Quark Mass Effects Research Articles

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.

Towards the understanding of fully-heavy tetraquark states from various models

We use a color-magnetic interaction model (CMIM), a traditional constituent quark model (CQM) and a multiquark color flux-tube model (MCFTM) to systematically investigate the properties of the states $[Q_1Q_2][\bar{Q}_3\bar{Q}_4]$ ($Q=c,b$). The dynamical investigation indicates that the CMIM can not completely absorb QCD dynamical effects through the effective constituent quark mass and overestimates the color-magnetic interaction in the states under the assumption of the same spatial configurations. The Coulomb interaction plays a critical role in the dynamical model calculations on the heavy hadrons, which induces the fact that none of bound states $[Q_1Q_2][\bar{Q}_3\bar{Q}_4]$ can be found in the dynamical models. The color configuration $\left[[Q_1Q_2]_{\mathbf{6}_c}[\bar{Q}_3\bar{Q}_4]_{\bar{\mathbf{6}}_c}\right]_{\mathbf{1}}$ should be taken seriously in the ground states due to the strong Coulomb attraction between the $[Q_1Q_2]_{\mathbf{6}_c}$ and $[\bar{Q}_3\bar{Q}_4]_{\bar{\mathbf{6}}_c}$. The color configuration $\left[[Q_1Q_2]_{\bar{\mathbf{3}}_c}[\bar{Q}_2\bar{Q}_4]_{\mathbf{3}_c}\right]_{\mathbf{1}}$ is absolutely dominant in the excited states because of the strong Coulomb attraction within the $[Q_1Q_2]_{\bar{\mathbf{3}}_c}$ and $[\bar{Q}_2\bar{Q}_4]_{\mathbf{3}_c}$. The $J/\Psi$-pair resonances recently observed by LHCb are difficult to be accommodated in the CMIM. The broad structure ranging from 6.2 to 6.8 GeV can be described as the ground tetraquark state $[cc][\bar{c}\bar{c}]$ in the various dynamical models. The narrow structure $X(6900)$ can be identified as the excited state $[cc][\bar{c}\bar{c}]$ with $L=1$ ($L=2$) in the CQM (MCFTM).

Weak magnetic field corrections to light vector or axial mesons mixings and vector meson dominance

Weak magnetic-field-induced corrections to effective coupling constants describing light vector meson mixing and vector meson dominance (VMD) are derived. The magnetic field must be weak with respect to an effective quark mass M* such that: or . On that basis, a flavor SU(2) quark–quark interaction due to a non-perturbative one gluon exchange is considered. By means of methods usually applied to the Nambu—Jona-Lasinio and global color models, the equations for leading light vector/axial meson coupling to a background electromagnetic field are derived. The corresponding effective coupling constants are resolved in structureless mesons and long-wavelength limits. Some of the resulting coupling constants are redefined, so as to become magnetic-field-induced corrections to vector or axial meson couplings. Due to the approximated chiral symmetry of the model, light axial meson mixing induced by the magnetic field is also obtained. Numerical estimates are presented for the coupling constants and some of the corresponding momentum-dependent form factors. The contributions of the induced VMD and vector meson mixing couplings for the low-momentum pion electromagnetic form factor and for the (off-shell) charge symmetry violation potential at the constituent quark level are estimated. The relative overall weak magnetic-field-induced anisotropic corrections are of the order of , where n = 2 or n = 1, respectively.

Dilepton production rate calculation using MEQM in heavy-ion collision

It is established that a strong magnetic field is generated along with quark–gluon plasma in heavy-ion collision. This unique scenario offers an opportunity to study and analyze the impact of the magnetic field on the evolution of the plasma. We calculate the dilepton yield from quark–gluon plasma in a magnetic environment by considering a suitably modified magnetized effective quark mass (MEQM). Further, we study the dilepton yield for different values of magnetic field and different values of chemical potential with MEQM. The results obtained are very encouraging and we compare it with recently reported theoretical results.

Quark mass effects in two-loop Higgs amplitudes

We provide two two-loop amplitudes relevant for precision Higgs physics. The first is the two-loop amplitude for Higgs boson production through gluon fusion with exact dependence on the top quark mass up to squared order in the dimensional regulator ε. The second result we provide is the two-loop amplitude for the decay of a Higgs boson into a pair of massive bottom quarks through the Higgs-to-gluon coupling in the infinite top mass limit. Both amplitudes are computed by finding canonical bases of master integrals, which we evaluate explicitly in terms of harmonic polylogarithms. We obtain the bare, renormalized and IR-subtracted amplitude and provide the results in terms of building blocks suitable for changing renormalization schemes.

