Light Quark Masses Research Articles

Decays of an exotic 1−+ hybrid meson resonance in QCD

We present the first determination of the hadronic decays of the lightest exotic ${J}^{PC}={1}^{\ensuremath{-}+}$ resonance in lattice QCD. Working with SU(3) flavor symmetry, where the up, down and strange-quark masses approximately match the physical strange-quark mass giving ${m}_{\ensuremath{\pi}}\ensuremath{\sim}700\text{ }\text{ }\mathrm{MeV}$, we compute finite-volume spectra on six lattice volumes which constrain a scattering system featuring eight coupled channels. Analytically continuing the scattering amplitudes into the complex-energy plane, we find a pole singularity corresponding to a narrow resonance which shows relatively weak coupling to the open pseudoscalar--pseudoscalar, vector--pseudoscalar and vector--vector decay channels, but large couplings to at least one kinematically closed axial-vector--pseudoscalar channel. Attempting a simple extrapolation of the couplings to physical light-quark mass suggests a broad ${\ensuremath{\pi}}_{1}$ resonance decaying dominantly through the ${b}_{1}\ensuremath{\pi}$ mode with much smaller decays into ${f}_{1}\ensuremath{\pi}$, $\ensuremath{\rho}\ensuremath{\pi}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}$ and $\ensuremath{\eta}\ensuremath{\pi}$. A large total width is potentially in agreement with the experimental ${\ensuremath{\pi}}_{1}(1564)$ candidate state observed in $\ensuremath{\eta}\ensuremath{\pi}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}$, which we suggest may be heavily suppressed decay channels.

Singlet dark matter in the SU(6)/SO(6) composite Higgs model

Singlet scalar Dark Matter can naturally arise in composite Higgs models as an additional stable pseudo-Nambu-Goldstone boson. We study the properties of such a candidate in a model based on $SU(6)/SO(6)$, with the light quark masses generated by 4-fermion interactions. The presence of non-linearities in the couplings allows to saturate the relic density for masses $400 < m_{\rm DM} < 1000$ GeV, and survive the bound from Direct Detection and Indirect Detection. The viable parameter regions are in reach of the sensitivities of future upgrades, like XENONnT and LZ.

Flavor nonsinglet parton distribution functions from lattice QCD at physical quark masses via the pseudodistribution approach

One of the great challenges of QCD is to determine the partonic structure of the nucleon from first principles. In this work, we provide such a determination of the flavor non-singlet ($u-d$) unpolarized parton distribution function (PDF), utilizing the non-perturbative formulation of QCD on the lattice. We apply Radyushkin's pseudo-distribution approach to lattice results obtained using simulations with the light quark mass fixed to its physical value; this is the first ever attempt for this approach directly at the physical point. The extracted coordinate-space matrix elements are used to find the relevant physical Ioffe time distributions from a matching procedure. The full Bjorken-$x$ dependence of PDFs is resolved using several reconstruction methods to tackle the ill-conditioned inverse problem encountered when using discrete lattice data. We consider both the valence distribution $q_v$ and the combination with antiquarks $q_v+2\bar{q}$, related to, respectively, the real and imaginary part of extracted matrix elements. Good agreement is found with PDFs from global fits already within statistical uncertainties and it is further improved by quantifying several systematic effects. The results presented here are the first ever \emph{ab initio} determinations of PDFs fully consistent with global fits in the whole $x$-range. Thus, they pave the way to investigating a wider class of partonic distributions, such as e.g.\ singlet PDFs and generalized parton distributions. Therefore, essential and yet missing first-principle insights can be achieved, complementing the rich experimental programs dedicated to the structure of the nucleon.

Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD.

