Bottom Quark Mass Research Articles

Heavy quark mass near the phase transition

Abstract Assuming that the number densities of heavy flavor in hadron gas and in QGP are same at $T_c$, we obtain the effective mass of heavy quark at $T_c$ from the comparison with the hadron resonance gas model which well describes particle yield in heavy-ion collisions. We find that charm quark mass at vanishing baryon chemical potential is around 1.8 GeV which is much heavier than QCD bare mass and close to $D$ meson mass. The mass slightly increases with increasing baryon chemical potential and then decreases.
On the other hand, anticharm quark mass constantly decreases with increasing baryon chemical potential. Bottom quark mass has a similar pattern. Extending the hadron resonance gas model to a bit higher temperature beyond $T_c$, the effective masses of charm and bottom quarks decrease with increasing temperature.

Quark mass effects in Higgs production

We examine the effect of finite top- and bottom-quark masses on the Higgs production cross section in the gluon-gluon fusion channel. We employ both MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{MS}} $$\\end{document} and on-shell renormalisation for the quark masses and provide a thorough comparison. Furthermore, we explore alternative treatments of quark masses, in particular in the four-flavour scheme, and investigate their impact on the cross section. Our work also presents novel predictions for differential cross sections in the Higgs rapidity. The results lead to a significant reduction of scale uncertainties, and our analysis enables us to offer well-grounded recommendations for future research in this area.

Nonleptonic B-meson decays to next-to-next-to-leading order

We compute next-to-next-to-leading order QCD corrections to the partonic processes b → cu¯d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ c\\overline{u}d $$\\end{document} and b → cc¯s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ c\\overline{c}s $$\\end{document}, which constitute the dominant decay channels in standard model predictions for B-meson lifetimes within the heavy quark expansion. We consider the contribution from the four-quark operators O1 and O2 in the ∆B = 1 effective Hamiltonian. The decay rates are obtained from the imaginary parts of four-loop propagator-type diagrams. We compute the corresponding master integrals using the “expand and match” approach which provides semi-analytic results for the physical charm and bottom quark masses. We show that the dependence of the decay rate on the renormalization scale is significantly reduced after including the next-to-next-to-leading order corrections. Furthermore, we compute next-to-next-to-leading order corrections to the Cabibbo-Kobayashi-Maskawa-suppressed decay channels b → uc¯s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ u\\overline{c}s $$\\end{document} and b → uu¯d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ u\\overline{u}d $$\\end{document}.

Analysis of 2S singly heavy baryons in HQET

In this paper, we have employed HQET to determine the masses of radially excited ([Formula: see text]) S-wave charm and bottom baryons. The HQET Lagrangian containing the non-perturbative parameters is shown with heavy baryon fields. The non-perturbative parameters, couplings, and decay widths are also studied for the S-wave singly heavy baryons. The HQET parameters [Formula: see text], [Formula: see text] and [Formula: see text] are calculated for the ground state ([Formula: see text]) using the masses of S-wave baryons. The [Formula: see text] mass short-distance mass scheme is employed to estimate the heavy quark masses and non-perturbative parameters. The mass term ratios of [Formula: see text] and [Formula: see text] mesons and baryons containing parameters [Formula: see text] and [Formula: see text] are studied by varying the bottom quark mass. This analysis shows that heavy quarks behave the same inside mesons and baryons in both 1S and 2S states. The HQET symmetry of [Formula: see text] is used to find the parameters and masses for [Formula: see text] S-wave baryons. The variation of mass of 2S baryons with the non-perturbative parameters [Formula: see text] and [Formula: see text] is discussed. The Regge trajectories are also plotted in the [Formula: see text] plane using masses of [Formula: see text] and 2 charm and bottom baryons. The Regge trajectories are parallel and equidistant lines in the [Formula: see text] plane. We have also studied the strong decays of charm and bottom baryons for both [Formula: see text] and [Formula: see text] states. We have estimated the coupling constants [Formula: see text] and [Formula: see text] for [Formula: see text], and [Formula: see text] for [Formula: see text]. We have also shown the semi-electronic decay rates of charm baryons in the spectator heavy quark approximation for [Formula: see text], [Formula: see text], and [Formula: see text] transitions. The decay rates for [Formula: see text] transitions are of the same order as [Formula: see text] transitions. This analysis agrees well with the available theoretical and experimental data.

