Renormalization Group Analysis in NRQCD for Colored Scalars

The vNRQCD Lagrangian for colored heavy scalar fields in the fundamental representation of QCD and the renormalization group analysis of the corresponding operators are presented. The results are an important ingredient for renormalization group improved computations of scalar-antiscalar bound state energies and production rates at next-to-next-to-leading-logarithmic (NNLL) order.Comment: 19 pages, 8 figures; revtex4. References added; version to appear in Phys. Rev.

Perturbative corrections to the determination of Vub from the P+ spectrum in B->X_u l nu

We investigate the relation between the E_gamma spectrum in B->X_s gamma decay and the P+ spectrum in semileptonic B->X_u l nu decay (P+ is the hadronic energy minus the absolute value of the hadronic three-momentum), which provides in principle the theoretically simplest determination of Vub from any of the "shape function regions" of B->X_u l nu spectra. We calculate analytically the P+ spectrum to order alpha_s^2 beta_0, and study its relation to the B->X_s gamma photon spectrum to eliminate the leading dependence on nonperturbative effects. We compare the result of fixed order perturbation theory to the next-to-leading log renormalization group improved calculation, and argue that fixed order perturbation theory is likely to be a more appropriate expansion. Implications for the perturbative uncertainties in the determination of Vub from the P+ spectrum are discussed.Comment: reference added, to appear in PR

Charm and Bottom Masses from Sum Rules with a Convergence Test

In this talk we discuss results of a new extraction of the MS-bar charm quark mass using relativistic QCD sum rules at O(as**3) based on moments of the vector and the pseudoscalar current correlators and using the available experimental measurements from e+e- collisions and lattice results, respectively. The analysis of the perturbative uncertainties is based on different implementations of the perturbative series and on independent variations of the renormalization scales for the mass and the strong coupling following a work we carried out earlier. Accounting for the perturbative series that result from this double scale variation is crucial since some of the series can exhibit extraordinarily small scale dependence, if the two scales are set equal. The new aspect of the work reported here adresses the problem that double scale variation might also lead to an overestimate of the perturbative uncertainties. We supplement the analysis by a convergence test that allows to quantify the overall convergence of QCD perturbation theory for each moment and to discard series that are artificially spoiled by specific choices of the renormalization scales. We also apply the new method to an extraction of the MS-bar bottom quark mass using experimental moments that account for a modeling uncertainty associated to the continuum region where no experimental data is available. We obtain m_c(m_c) = 1.287 +- 0.020 GeV and m_b(m_b) = 4.167 +- 0.023 GeV.Comment: 6 pages, 2 figures. Presented at the International Workshop on the CKM Unitarity Triangle Vienna, Austria, September 8-12, 201

Variable Flavor Number Scheme for Final State Jets

We discuss a variable flavor number scheme (VFNS) for final state jets which can account for the effects of arbitrary finite quark masses in inclusive jet observables. The scheme is a generalization of the VFNS scheme for PDFs applied to setups with additional dynamical scales and relies on appropriate renormalization conditions for the matrix elements in the factorization theorem. We illustrate general properties by means of the example of deep-inelastic scattering (DIS) in the endpoint region $x\rightarrow 1$ and event shapes in the dijet limit, in particular the calculations of threshold corrections, consistency conditions and relations to mass singularities found in fixed-order massive calculations.Comment: 7 pages, 4 figures, Proceedings of the XXII. International Workshop on Deep-Inelastic Scattering and Related Subjects, 28 April - 2 May 2014, Warsaw, Polan

On the Light Massive Flavor Dependence of the Large Order Asymptotic Behavior and the Ambiguity of the Pole Mass