We introduce novel relations between the derivatives [∂^{n}ρ(λ,m_{l})/∂m_{l}^{n}] of the Dirac eigenvalue spectrum [ρ(λ,m_{l})] with respect to the light sea quark mass (m_{l}) and the (n+1)-point correlations among the eigenvalues (λ) of the massless Dirac operator. Using these relations we present lattice QCD results for ∂^{n}ρ(λ,m_{l})/∂m_{l}^{n} (n=1, 2, 3) for m_{l} corresponding to pion masses m_{π}=160-55 MeV and at a temperature of about 1.6 times the chiral phase transition temperature. Calculations were carried out using (2+1) flavors of highly improved staggered quarks with the physical value of strange quark mass, three lattice spacings a=0.12, 0.08, 0.06fm, and lattices having aspect ratios 4-9. We find that ρ(λ→0,m_{l}) develops a peaked structure. This peaked structure arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum, becomes sharper as a→0, and its amplitude is proportional to m_{l}^{2}. We demonstrate that this ρ(λ→0,m_{l}) is responsible for the manifestations of axial anomaly in two-point correlation functions of light scalar and pseudoscalar mesons. After continuum and chiral extrapolations we find that axial anomaly remains manifested in two-point correlation functions of scalar and pseudoscalar mesons in the chiral limit.

DK I = 0, Doverline{K} I = 0, 1 scattering and the {D}_{s0}^{ast } (2317) from lattice QCD

Elastic scattering amplitudes for I = 0 DK and I = 0, 1 Doverline{K} are computed in S, P and D partial waves using lattice QCD with light-quark masses corresponding to mπ = 239 MeV and mπ = 391 MeV. The S-waves contain interesting features including a near-threshold JP = 0+ bound state in I = 0 DK, corresponding to the {D}_{s0}^{ast } (2317), with an effect that is clearly visible above threshold, and suggestions of a 0+ virtual bound state in I = 0 Doverline{K} . The S-wave I = 1 Doverline{K} amplitude is found to be weakly repulsive. The computed finite-volume spectra also contain a deeply-bound D* vector resonance, but negligibly small P -wave DK interactions are observed in the energy region considered; the P and D-wave Doverline{K} amplitudes are also small. There is some evidence of 1+ and 2+ resonances in I = 0 DK at higher energies.

Energy-energy correlation in hadronic Higgs decays: analytic results and phenomenology at NLO

In this work we complete the investigation of the recently introduced energy-energy correlation (EEC) function in hadronic Higgs decays at next-to-leading order (NLO) in fixed-order perturbation theory in the limit of vanishing light quark masses. The full analytic NLO result for the previously unknown EEC in the H → qoverline{q} + X channel is given in terms of classical polylogarithms and cross-checked against a numerical calculation. In addition to that, we discuss further corrections to predictions of the Higgs EEC event shape variable, including quark mass corrections, effects of parton shower and hadronization. We also estimate the statistical error on the measurements of the Higgs EEC at future Higgs factories and compare with the current perturbative uncertainty.

Universal Scaling Properties of QCD Close to the Chiral Limit

We present a lattice QCD based determination of the chiral phase transition temperature in QCD with two massless (up and down) and one strange quark having its physical mass. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range of $58~{\rm MeV}\lesssim m_\pi\lesssim 163~{\rm MeV}$. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling relations. After thermodynamic, continuum and chiral extrapolations we find the chiral phase transition temperature $T_c^0=132^{+3}_{-6}$ MeV. We also show some preliminary calculations that use the conventional estimator for the pseudo-critical temperature and compare with the new estimators for $T_c^0$. Furthermore, we show results for the ratio of the chiral order parameter and its susceptibility and argue that this ratio can be used to differentiate between $O(N)$ and $Z_2$ universality classes in a non-parametric manner.

Construction of bbu¯d¯ tetraquark states on lattice with NRQCD bottom and HISQ up and down quarks

We construct $bb\bar{u}\bar{d}$ states on lattice using NRQCD action for bottom and HISQ action for the light up/down quarks. The NRQCD-HISQ tetraquark operators are constructed for "bound" $[bb][\bar{u}\bar{d}]$ and "molecular" $[b\bar{u}] [b\bar{d}]$ states. Corresponding to these different operators, two different appropriately tuned light quark masses are needed to obtain the desired spectra. We explain this requirement of different $m_{u/d}$ in the light of relativised quark model involving Hartree-Fock calculation. The mass spectra of double bottom tetraquark states are obtained on MILC $N_f=2+1$ Asqtad lattices at three different lattice spacings. Variational analysis has been carried out to obtain the relative contribution of "bound" and "molecular" states to the energy eigenstates.