B meson mixing at NNLO: technical aspects

We provide details to several technical aspects which are important for the calculation of next-to-next-to-leading order corrections to the mixing of neutral B mesons. This includes the computation of the master integrals for finite charm and bottom quark masses, projectors for products of up to 22 γ matrices and tensor integrals with up to rank 11.

B→D*ℓνℓ semileptonic form factors from lattice QCD with Möbius domain-wall quarks

We calculate the form factors for the B→D*ℓνℓ decay in 2+1 flavor lattice QCD. For all quark flavors, we employ the Möbius domain-wall action, which preserves chiral symmetry to a good precision. Our gauge ensembles are generated at three lattice cutoffs a−1∼2.5, 3.6, and 4.5 GeV with pion masses as low as Mπ∼230 MeV. The physical lattice size L satisfies the condition MπL≥4 to control finite volume effects (FVEs), while we simulate a smaller size at the smallest Mπ to directly examine FVEs. The bottom quark masses are chosen in a range from the physical charm quark mass to 0.7a−1 to control discretization effects. We extrapolate the form factors to the continuum limit and physical quark masses based on heavy meson chiral perturbation theory at next-to-leading order. Then the recoil parameter dependence is parametrized using a model independent form leading to our estimate of the decay rate ratio between the tau (ℓ=τ) and light lepton (ℓ=e, μ) channels R(D*)=0.252(22) in the Standard Model. A simultaneous fit with recent data from the Belle experiment yields |Vcb|=39.19(91)×10−3, which is consistent with previous exclusive determinations, and shows good consistency in the kinematical distribution of the differential decay rate between the lattice and experimental data. Published by the American Physical Society 2024

Analytic decay width of the Higgs boson to massive bottom quarks at next-to-next-to-leading order in QCD

The Higgs boson decay to a massive bottom quark pair provides the dominant contribution to the Higgs boson width. We present an exact result for such a decay induced by the bottom quark Yukawa coupling with next-to-next-to-leading order (NNLO) QCD corrections. We have adopted the canonical differential equations in the calculation and obtained the result in terms of multiple polylogarithms. We also compute the contribution from the decay to four bottom quarks which consists of complete elliptic integrals or their one-fold integrals. The result in the small bottom quark mass limit coincides with the previous calculation using the large momentum expansion. The threshold expansion exhibits power divergent terms in the bottom quark velocity, which has a structure different from that in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${e}^{+}{e}^{-}\ o t\\overline{t }$$\\end{document} but can be reproduced by computing the corresponding Coulomb Green function. The NNLO corrections significantly reduce the uncertainties from both the renormalization scale and the renormalization scheme of the bottom quark Yukawa coupling. Our result can be applied to a heavy scalar decay to a top quark pair.

Complete analysis on QED corrections to Bq → τ+τ−

Motivated by a dynamical enhancement of the electromagnetic corrections by a power of ΛQCD/mb in Bd,s→ μ+μ− at next-to-leading order (NLO), we extend the QED factorization effects on the leptonic B meson decays with light muon leptons to tauonic final states, Bd,s→ τ+τ−, using soft-collinear effective theory (SCET). This extension is necessary owing to the appearance of the large τ mass, which will lead to different power counting in SCET and also different results. We provide a complete NLO electromagnetic corrections to Bd,s→ τ+τ−, which include hard functions and hard-collinear functions below the bottom quark mass scale μb. The power enhanced electromagnetic effects from hard-collinear contributions on Bd,s→ μ+μ− discussed before also exist in Bd,s→ τ+τ−. However the logarithm term arising from contributions of hard-collinear photon and lepton virtualities for Bd,s→ τ+τ− is not large as it is in muon case due to the hard-collinear scale of τ mass, which lead to only approximately 0.04% QED corrections to the branching fraction of Bd,s→ τ+τ− compared with overall reduction about 0.5% in Bd,s→ μ+μ−.

