Finite Quark Mass Effects Research Articles

The renormalised mathrm{O}(a) improved vector current in three-flavour lattice QCD with Wilson quarks

We present the results of a non-perturbative determination of the improvement coefficient c_mathrm{V} and the renormalisation factor Z_mathrm{V}, which define the renormalised vector current in three-flavour mathrm{O}(a) improved lattice QCD with Wilson quarks and tree-level Symanzik-improved gauge action. In case of the improvement coefficient, we consider both lattice descriptions of the vector current, the local as well as the conserved (i.e., point-split) one. Our improvement and normalisation conditions are based on massive chiral Ward identities and numerically evaluated in the Schrödinger functional setup, which allows to eliminate finite quark mass effects in a controlled way. In order to ensure a smooth dependence of the renormalisation constant and improvement coefficients on the bare gauge coupling, our computation proceeds along a line of constant physics, covering the typical range of lattice spacings 0.04,mathrm{fm}lesssim alesssim 0.1,mathrm{fm} that is useful for phenomenological applications. Especially for the improvement coefficient of the local vector current, we report significant differences between the one-loop perturbative estimates and our non-perturbative results.

Relation between the MS¯ and the kinetic mass of heavy quarks

We compute the relation between the pole mass and the kinetic mass of a heavy quark to three loops. Using the known relation between the pole and the $\overline{\rm MS}$ mass we obtain precise conversion relations between the $\overline{\rm MS}$ and kinetic masses. The kinetic mass is defined via the moments of the spectral function for the scattering involving a heavy quark close to threshold. This requires the computation of the imaginary part of a forward scattering amplitude up to three-loop order. We discuss in detail the expansion procedure and the reduction to master integrals. For the latter analytic results are provided. We apply our result both to charm and bottom quark masses. In the latter case we compute and include finite charm quark mass effects. Furthermore, we determine the large-$\beta_0$ result for the conversion formula at four-loop order. For the bottom quark we estimate the uncertainty in the conversion between the $\overline{\rm MS}$ and kinetic masses to about 15 MeV which is an improvement by a factor two to three as compared to the two-loop formula. The improved precision is crucial for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ at Belle II.

Finite quark-mass effects in Higgs boson production with dijets at large energies

The production of a Higgs boson in association with at least two jets receives contributions both from the fusion of weak vector bosons (VBF) and from QCD processes, especially gluon fusion (GF). The former process is important for measuring the coupling of the Higgs boson to weak bosons, whereas the latter process plays an important role in determining any CP-admixtures in the Higgs sector. In this paper we go beyond the current state-of-the-art for fixed order calculations of the GF process (i.e. one loop H + 2j including full quark mass effects) by including the all-order effects in leading log(ŝ/pt2), together with full quark mass and loop-propagator kinematic effects. We calculate the mass-dependent components and implement the resummation within the framework of High Energy Jets.The high-energy effects suppress the prediction compared to fixed order at large Δy12 and mjj (and therefore within the usual VBF cuts of widely separated jets), just as found in the limit of mt → ∞. The mass dependence is more significant than at fixed order, because the systematic inclusion of the leading logarithms in ŝ/pt2 results in a hardening of the transverse momentum of the Higgs boson, which in turn probes in more detail the loop-structure of the coupling. In particular, the full mass dependence reduces the cross section within VBF cuts by 11% compared to a calculation based just on the infinite top mass limit, but the impact of the bottom quark remains small. This all implies that the gluon-fusion contribution within VBF-cuts is less severe than current estimates suggest.

Bottom and charm mass determinations from global fits to Qoverline{Q} bound states at N3LO

The bottomonium spectrum up to n = 3 is studied within Non-Relativistic Quantum Chromodynamics up to N3LO. We consider finite charm quark mass effects both in the QCD potential and the overline{mathrm{MS}} -pole mass relation up to third order in the Y-scheme counting. The u = 1/2 renormalon of the static potential is canceled by expressing the bottom quark pole mass in terms of the MSR mass. A careful investigation of scale variation reveals that, while n = 1, 2 states are well behaved within perturbation theory, n = 3 bound states are no longer reliable. We carry out our analysis in the nℓ = 3 and nℓ = 4 schemes and conclude that, as long as finite mc effects are smoothly incorporated in the MSR mass definition, the difference between the two schemes is rather small. Performing a fit to boverline{b} bound states we find {overline{m}}_bleft({overline{m}}_bright) = 4.216 ± 0.039 GeV. We extend our analysis to the lowest lying charmonium states finding {overline{m}}_cleft({overline{m}}_cright) = 1.273 ± 0.054 GeV. Finally, we perform simultaneous fits for {overline{m}}_b and αs finding {alpha}_s^{left({n}_f=5right)}left({m}_Zright)=0.1178pm 0.0051 . Additionally, using a modified version of the MSR mass with lighter massive quarks we are able to predict the uncalculated mathcal{O}left({alpha}_s^4right) virtual massive quark corrections to the relation between the overline{mathrm{MS}} and pole masses.