On the singular behavior of the chirality-odd twist-3 parton distribution e(x)

The first moment of the chirality-odd twist-3 parton distribution e(x) is related to the pion-nucleon σ-term, which is important for phenomenology. However, the possible existence of a singular contribution proportional to δ(x) in the distribution prevents the determination of the σ-term with e(x) extracted from experimental data. There are two approaches to show the existence: the first one is based on an operator identity; the second one is based on a perturbative calculation of a single quark state with finite quark mass. We show that all contributions proportional to δ(x) in the first approach are canceled. For the second approach we find that e(x) of a multiparton state with a massless quark has no contribution with δ(x). Considering that a proton is essentially a multiparton state, the effect of the contribution with δ(x) is expected to be suppressed by light quark masses with arguments from perturbation theory. A detailed discussion of the difference between cut diagrams and uncut diagrams of e(x) is provided.

Pion-mass dependence of the nucleon-nucleon interaction

Nucleon-nucleon interactions, both bare and effective, play an important role in our understanding of the non-perturbative strong interaction, as well as nuclear structure and reactions. In recent years, tremendous efforts have been seen in the lattice QCD community to derive nucleon-nucleon interactions from first principles. Because of the daunting computing resources needed, most of such simulations were still performed with larger than physical light quark masses. In the present work, employing the recently proposed covariant chiral effective field theory (ChEFT), we study the light quark mass dependence of the nucleon-nucleon interaction extracted by the HALQCD group. It is shown that the pion-full version of the ChEFT can describe the lattice QCD data with mπ=469 MeV and their experimental counterpart reasonably well, while the pion-less version can describe the lattice QCD data with mπ=672,837,1015,1171 MeV, for both the S01 and S13-D13 channels. The slightly better description of the single channel than the triplet channel indicates that higher order studies are necessary for the latter. Our results confirmed previous studies that the nucleon-nucleon interaction becomes more attractive for both the singlet and triplet channels as the pion mass decreases towards its physical value. It is shown that the virtual bound state in the S01 channel remains virtual down to the chiral limit, while the deuteron only appears for a pion mass smaller than about 400 MeV. It seems that proper chiral extrapolations of nucleon-nucleon interaction are possible for pion masses smaller than 500 MeV, similar to the mesonic and one-baryon sectors.

Hadronic light-by-light contribution to (g-2)_mu from lattice QCD with SU(3) flavor symmetry

We perform a lattice QCD calculation of the hadronic light-by-light contribution to (g-2)_mu at the SU(3) flavor-symmetric point m_pi =m_Ksimeq 420,MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computing the connected contribution, and introduce a sparse-grid technique for computing the disconnected contribution. Thanks to our previous calculation of the pion transition form factor, we are able to correct for the residual finite-size effects and extend the tail of the integrand. We test our understanding of finite-size effects by using gauge ensembles differing only by their volume. After a continuum extrapolation based on four lattice spacings, we obtain a_mu ^{mathrm{hlbl}}= (65.4pm 4.9 pm 6.6)times 10^{-11}, where the first error results from the uncertainties on the individual gauge ensembles and the second is the systematic error of the continuum extrapolation. Finally, we estimate how this value will change as the light-quark masses are lowered to their physical values.

Going beyond the minimal texture of quark mass matrices in the era of precision measurements

Abstract An attempt has been made to carry out a detailed analysis of quark mass matrices having structure beyond the minimal texture. In particular, keeping in mind precision measurements of Cabibbo–Kobayashi–Maskawa parameters as well as refinements in the ranges of light quark masses, we have examined the viability of all possible combinations of Hermitian texture 5 zero quark mass matrices. Interestingly, one finds that all these possibilities are now excluded by the present quark mixing data, thereby having important implications for model building.

Parametrically narrow tetraquark states containing one heavy quark and one heavy antiquark

This paper focuses on tetraquarks containing one heavy quark and one heavy antiquark in the formal limit where the heavy quark masses go to infinity. It extends the theoretical framework developed for tetraquark containing two heavy quarks based on semi-classical analysis and the Born-Oppenheimer approximation. It is shown that for sufficiently small light quark masses, parametrically narrow $q\bar{q}'Q\bar{Q}$ tetraquarks must exist in the formal limit of arbitrarily large heavy quark masses. The analysis is model-independent; it requires no assumptions about the structure of the state or the mechanism of its decay beyond what can be deduced directly from QCD. The formal analysis here is only directly applicable to tetraquarks with large angular momentum and hence does not directly apply to experimentally observed tetraquark candidates. We also discuss the condition needed for a version of the analysis to apply for low angular momenta states. Whether this condition holds can be explored via lattice calculations. Current lattice calculations suggest that the condition is not met. If these preliminary calculations are confirmed, there are strong implications for the nature of the observed tetraquark resonances containing $\bar{c}c$ or $\bar{b}b$ pairs. It raises the possibility that the observed tetraquarks exist and are narrow not because the charm and bottom quarks are extremely heavy, but because they are sufficiently light.