Next-to-leading-order QCD corrections to Higgs production in association with a jet

We compute the next-to-leading-order (NLO) QCD corrections to the Higgs pT distribution in Higgs production in association with a jet via gluon fusion at the LHC, with exact dependence on the mass of the quark circulating in the heavy-quark loops. The NLO corrections are presented including the top-quark mass, and for the first time, the bottom-quark mass as well. Further, besides the on-shell mass scheme, we consider for the first time a running mass renormalisation scheme. The computation is based on amplitudes which are valid for arbitrary heavy-quark masses.

Dispersive constraints on fermion masses

We demonstrate that fermion masses in the Standard Model (SM) can be constrained by the dispersion relations obeyed by hadronic and semileptonic decay widths of a fictitious heavy quark $Q$ with an arbitrary mass. These relations, imposing stringent connections between the high-mass and low-mass behaviors of decay widths, correlate a heavy quark mass and the chiral symmetry breaking scale. Given the known input from leading-order heavy quark expansion and a hadronic threshold for decay products, we solve for a physical heavy quark decay width. It is shown that the charm (bottom) quark mass $m_c= 1.35$ GeV ($m_b= 4.0$ GeV) can be determined by the dispersion relation for the $Q\to du\bar d$ ($Q\to c\bar ud$) decay with the threshold $2m_\pi$ ($m_\pi+m_D$), where $m_\pi$ ($m_D$) denotes the pion ($D$ meson) mass. Requiring that the dispersion relation for the $Q\to su\bar d$ ($Q\to d\mu^+\nu_\mu$, $Q\to u\tau^-\bar\nu_\tau$) decay with the threshold $m_\pi+m_K$ ($m_\pi+m_\mu$, $m_\pi+m_\tau$) yields the same heavy quark mass, $m_K$ being the kaon mass, we constrain the strange quark (muon, $\tau$ lepton) mass to be $m_s= 0.12$ GeV ($m_\mu=0.11$ GeV, $m_\tau= 2.0$ GeV). Moreover, all the predicted decay widths corresponding to the above masses agree with the data. It is pointed out that our formalism is similar to QCD sum rules for probing resonance properties, and that the Pauli interference (weak annihilation) provides the higher-power effect necessary for establishing the solutions of the hadronic (semilaptonic) decay widths. This work suggests that the parameters in the SM may not be free, but arranged properly to achieve internal dynamical consistency.

Decay constant of [formula omitted] accurate up to [formula omitted

In this paper, we evaluate, up to QCD next-to-next-to-next-to-leading order, the Bc⁎ decay constant, which, within the nonrelativistic QCD (NRQCD) framework, is factorized as the product of the short-distance coefficient (SDC) and the long-distance matrix element. For the first time, the renormalization constant and the anomalous dimension for the NRQCD vector current composed of cb¯, which are functions of the charm quark mass mc, the bottom quark mass mb and the factorization scale μΛ, are obtained analytically at O(αs2) and O(αs3). The SDC is calculated up to O(αs3) in perturbative expansion. Explicitly, the O(αs2) correction to the SDC is analytically calculated in terms of logarithmic and polylogarithmic functions of r≡mb/mc, and the O(αs3) correction to the SDC is numerically calculated at a series of values of r, ranging from 2.1 to 4.0. Surprisingly, we find that the nontrivial part of the SDC at O(αs3) can be well estimated by a linear function of r. In addition, we find that the O(αs2) and O(αs3) corrections to the decay constant and decay width are considerable and very significant, which indicates a very poor convergence for the perturbative expansion.

High energy resummed predictions for the production of a Higgs boson with at least one jet

We present all-order predictions for Higgs boson production plus at least one jet which are accurate to leading logarithm in hat{s}/{left|{p}_{perp}right|}^2 . Our calculation includes full top and bottom quark mass dependence at all orders in the logarithmic part, and to highest available order in the tree-level matching. The calculation is implemented in the framework of High Energy Jets (HEJ). This is the first cross section calculated with log( hat{s} ) resummation and matched to fixed order for a process requiring just one jet, and our results also extend the region of resummation for processes with two jets or more. This is possible because the resummation is performed explicitly in phase space. We compare the results of our new calculation to LHC data and to next-to-leading order predictions and find a numerically significant impact of the logarithmic corrections in the shape of key distributions, which remains after normalisation of the cross section.

