The photon polarization in B -> X gamma in the standard model

The standard model prediction for the $B\to X_{s,d}\gamma$ decay amplitude with a right-handed photon is believed to be tiny, suppressed by $m_{s,d}/m_b$, compared to the amplitude with a left-handed photon. We show that this suppression is fictitious: in inclusive decays, the ratio of these two amplitudes is only suppressed by $g_s/(4\pi)$, and in exclusive decays by $\Lambda_{QCD}/m_b$. The suppression is not stronger in $B\to X_d\gamma$ decays than it is in $B\to X_s\gamma$. We estimate that the time dependent CP asymmetries in $B\to K^*\gamma$, $\rho\gamma$, $K_S\pi^0\gamma$, and $\pi^+\pi^-\gamma$ are of order 0.1 and that they have significant uncertainties.Comment: Clarifications in the exclusive section, references adde

Rational Asset Price Bubbles

The solution to a linear model in which supply and/or demand depends on rational expectations of future prices can involve three parts, which we denote as the fundamental component, the deterministic bubble component, and the stochastic bubble component. This paper explores the properties of these solution components, emphasizing the distinction between deterministic bubbles and stochastic bubbles, for a model of inflation and for a model of the evolution of price and quantity in the market fora storable commodity, such as gold. The analysis focuses on stochastic bubbles as a possibility peculiarly associated with models that involve rational expectations. In both the inflation model and the gold model, although the analysis points to no compelling reason to rule out rational stochastic bubbles apriori, conventional behavioral assumptions imply that anyrational bubbles that arise, whether deterministic or stochastic,are explosive. The paper discusses problems of implementing econometric tests for the existence of rational bubbles, and, as an alternative to these tests, suggests "diagnostic checking" of the stationarity properties of time series. Although these diagnostic checks do not constitute definitive hypothesis testing, we conjecture they would provide strong evidence against rational bubbles outside the context of hyperinflation.

Rational Inflationary Bubbles

This paper analyzes the possible inception of rational inflationary bubbles under the assumption that the empirically relevant environment precludes the existence of rational deflationary bubbles. The analysis shows that if a rational inflationary bubble exists, then it must have started on the date of initial issuance of the fiat money. Moreover, the existence of a rational inflationary bubble would imply that, prior to the initial issuance of the fiat money, agents who anticipated its introduction expected a rational inflationary bubble to occur. The analysis also shows that once a rational inflationary bubble bursts it cannot restart. The analysis, however, does not preclude the existence of a rational inflationary bubble that shrinks periodically, but never bursts. The limitations on the inception and existence of rational inflationary bubbles also apply to rational exchange-rate bubbles.

Rational Bubbles in Stock Prices?

This paper reports empirical tests for the existence of rational bubbles in stock prices. The analysis focuses on a familiar model that defines market fundamentals to be the expected present value of dividends, discounted at a constantrate, and defines a rational bubble to be a self-confirming divergence of stock prices from market fundamentals in response to extraneous variables. The tests are based on the theoretical result that, if rational bubbles exist, time series obtained by differencing real stock prices do not have stationary means. Analysis of the data in both the time domain and the frequency domain suggests that the time series of aggregate real stock prices is nonstationary in levels but stationary in first differences. Applications of the time domain tests to simulated nonstationary time series that would be implied by rational bubbles indicates that the tests have power to detect relevant nonstationarity when it is present. Furthermore, application of the time-domain and frequency-domain tests to the time series of aggregate real dividends also indicates nonstationarity in levels but stationarity in first differences -- suggesting that market fundamentals can account for the stationarity properties of real stock prices. These findings imply that rational bubbles do not exist in stock prices. Accordingly,any evidence that stock price fluctuations do not accord with market fundamentals (asspecified above) is attributable to misspecification of market fundamentals.

