Constraining Form Factors with the Method of Unitarity Bounds

The availability of a reliable bound on an integral involving the square of the modulus of a form factor on the unitarity cut allows one to constrain the form factor at points inside the analyticity domain and its shape parameters, and also to isolate domains on the real axis and in the complex energy plane where zeros are excluded. In this lecture note, we review the mathematical techniques of this formalism in its standard form, known as the method of unitarity bounds, and recent developments which allow us to include information on the phase and modulus along a part of the unitarity cut. We also provide a brief summary of some results that we have obtained in the recent past, which demonstrate the usefulness of the method for precision predictions on the form factors.Comment: 12 pages, 2 figures; Lecture given at the DAE-BRNS Workshop on Hadron Physics, Bhabha Atomic Research Centre, Mumbai, India, October 31-November 4, 2011, submitted to Proceeding

Semileptonic charm decays D \to \pi l \nu_{\l} and D→KlνlD \to K l \nu_l from QCD Light-Cone Sum Rules

We present a new calculation of the $D\to\pi$ and $D \to K$ form factors from QCD light-cone sum rules. The $\overline{MS}$ scheme for the $c$-quark mass is used and the input parameters are updated. The results are $f^+_{D\pi}(0)= 0.67^{+0.10}_{-0.07}$, $f^+_{DK}(0)=0.75^{+0.11}_{-0.08}$ and $f^+_{D\pi}(0)/f^+_{DK}(0)=0.88 \pm 0.05$. Combining the calculated form factors with the latest CLEO data, we obtain $|V_{cd}|=0.225\pm 0.005 \pm 0.003 ^{+0.016}_{-0.012}$ and $|V_{cd}|/|V_{cs}|= 0.236\pm 0.006\pm 0.003\pm 0.013$ where the first and second errors are of experimental origin and the third error is due to the estimated uncertainties of our calculation. We also evaluate the form factors $f^-_{D\pi}$ and $f^-_{DK}$ and predict the slope parameters at $q^2=0$. Furthermore, calculating the form factors from the sum rules at $q^2<0$, we fit them to various parameterizations. After analytic continuation, the shape of the $D\to \pi,K$ form factors in the whole semileptonic region is reproduced, in a good agreement with experiment.Comment: 34 pages, 5 figure

Revegetation of Fluvial Mine Tailing Deposits: The Use of Five Riparian Shrub Species

Fluvial deposition of mine tailings has caused extensive damage to riparian ecosystems throughout the West. Willows are often used for revegetation of fluvial mine tailing deposits but some species accumulate toxic concentrations of metals in leaves and stems. A greenhouse experiment was conducted to determine the value of thinleaf alder [Alnus incana (L.) Moench spp. tinuifolia (Nutt.) Breitung], water birch (Betula occidentalis Hook.), red osier dogwood (Cornus sericea L. spp. sericea), and shrubby cinquefoil [Dasiphora fruticosa (L.) Rybd.] compared to Geyer willow (Salix geyeriana Andersson) for revegetation of fluvial tailing deposits along the Upper Arkansas River. Bare root shrubs were grown in tailings amended with lime and composted biosolids. Tailings were collected from three acidic and metal contaminated deposits along the Arkansas River south of Leadville, Colorado. All shrubs survived the two month experiment. Averaged across source deposits, total biomass during the experiment increased for alder, birch, dogwood, cinquefoil, and willow by 831, 689, 579, 525, and 683%, respectively. All species concentrated Pb and Zn belowground. Dogwood assimilated little Zn (44.0 mg kg-1) into its leaves and stems, but showed signs of nutrient deficiency which could have been induced by metal stress. Alder and cinquefoil partitioned Pb aboveground, 30.3 and 26.1 mg kg-1, respectively, which is unusual, but concentrations were below toxicity thresholds for humans and animals. All species evaluated did not exhibit greater growth when compared to Geyer willow, but the other four riparian species had metal partitioning characteristics valuable for managers planning for in situ restoration of mine tailing deposits

Spectral density in resonance region and analytic confinement

We study the role of finite widths of resonances in a nonlocal version of the Wick-Cutkosky model. The spectrum of bound states is known analytically in this model and forms linear Regge tragectories. We compute the widths of resonances, calculate the spectral density in an extension of the Breit-Wigner {\it ansatz} and discuss a mechanism for the damping of unphysical exponential growth of observables at high energy due to finite widths of resonances.Comment: 13 pages, RevTeX, 6 figures. Revised version with typographical corrections and additional comments in conclusion

