A massive variable flavour number scheme for the Drell-Yan process

The prediction of differential cross-sections in hadron-hadron scattering processes is typically performed in a scheme where the heavy-flavour quarks (c, b, tc,b,t) are treated either as massless or massive partons. In this work, a method to describe the production of colour-singlet processes which combines these two approaches is presented. The core idea is that the contribution from power corrections involving the heavy-quark mass can be numerically isolated from the rest of the massive computation. These power corrections can then be combined with a massless computation (where they are absent), enabling the construction of differential cross-section predictions in a massive variable flavour number scheme. As an example, the procedure is applied to the low-mass Drell-Yan process within the LHCb fiducial region, where predictions for the rapidity and transverse-momentum distributions of the lepton pair are provided. To validate the procedure, it is shown how the n_fnf-dependent coefficient of a massless computation can be recovered from the massless limit of the massive one. This feature is also used to differentially extract the massless N^3LON3LO coefficient of the Drell-Yan process in the gluon-fusion channel.

Doubly heavy baryons in Born-Oppenheimer EFT

We report on the recent progress on the computation of the doubly heavy baryon spectrum in effective field theory. The effective field theory is built upon the heavy-quark mass and adiabatic expansions. The potentials can be expressed as NRQCD Wilson loops with operator insertions. These are nonperturbative objects and so far only the one corresponding to the static potential has been computed with lattice QCD. We review the proposal for a parametrization of the potentials based in an interpolation between the shortand long-distance regimes. The long-distance description is obtained with a newly proposed Effective String Theory which coincides with the previous ones for pure gluodynamics but it is extended to contain a fermion field. We show the doubly heavy baryon spectrum with hyperfine contributions obtained using these parametrizations for the hyperfine potentials.

Heavy quark jet production near threshold

In this paper, we study the fragmentation of a heavy quark into a jet near threshold, meaning that final state jet carries most of the energy of the fragmenting heavy quark. Using the heavy quark fragmentation function, we simultaneously resum large logarithms of the jet radius R and 1 − z, where z is the ratio of the jet energy to the initiating heavy quark energy. There are numerically significant corrections to the leading order rate due to this resummation. We also investigate the heavy quark fragmentation to a groomed jet, using the soft drop grooming algorithm as an example. In order to do so, we introduce a collinear-ultrasoft mode sensitive to the grooming region determined by the algorithm’s zcut parameter. This allows us to resum large logarithms of zcut/(1 − z), again leading to large numerical corrections near the endpoint. A nice feature of the analysis of the heavy quark fragmenting to a groomed jet is the heavy quark mass m renders the algorithm infrared finite, allowing a perturbative calculation. We analyze this for EJR ∼ m and EJR » m, where EJ is the jet energy. To do the latter case, we introduce an ultracollinear-soft mode, allowing us to resum large logarithms of EJR/m. Finally, as an application we calculate the rate for e+e− collisions to produce a heavy quark jet in the endpoint region, where we show that grooming effects have a sizable contribution near the endpoint.

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

We 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.

1-loop matching of a thermal Lorentz force

Studying the diffusion and kinetic equilibration of heavy quarks within a hot QCD medium profits from the knowledge of a coloured Lorentz force that acts on them. Starting from the spatial components of the vector current, and carrying out two matching computations, one for the heavy quark mass scale (M) and another for thermal scales $$ \left(\sqrt{MT},T\right) $$ MT T , we determine 1-loop matching coefficients for the electric and magnetic parts of a Lorentz force. The magnetic part has a non-zero anomalous dimension, which agrees with that extracted from two other considerations, one thermal and the other in vacuum. The matching coefficient could enable a lattice study of a colour-magnetic 2-point correlator.

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

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.

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

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.

Consistent treatment of rapidity divergence in soft-collinear effective theory

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.

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

The 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.

Mass-suppressed effects in heavy quark diffusion

Many lattice studies of heavy quark diffusion originate from a colour-electric correlator, obtained as a leading term after an expansion in the inverse of the heavy-quark mass. In view of the fact that the charm quark is not particularly heavy, we consider subleading terms in the expansion. Working out correlators up to $$ \mathcal{O} $$ O (1/M2), we argue that the leading corrections are suppressed by $$ \mathcal{O} $$ O (T/M), and one of them can be extracted from a colour-magnetic correlator. The corresponding transport coefficient is non-perturbative already at leading order in the weak-coupling expansion, and therefore requires a non­perturbative determination.