Bottom hadrons from lattice QCD with domain wall and NRQCD fermions
Stefan Meinel, William Detmold, C. -J. David Lin, Matthew Wingate
备注：
7 pages, 8 figures; talk presented at the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, China. This version: reference added
Dynamical 2+1 flavor lattice QCD is used to calculate the masses of bottom hadrons, including B mesons, singly and doubly bottom baryons, and for the first time also the triply-bottom baryon Omega_bbb. The domain wall action is used for the up-, down-, and strange quarks (both valence and sea), while the bottom quark is implemented with non-relativistic QCD. A calculation of the bottomonium spectrum is also presented.
We determine the mass spectra of heavy baryons containing one or more bottom quarks along with their hyperfine splittings and various mass differences on MILC 2+1 Asqtad lattices at three different lattice spacings. NRQCD action is used for bottom quarks whereas relativistic HISQ action for the lighter up/down, strange and charm quarks. We consider all possible combinations of bottom and lighter quarks to construct the bottom baryon operators for the states $J^P=1/2^+$ and $3/2^+$.
We study S-wave and P-wave bottomonium spectral functions at non-zero temperature in 2+1 flavor QCD using the NRQCD formulation for bottom quarks. We use a novel Bayesian approach to reconstruct the spectral functions and find that $χ_{b1}$ survives up to $T=249 {\rm MeV}$. We also study the effect of different temporal discretizations of the NRQCD formalism on the bottomonium correlation functions
We give results for B, Bs, Bc and bottomonium spectroscopy using NRQCD heavy quarks and HISQ valence and sea quarks. Five MILC ensembles of gluon configurations with three values of the lattice spacing and m(light)/m(strange) values down to 0.1 are used that include 2+1+1 flavours of sea quark. Systematic errors in the NRQCD action are improved through the radiative correction of the coefficients of terms at v^4. Improved results for S-wave and P-wave bottomonium states are discussed as well as a prediction for the full D-wave spectrum. Preliminary results for the ground state B meson masses a…
We report progress in the calculation of the thermal interquark potential of bottomonium using the HAL QCD method applied to bottom quarks in the non-relativistic approximation (i.e. NRQCD). We exploit the fast Fourier transform algorithm, using a momentum space representation, to efficiently calculate NRQCD correlation functions of non-local mesonic S-wave states, and thus obtain the potential for temperatures in both the hadronic and plasma phases. This work was performed on our anisotropic 2+1 flavour ''Generation 2'' FASTSUM ensembles.
We report our preliminary progress in the calculation of the interquark potential of bottomonium at non-zero temperature using the HAL QCD method. We use NRQCD correlation functions of non-local mesonic S-wave states to obtain the central potential as a function of temperature. These results have been obtained using our anisotropic 2+1 flavour "Generation 2" FASTSUM ensembles.
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 …
The behavior of bottomonium state correlators at non-zero temperature, $140.4 (β= 6.664) \le T \le 221 (β= 7.280)$ (MeV), where the transition temperature is $154(9)$ (MeV), is studied, using lattice NRQCD on $48^3 \times 12$ HotQCD HiSQ action configurations with light dynamical $N_f = 2 + 1$ ($m_{u,s}/m_s = 0.05$) staggered quarks. In order to understand finite temperature effects on quarkonium states, zero temperature behavior of bottomonium correlators is compared based on $32^4$ ($β= 6.664, 6.800$ and $6.950$) and $48^3 \times 64$ ($β= 7.280)$ lattices. We find that temperature effects on…
Using Non-Relativistic QCD (NRQCD), we study heavy quark mass dependence of S-wave and P-wave bottomonium correlators for 0.42Tc <= T <= 2.09Tc and study spectral functions of S-wave bottomonium states moving in a thermal bath at these temperatures using Maximum Entropy Method with NRQCD kernel. For the studied momentum range, the energy of moving states shows quadratic momentum-dependence and the width of moving states does not show significant changes as the momentum of bottomonium is increased. Also, we find that in correlator ratios, the temperature effect is larger than the effect caused …
On a cubic lattice the zero-momentum meson states have one of 20 possible Lambda^{PC} combinations where Lambda labels the irreducible representation of the octahedral group. Each continuum bottomonium state with specific J^{PC} quantum numbers is contained within one or more of the lattice Lambda^{PC} states. In this work, bottomonium quark-antiquark operators are constructed for all 20 lattice Lambda^{PC} combinations which allows many continuum high angular momentum states to be accessible as ground states of their associated lattice channels. From a dynamical simulation, realistic results …
We extend our study of bottomonium spectral functions in the quark-gluon plasma to nonzero momentum. We use lattice QCD simulations with two flavours of light quark on highly anisotropic lattices and treat the bottom quark with nonrelativistic QCD (NRQCD). We focus on S wave (Upsilon and eta_b) channels and consider nonrelativistic velocities, v/c < 0.2. A comparison with predictions from effective field theory is made.
