Estimated Branching Ratios Research Articles

Lambda _brightarrow p transition form factors in perturbative QCD

We reanalyze the Lambda _brightarrow p transition form factors in the perturbative QCD (PQCD) approach by including higher-twist light-cone distribution amplitudes (LCDAs) of a Lambda _b baryon and a proton. The previous PQCD evaluation performed decades ago with only the leading-twist Lambda _b baryon and proton LCDAs gave the form factors, which are two orders of magnitude smaller than indicated by experimental data. We find that the twist-4 Lambda _b baryon LCDAs and the twist-4 and -5 proton LCDAs contribute dominantly, and the enhanced form factors become consistent with those from lattice QCD and other nonperturbative methods. The estimated branching ratios of the semileptonic decays Lambda _brightarrow pell {bar{nu }}_ell and the hadronic decay Lambda _brightarrow ppi are also close to the data. It implies that the b quark mass is not really heavy enough, and higher-power contributions play a crucial role, similar to the observation made in analyses of B meson transition form factors. With the formalism established in this work, we are ready to study various exclusive heavy baryon decays systematically in the PQCD approach.

Scale-, time- and asset-dependence of Hawkes process estimates on high frequency price changes

The statistical estimate of the branching ratio η of the Hawkes model, when fitted to windows of mid-price changes, has been reported to approach criticality () as the fitting window becomes large. In this study – using price changes from the EUR/USD currency pair traded on the Electronic Broking Services (EBS) interbank trading platform and the S&P 500 E-mini futures contract traded at the Chicago Mercantile Exchange (CME) – it is shown that the estimated branching ratio depends little upon window size and is usually far from criticality. This is done by controlling for exogenous non-stationarities/heterogeneities at inter- and intraday scales, accomplished by using information criteria to select the degree of flexibility of the Hawkes immigration intensity, either piecewise constant or adaptive logspline, estimated using an expectation maximization (EM) algorithm. The (positive) bias incurred by keeping the immigration intensity constant is small for time scales up to two hours, but can become as high as 0.3 for windows spanning days. This emphasizes the importance of choosing an appropriate model for the immigration intensity in the application of Hawkes processes to financial data and elsewhere. The branching ratio is also found to have an intraday seasonality, where it appears to be higher during times where market activity is dominated by supposedly reflexive automated decisions and a lack of fundamental news and trading. The insights into the microstructure of the two considered markets derived from our Hawkes process fits suggest that equity futures exhibit more complex non-stationary features, are more endogenous, persistent and traded at higher speed than spot foreign exchange. We complement our point process study with EM-estimates of integer-valued autoregressive (INAR) time series models at even longer scales of months. Transferring our methodologies to the aggregate bin-count setting confirms that, even at these very long scales, criticality can be rejected.

Judd-Ofelt itemization and influence of energy transfer on Sm3+ ions activated B2O3–ZnF2–SrO–SiO2 glasses for orange-red emitting devices

Augmenting the photoluminescence (PL) properties of Samarium (Sm3+) doped Zinc Strontium fluoro-borosilicate glass (ZSFBSi glass) by varying the Sm3+ ions concentration unlocks new prospects for their application as luminescent devices. This paper presents absorption, photoluminescence (PL), energy transfer and color chromaticity parameterization of ZSFBSi glass doped with Sm3+ ions concentrations. The Judd-Ofelt (J-O) theory in correlation with absorption as well as PL spectra leads to the estimation of radiative parameters of the excited luminescent states of Sm3+ ions needed to understand the luminescent potentiality of the as-prepared glasses. The absorption spectral data reveals the nature of bonding between Sm3+ ions and oxygen ligands in the as-quenched glasses as ionic and the result is consistent with the J-O analysis. The PL spectra of as-quenched glasses exhibit greenish-yellow, orange-red, light red and red color ascribed to 4G5/2 → 6H5/2, 6H7/2, 6H9/2, 6H11/2 emission bands at 563, 599, 646 and 706 nm, respectively. The PL intensity enhances with an escalation in Sm3+ ions content until 1.0 mol% and reduces thereafter, owing to a proficient energy transfer (ET) process. The Dexter theory and Inokuti-Hirayama (I–H) model identified the foremost ET process associated with the as-quenched glasses as dipole-dipole in nature. The CIE color coordinates (x, y) and Correlated Color Temperature (CCT) were calculated to cognize the effectiveness of as-quenched glasses in radiative cool white emission. The estimated branching ratios, emission cross-sections, gain bandwidth, quantum efficiency, optical gain, color coordinates and CCT finally reveals that the as-quenched glasses can be used in luminescent devices and amide all, 1.0 mol% Sm2O3 in ZSFBSi glass is highly appropriate for white LEDs as well as orange-red luminescent devices.

