Λc→N\Lambda_c \to N form factors from lattice QCD and phenomenology of Λc→nℓ+νℓ\Lambda_c \to n \ell^+ \nu_\ell and Λc→pμ+μ−\Lambda_c \to p \mu^+ \mu^- decays

A lattice QCD determination of the $\Lambda_c \to N$ vector, axial vector, and tensor form factors is reported. The calculation was performed with $2+1$ flavors of domain wall fermions at lattice spacings of $a\approx 0.11\:{\rm fm},\:0.085\:{\rm fm}$ and pion masses in the range $230\:{\rm MeV} \lesssim m_\pi \lesssim 350$ MeV. The form factors are extrapolated to the continuum limit and the physical pion mass using modified $z$ expansions. The rates of the charged-current decays $\Lambda_c \to n\, e^+ \nu_e$ and $\Lambda_c \to n\, \mu^+ \nu_\mu$ are predicted to be $\left( 0.405 \pm 0.016_{\,\rm stat} \pm 0.020_{\,\rm syst} \right)|V_{cd}|^2 \:{\rm ps}^{-1}$ and $\left( 0.396 \pm 0.016_{\,\rm stat} \pm 0.020_{\,\rm syst} \right)|V_{cd}|^2 \:{\rm ps}^{-1}$, respectively. The phenomenology of the rare charm decay $\Lambda_c \to p\, \mu^+ \mu^-$ is also studied. The differential branching fraction, the fraction of longitudinally polarized dimuons, and the forward-backward asymmetry are calculated in the Standard Model and in an illustrative new-physics scenario.Comment: 21 pages, 7 figures, form factor parameters included as ancillary file

Λc→Λℓ+νℓ\Lambda_c \to \Lambda \ell^+ \nu_\ell form factors and decay rates from lattice QCD with physical quark masses

The first lattice QCD calculation of the form factors governing $\Lambda_c \to \Lambda \ell^+ \nu_\ell$ decays is reported. The calculation was performed with two different lattice spacings and includes one ensemble with a pion mass of 139(2) MeV. The resulting predictions for the $\Lambda_c \to \Lambda e^+ \nu_e$ and $\Lambda_c \to \Lambda \mu^+ \nu_\mu$ decay rates divided by $|V_{cs}|^2$ are $0.2007(71)(74)\:{\rm ps}^{-1}$ and $0.1945(69)(72)\:{\rm ps}^{-1}$, respectively, where the two uncertainties are statistical and systematic. Taking the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ from a global fit and the $\Lambda_c$ lifetime from experiments, this translates to branching fractions of $\mathcal{B}(\Lambda_c\to\Lambda e^+\nu_e)=0.0380(19)_{\rm LQCD\:\:}(11)_{\tau_{\Lambda_c}}$ and $\mathcal{B}(\Lambda_c\to\Lambda \mu^+\nu_\mu)=0.0369(19)_{\rm LQCD\:\:}(11)_{\tau_{\Lambda_c}}$. These results are consistent with, and two times more precise than, the measurements performed recently by the BESIII Collaboration. Using instead the measured branching fractions together with the lattice calculation to determine the CKM matrix element gives $|V_{cs}|= 0.949(24)_{\rm LQCD\:\:}(14)_{\tau_{\Lambda_c}}(49)_{\mathcal{B}}$.Comment: 6 pages, 3 figures, form factor parameters included as ancillary file

Excited-state spectroscopy of triply-bottom baryons from lattice QCD

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 extrapolations of the bbb spectrum to realistic values of the light sea-quark masses are performed. All spin-dependent energy splittings are resolved with total uncertainties of order 1 MeV, and the dependence of these splittings on the couplings in the NRQCD action is analyzed.Comment: 26 pages, 15 figures; added uncertainty due to choice of fit range; accepted by PR

Omega_bbb excited-state spectroscopy from lattice QCD

Triply heavy baryons are very interesting systems analogous to heavy quarkonia, but are difficult to access experimentally. Lattice QCD can provide precise predictions for these systems, which can be compared to other theoretical approaches. In this work, the spectrum of excited states of the Omega_bbb baryon is calculated using lattice NRQCD for the b quarks, and using a domain-wall action for the u, d and s sea quarks. The calculations are done for multiple values of the sea-quark masses, and for two different lattice spacings. The energies of states with angular momentum up to J=7/2 are calculated, and the effects of rotational symmetry breaking by the lattice are analyzed. Precise results are obtained even for the small spin-dependent energy splittings, and the contributions of individual NRQCD interactions to these energy splittings are studied. The results are compared to potential-model calculations.Comment: 8 pages, 5 figure

Λb→Λℓ+ℓ−\Lambda_b \to \Lambda \ell^+ \ell^- form factors, differential branching fraction, and angular observables from lattice QCD with relativistic bb quarks