Non-perturbative determination of cV, ZV and ZS/ZP in Nf = 3 lattice QCD

We report on non-perturbative computations of the improvement coefficient cV and the renormalization factor ZV of the vector current in three-flavour O(a) improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge action. To reduce finite quark mass effects, our improvement and normalization conditions exploit massive chiral Ward identities formulated in the Schrödinger functional setup, which also allow deriving a new method to extract the ratio ZS/ZP of scalar to pseudoscalar renormalization constants. We present preliminary results of a numerical evaluation of ZV and cV along a line of constant physics with gauge couplings corresponding to lattice spacings of about 0:09 fm and below, relevant for phenomenological applications.

Tetraquarks in holographic QCD

Using a soft-wall AdS/QCD approach we derive the Schr\"odinger-type equation of motion for the tetraquark wave function, which is dual to the dimension-4 AdS bulk profile. The latter coincides with the number of constituents in the leading Fock state of the tetraquark. The obtained equation of motion is solved analytically, providing predictions for both the tetraquark wave function and its mass. A low mass limit for possible tetraquark states is given by $M \ge 2 \kappa = 1$ GeV, where $\kappa = 0.5$ GeV is the typical value of the scale parameter in soft-wall AdS/QCD. We confirm results of the COMPASS Collaboration recently reported on the discovery of the $a_1(1414)$ state, interpreted as a tetraquark state composed of light quarks and having $J^{PC} = 1^{++}$. Our prediction for the mass of this state, $M_{a_1} = \sqrt{2}$ GeV $\simeq 1.414$ GeV, is in good agreement with the COMPASS result $M_{a_1} = 1.414^{+0.015}_{-0.013}$ GeV. Next we included finite quark mass effects, which are essential for the tetraquark states involving heavy quarks.

Improved analysis of the (O7,O7) contribution to B¯→Xsγγ at O(αs)

The present study is devoted for an improved analysis of the self-interference contribution of the electromagnetic dipole operator ${\mathcal{O}}_{7}$ to the double differential decay width $d\mathrm{\ensuremath{\Gamma}}/(d{s}_{1}d{s}_{2})$ for the inclusive $\overline{B}\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}\ensuremath{\gamma}$ process, where the kinematical variables ${s}_{1}$ and ${s}_{2}$ are defined as ${s}_{i}=({p}_{b}\ensuremath{-}{q}_{i}{)}^{2}/{m}_{b}^{2}$ with ${p}_{b}$, ${q}_{1}$, ${q}_{2}$ being the momenta of the $b$-quark and two photons. This calculation completes the next-to-leading-logarithmic (NLL) QCD prediction of the numerically important self-interference contribution of ${\mathcal{O}}_{7}$ by keeping the full dependence on the strange-quark mass ${m}_{s}$, which is introduced to control possible collinear configurations of one of the photons with the strange quark. Our results are given for exact ${m}_{s}$, in contrast to an earlier work where only logarithmic and constant terms in ${m}_{s}$ were retained. This improved NLL result for the $({\mathcal{O}}_{7},{\mathcal{O}}_{7})$-interference contribution shows that finite ${m}_{s}$ effects are only sizable near the kinematical endpoints of the spectrum $d\mathrm{\ensuremath{\Gamma}}/(d{s}_{1}d{s}_{2})$. At the level of the branching ratio, in the phase-space region considered in this paper, it is observed that $\text{Br}[\overline{\mathrm{B}}\ensuremath{\rightarrow}{\mathrm{X}}_{\mathrm{s}}\ensuremath{\gamma}\ensuremath{\gamma}]$ does not develop a sizable ${m}_{s}$ dependence: the impact on this branching ratio is less than 5% when ${m}_{s}$ is varied between 400--600 MeV. For the same phase-space region finite strange quark mass effects for the branching ratio are less than 7%.

Quark mass effect on axial charge dynamics

We studied effect of finite quark mass on the dynamics of axial charge using the D3/D7 model in holography. The mass term in axial anomaly equation affects both the fluctuation (generation) and dissipation of axial charge. We studied the dependence of the effect on quark mass and external magnetic field. For axial charge generation, we calculated the mass diffusion rate, which characterizes the helicity flipping rate. The rate is a non-monotonous function of mass and can be significantly enhanced by the magnetic field. The diffusive behavior is also related to a divergent susceptibility of axial charge. For axial charge dissipation, we found that in the long time limit, the mass term dissipates all the charge effectively generated by parallel electric and magnetic fields. The result is consistent with a relaxation time approximation. The rate of dissipation through mass term is a monotonous increasing function of both quark mass and magnetic field.