Bottom quark mass effects in associated WH production with the H→bb¯ decay through NNLO QCD

We present a computation of NNLO QCD corrections to the production of a Higgs boson in association with a $W$ boson at the LHC followed by the decay of the Higgs boson to a $b\bar{b}$ pair. At variance with previous NNLO QCD studies of the same process, we treat $b$ quarks as massive. An important advantage of working with massive $b$ quarks is that it makes the use of flavor jet algorithms unnecessary and allows us to employ conventional jet algorithms to define $b$ jets. We compare NNLO QCD descriptions of the associated $WH(b\bar{b})$ production with massive and massless $b$ quarks and also contrast them with the results provided by parton showers. We find ${\cal O}(5\%)$ differences in fiducial cross sections computed with massless and massive $b$ quarks. We also observe that much larger differences between massless and massive results, as well as between fixed-order and parton-shower results, can arise in selected kinematic distributions.

Exclusive production of ϕ meson in the γ*p→ϕp reaction at large photon virtualities within kT -factorization approach

We apply the $k_T$-factorization approach to the production of $\phi$ meson in deep-inelastic scattering. The helicity-conserving $\gamma^*(T,L) \to \phi$ impact factor is calculated for longitudinal and transverse photon polarization using $\phi$ meson distribution amplitudes. Different unintegrated gluon distributions are used in the calculations. The formalism for massless quarks/antiquarks gives too large transverse and longitudinal cross sections for photon virtualities below $Q^2\sim 8 \, \rm{GeV}^2$. We suggest how to improve the description of the HERA data by introducing effective strange quark masses into the formalism. We derive the corresponding massive impact factor by comparing to the light-cone wave function representation used in previous $k_T$-factorization calculations and the color-dipole approaches. As a byproduct we present expressions for higher twist-amplitudes as weighted integrals over the light-cone wave function. The quark mass $m_q \approx 0.5$ GeV allows to improve the description of both longitudinal and transverse cross section down to $Q^2 \sim$ 4 GeV$^2$. We present also the polarized cross section ratio $\sigma_L/\sigma_T$ and the behavior of the total cross section $\sigma_{tot} = \sigma_{L} + \sigma_{T}$ as a function of photon virtuality.

Top Quark Mass Effects in Higgs Boson Production at Four-Loop Order: Virtual Corrections

We compute four-loop corrections to the Higgs boson gluon vertex, including finite top quark mass effects. Analytic results are presented which serve as a building block for the next-to-next-to-next-to-leading order corrections to Higgs boson production at the Large Hadron Collider at CERN.

Weak magnetic field corrections to pion and constituent quarks form factors

A quark–quark interaction due to nonperturbative one gluon exchange is considered for the derivation of leading weak magnetic field induced anisotropic corrections to usual pion—constituent quarks form factors. Besides that, few chiral and isospin symmetry breaking effective couplings which emerge only due to the weak magnetic field are also found. Numerical estimations for these magnetic field corrections are presented. All of these corrections are ultraviolet finite and their relative values are found to be of order of being n = 1 for the vector and axial pion couplings and n = 2 for the pseudoscalar and scalar ones. The corresponding anisotropic corrections to the constituent quark and pion strong averaged quadratic radii in the plane perpendicular to the magnetic field are also calculated as functions of the quark effective mass.

Heavy holographic QCD

We study the phase structure of the Witten-Sakai-Sugimoto model in the plane of temperature and baryon chemical potential, including the effect of a nonzero current quark mass. Our study is performed in the decompactified limit of the model, which, at least regarding the chiral phase transition, appears to be closer to real-world QCD than the original version. Following earlier studies, we account for the quark mass in an effective way based on an open Wilson line operator whose expectation value is identified with the chiral condensate. We find that the quark mass stabilizes a configuration with string sources and point out that this phase plays an important role in the phase diagram. Furthermore, we show that the quark mass breaks up the first-order chiral phase transition curve and introduces critical points to the phase diagram. Similarities of the phase structure to other holographic approaches and to lattice simulations of “heavy QCD” are found and discussed. By making holographic QCD more realistic, our results open the door to a better understanding of real-world strongly coupled hot and dense matter.