We study the fate of P wave bottomonium states in the quark-gluon plasma, using a spectral function analysis of euclidean lattice correlators. The correlators are obtained from lattice QCD simulations with two light quark flavours on highly anisotropic lattices, treating the bottom quark nonrelativistically. We find clear indications of melting immediately after the deconfinement transition.
We present a progress report on new calculations of B and B_s meson decay constants employing NRQCD heavy and HISQ light valence quarks and using MILC N_f = 2+1 AsqTad lattices. Bare quark masses have been retuned in accord with HPQCD's new r_1 scale. We find significant reductions in discretization effects compared to previous calculations with AsqTad light valence quarks. Matching of the NRQCD/HISQ heavy-light axial vector current is carried out at one-loop order including all relevant dimension 4 current corrections.
We study the role of the lattice artifacts associated with the Coulomb binding effects in the analysis of the heavy quarkonium within lattice NRQCD. We find that a "naive" perturbative matching generates spurious linear Coulomb artifacts, which result in a large systematic error in the lattice predictions for the heavy quarkonium spectrum. This effect is responsible, in particular, for the discrepancy between the recent determinations of the bottomonium hyperfine splitting in the radiatively improved lattice NRQCD [1, 2]. We show that the correct matching procedure which provides full control …
We present an overview of bottomonium spectral functions in the quark-gluon plasma, obtained by the FASTSUM collaboration, using lattice QCD simulations with two light quark flavours on anisotropic lattices. The bottom quark is treated nonrelativistically. While we find that the S wave ground states survive up to the highest temperature we consider, we have strong indications that P wave states melt immediately above Tc.
We present recent results on the in-medium modification of S- and P-wave bottomonium states around the deconfinement transition. Our study uses lattice QCD with $N_f=2+1$ light quark flavors to describe the non-perturbative thermal QCD medium between $140$MeV$<T<249$MeV and deploys lattice regularized non-relativistic QCD (NRQCD) effective field theory to capture the physics of heavy quark bound states immersed therein. The spectral functions of the $^3S_1$ $(Υ)$ and $^3P_1$ $(χ_{b1})$ bottomonium states are extracted from Euclidean time Monte Carlo simulations using a novel Bayesian prescript…
We apply the background field (BF) method to Non-Relativistic QCD (NRQCD) on the lattice in order to determine the one-loop radiative corrections to the coefficients of the NRQCD action in a manifestly gauge-covariant manner by matching the NRQCD prediction for particular on-shell processes with those of relativistic continuum QCD. We explain how the BF method is implemented in automated perturbation theory and discuss the technique for matching the relativistic and non-relativistic theories. We compute the one-loop radiative corrections to the sigma.B and Darwin terms for the NRQCD action cur…
We report on progress of a lattice QCD calculation of the $B\to Dlν$ and $B_s\to D_s lν$ semileptonic form factors. We use a relativistic staggered action (HISQ) for light and charm quarks, and an improved non-relativistic (NRQCD) action for bottom, on the second generation MILC ensembles.
We investigate the properties of S-and P-wave bottomonium states in the vicinity of the deconfinement transition temperature. The light degrees of freedom are represented by dynamical lattice QCD configurations of the HotQCD collaboration with $N_f = 2 + 1$ flavors. Bottomonium correlators are obtained from bottom quark propagators, computed in nonrelativistic quantum chromodynamics (NRQCD) under the background of these gauge field configurations. The spectral functions for the $^3S_1$ ($Υ$) and $^3P_1$ ($χ_{b1}$) channel are extracted from the Euclidean time correlators using a novel Bayesian…
The HPQCD collaboration has used radiatively-improved NonRelativistic QCD (NRQCD) for $b$ quarks in bottomonium to determine the decay rate of $Υ$ and $Υ^\prime$ mesons to leptons in lattice QCD. Using time-moments of vector bottomonium current-current correlators, we are also able to determine the $b$ quark mass in the $\overline{\mathrm{MS}}$ scheme. We use the same NRQCD $b$ quarks and Highly Improved Staggered Quark (HISQ) light quarks -- with masses down to their physical values -- to give a complete picture of heavy-light meson decay constants including those for vector mesons. We also s…
We present updated results for the radiative improvement of the σ.B term and the spin-dependent four-fermion terms in the lattice NRQCD action, and first results for the radiative corrections to the NRQCD Darwin term and spin-independent four-fermion terms. The spin-dependent terms have significant impact on getting the correct hyperfine splitting for both bottomonium and heavy-light mesons, while the spin-independent terms suffer from a conspiracy between lattice artifacts and severe IR divergences that complicates their evaluation.