Scale-, time- and asset-dependence of Hawkes process estimates on high frequency price changes

The statistical estimate of the branching ratio η of the Hawkes model, when fitted to windows of mid-price changes, has been reported to approach criticality (η = 1) as the fitting window becomes large. In this study -- using price changes from the EUR/USD currency pair traded on the Electronic Broking Services (EBS) interbank trading platform and the S&P 500 E-mini futures contract traded at the Chicago Mercantile Exchange (CME) -- it is shown that the estimated branching ratio depends little upon window size and is usually far from criticality. This is done by controlling for exogenous non-stationarities/heterogeneities at inter- and intraday scales, accomplished by using information criteria to select the degree of flexibility of the Hawkes immigration intensity, either piecewise constant or adaptive logspline, estimated using an expectation maximization (EM) algorithm. The bias incurred by keeping the immigration intensity constant is small for time scales up to two hours, but can become as high as 0.3 for windows spanning days. This emphasizes the importance of choosing an appropriate model for the immigration intensity in the application of Hawkes processes to financial data and elsewhere. The branching ratio is also found to have an intraday seasonality, where it appears to be higher during times where market activity is dominated by supposedly reflexive automated decisions and a lack of fundamental news and trading. The insights into the microstructure of the two considered markets derived from our Hawkes process fits suggest that equity futures exhibit more complex non-stationary features, are more endogenous, persistent and traded at higher speed than spot foreign exchange. We complement our point process study with EM-estimates of integer-valued autoregressive (INAR) time series models at even longer scales of months. Transferring our methodologies to the aggregate bin-count setting confirms that even at these very long scales, criticality can be rejected.

Branching ratios for de-excitation processes of daughter nuclei following invisible dinucleon decays in 16O

Various theories beyond the standard model of particle physics predict the existence of baryon number violating processes resulting in nucleon decay. When occurring within an atomic nucleus, such a decay will be followed by secondary decays of the daughter nucleus unless its ground state is directly populated. In this paper, we estimate branching ratios for processes associated with dinucleon decays of the 16O nucleus. To this end, we use a simple shell model for the ground state of 16O. For decays from the configuration, which result in highly excited states in the daughter nucleus, we employ a statistical model with the Hauser–Feshbach theory. Our analysis indicates that the branching ratio for gamma-ray emission in the energy range between 5 and 9 MeV, which is relevant to low-threshold water Cherenkov experiments such as SNO+, is 4.53%, 35.7%, and 20.2% for the nn, pp, and pn decays in 16O, respectively. In particular, emission of 6.09 and 7.01 MeV gamma-rays from 14C, and 6.45 and 7.03 MeV gamma-rays from 14N, have branching ratios of as large as 10.9%, 20.1%, 7.73% and 8.90%, respectively.

Dynamics of the C(3P) + Ethylene Reaction: A Trajectory Surface Hopping Study.