Charmonium, Bc and X(3872) Transport at the LHC

We deploy a kinetic-rate equation to evaluate the transport of J/ψ, ψ(2S), Bc and X (3872) in ultrarelativistic heavy-ion collisions and compare their production yields to experimental data from the Large Hadron Collider. The rate equation has two main transport parameters: the equilibrium limit and reaction rate for each state. The temperature-dependent equilibrium limits include charm- and bottom-quark fugacities based on their initial production. The reaction rates for charmonia, bottomonia and Bc rely on charm- and bottomquark masses and binding energies from a thermodynamic T-matrix approach. For the X (3872) particle, internal structure information is encoded in reaction rates and initial conditions in the hadronic phase via two different scenarios: a loosely bound hadronic molecule vs. a compact tetraquark.

Measurement of nonprompt and prompt D0 azimuthal anisotropy in Pb-Pb collisions at √SNN = 5.02 TeV

Heavy quarks are primarily produced via initial hard scatterings, and thus carry information about the early stages of the Quark-Gluon Plasma (QGP). Measurements of the azimuthal anisotropy of the final-state heavy flavor hadrons provide information about the initial collision geometry, its fluctuation, and more importantly, the mass dependence of energy loss in QGP. Due to the larger bottom quark mass as compared to the charm quark mass, separate measurements of charm and bottom hadron azimuthal anisotropy can shed new light on understanding the dependence of the heavy quark and medium interaction. Because of the high branching ratio and large D0 mass, measurements of D0 meson coming from bottom hadron decay (nonprompt D0) can cover a broad kinematic range and be a good proxy of the parent bottom hadrons results. In this talk, we report on the prompt D0 and the first nonprompt D0 measurements of the azimuthal anisotropy elliptic (v2) and triangular (v3) coefficients of nonprompt D0 in PbPb collisions at √SNN = 5.02 TeV. The measurements are performed as functions of transverse momentum pT, in three centrality classes, from central to midcentral collisions. Compared to the prompt D0 results, the nonprompt D0 v2 flow coefficients are systematically lower but have a similar dependence on pT and centrality. A non-zero v3 coefficient of the nonprompt D0 is observed. The obtained results are compared with theoretical predictions. The comparison could provide new constraints on the theoretical description of the interaction between heavy quarks and the medium.

Bottom quark mass with calibrated uncertainty

We determine the bottom quark mass {hat{m}}_b from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD to {{mathcal {O}}} ({hat{alpha }}_s^3). Our approach is based on the mutual consistency across a set of moments where experimental data are required for the resonance contributions only. Additional experimental information from the continuum region can then be used for stability tests and to assess the theoretical uncertainty. We find {hat{m}}_b({hat{m}}_b) = (4180.2 pm 7.9) MeV for {hat{alpha }}_s(M_Z) = 0.1182.

O(αs) perturbative and nonperturbative corrections to polarized semileptonic Λb decay distributions

In this paper we calculate first order radiative QCD corrections to the decay process $b\to cW^-(\to\ell^-\bar\nu_\ell)$ of a polarized bottom quark. Taking into account both the bottom and charm quark masses, the analytical expressions given in this paper allow for a detailed analysis of the differential decay rate of the polarized quark in dependence on the polar and azimuthal angles of the lepton pair and the angle of the polarization vector of the quark relative to the momentum direction of the $W$ boson. The results are given for different polarization states of the charged lepton. In addition, we calculated nonperturbative corrections and estimated their contribution.

$\mathcal{O}(α_s^3)$ corrections to semileptonic $b \to c$ decays in the heavy daughter approximation

We present our recent calculation of the third order corrections to the semileptonic b \to cb→c and the muon decays. The calculation has been performed in an expansion around the limit m_c \sim m_bmc∼mb, but shows decent convergence even for m_c=0mc=0 from which the contribution to the muon decay can be extracted. For the semileptonic b \to cb→c decay we find large perturbative corrections in the on-shell scheme which can be significantly reduced by changing to the kinetic scheme for the bottom quark mass. These results are important input for the inclusive determination of |V_{cb}||Vcb| and the Fermi coupling constant G_FGF.

M_{b} at m_{H}: The Running Bottom Quark Mass and the Higgs Boson.