We present the first application of the background field method to Non-Relativistic QCD (NRQCD) on the lattice in order to determine the one-loop radiative corrections to the coefficients of the NRQCD action in a manifestly gauge-covariant manner. The coefficient of the $σ\cdot B$ term in the NRQCD action is computed at the one-loop level; the resulting shift of the hyperfine splitting of bottomonium is found to bring the lattice predictions in line with experiment.
We present a calculation of the hyperfine splittings in bottomonium using lattice Nonrelativistic QCD. The calculation includes spin-dependent relativistic corrections through O(v^6), radiative corrections to the leading spin-magnetic coupling and, for the first time, non-perturbative 4-quark interactions which enter at alpha_s^2 v^3. We also include the effect of u,d,s and c quark vacuum polarisation. Our result for the 1S hyperfine splitting is M(Upsilon,1S) - M(eta_b,1S)= 60.0(6.4) MeV. We find the ratio of 2S to 1S hyperfine splittings (M(Upsilon,2S) - M(eta_b,2S))/ (M(Upsilon,1S) - M(eta_…
Recently, realistic lattice QCD calculations with 2+1 flavors of domain wall fermions and the Iwasaki gauge action have been performed by the RBC and UKQCD collaborations. Here, results for the bottomonium spectrum computed on their gauge configurations of size 24^3x64 with a lattice spacing of approximately 0.11 fm and four different values for the light quark mass are presented. Improved lattice NRQCD is used to treat the b quarks inside the bottomonium. The results for the radial and orbital energy splittings are found to be in good agreement with experimental measurements, indicating that …
To study the in-medium modification of quarkonium properties, charmonium correlators at $140.4 (β=6.664) \le T \le 221 (β= 7.280)$ (MeV) are calculated using the NRQCD formalism on $48^3 \times 12$ gauge configurations with dynamical $N_f = 2 + 1$ flavors of Highly Improved Staggered Quarks (HISQ). To determine the "zero energy shift" for these lattices, we perform a fine zero temperature scan ($β=6.664, 6.740, 6.800, 6.880, 6.950, 7.030, 7.150$ and $7.280$). We find that the temperature dependence of charmonium correlators is stronger than the temperature dependence of bottomonium correlators…
We present the status of our ongoing calculation of the zero-recoil form factor for the semileptonic decay $\bar{B}^0\rightarrow D^{*+}l^-\barν$ using lattice QCD with 2+1+1 flavours of highly improved staggered quarks in the sea (the MILC HISQ configurations) and using non-relativistic QCD for the bottom quark. We combine our result for $ F(1)$ with the latest HFAG average of $η_{EW} F(1)|V_{cb}|$ to get a preliminary value for $|V_{cb}|$.