The Impossibility of Rational Bubbles

A rational bubble would involve a self-confirming belief that an asset price depends on information that includes variables or parameters that are not part of market fundamentals. The existing literature shows that, if market fundamentals are economically interesting, i.e., forward looking, any rational bubbles would be either explosive or implosive. Further arguments based on the existing literature show that utility maximizing behavior implies finite bounds on asset prices and, accordingly, precludes both explosive and implosive rational price expectations, except for the possible case of an implosion in the value of fiat money. These arguments rule out both positive and negative rational bubbles, except for the poissibility of rational inflationary bubbles.This paper extends the theoretical analysis of rational bubbles in two ways. First, it shows that, although a supply response of the current asset stock to the current asset price dampens fluctuations in market fundamentals, such a response would cause a rational bubble to explode or to implode even faster.Thus, the explosiveness or implosiveness of rational bubbles isnot an artifact of assuming that the asset stock evolves autonomously. Second, and more importantly, the present analysis considers the inception of rational bubbles and shows that, for anegative rational bubble -- such as a rational inflationary bubble -- to get started, a positive rational bubble also would have to have positive probability. Specifically, the expected initial absolute value of a potential negative rational bubble cannot exceed the expected, initial value of a potential positive rational bubble.This result dramatically expands the theoretical basis for precluding rational bubbles. Specifically, because utility maximization directly rules out rational deflationary bubbles, the inception of a rational inflationary bubbles is also precluded.

Implications of the non-universal Z boson in FCNC mediated rare decays

We analyze the effect of the non-universal $Z$ boson in the rare decays $B_s \to l^+ l^-$, $B_s \to l^+ l^- \gamma$ and $Z \to b \bar s$ decays. These decays involve the FCNC mediated $b \to s$ transitions, and are found to be very small in the standard model. The smallness of these decays in the standard model makes them sensitive probe for new physics. We find an enhancement of at least an order in these branching ratios because of the non-universal $Zbs$ coupling.Comment: 15 pages, 4 figures, minor changes in the text, references added, to appear in PR

Rational Bubbles in the Price of Gold

This paper describes a theoretical and empirical study of the possibility of rational bubbles in the relative price ofgold. The critical implication of the theoretical analysis is that, if rational bubbles exist, the time series of the relative price of gold, as well as any time series obtained by differencing a finite number of times, is nonstationary. The empirical evidence relating to this nonstationarity property involves diagnostic checks for stationarity carried out in both the time domain and the frequency domain. This evidence strongly suggests that the process generating the first difference of the log of the relative price of gold is stationary, a finding that is inconsistent with the existence of rational bubbles. More broadly, the empirical analysis finds a close correspondence between the time series properties of the relative price of gold and the time series properties of real interest rates,which the theory relates to the time series properties of the fundamental component of the relative price of gold. In sum, the evidence is consistent with the combined conclusion that the relative price of gold corresponds to market fundamentals, that the process generating first differences of market fundamentals is stationary, and that actual price movements do not involve rational bubbles.

On the Inception of Rational Bubbles in Stock Prices

This paper analyzes the theoretical possibility of rational bubbles in stock prices in a model in which stockholders have infinite planning horizons and in which free disposal of equity rules out the existence of negative rational bubbles. The analysis shows that in this framework if a positive rational bubble exists, then it started on the first date of trading of the stock. Thus, the existence of a rational bubble at any date would imply that the stock has been overvalued relative to market fundamentals since the first date of trading and that prior to the first date of trading potential stockholders who anticipated the initial pricing of the stock expected that the stock would be overvalued relative to market fundamentals. The analysis also shows that any rational bubble will eventually burst and will not restart. Thus, even if a positive rational bubble exists, stockholders know that after a random, but almost surely finite, date the stock price will conform to market fundamentals forever.

Neutrino masses and R-parity violation

We review different contributions to the neutrino masses in the context of R-parity violating supersymmetry in a basis independent manner. We comment on the generic spectrum expected in such a scenario comparing different contributions.Comment: Invited brief review for Mod. Phys. Lett. A, 15 pages, uses axodraw.st