Deconfinement and chiral phase transitions in quark matter with a strong electric field

The deconfinement and chiral phase transitions are studied in the context of the electrized quark matter at finite temperature in the two-flavor Polyakov-Nambu--Jona-Lasinio model. Using the mean field approximation and an electric field independet regularization we show that the effect of temperature and/or electric fields is to partially restore the chiral symmetry. The deconfinement phase transition is slightly affected by the magnitude of the electric field. To this end we show how the effective quark masses and the expectation value of the Polyakov Loop are affected by the electric fields at finite temperatures. As a very interesting result, the pseudocritical temperatures for chiral symmetry restoration and deconfinement decrease as we increase the magnitude of the electric fields, however, both start to increase after some critical value of the electric field.

Top quark mass effects in gg→ZZ at two loops and off-shell Higgs boson interference

We consider top-quark mass effects in the Higgs-interference contribution to $Z$-boson pair production in gluon fusion. While this production mechanism is formally of next-to-next-to leading order, its contribution is numerically important above the top threshold $M_{ZZ}^2=4m_t^2$. This region is essential to constrain the width of the Higgs boson and good control over the top-quark mass dependence is crucial. We determine the form factors that are relevant for the interference contribution at two-loop order using a method based on a conformal mapping and Pad\'e approximants constructed from the expansions of the amplitude for large top mass and around the top threshold.

Parton showers and matching uncertainties in top quark pair production with Herwig 7

We evaluate the theoretical uncertainties in next-to-leading order plus parton shower predictions for top quark pair production and decay in hadronic collisions. Our work is carried out using the Herwig 7 event generator and presents an in-depth study of variations in matching schemes with two systematically different shower algorithms, the traditional angular-ordered and alternative dipole shower. We also present all of the required extensions of the Herwig dipole shower algorithm to properly take into account quark mass effects, as well as its ability to perform top quark decays. The predictions are compared at parton level as well as to Large Hadron Collider data, including in the boosted regime. We find that the regions where predictions with a non-top-quark-specific tune differ drastically from data are plagued by large uncertainties which are consistent between our two shower and matching algorithms.

Effective repulsion in dense quark matter from nonperturbative gluon exchange

A moderately strong vector repulsion between quarks in dense quark matter is needed to explain how a quark core can support neutron stars heavier than two solar masses. We study this repulsion, parametrized by a four-fermion interaction with coupling g_V, in terms of non-perturbative gluon exchange in QCD in the Landau gauge. Matching the energy of quark matter, g_V n_q^2 (where n_q is the number density of quarks) with the quark exchange energy calculated in QCD with a gluon propagator parametrized by a finite gluon mass m_g and a frozen coupling alpha_s, at moderate quark densities, we find that gluon masses m_g in the range 200 - 600 MeV and alpha_s = 2 - 4 lead to a g_V consistent with neutron star phenomenology. Estimating the effects of quark masses and a color-flavor-locked (CFL) pairing gap, we find that g_V can be well approximated by a flavor-symmetric, decreasing function of density. We briefly discuss similar matchings for the isovector repulsion and for the pairing attraction.

Nuclear parton distributions from lepton-nucleus scattering and the impact of an electron-ion collider

We present a first determination of the nuclear parton distribution functions (nPDF) based on the NNPDF methodology: nNNPDF1.0. This analysis is based on neutral-current deep-inelastic structure function data and is performed up to NNLO in QCD calculations with heavy quark mass effects. For the first time in the NNPDF fits, the chi ^2 minimization is achieved using stochastic gradient descent with reverse-mode automatic differentiation (backpropagation). We validate the robustness of the fitting methodology through closure tests, assess the perturbative stability of the resulting nPDFs, and compare them with other recent analyses. The nNNPDF1.0 distributions satisfy the boundary condition whereby the NNPDF3.1 proton PDF central values and uncertainties are reproduced at A=1, which introduces important constraints particularly for low-A nuclei. We also investigate the information that would be provided by an Electron-Ion Collider (EIC), finding that EIC measurements would significantly constrain the nPDFs down to xsimeq 5times 10^{-4}. Our results represent the first-ever nPDF determination obtained using a Monte Carlo methodology consistent with that of state-of-the-art proton PDF fits, and provide the foundation for a subsequent global nPDF analyses including also proton-nucleus data.