We formulate Non-Relativistic Quantum Chromodynamics (NRQCD) on a lattice which is boosted relative to the usual discretization frame. Moving NRQCD (mNRQCD) allows us to treat the momentum for the heavy quark arising from the frame choice exactly. We derive mNRQCD through O(1/m^2,v^4), as accurate as the NRQCD action in present use, both in the continuum and on the lattice with O(a^4) improvements. We have carried out extensive tests of the formalism through calculations of two-point correlators for both heavy-heavy (bottomonium) and heavy-light (B_s) mesons in 2+1 flavor lattice QCD and obtai…
Along the years, the Cornell Model has been extraordinarily successful in describing hadronic phenomenology, in particular in physical situations for which an effective theory of the strong interactions such as NRQCD cannot be applied. As a consequence of its achievements, a relevant question is whether its model parameters can somehow be related to fundamental constants of QCD. We shall give a first answer in this article by comparing the predictions of both approaches. Building on results from a previous study on heavy meson spectroscopy, we calibrate the Cornell model employing NRQCD predic…
We have developed two methods for handling $b$ quarks in lattice QCD. One uses NRQCD (now improved to include radiative corrections) and the other uses Highly Improved Staggered Quarks (HISQ), extrapolating to the $b$ quark from lighter masses and using multiple lattice spacings to control discretisation errors. Comparison of results for the two different methods gives confidence in estimates of lattice QCD systematic errors, since they are very different in these two cases. Here we show results for heavyonium hyperfine splittings and vector current-current correlator moments using HISQ quarks…
The spectrum of baryons containing three b quarks is calculated in nonperturbative QCD, using the lattice regularization. The energies of ten excited bbb states with J^P = 1/2^+, 3/2^+, 5/2^+, 7/2^+, 1/2^-, and 3/2^- are determined with high precision. A domain-wall action is used for the up-, down- and strange quarks, and the bottom quarks are implemented with NRQCD. The computations are done at lattice spacings of a \approx 0.11 fm and a \approx 0.08 fm, and the results demonstrate the improvement of rotational symmetry as a is reduced. A large lattice volume of (2.7 fm)^3 is used, and extra…
We continue our study of heavy-light four-quark states and find evidence from lattice QCD for the existence of a strong-interaction-stable $I(J^P)=0(1^+)$ $ud\bar{c}\bar{b}$ tetraquark with mass in the range of 15 to 61 MeV below $\bar{D}B^*$ threshold. Since this range includes the electromagnetic $\bar{D}Bγ$ decay threshold, current uncertainties do not allow us to determine whether such a state would decay electromagnetically, or only weakly. We also perform a study at fixed pion mass, with NRQCD for the heavy quarks, simulating $qq^\prime \bar{b}^\prime \bar{b}$ and $q q^\prime \bar{b}^\pr…
The bottomonium spectrum is computed in dynamical 2+1 flavor lattice QCD, using NRQCD for the b quarks. The main calculations in this work are based on gauge field ensembles generated by the RBC and UKQCD collaborations with the Iwasaki action for the gluons and a domain-wall action for the sea quarks. Lattice spacing values of approximately 0.08 fm and 0.11 fm are used, and simultaneous chiral extrapolations to the physical pion mass are performed. As a test for gluon discretization errors, the calculations are repeated on two ensembles generated by the MILC collaboration with the Luscher-Wei…
We investigate heavy-light four-quark systems $ud\bar b \bar b$ with bottom quarks of finite mass which are treated in the framework of NRQCD. We focus on $I(J^P)=0(1^+)$, where we recently found evidence for the existence of a tetraquark state using static bottom quarks. Furthermore, we report on an investigation of the $u \bar d b \bar b$ four-quark system with quantum numbers $I(J^P)=1(1^+)$ again using static bottom quarks.
We study bottomonium spectral functions in the quark-gluon plasma in the Upsilon and eta_b channels, using lattice QCD simulations with two flavours of light quark on highly anisotropic lattices. The bottom quark is treated with nonrelativistic QCD (NRQCD). In the temperature range we consider, 0.42 < T/T_c < 2.09, we find that the ground states survive, whereas the excited states are suppressed as the temperature is increased. The position and width of the ground states are compared to analytical effective field theory (EFT) predictions. Systematic uncertainties of the maximum entropy method …
We present the final results of our high statistics study on the properties of bottomonium and charmonium at finite temperature. We focus on the temperature range around the crossover transition $150\leq T\leq 410$MeV, relevant for current heavy ion collision experiments. The QCD medium degrees of freedom which consist of dynamical u,d, and s quarks and gluons are captured by realistic state-of-the art ($m_π\approx 161$MeV) lattice QCD simulations of the HotQCD collaboration. For the heavy quarks we deploy the non-relativistic effective field theory of QCD, NRQCD. The in-medium properties of q…
We report the ground state masses of hadrons containing at least one charm and one bottom quark using lattice quantum chromodynamics. These include mesons with spin (J)-parity (P) quantum numbers J(P): 0(-), 1(-), 1(+) and 0(+) and the spin-1/2 and 3/2 baryons. Among these hadrons only the ground state of 0(-) is known experimentally and therefore our predictions provide important information for the experimental discovery of all other hadrons with these quark contents.