Magnetic effects of QCD parameters from fnite energy sum rules

One of the advantages of the fnite energy sum rules is the fact that every operator in the operator product expansion series can be selected individually by the use of an appropriate kernel function which removes other operator poles. This characteristic is maintained by QCD systems in the presence of external homogeneous magnetic feld, providing interesting information about the magnetic evolution of QCD and hadronic parameters. In this work fnite energy sum rules are applied on QCD in the light quark sector, combining axial and pseudoscalar channels in the presence of an external homogeneous magnetic feld, obtaining the magnetic evolution of the light quark masses, pion mass, the pion decay constant, the gluon condensate and the continuum hadronic threshold.

Precision calculations of B→V form factors from soft-collinear effective theory sum rules on the light-cone

Applying the vacuum-to-$B$-meson correlation functions with an interpolating current for the light vector meson we construct the light-cone sum rules (LCSR) for the "effective" form factors $\xi_{\parallel}(n \cdot p)$, $\xi_{\perp}(n \cdot p)$, $\Xi_{\parallel}(\tau, n \cdot p)$ and $\Xi_{\perp}(\tau, n \cdot p)$, defined by the corresponding hadronic matrix elements in soft-collinear effective theory (SCET), entering the leading-power factorization formulae for QCD form factors responsible for $B \to V \ell \bar \nu_{\ell}$ and $B \to V \ell \bar \ell$ decays at large hadronic recoil at next-to-leading-order in QCD. The light-quark mass effect for the local SCET form factors $\xi_{\parallel}(n \cdot p)$ and $\xi_{\perp}(n \cdot p)$ is also computed from the LCSR method with the $B$-meson light-cone distribution amplitude $\phi_B^{+}(\omega, \mu)$ at ${\cal O}(\alpha_s)$. Furthermore, the subleading power corrections to $B \to V$ form factors from the higher-twist $B$-meson light-cone distribution amplitudes are also computed with the same method at tree level up to the twist-six accuracy. Having at our disposal the LCSR predictions for $B \to V$ form factors, we further perform new determinations of the CKM matrix element $|V_{ub}|$ from the semileptonic $B \to \rho \, \ell \, \bar \nu_{\ell}$ and $B \to \omega \, \ell \, \bar \nu_{\ell}$ decays, and predict the normalized differential branching fractions and the $q^2$-binned $K^{\ast}$ longitudinal polarization fractions of the exclusive rare $B \to K^{\ast} \, \nu_{\ell} \, \bar \nu_{\ell}$ decays.

Skewness, kurtosis, and the fifth and sixth order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data

We present new results on up to $6^{th}$ order cumulants of net baryon-number fluctuations at small values of the baryon chemical potential, $\mu_B$, obtained in lattice QCD calculations with physical values of light and strange quark masses. Representation of the Taylor expansions of higher order cumulants in terms of the ratio of the two lowest order cumulants, $M_B/\sigma_B^2=\chi_1^B(T,\mu_B)/\chi_2^B(T,\mu_B)$, allows for a parameter free comparison with data on net proton-number cumulants obtained by the STAR Collaboration in the Beam Energy Scan at RHIC. We show that recent high statistics data on skewness and kurtosis ratios of net proton-number distributions, obtained at beam energy $\sqrt{s_{_{NN}}}=54.4$ GeV, agree well with lattice QCD results on cumulants of net baryon-number fluctuations close to the pseudo-critical temperature, $T_{pc}(\mu_B)$, for the chiral transition in QCD. We also present first results from a next-to-leading order expansion of $5^{th}$ and $6^{th}$ order cumulants on the line of pseudo-critical temperatures.