The direct dynamics trajectory surface hopping (DDTSH) method has been employed to study the reaction of C(3P) with ethylene (C2H4). Our trajectory simulations show that at a reagent collision energy of 7.36 kcal/mol, there are two possible product channels: propargyl (H2CCCH) + H and carbene (CH2) + acetylene (HCCH). Estimated branching ratios based on trajectory propagations indicate that propargyl radical formation is the dominant channel contributing (94.1 ± 5.2) % of the overall products formation with (5.9 ± 1.7)% contribution from the minor CH2 + HCCH channel. These findings are consistent with earlier experimental observations and theoretical predictions that propargyl (H2CCCH) formation is the dominant channel for the C(3P) + C2H4 collision reaction. Our trajectory simulations, however, unravel five distinctly different dynamical pathways, unlike earlier experimental and theoretical predictions of only two pathways proposed for the formation of propargyl radical, and three different dynamics are followed for the CH2 + HCCH channel (this channel was not detected experimentally). The computed translational energy distribution for the propargyl + H channel is narrower and showed peak maximum at a lower energy compared to the experimental one. While the center of mass product angular distribution based on our trajectory propagation is nearly isotropic in nature indicating formation of long-lived intermediate complexes, the experimental one was reported to be backward-forward distributed with more intensity in the forward direction indicating the formation of an osculating complex. Our trajectory surface hopping calculations confirm that the effect of intersystem crossing (ISC) is not important for the title reaction presumably because of weak spin-orbit coupling values (<10 cm-1) for the (C + C2H4) system. No trace of cyclic products formation was obtained from our trajectory simulations, which however was predicted to be a minor (2%) product channel, experimentally.

Systematic investigation of cluster radioactivity for uranium isotopes

The most probable cluster decays that can be observed for 217–238U isotopes are investigated. We identified the more-probable decays that commonly manifest themselves via cold valleys in the driving potentials with respect to the mass number and the atomic number, individually. The calculations are performed using the Skyrme-SLy4 nucleon–nucleon interaction, within the frame work of the performed cluster model. Among the indicated favored decays that involve emitted light clusters heavier than α-particle, twenty six decay modes display calculated half-life less than 1022 years, with branching ratio larger than 10−14%. The estimated branching ratio for the α-decay of 237U, that did not observed yet, is B=2.1×10−10% (Tα=8.7×109 years). The indicated most probable decays that did not observed yet include the 22Ne decay of 232U, 25Ne and 32Si decays of 233U, 24Ne and 29Mg decays of 235U, and the 34Si and 30Mg decay modes of 238U, with 10−14<B(%)<10−7.

White light emitting lanthanum aluminate nanophosphor: Near ultra violet excited photoluminescence and photometric characteristics

LaAlO3:Dy3+ (1–11mol%) nanophosphors (NPs) were synthesized using solution combustion route and the final product was well characterized. The bandgap energy (Eg) was estimated using diffuse reflection data and the value was found to be in the range 5.70 – 5.90eV. Upon ~ 353nm [6H15/2 → 6P5/2] excitation, a characteristic emissions peaks of Dy3+ ions were recorded at ~ 480, 576 and 673nm and ascribed to transitions from 4F9/2 to 6H15/2,6H13/2 and 6H11/2 respectively. Judd–Ofelt parameters (Ω2, Ω4 and Ω6), transition probabilities (AT), quantum efficiency (η), luminescence lifetime (τrad), branching ratio (β), color chromaticity coordinates (CIE) and correlated color temperature (CCT) values were estimated from the emission spectra and discussed in detail. The estimated branching ratio was found to be ∼75%, as a result the phosphor may be potentially useful for display device applications. Further, the optimized LaAlO3:Dy3+ (5mol%) nanophosphor can be effectively used in the white light emitting diodes (WLEDs) under NUV excitation.