Relativistic Restrictions on the Distinguishability of Orthogonal Quantum States

We analyze the restrictions on the distinguishability of quantum states imposed by special relativity. An explicit expression relating the error probability for distinguishing between two orthogonal single-photon states with the time $T$ elapsed from the start of the measurement procedure until the measurement result is obtained by the observer.Comment: 9 pages, 1 figure (misprints in formulas corrected

Model-Independent Semileptonic Form Factors Using Dispersion Relations

We present a method for parametrizing heavy meson semileptonic form factors using dispersion relations, and from it produce a two-parameter description of the B -> B elastic form factor. We use heavy quark symmetry to relate this function to B -> D* l nu form factors, and extract |V_cb|=0.0355^{+0.0029}_{-0.0025} from experimental data with a least squares fit. Our method eliminates model-dependent uncertainties inherent in choosing a parametrization for the extrapolation of the differential decay rate to threshold.Comment: uses lanlmac(harvmac) and epsf, 12 pages, 1 eps figure included (Talk by BG at the 6-th International Symposium on Heavy Flavour Physics, Pisa, Italy, 6--10 June, 1995

Unitarity Constraints on the B and B^* Form Factors from QCD Analyticity and Heavy Meson Spin Symmetry

A method of deriving bounds on the weak meson form factors, based on perturbative QCD, analyticity and unitarity, is generalized in order to fully exploit heavy quark spin symmetry in the ground state $(L=0)$ doublet of pseudoscalar $(B)$ and vector $(B^*)$ mesons. All the relevant form factors of these mesons are taken into account in the unitarity sum. They are treated as independent functions along the timelike axis, being related by spin symmetry only near the zero recoil point. Heavy quark vacuum polarisation up to three loops in perturbative QCD and the experimental cross sections $\sigma(e^+e^- \rightarrow \Upsilon)$ are used as input. We obtain bounds on the charge radius of the elastic form factor of the $B$ meson, which considerably improve previous results derived in the same framework.Comment: 13 pages LaTex, 1 figure as a separate ps fil

Towards a Generalized Distribution Formalism for Gauge Quantum Fields

We prove that the distributions defined on the Gelfand-Shilov spaces, and hence more singular than hyperfunctions, retain the angular localizability property. Specifically, they have uniquely determined support cones. This result enables one to develop a distribution-theoretic techniques suitable for the consistent treatment of quantum fields with arbitrarily singular ultraviolet and infrared behavior. The proofs covering the most general case are based on the use of the theory of plurisubharmonic functions and Hormander's estimates.Comment: 12 p., Department of Theoretical Physics, P.N.Lebedev Physical Institute, Leninsky prosp. 53, Moscow 117924, Russi

New Constraints on Dispersive Form Factor Parameterizations from the Timelike Region

We generalize a recent model-independent form factor parameterization derived from rigorous dispersion relations to include constraints from data in the timelike region. These constraints dictate the convergence properties of the parameterization and appear as sum rules on the parameters. We further develop a new parameterization that takes into account finiteness and asymptotic conditions on the form factor, and use it to fit to the elastic \pi electromagnetic form factor. We find that the existing world sample of timelike data gives only loose bounds on the form factor in the spacelike region, but explain how the acquisition of additional timelike data or fits to other form factors are expected to give much better results. The same parameterization is seen to fit spacelike data extremely well.Comment: 24 pages, latex (revtex), 3 eps figure

Dispersive Bounds on The Shape Of Lambda_b to Lambda_c l {\bar \nu_l} Formfactors

We derive a theoretically allowed domain for the charge radius $\rho$ and curvature $c$ of the Isgur-Wise function describing the decay $\Lambda_b \to \Lambda_c l {\bar \nu_l}$. Our method uses crossing symmetry, dispersion relations and analyticity in the context of the Heavy Quark Effective Theory but is independent of the specifics of any given model. The experimentally determined values of the $\Upsilon$ masses have been used as input information. The results are of interest for testing different models employed to calculate the heavy baryon formfactors which are used for the extraction of $| V_{cb} |$ from the experimental data.Comment: 18 pages, 1 figure included via psfi