Using $(2+1)$-flavor lattice QCD, we compute the 10 form factors describing the $\Lambda_b \to \Lambda$ matrix elements of the $b \to s$ vector, axial vector, and tensor currents. The calculation is based on gauge field ensembles generated by the RBC and UKQCD Collaborations with a domain-wall action for the $u$, $d$, and $s$ quarks and the Iwasaki gauge action. The $b$ quark is implemented using an anisotropic clover action, tuned nonperturbatively to the physical point, and the currents are renormalized with a mostly nonperturbative method. We perform simultaneous chiral, continuum, and kinematic extrapolations of the form factors through modified $z$ expansions. Using our form factor results, we obtain precise predictions for the $\Lambda_b \to \Lambda(\to p^+ \pi^-) \mu^+ \mu^-$ differential branching fraction and angular observables in the Standard Model.Comment: 33 pages, 9 figures, form factor parameters included as ancillary file

Using Λb→Λμ+μ−\Lambda_b\to \Lambda\mu^+\mu^- data within a Bayesian analysis of ∣ΔB∣=∣ΔS∣=1|\Delta B| = |\Delta S| = 1 decays

We study the impact of including the baryonic decay $\Lambda_b\to \Lambda(\to p \pi^-)\mu^+\mu^-$ in a Bayesian analysis of $|\Delta B | = |\Delta S| = 1$ transitions. We perform fits of the Wilson coefficients $C_{9}$, $C_{9'}$, $C_{10}$ and $C_{10'}$, in addition to the relevant nuisance parameters. Our analysis combines data for the differential branching fraction and three angular observables of $\Lambda_b\to \Lambda(\to p \pi^-)\mu^+\mu^-$ with data for the branching ratios of $B_s \to \mu^+\mu^-$ and inclusive $b \to s\ell^+\ell^-$ decays. Newly available precise lattice QCD results for the full set of $\Lambda_b \to \Lambda$ form factors are used to evaluate the observables of the baryonic decay. Our fits prefer shifts to $C_{9}$ that are opposite in sign compared to those found in global fits of only mesonic decays, and the posterior odds show no evidence of physics beyond the Standard Model. We investigate a possible hadronic origin of the observed tensions between theory and experiment.Comment: 9 pages, 2 figures; v2 as published: added some clarifications, changed setup for model comparisons, expanded conclusion

Heavy quark physics on the lattice with improved nonrelativistic actions

Hadrons containing heavy quarks, in particular b quarks, play an important role in high energy physics. Measurements of their electroweak interactions are used to test the Standard Model and search for new physics. For the comparison of experimental results with theoretical predictions, nonperturbative calculations of hadronic matrix elements within the theory of quantum chromodymanics are required. Such calculations can be performed from first principles by formulating QCD on a Euclidean spacetime grid and computing the path integral numerically. Including b quarks in lattice QCD calculations requires special techniques as the lattice spacing in present computations usually can not be chosen fine enough to resolve their Compton wavelength. In this work, improved nonrelativistic lattice actions for heavy quarks are used to perform calculations of the bottom hadron mass spectrum and of form factors for heavy-to-light decays. In heavy-to-light decays, additional complications arise at high recoil, when the momentum of the light meson reaches a magnitude comparable to the cutoff imposed by the lattice. Discretisation errors at high recoil can be reduced by working in a frame of reference where the heavy and light mesons move in opposite directions. Using a formalism referred to as moving nonrelativistic QCD (mNRQCD), the nonrelativistic expansion for the heavy quark can be performed around a state with an arbitrary velocity. This dissertation begins with a review of the fundamentals of lattice QCD. Then, the construction of effective Lagrangians for heavy quarks in the continuum and on the lattice is discussed in detail. A highly improved lattice mNRQCD action is derived and its effectiveness is demonstrated by nonperturbative tests involving both heavy-heavy and heavy-light mesons at several frame velocities. This mNRQCD action is then used in combination with a staggered action for the light quarks to calculate hadronic matrix elements relevant for rare B decays, including B --> K* gamma and B --> K l l. A major contribution to the uncertainty of the results also comes from statistical errors. The effectiveness of random-wall sources to reduce these errors is studied. As another application of a nonrelativistic heavy quark action, the spectrum of bottomonium is calculated and masses of several bottom baryons are predicted. In these computations, the light quarks are implemented with a domain wall action.I thank St John's College Cambridge, the Cambridge European Trust and the Engineering and Physical Sciences Research Council for financial support. This work has made use of high performance computing resources provided by the Fermilab Lattice Gauge Theory Computational Facility (http://www.usqcd.org/fnal), the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk), the National Energy Research Scientific Computing Center (http://www.nersc.gov/), the National Center for Supercomputing Applications (http://www.ncsa.illinois.edu/) and Teragrid (http://www.teragrid.org/)