A benign approach for tailoring the photometric properties and Judd-Ofelt analysis of LaAlO3:Sm3+ nanophosphors for thermal sensor and WLED applications

Sm3+ doped (1–9mol%) Lanthanum aluminate (LaAlO3) nanophosphor was prepared by solution combustion synthesis and characterized by photoluminescence (PL), powder X-ray diffraction (PXRD), UV–vis (UV-vis), scanning and transmission electron microscopy (SEM and TEM). PL excitation and emission spectra, quantum efficiency, luminescence life time were studied to investigate the luminescence properties of LaAlO3:Sm3+ nanophosphor, effectively excited by near UV wavelength 406nm. The combination of different coloured emissions in visible region presents a desired white light which leads to the WLED application. The chromaticity coordinates of the optimized concentration of Sm3+ was estimated to be (0.3684, 0.4066) and the corresponding correlated color temperature (CCT) was found to be ∼4485K which favors in warm white light emissive display applications. The luminescence quantum efficiency was calculated from the emission spectra using Judd–Ofelt (J-O) theory. From the analysis the estimated branching ratio (∼56%) was greater than 50%, as a result the phosphor was highly suitable for display devices. The present phosphor was highly useful as thermal sensor in the temperature interval between 100 to 400°C as estimated from decay time measurements.

Search for the B s 0 → e + e − and B d 0 → e + e − Decays in Flavor-Changing Z′ Model

The precise prediction of the branching ratios of the very rare decays B 0 → e + e − and B 0 → e + e − is an important ingredient for high energy research beyond standard model (SM). Recently, the CDF collaboration has reported upper limits for the branching ratios B ( B 0 → e + e − ) < 2.8 × 10− 7 and B ( B 0 → e + e − ) < 8.3 × 10− 8 at 90 % confidence level. These branching ratios are approximately seven orders of magnitude larger than the SM predictions, providing in this way a direction in which the SM could be extended. In this paper, the B 0 → e + e − and B 0 → e + e − rare decays in flavor-changing Z′ model are studied. Our estimated branching ratios are enhanced from their SM values and provide signals for new physics.

X-ray absorption spectroscopy systematics at the tungsten L-edge.

A series of mononuclear six-coordinate tungsten compounds spanning formal oxidation states from 0 to +VI, largely in a ligand environment of inert chloride and/or phosphine, was interrogated by tungsten L-edge X-ray absorption spectroscopy. The L-edge spectra of this compound set, comprised of [W0(PMe3)6], [WIICl2(PMePh2)4], [WIIICl2(dppe)2][PF6] (dppe = 1,2-bis(diphenylphosphino)ethane), [WIVCl4(PMePh2)2], [WV(NPh)Cl3(PMe3)2], and [WVICl6], correlate with formal oxidation state and have usefulness as references for the interpretation of the L-edge spectra of tungsten compounds with redox-active ligands and ambiguous electronic structure descriptions. The utility of these spectra arises from the combined correlation of the estimated branching ratio of the L3,2-edges and the L1 rising-edge energy with metal Zeff, thereby permitting an assessment of effective metal oxidation state. An application of these reference spectra is illustrated by their use as backdrop for the L-edge X-ray absorption spectra of [WIV(mdt)2(CO)2] and [WIV(mdt)2(CN)2]2– (mdt2– = 1,2-dimethylethene-1,2-dithiolate), which shows that both compounds are effectively WIV species even though the mdt ligands exist at different redox levels in the two compounds. Use of metal L-edge XAS to assess a compound of uncertain formulation requires: (1) Placement of that data within the context of spectra offered by unambiguous calibrant compounds, preferably with the same coordination number and similar metal ligand distances. Such spectra assist in defining upper and/or lower limits for metal Zeff in the species of interest. (2) Evaluation of that data in conjunction with information from other physical methods, especially ligand K-edge XAS. (3) Increased care in interpretation if strong π-acceptor ligands, particularly CO, or π-donor ligands are present. The electron-withdrawing/donating nature of these ligand types, combined with relatively short metal–ligand distances, exaggerate the difference between formal oxidation state and metal Zeff or, as in the case of [WIV(mdt)2(CO)2], exert the subtle effect of modulating the redox level of other ligands in the coordination sphere.

