emphasize that coefficients of the quark mass relation contain proportional to π2 effects, which result from analytical continuation from the Euclidean region, where the scales of the running masses and QCD coupling constant are initially fixed, to the Minkowskian region, where the pole masses and the running QCD parameters are determined. For the t-quark the asymptotic nature of the non-resummed PT mass relation does not manifest itself at six-loops, while for the b-quark the minimal PT term appears at the probed by direct calculations four-loop level. The recent infrared renormalon based studies support these conclusions.

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An investigation of the $$\alpha _S$$ and heavy quark mass dependence in the MSHT20 global PDF analysis

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09533-7 ◽

2021 ◽

Vol 81 (8) ◽

Author(s):

T. Cridge ◽

L. A. Harland-Lang ◽

A. D. Martin ◽

R. S. Thorne

Keyword(s):

Heavy Quark ◽

Cross Sections ◽

Scattering Data ◽

Data Sets ◽

Quark Masses ◽

Heavy Quark Mass ◽

Pdf Analysis ◽

Definition Of ◽

The Individual ◽

The Masses

AbstractWe investigate the MSHT20 global PDF sets, demonstrating the effects of varying the strong coupling $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) and the masses of the charm and bottom quarks. We determine the preferred value, and accompanying uncertainties, when we allow $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) to be a free parameter in the MSHT20 global analyses of deep-inelastic and related hard scattering data, at both NLO and NNLO in QCD perturbation theory. We also study the constraints on $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) which come from the individual data sets in the global fit by repeating the NNLO and NLO global analyses at various fixed values of $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) , spanning the range $$\alpha _S(M_Z^2)=0.108$$ α S ( M Z 2 ) = 0.108 to 0.130 in units of 0.001. We make all resulting PDFs sets available. We find that the best fit values are $$\alpha _S(M_Z^2)=0.1203\pm 0.0015$$ α S ( M Z 2 ) = 0.1203 ± 0.0015 and $$0.1174\pm 0.0013$$ 0.1174 ± 0.0013 at NLO and NNLO respectively. We investigate the relationship between the variations in $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) and the uncertainties on the PDFs, and illustrate this by calculating the cross sections for key processes at the LHC. We also perform fits where we allow the heavy quark masses $$m_c$$ m c and $$m_b$$ m b to vary away from their default values and make PDF sets available in steps of $$\Delta m_c =0.05~\mathrm GeV$$ Δ m c = 0.05 G e V and $$\Delta m_b =0.25~\mathrm GeV$$ Δ m b = 0.25 G e V , using the pole mass definition of the quark masses. As for varying $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) values, we present the variation in the PDFs and in the predictions. We examine the comparison to data, particularly the HERA data on charm and bottom cross sections and note that our default values are very largely compatible with best fits to data. We provide PDF sets with 3 and 4 active quark flavours, as well as the standard value of 5 flavours.

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Heavy-flavor hadro-production with heavy-quark masses renormalized in the $$ \overline{\mathrm{MS}} $$, MSR and on-shell schemes

Journal of High Energy Physics ◽

10.1007/jhep04(2021)043 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

M. V. Garzelli ◽

L. Kemmler ◽

S. Moch ◽

O. Zenaiev

Keyword(s):

Heavy Quark ◽

Cross Sections ◽

Top Quark ◽

Quark Mass ◽

Production Cross ◽

Hadron Collider ◽

Distribution Functions ◽

Heavy Flavor ◽

Parton Distribution Functions ◽

Heavy Quark Mass

Abstract We present predictions for heavy-quark production at the Large Hadron Collider making use of the $$ \overline{\mathrm{MS}} $$ MS ¯ and MSR renormalization schemes for the heavy-quark mass as alternatives to the widely used on-shell renormalization scheme. We compute single and double differential distributions including QCD corrections at next-to-leading order and investigate the renormalization and factorization scale dependence as well as the perturbative convergence in these mass renormalization schemes. The implementation is based on publicly available programs, MCFM and xFitter, extending their capabilities. Our results are applied to extract the top-quark mass using measurements of the total and differential $$ t\overline{t} $$ t t ¯ production cross-sections and to investigate constraints on parton distribution functions, especially on the gluon distribution at low x values, from available LHC data on heavy-flavor hadro-production.

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Consistent treatment of rapidity divergence in soft-collinear effective theory

Journal of High Energy Physics ◽

10.1007/jhep03(2021)300 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Junegone Chay ◽

Chul Kim

Keyword(s):

Heavy Quark ◽

Soft Mode ◽

Form Factors ◽

Effective Theory ◽

Large Rapidity ◽

Soft Modes ◽

Heavy Quark Mass ◽

Soft Collinear Effective Theory ◽

Matching Procedure ◽

Consistent Treatment

Abstract In soft-collinear effective theory, we analyze the structure of rapidity divergence due to the collinear and soft modes residing in disparate phase spaces. The idea of an effective theory is applied to a system of collinear modes with large rapidity and soft modes with small rapidity. The large-rapidity (collinear) modes are integrated out to obtain the effective theory for the small-rapidity (soft) modes. The full SCET with the collinear and soft modes should be matched onto the soft theory at the rapidity boundary, and the matching procedure becomes exactly the zero-bin subtraction. The large-rapidity region is out of reach for the soft mode, which results in the rapidity divergence. The rapidity divergence in the collinear sector comes from the zero-bin subtraction, which ensures the cancellation of the rapidity divergences from the soft and collinear sectors. In order to treat the rapidity divergence, we construct the rapidity regulators consistently for all the modes. They are generalized by assigning independent rapidity scales for different collinear directions. The soft regulator incorporates the correct directional dependence when the innate collinear directions are not back-to-back, which is discussed in the N-jet operator. As an application, we consider the Sudakov form factor for the back-to-back collinear current and the soft-collinear current, where the soft rapidity regulator for a soft quark is developed. We extend the analysis to the boosted heavy quark sector and exploit the delicacy with the presence of the heavy quark mass. We present the resummed results of large logarithms in the form factors for various currents with the light and the heavy quarks, employing the renormalization group evolution on the renormalization and the rapidity scales.

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Quarkonia Formation in a Holographic Gravity–Dilaton Background Describing QCD Thermodynamics

Particles ◽

10.3390/particles4020015 ◽

2021 ◽

Vol 4 (2) ◽

pp. 159-177

Author(s):

Rico Zöllner ◽

Burkhard Kämpfer

Keyword(s):

Quark Mass ◽

Heavy Ion ◽

Mass Dependence ◽

Holographic Model ◽

Spectral Functions ◽

Special Aspect ◽

Quark Masses ◽

Ion Collisions ◽

Heavy Quark Mass ◽

Quark Mass Dependence

A holographic model of probe quarkonia is presented, where the dynamical gravity–dilaton background was adjusted to the thermodynamics of 2 + 1 flavor QCD with physical quark masses. The quarkonia action was modified to account for the systematic study of the heavy-quark mass dependence. We focused on the J/ψ and Υ spectral functions and related our model to heavy quarkonia formation as a special aspect of hadron phenomenology in heavy-ion collisions at LHC.

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