High precision determination of the gluon fusion Higgs boson cross-section at the LHC

We present the most precise value for the Higgs boson cross-section in the gluon-fusion production mode at the LHC. Our result is based on a perturbative expansion through N3LO in QCD, in an effective theory where the top-quark is assumed to be infinitely heavy, while all other Standard Model quarks are massless. We combine this result with QCD corrections to the cross-section where all finite quark-mass effects are included exactly through NLO. In addition, electroweak corrections and the first corrections in the inverse mass of the top-quark are incorporated at three loops. We also investigate the effects of threshold resummation, both in the traditional QCD framework and following a SCET approach, which resums a class of π2 contributions to all orders. We assess the uncertainty of the cross-section from missing higher-order corrections due to both perturbative QCD effects beyond N3LO and unknown mixed QCD-electroweak effects. In addition, we determine the sensitivity of the cross-section to the choice of parton distribution function (PDF) sets and to the parametric uncertainty in the strong coupling constant and quark masses. For a Higgs mass of m H = 125 GeV and an LHC center-of-mass energy of 13 TeV, our best prediction for the gluon fusion cross-section is $$ \sigma =48.58\;{\mathrm{pb}}_{-3.27\;\mathrm{p}\mathrm{b}}^{+2.22\;\mathrm{p}\mathrm{b}}\left(\mathrm{theory}\right)\pm 1.56\;\mathrm{p}\mathrm{b}\left(3.20\%\right)\left(\mathrm{P}\mathrm{D}\mathrm{F}+{\alpha}_s\right). $$

Finite quark-mass effects in the NNLOPS POWHEG+MiNLO Higgs generator

We include finite top- and bottom-mass effects in the next-to-next-to-leading order parton shower (NNLOPS) event generator for inclusive Higgs boson production in gluon fusion based upon the POWHEG+MiNLO approach. Since fixed-order results for quark-mass effects only reach NLO accuracy, we add them to the NNLOPS generator at that accuracy. We explore uncertainties related to the unknown all-order logarithmic structure of bottom-mass effects by comparing the assumption of full exponentiation to no exponentiation at all. Phenomenological results showing the effects of finite quark-masses in the NNLOPS simulation are presented. These suggest that the aforementioned uncertainty is well contained within the envelope of plain renormalization and factorization scale uncertainties.

O(α s ) corrections to the decays of polarized W ± and Z bosons into massive quark pairs

We present O(\alpha_s) results on the decays of polarized W^+- and Z bosons into massive quark pairs. The NLO QCD corrections to the polarized decay functions are given up to the second order in the quark mass expansion. We find a surprisingly strong dependence of the NLO polarized decay functions on finite quark mass effects even at the relatively large mass scale of the W^+- and Z bosons. As a main application we consider the decay t -> b + W^+ involving the helicity fractions \rho_{mm} of the W^+ boson followed by the polarized decay W^+(\uparrow) -> q_1 qbar_2 for which we determine the O(\alpha_s) polar angle decay distribution. We also discuss NLO polarization effects in the production/decay process e^+e^- -> Z(\uparrow) -> q qbar.

Helicity fractions ofWbosons from top quark decays at next-to-next-to-leading order in QCD

Decay rates of unpolarized top quarks into longitudinally and transversally polarized W bosons are calculated to second order in the strong coupling constant alpha_s. Including the finite bottom quark mass and electroweak effects, the Standard Model predictions for the W boson helicity fractions are F_L=0.687(5), F_+=0.0017(1), and F_-=0.311(5).

HPro: A NLO Monte-Carlo for Higgs production via gluon fusion with finite heavy quark masses

We compute fully differential next-to-leading order QCD cross-sections for Higgs boson production via gluon fusion in the Standard Model. We maintain the full dependence of the cross-sections on the top and bottom quark mass. We find that finite quark mass effects are important given the achieved precision of QCD predictions for gluon fusion. Our Monte-Carlo program, HPro, can correct existing NNLO fully differential calculations, which employ the approximation of an infinitely heavy top and a vanishing bottom quark Yukawa coupling, for heavy quark finite mass effects through NLO.