Study of B s 0 → µ+µ− and B d 0 → µ+µ− decays in flavor-changing Z′ models

Recently, the first evidence for the decay Bs0 → μ+μ− has been announced by the LHCb Collaboration and the measured branching ratio B(s0 → μ+) = (3.2−1.2+1.5) × 10−9 is in good agreement with the standard model (SM) expectation. It has also reported an upper limit for B(Bd0 → μ+μ−) < 9.4 × 10−10 at 95% confidence level. In this paper, we study the Bs0 → μ+μ− and Bd0 → μ+μ− rare decays in flavor-changing Z′ model. Our estimated branching ratios are enhanced from their SM values and provide signals for new physics.

Bound Beta-decay of the Free Neutron: BoB

Abstract For many years neutron decay has been investigated as a possible pathway to the exploration of new physics. One such example is the bound beta-decay (BoB) of the neutron into a hydrogen atom and an anti-neutrino. This two-body decay mode offers a very elegant method to study neutrino helicities, just as the Goldhaber experiment has done. However, this rare decay has not yet been observed so far owing to the challenges of measuring a decay involving only electrically neutral particles with an estimated branching ratio of only 10-6 of the three-body decay mode. Specifically an intense source of thermal neutrons would be required for such an experiment, such as the FRMII in Garching, the ILL in Grenoble or the ESS in Lund. This paper provides a summary of the novel experimental scheme that we propose to observe the BoB neutron decay, addressing all necessary problems in a very coherent way.

A VUV photoionization study of the multichannel reaction of phenyl radicals with 1,3-butadiene under combustion relevant conditions

We studied the reaction of phenyl radicals (C(6)H(5)) with 1,3-butadiene (H(2)CCHCHCH(2)) exploiting a high temperature chemical reactor under combustion-like conditions (300 Torr, 873 K). The reaction products were probed in a supersonic beam by utilizing VUV radiation from the Advanced Light Source and by recording the experimental PIE curves at mass-to-charge ratios of m/z = 130 (C(10)H(10)(+)), 116 (C(9)H(8)(+)), and 104 (C(8)H(8)(+)). Our data suggest that the atomic hydrogen (H), methyl (CH(3)), and vinyl (C(2)H(3)) losses are open with estimated branching ratios of about 86 ± 4%, 8 ± 2%, and 6 ± 2%, respectively. The isomer distributions were probed further by fitting the experimentally recorded PIE curves with a linear combination of the PIE curves of individual C(10)H(10), C(9)H(8), and C(8)H(8) isomers. These fits indicate the formation of three C(10)H(10) isomers (trans-1,3-butadienylbenzene, 1,4-dihydronaphthalene, 1-methylindene), three C(9)H(8) isomers (indene, phenylallene, 1-phenyl-1-methylacetylene), and a C(8)H(8) isomer (styrene). A comparison with results from recent crossed molecular beam studies of the 1,3-butadiene-phenyl radical reaction and electronic structure calculations suggests that trans-1,3-butadienylbenzene (130 amu), 1,4-dihydronaphthalene (130 amu), and styrene (104 amu) are reaction products formed as a consequence of a bimolecular reaction between the phenyl radical and 1,3-butadiene. 1-Methylindene (130 amu), indene (116 amu), phenylallene (116 amu), and 1-phenyl-1-methylacetylene (116 amu) are synthesized upon reaction of the phenyl radical with three C(4)H(6) isomers: 1,2-butadiene (H(2)CCCH(CH(3))), 1-butyne (HCCC(2)H(5)), and 2-butyne (CH(3)CCCH(3)); these C(4)H(6) isomers can be formed from 1,3-butadiene via hydrogen atom assisted isomerization reactions or via thermal rearrangements of 1,3-butadiene involving hydrogen shifts in the high temperature chemical reactor.