QCD spin effects in the heavy hybrid potentials and spectra

The spin-dependent operators for heavy quarkonium hybrids have been recently obtained in a nonrelativistic effective field theory approach up to next-to-leading order in the heavy-quark mass expansion. In the effective field theory for hybrids several operators not found in standard quarkonia appear, including an operator suppressed by only one power of the heavy-quark mass. We compute the matching coefficients for these operators in the short heavy-quark-antiquark distance regime, $r\ll 1/\Lambda_{\rm QCD}$, by matching weakly-coupled potential NRQCD to the effective field theory for hybrids. In this regime the perturbative and nonperturbative contributions to the matching coefficients factorize, and the latter can be expressed in terms of purely gluonic correlators whose form we explicitly calculate with the aid of the transformation properties of the gluon fields under discrete symmetries. We detail our previous comparison with direct lattice computations of the charmonium hybrid spectrum, from which the unknown nonperturbative contributions can be obtained, and extend it to data sets with different light-quark masses.

Nature of the phase transition for finite temperature Nf=3 QCD with nonperturbatively O(a) improved Wilson fermions at Nt=12

We study the nature of the finite temperature phase transition for three-flavor QCD. In particular we investigate the location of the critical endpoint along the three flavor symmetric line in the light quark mass region of the Columbia plot. In the study, the Iwasaki gauge action and the nonperturvatively O($a$) improved Wilson-Clover fermion action are employed. We newly generate data at $N_{\rm t}=12$ and set an upper bound of the critical pseudoscalar meson mass in the continuum limit $m_{\rm PS,E}\lesssim 110$MeV.

An update on fine-tunings in the triple-alpha process

The triple-alpha process, whereby evolved stars create carbon and oxygen, is believed to be fine-tuned to a high degree. Such fine-tuning is suggested by the unusually strong temperature dependence of the triple-alpha reaction rate at stellar temperatures. This sensitivity is due to the resonant character of the triple-alpha process, which proceeds through the so-called “Hoyle state” of {}^{12}mathrm{C} with spin-parity 0^+. The question of fine-tuning can be studied within the ab initio framework of nuclear lattice effective field theory, which makes it possible to relate ad hoc changes in the energy of the Hoyle state to changes in the fundamental parameters of the nuclear Hamiltonian, which are the light quark mass m_q and the electromagnetic fine-structure constant alpha _mathrm{em}. Here, we update the effective field theory calculation of the sensitivity of the triple-alpha process to small changes in the fundamental parameters. In particular, we consider recent high-precision lattice QCD calculations of the nucleon axial coupling g_A, as well as new and more comprehensive results from stellar simulations of the production of carbon and oxygen. While the updated stellar simulations allow for much larger ad hoc shifts in the Hoyle state energy than previously thought, recent lattice QCD results for the nucleon S-wave singlet and triplet scattering lengths now disfavor the “no fine-tuning scenario” for the light quark mass m_q.

Light quark masses in {N_mathrm{f}=2+1} lattice QCD with Wilson fermions

We present a lattice QCD determination of light quark masses with three sea-quark flavours (N_mathrm{f}=2+1). Bare quark masses are known from PCAC relations in the framework of CLS lattice computations with a non-perturbatively improved Wilson-Clover action and a tree-level Symanzik improved gauge action. They are fully non-perturbatively improved, including the recently computed Symanzik counter-term b_{mathrm{A}} - b_{mathrm{P}}. The mass renormalisation at hadronic scales and the renormalisation group running over a wide range of scales are known non-perturbatively in the Schrödinger functional scheme. In the present paper we perform detailed extrapolations to the physical point, obtaining (for the four-flavour theory) m_{mathrm{u}/mathrm{d}}(2~mathrm{GeV})= 3.54(12)(9)~mathrm{MeV} and m_{mathrm{s}}(2~mathrm{GeV}) = 95.7(2.5)(2.4)~mathrm{MeV} in the overline{mathrm{MS}} scheme. For the mass ratio we have m_{mathrm{s}}/m_{mathrm{u}/mathrm{d}}= 27.0(1.0)(0.4). The RGI values in the three-flavour theory are M_{mathrm{u}/mathrm{d}}= 4.70(15)(12)~mathrm{MeV} and M_{mathrm{s}}= 127.0(3.1)(3.2)~mathrm{MeV}.