Electroweak and finite quark-mass effects on the Higgs boson transverse momentum distribution

We perform a detailed study of the various one-loop contributions leading to production of the standard model Higgs boson in association with a hard jet. This production mode contributes to the current Tevatron exclusion limit of the standard model Higgs with $160\text{ }\text{ }\mathrm{GeV}\ensuremath{\le}{M}_{H}\ensuremath{\le}170\text{ }\text{ }\mathrm{GeV}$, and will also be important for discovery and interpretation of new scalar bosons at the Large Hadron Collider (LHC). We include top- and bottom-quark initiated contributions, maintaining the exact dependence on the quark masses, and also study previously neglected $W$- and $Z$-boson mediated effects which shift the $qg$ and $q\overline{q}$ production modes. We consider the deviations from commonly used approximations for the Higgs boson transverse momentum spectrum caused by the finite top-quark mass, bottom-quark contributions, and electroweak gauge boson terms. All three effects act to decrease the Higgs boson transverse momentum distribution for observable momenta, with shifts reaching $\ensuremath{-}8%$ at the Tevatron and $\ensuremath{-}30%$ at the LHC. The shifts have a significant dependence on the Higgs ${p}_{T}$, and are especially important if large momenta are selected by experimental cuts.

Heavy-quark colorimetry of QCD matter

We consider propagation of heavy quarks in QCD matter. Because of large quark mass, the radiative quark energy loss appears to be qualitatively different from that of light quarks at all energies of practical importance. Finite quark mass effects lead to an in-medium enhancement of the heavy-to-light D/\pi ratio at moderately large (5--10 GeV) transverse momenta. For hot QCD matter a large enhancement is expected, whose magnitude and shape are exponentially sensitive to the density of colour charges in the medium.

Radiative corrections to the structure functions and sum rules in polarized dis

The one-loop NLO radiative corrections (RC) to the observables in polarized DIS using assumption that a quark is an essential massive particle are considered. If compared with classical QCD formulae the obtained results are identical for the unpolarized and different for polarized sum rules, that can be explained as the influence of the finite quark mass effects on NLO QCD corrections. The explicit expression for one-loop NLO QCD contribution to the structure function g 2 is presented.

Two-loop scale dependence of the static QCD potential including quark masses

The interaction potential V(Q^2) between static test charges can be used to define an effective charge $\alpha_V(Q^2)$ and a physically-based renormalization scheme for quantum chromodynamics and other gauge theories. In this paper we use recent results for the finite-mass fermionic corrections to the heavy-quark potential at two-loops to derive the next-to-leading order term for the Gell Mann-Low function of the V-scheme. The resulting effective number of flavors $N_F(Q^2/m^2)$ in the $\alpha_V$ scheme is determined as a gauge-independent and analytic function of the ratio of the momentum transfer to the quark pole mass. The results give automatic decoupling of heavy quarks and are independent of the renormalization procedure. Commensurate scale relations then provide the next-to-leading order connection between all perturbatively calculable observables to the analytic and gauge-invariant $\alpha_V$ scheme without any scale ambiguity and a well defined number of active flavors. The inclusion of the finite quark mass effects in the running of the coupling is compared with the standard treatment of finite quark mass effects in the $\bar{MS}$ scheme.

Finite quark mass effects in the improved ladder Bethe-Salpeter amplitudes

We study the finite quark mass effects of the low-energy QCD using the improved ladder Schwinger-Dyson and Bethe-Salpeter equations which are derived in the manner consistent with the vector and axial-vector Ward-Takahashi identities. The non-perturbative mass-independent renormalization allows us to calculate the quark condensate for a non-zero quark mass. We explicitly show that the PCAC relation holds. The key ingredients are the Cornwall-Jackiw-Tomboulis effective action, the generalized Noether current and the introduction of the regularization function to the Lagrangian. The reasonable values of the pion mass, the pion decay constant and the quark condensate are obtained with a rather large $\Lambda_{QCD}$. The pion mass square and the pion decay constant are almost proportional to the current quark mass up to the strange quark mass region. It suggests that the chiral perturbation is applicable up to the strange quark mass region. We study the validity of the approximation often used in solving the Bethe-Salpeter equations too.

Heavy quark fragmentation in deep inelastic scattering

We perform an analysis of semi-inclusive production of charm (D-mesons) in neutral current (NC) and charged current (CC) deep inelastic scattering (DIS) at full O(alpha_s^1). Our calculation is based on the heavy quark scheme developed by Aivazis, Collins, Olness and Tung (ACOT) where we include an O(alpha_s^1) calculation of quark scattering contributions for general masses and couplings. We review the relevant massive formulae and subtraction terms and discuss their massless limits. We show how the charm fragmentation function can be measured in CC DIS and we investigate whether the charm production dynamics may be tested in NC DIS. We also discuss finite initial state quark mass effects in CC and NC DIS.

Perturbative renormalization factors of bilinear operators for massive Wilson quarks on the lattice

Renormalization factors for local vector and axial vector currents for the Wilson quark action are perturbatively calculated to one loop order including finite quark masses from the ratio of the on-shell quark matrix elements in the Feynman gauge defined on the lattice and in the continuum. For large quark masses of order unity in lattice units, we find that finite quark mass effects are quite large: one-loop coefficients of the renormalization factors differ by 100% compared to those in the massless limit.