Quark propagator with two flavors of O(a) -improved Wilson fermions

We compute the Landau gauge quark propagator from lattice QCD with two flavors of dynamical O(a)-improved Wilson fermions. The calculation is carried out with lattice spacings ranging from 0.06 fm to 0.08 fm, with quark masses corresponding to pion masses of 420, 290 and 150 MeV, and for volumes of up to (4.5fm)^4. Our ensembles allow us to evaluate lattice spacing, volume and quark mass effects. We find that the quark wave function which is suppressed in the infrared, is further suppressed as the quark mass is reduced, but the suppression is weakened as the volume is increased. The quark mass function M(p^2) shows only a weak volume dependence. Hypercubic artefacts beyond O(a) are reduced by applying both cylinder cuts and H4 extrapolations. The H4 extrapolation shifts the quark wave function systematically upwards but does not perform well for the mass function.

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.

Light and heavy flavor dijet production and dijet mass modification in heavy ion collisions

Back-to-back light and heavy flavor dijet measurements are promising experimental channels to accurately study the physics of jet production and propagation in a dense QCD medium. They can provide new insights into the path length, color charge, and mass dependence of quark and gluon energy loss in the quark-gluon plasma produced in reactions of ultra-relativistic nuclei. To this end, we perform a comprehensive study of both light and heavy flavor dijet production in heavy ion collisions. We propose the modification of dijet invariant mass distributions in such reactions as a novel observable that shows enhanced sensitivity to the QGP transport properties and heavy quark mass effects on in-medium parton showers. This is achieved through the addition of the jet quenching effects on the individual jets as opposed to their subtraction. The latter drives the subtle effects on more conventional observables, such as the dijet momentum imbalance shifts, which we also calculate here. Results are presented in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV for comparison to data at the Large Hadron Collider and in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV to guide the future sPHENIX program at the Relativistic Heavy Ion Collider.

Lattice computation of the electromagnetic contributions to kaon and pion masses

We present a lattice calculation of the electromagnetic (EM) effects on the masses of light pseudoscalar mesons. The simulations employ $2+1$ dynamical flavors of asqtad QCD quarks and quenched photons. Lattice spacings vary from $\ensuremath{\approx}0.12\text{ }\text{ }\mathrm{fm}$ to $\ensuremath{\approx}0.045\text{ }\text{ }\mathrm{fm}$. We compute the quantity $\ensuremath{\epsilon}$, which parametrizes the corrections to Dashen's theorem for the ${K}^{+}$--${K}^{0}$ EM mass splitting, as well as ${\ensuremath{\epsilon}}_{{K}^{0}}$, which parametrizes the EM contribution to the mass of the ${K}^{0}$ itself. An extension of the nonperturbative EM renormalization scheme introduced by the BMW group is used in separating EM effects from isospin-violating quark mass effects. We correct for leading finite-volume effects in our realization of lattice electrodynamics in chiral perturbation theory, and remaining finite-volume errors are relatively small. While electroquenched effects are under control for $\ensuremath{\epsilon}$, they are estimated only qualitatively for ${\ensuremath{\epsilon}}_{{K}^{0}}$ and constitute one of the largest sources of uncertainty for that quantity. We find $\ensuremath{\epsilon}=0.78(1{)}_{\text{stat}}(\genfrac{}{}{0}{}{+8}{\ensuremath{-}11}{)}_{\text{syst}}$ and ${\ensuremath{\epsilon}}_{{K}^{0}}=0.035(3{)}_{\text{stat}}(20{)}_{\text{syst}}$. We then use these results on $2+1+1$ flavor pure QCD highly improved staggered quark (HISQ) ensembles and find ${m}_{u}/{m}_{d}=0.4529(48{)}_{\text{stat}}(\genfrac{}{}{0}{}{+150}{\ensuremath{-}67}{)}_{\text{syst}}$.

Pion constituent quark couplings strong form factors: A dynamical approach

Form factors for pions interactions with constituent quarks are investigated as the leading effective couplings obtained from a one loop background field method applied to a global color model. Two pion field definitions are considered and the resulting eleven form factors are expressed in terms of components of the quark and gluon propagators that compose only two momentum dependent functions. A momentum dependent Goldberger Treiman relation is also obtained as one of the ratios between the form factors. The resulting form factors with pion momenta up to 1.5 GeV are exhibited for different quark effective masses and two different non-perturbative gluon propagators and they present similar behavior to fittings of experimental data from nucleons form factors. The corresponding pseudoscalar averaged quadratic radii (a.q.r.) and correction to the axial a.q.r. are presented as functions of the sea quark effective mass, being equal respectively to the scalar and vector ones at the present level of calculation.