We present a new measurement of the bottom quark mass in the MS[over ¯] scheme at the renormalization scale of the Higgs boson mass from measurements of Higgs boson decay rates at the LHC: m_{b}(m_{H})=2.60_{-0.31}^{+0.36} GeV. The measurement has a negligible theory uncertainty and excellent prospects to improve at the HL-LHC and a future Higgs factory. Confronting this result and m_{b}(m_{b}) from low-energy measurements and m_{b}(m_{Z}) from Z-pole data, with the prediction of the scale evolution of the renormalization group equations, we find strong evidence for the "running" of the bottom quark mass.

Tcc+ and its partners

Inspired by the ${T}_{cc}^{+}$ signal discovered by the LHCb Collaboration, we systematically investigate the doubly heavy tetraquark states with the molecule configuration $[{Q}_{1}{\overline{q}}_{2}{]}_{{\mathbf{1}}_{c}}[{Q}_{3}{\overline{q}}_{4}{]}_{{\mathbf{1}}_{c}}$ ($Q=c$ and $b$, $q=u$, $d$, and $s$) in a nonrelativistic quark model. The model involves a color screening confinement potential, meson-exchange interactions, and one-gluon-exchange interactions. The state ${T}_{cc}^{+}$ with $I{J}^{P}=0{1}^{+}$ is a very loosely bound deuteronlike state with a binding energy around 0.34 MeV and a huge size of 4.32 fm. Both the meson exchange force and the coupled channel effect play a pivotal role. Without the meson exchange force, there does not exist the ${T}_{cc}^{+}$ molecular state. In strong contrast, the QCD valence bond forms clearly in the ${T}_{bb}^{\ensuremath{-}}$ system when we turn off the meson-exchange force, which is very similar to the hydrogen molecule in QED. Moreover, the ${T}_{bb}^{\ensuremath{-}}$ becomes a heliumlike QCD-atom if we increase the bottom quark mass by a factor of three. Especially, the states ${T}_{bb}^{\ensuremath{-}}$ with ${01}^{+}$, ${T}_{bc}^{0}$ with ${00}^{+}$ and ${01}^{+}$, and the $V$-spin antisymmetric states ${T}_{bbs}^{\ensuremath{-}}$ with $\frac{1}{2}{1}^{+}$, ${T}_{bcs}^{0}$ with $\frac{1}{2}{0}^{+}$ and $\frac{1}{2}{1}^{+}$ can form a compact, hydrogen moleculelike or deuteronlike bound state with different binding dynamics. The high-spin states ${T}_{bc}^{0}$ with ${02}^{+}$ and ${T}_{bcs}^{0}$ with $\frac{1}{2}{2}^{+}$ can decay into $D$-wave $\overline{B}D$ and ${\overline{B}}_{s}D$ although they are below the thresholds ${\overline{B}}^{*}{D}^{*}$ and ${\overline{B}}_{s}^{*}{D}^{*}$, respectively. The isospin and $V$-spin symmetric states are unbound. We also calculate their magnetic moments and axial charges.

Bottom tetraquark production at RHIC?

Background: A resonance has been observed by the ANDY Collaboration at the Relativistic Heavy-Ion Collider at Brookhaven National Laboratory in Cu+Au collisions at center-of-mass energy $\sqrt{s} = 200$ GeV and at forward rapidity with an average mass of 18.15 GeV. The Collaboration suggests that it is a $b \overline b b \overline b$ tetraquark state decaying to two $\Upsilon$(1S) states, each measured through the $\Upsilon \rightarrow ggg$ channel. Purpose: Their suggestion is investigated assuming that the two $\Upsilon$ states are produced through the materialization of a $|uud b\overline b b \overline b \rangle$ Fock state in the projectile. Methods: The $\Upsilon$ pair mass and rapidity distributions arising from such a state are calculated. The production of an $X_b(b \overline b b \overline b)$ tetraquark state from the same Fock configuration is also investigated. The dependence on bottom quark mass and their transverse momentum range is also studied. Results: It is found that double $\Upsilon$ production from these $|uud b \overline b b \overline b \rangle$ states peak in the rapidity range of the ANDY detector. The $\Upsilon$ pair and $X_b$ masses are, however, higher than the mass reported by the ANDY Collaboration. Conclusions: The results obtained from these calculations are incompatible with the ANDY result. They are, however, compatible with previous predictions of $b \overline b b \overline b$ tetraquark masses.