B-meson semi-inclusive decay to2−+charmonium in nonrelativistic QCD andX(3872)

The semi-inclusive B-meson decay into spin-singlet D-wave $2^{-+}$ charmonium, $B\to \eta_{c2}+X$, is studied in nonrelativistic QCD (NRQCD). Both color-singlet and color-octet contributions are calculated at next-to-leading order (NLO) in the strong coupling constant $\alpha_s$. The non-perturbative long-distance matrix elements are evaluated using operator evolution equations. It is found that the color-singlet $^1D_2$ contribution is tiny, while the color-octet channels make dominant contributions. The estimated branching ratio $B(B\to \eta_{c2}+X)$ is about $0.41\,\times10^{-4}$ in the Naive Dimensional Regularization (NDR) scheme and $1.24\,\times10^{-4}$ in the t'Hooft-Veltman (HV) scheme, with renormalization scale $\mu=m_b=4.8$\,GeV. The scheme-sensitivity of these numerical results is due to cancelation between ${}^1S_0^{[8]}$ and ${}^1P_1^{[8]}$ contributions. The $\mu$-dependence curves of NLO branching ratios in both schemes are also shown, with $\mu$ varying from $\frac{m_b}{2}$ to $2m_b$ and the NRQCD factorization or renormalization scale $\mu_{\Lambda}$ taken to be $2m_c$. Comparison of the estimated branching ratio of $B\to \eta_{c2}+X$ with the observed branching ratio of $B \to X(3872)+K$ may lead to the conclusion that X(3872) is unlikely to be the $2^{-+}$ charmonium state $\eta_{c2}$.

Effect of Z′-mediated flavor-changing neutral current on B → ππ decays

We study the effect of -mediated flavor-changing neutral current on the decays. The branching ratios of these decays can be enhanced remarkably in the non-universal model. Our estimated branching ratios are enhanced significantly from their standard model (SM) value. For = 1, the branching ratios are very close to the recently observed experimental values and for higher values of branching ratios are more. Our calculated branching ratios and are also enhanced from the SM value as well as the recently observed experimental values. These enhancements of branching ratios from their SM value give the possibility of new physics.

The reactions of SO3 with HO2 radical and H2O⋯HO2 radical complex. Theoretical study on the atmospheric formation of HSO5 and H2SO4

The influence of a single water molecule on the gas-phase reactivity of the HO(2) radical has been investigated by studying the reactions of SO(3) with the HO(2) radical and with the H(2)O...HO(2) radical complex. The naked reaction leads to the formation of the HSO(5) radical, with a computed binding energy of 13.81 kcal mol(-1). The reaction with the H(2)O...HO(2) radical complex can give two different products, namely (a) HSO(5) + H(2)O, which has a binding energy that is computed to be 4.76 kcal mol(-1) more stable than the SO(3) + H(2)O...HO(2) reactants (Delta(E + ZPE) at 0K) and an estimated branching ratio of about 34% at 298K and (b) sulfuric acid and the hydroperoxyl radical, which is computed to be 10.51 kcal mol(-1) below the energy of the reactants (Delta(E + ZPE) at 0K), with an estimated branching ratio of about 66% at 298K. The fact that one of the products is H(2)SO(4) may have relevance in the chemistry of the atmosphere. Interestingly, the water molecule acts as a catalyst, [as it occurs in (a)] or as a reactant [as it occurs in (b)]. For a sake of completeness we have also calculated the anharmonic vibrational frequencies for HO(2), HSO(5), the HSO(5)...H(2)O hydrogen bonded complex, H(2)SO(4), and two H(2)SO(4)...H(2)O complexes, in order to help with the possible experimental identification of some of these species.