We provide a systematic renormalization group formalism for the mass effects in the relation of the pole mass $m_Q^{\rm pole}$ and short-distance masses such as the $\overline{\rm MS}$ mass $\overline{m}_Q$ of a heavy quark $Q$, coming from virtual loop insertions of massive quarks lighter than $Q$. The formalism reflects the constraints from heavy quark symmetry and entails a combined matching and evolution procedure that allows to disentangle and successively integrate out the corrections coming from the lighter massive quarks and the momentum regions between them and to precisely control the large order asymptotic behavior. With the formalism we systematically sum logarithms of ratios of the lighter quark masses and $m_Q$, relate the QCD corrections for different external heavy quarks to each other, predict the ${\cal O}(\alpha_s^4)$ virtual quark mass corrections in the pole-$\overline{\rm MS}$ mass relation, calculate the pole mass differences for the top, bottom and charm quarks with a precision of around $20$ MeV and analyze the decoupling of the lighter massive quark flavors at large orders. The summation of logarithms is most relevant for the top quark pole mass $m_t^{\rm pole}$, where the hierarchy to the bottom and charm quarks is large. We determine the ambiguity of the pole mass for top, bottom and charm quarks in different scenarios with massive or massless bottom and charm quarks in a way consistent with heavy quark symmetry, and we find that it is $250$ MeV. The ambiguity is larger than current projections for the precision of top quark mass measurements in the high-luminosity phase of the LHC.Comment: 45 pages + appendix, 6 figures, v2: journal versio

Bottom and Charm Mass Determinations with a Convergence Test

We present new determinations of the MS-bar charm quark mass using relativistic QCD sum rules at O(alpha_s^3) from the moments of the vector and the pseudoscalar current correlators. We use available experimental measurements from e+e- collisions and lattice simulation results, respectively. Our analysis of the theoretical uncertainties is based on different implementations of the perturbative series and on independent variations of the renormalization scales for the mass and the strong coupling. Taking into account the resulting set of series to estimate perturbative uncertainties is crucial, since some ways to treat the perturbative expansion can exhibit extraordinarily small scale dependence when the two scales are set equal. As an additional refinement, we address the issue that double scale variation could overestimate the perturbative uncertainties. We supplement the analysis with a test that quantifies the convergence rate of each perturbative series by a single number. We find that this convergence test allows to determine an overall and average convergence rate that is characteristic for the series expansions of each moment, and to discard those series for which the convergence rate is significantly worse. We obtain mc(mc) = 1.288 +- 0.020 GeV from the vector correlator. The method is also applied to the extraction of the MS-bar bottom quark mass from the vector correlator. We compute the experimental moments including a modeling uncertainty associated to the continuum region where no data is available. We obtain mb(mb) = 4.176 +- 0.023 GeV.Comment: 53 pages, 16 figures, 19 tables; v2 typos fixed, references added, modification of section 6.3, results for bottom moments and bottom mass updated, matches published versio

Approximating the radiatively corrected Higgs mass in the Minimal Supersymmetric Model

To obtain the most accurate predictions for the Higgs masses in the minimal supersymmetric model (MSSM), one should compute the full set of one-loop radiative corrections, resum the large logarithms to all orders, and add the dominant two-loop effects. A complete computation following this procedure yields a complex set of formulae which must be analyzed numerically. We discuss a very simple approximation scheme which includes the most important terms from each of the three components mentioned above. We estimate that the Higgs masses computed using our scheme lie within 2 GeV of their theoretically predicted values over a very large fraction of MSSM parameter space.Comment: 31 pages, 10 embedded figures, latex with psfig.sty the complete postscript file of this preprint, including figures, is available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ttp95-09/ttp95-09.ps or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints

B decays in the upsilon expansion

Theoretical predictions for B decay rates are rewritten in terms of the Upsilon(1S) meson mass instead of the b quark mass, using a modified perturbation expansion. The theoretical consistency of this expansion is shown both at low and high orders. Our method improves the behavior of the perturbation series for semileptonic and nonleptonic inclusive decay modes, as well as for exclusive decay form factors. The results are applied to the determination of the semileptonic B branching ratio, charm counting, the ratio of B -> X tau nu and B -> X e nu decay rates, and form factor ratios in B -> D* e nu decay. We also comment on why it is not possible to separate perturbative and nonperturbative effects in QCD.Comment: 21 page