Product distributions from the OH radical‐induced oxidation of n‐pentane and isopentane (2‐methylbutane) in air

AbstractHydroxyl radicals, generated by photolysis of H2O2, were reacted with n‐pentane and isopentane in air in the absence of nitrogen oxides. The observed product distributions were compared with similar data derived by computer simulations, based on the known reaction mechanisms, to determine relative probabilities for hydrogen abstraction at different sites of the parent compounds and to estimate branching ratios and relative rate coefficients for cross‐combination reactions between different peroxy radicals. For n‐pentane, the distribution of the pentanols indicates probabilities for hydrogen abstraction, in percent, of q1 = 9.1 ± 0.7, q2 = 56.1 ± 1.8, and q3 = 34.8 ± 1.3, which agree with predictions based on the algorithm proposed by Atkinson. Branching ratios needed to harmonize calculated and observed product distributions are somewhat larger than, although still within the error ranges of, the values found by us previously. Comparison between experimental and calculated data confirms the isomerization and decomposition constants recently established for the three pentoxyl radical isomers. The product distribution for isopentane, which is dominated by acetone, acetaldehyde, 2‐methyl‐butan‐2‐ol, and 2‐methyl‐butan‐2‐hydroperoxide, is in harmony with the predicted oxidation mechanism. Probabilities for hydrogen abstraction from isopentane were estimated to occur to 12% at the primary, 28% at the secondary, and 60% at the tertiary sites, again in agreement with predictions based on the algorithm of Atkinson. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 677–688, 2006

B→η(′)lν decays and the flavor-singlet form factors

We study semileptonic decays B→η(′)lν, taking into account the flavor-singlet contribution (Fsinglet+) to the B→η(′) form factors, which arises from the two-gluon emission in a decaying B meson. It has been recently pointed out that, in addition to large weak annihilation effects, the unknown value of Fsinglet+ prevents accurate theoretical estimates in the analysis of B→η′K decays in QCD factorization. We present a certain method to determine Fsinglet+ with a reasonable accuracy, using B→η(′)lν and B→πlν decays. We also investigate the possible effect of Fsinglet+ on the estimated branching ratios (BRs) for B→η(′)lν and find that the BR for B→η′lν is particularly sensitive to the effect of Fsinglet+.

Vibrational spectroscopy of HOD in liquid D2O. VI. Intramolecular and intermolecular vibrational energy flow

In a previous theoretical study [J. Chem. Phys. 117, 5827 (2002)] we calculated the vibrational lifetimes of the three fundamentals of HOD in liquid D2O. In that calculation the D2O solvent was treated as rigid, not allowing for the possibility of intermolecular vibrational energy transfer as a relaxation mechanism. In this paper we use both flexible and rigid solvent models, enabling us to include the possibility of intermolecular vibrational energy transfer, and also to estimate branching ratios for vibrational and nonvibrational relaxation channels. Our theoretical value for the lifetime of the OH stretch decreases modestly from 2.7 ps (in the original calculation) to 2.3 ps, which should be compared to the experimental value of about 1 ps. The lifetime of the OD stretch decreases dramatically from 18 ps to 390 fs due to resonant energy transfer to the solvent stretch. Our lifetime value for the bend actually increases from 220 to 380 fs, not because of the vibrational energy transfer channel, but rather because we find that Fermi’s Golden Rule (used in the original calculation) breaks down for this very fast process. We have calculated all the state-to-state rate constants for the low-lying vibrational energy levels of HOD, which allows us to construct and solve the vibrational master equation. We find that after excitation of the OH stretch, population flows into the HOD bend states (and to a lesser extent the OD stretch of HOD) on the time scale of 1 ps, in agreement with recent infrared pump/Raman probe measurements of Dlott and co-workers. From our results we estimate that for each quantum of OH stretch excitation, 0.26 quanta of solvent stretch is excited by direct intermolecular energy transfer, and yet we find, surprisingly, that there is almost no direct excitation of solvent bend. On the other hand, we suggest that because of the intramolecular Fermi resonance in D2O, rapid intramolecular vibrational relaxation occurs from solvent stretch to solvent bend. This would account for the experimental observation of solvent stretch and bend excitations on the time scale of 1 ps after the OH stretch is excited.