arXiv subjects

I. Z. Rothstein

Publications and source records attributed to I. Z. Rothstein.

At least 19 recordsLinked to original sources

arXiv2001

Cosmological Solutions on Compactified AdS_5 with a Thermal Bulk

This paper is an investigation of the effects of a thermal bulk fluid in brane world models compactified on AdS_5. Our primary purpose is to study how such a fluid changes the bulk dynamics and to compare these effects with those generated by matter localized to the branes. We find an exact cosmological solution for a thermally excited massless bulk field, as well as perturbative solutions with matter on the brane and in the bulk. We then perturb around these solutions to find solutions for a massive bulk mode in the limit where the bulk mass (m_B) is small compared to the AdS curvature scale and T< m_B. We find that without a stabilizing potential there are no physical solutions for a thermal bulk fluid. We then include a stabilizing potential and calculate the shift in the radion as well as the time dependence of the weak scale as a function of the bulk mass. It is shown that, as opposed to a brane fluid, the bulk fluid contribution to the bulk dynamics is controlled by the bulk mass.

hep-th↗

arXiv2001

A Comment on the Extractions of V_{ub} from Radiative Decays

We present a model independent closed form expression for |V_{ub}|^2/|V_{tb} V_{ts}^*|^2, which includes the resummation of large endpoint logarithms as well as the interference effects from the operators $O_2$ and $O_8$. We demonstrate that the method to extract |V_{ub}| presented by the authors in hep-ph/9909404, and modified in this letter to include interference effects, is not just a refinement of the method introduced in hep-ph/9312311. We also discuss the model dependence of the latter proposal. Furthermore, we show that the resummation is not negligible and that the Landau pole does not introduce any significant uncertainties.

hep-ph↗

arXiv2000

Power counting and effective field theory for charmonium

We hypothesize that the correct power counting for charmonia is in the parameter Lambda_QCD/m_c, but is not based purely on dimensional analysis (as is HQET). This power counting leads to predictions which differ from those resulting from the usual velocity power counting rules of NRQCD. In particular, we show that while Lambda_QCD/m_c power counting preserves the empirically verified predictions of spin symmetry in decays, it also leads to new predictions which include: A hierarchy between spin singlet and triplet octet matrix elements in the J/psi system. A quenching of the net polarization in production at large transverse momentum. No end point enhancement in radiative decays. We discuss explicit tests which can differentiate between the traditional and new theories of NRQCD.

hep-ph↗

arXiv2000

Extracting |V_{ub}| from the Hadronic Mass Spectrum of Inclusive B decays

Following a strategy introduced earlier by the authors, we show that it is possible to extract |V_{ub}| from the cut hadronic mass spectrum of B decays without large systematic errors which usually arise from having to model the Fermi motion of the heavy quark. We present a closed form expression for |V_{ub}|/|V_{ts}| which is accurate up to corrections of order α_s^2, α_s ρ, (Λ/m_b)^2/ρ, where ρis the experimental cut (s_c/m_b^2) on the hadronic mass used to veto charmed decays. Modulo duality violation errors, which are intrinsic to all inclusive predictions, we estimate the theoretical error in the extraction to be at the 5% level.

hep-ph↗

arXiv2000

On the Resummed Hadronic Spectra of Inclusive B Decays

In this paper we investigate the hadronic mass spectra of inclusive B decays. Specifically, we study how an upper cut on the invariant mass spectrum, which is necessary to extract V_{ub}, results in the breakdown of the standard perturbative expansion due to the existence of large infrared logs. We first show how the decay rate factorizes at the level of the double differential distribution. Then, we present closed form expressions for the resummed cut rate for the inclusive decays B -> X_s gamma and B -> X_u e nu at next-to-leading order in the infrared logs. Using these results, we determine the range of cuts for which resummation is necessary, as well as the range for which the resummed expansion itself breaks down. We also use our results to extract the leading and next to leading infrared log contribution to the two loop differential rate. We find that for the phenomenologically interesting cut values, there is only a small region where the calculation is under control. Furthermore, the size of this region is sensitive to the parameter \barΛ. We discuss the viability of extracting V_{ub} from the hadronic mass spectrum.

hep-ph↗

arXiv1999

Extracting V_{ub} Without Recourse to Structure Functions

We present a closed form expression for |V_{ub}|^2/ |V_{tb} V_{ts}^*|^2 in terms of the endpoint photon and lepton spectra from the inclusive decays B -> X_sγand B -> X_u\ellν, respectively, which includes the resummation of the endpoint logs at next to leading order and is completely independent of the B meson structure function. The use of this expression for extracting V_{ub} would eliminate the large systematic errors usually incurred due to the modeling of the heavy quarks' Fermi motion.

hep-ph↗

arXiv1999

Bounds from Primordial Black Holes with a Near Critical Collapse Initial Mass Function

Recent numerical evidence suggests that a mass spectrum of primordial black holes (PBHs) is produced as a consequence of near critical gravitational collapse. Assuming that these holes formed from the initial density perturbations seeded by inflation, we calculate model independent upper bounds on the mass variance at the reheating temperature by requiring the mass density not exceed the critical density and the photon emission not exceed current diffuse gamma-ray measurements. We then translate these results into bounds on the spectral index n by utilizing the COBE data to normalize the mass variance at large scales, assuming a constant power law, then scaling this result to the reheating temperature. We find that our bounds on n differ substantially (δn > 0.05) from those calculated using initial mass functions derived under the assumption that the black hole mass is proportional to the horizon mass at the collapse epoch. We also find a change in the shape of the diffuse gamma-ray spectrum which results from the Hawking radiation. Finally, we study the impact of a nonzero cosmological constant and find that the bounds on n are strengthened considerably if the universe is indeed vacuum-energy dominated today.

astro-ph↗

arXiv1999

The Resummed Rate for B -> X_s gamma

In this paper we investigate the effect of the resummation of threshold logs on the rate for B -> X_s gamma. We calculate the differential rate dGamma/dE_gamma including the infinite set of terms of the form alpha_s^n log^{n+1}(1-x) and alpha_s^n log^n(1-x) in the Sudakov exponent. The resummation is potentially important since these logs turn into log(2E_{cut}/m_b), when the rate is integrated from the lower cut x=2E_{cut}/m_b to 1. The resummed rate is then convolved with models for the structure function to study whether or not the logs will be enhanced due to the fermi motion of the heavy quark. A detailed discussion of the accuracy of the calculation with and without the inclusion of the non-perturbative effects dictated by the B meson structure function is given. We also investigate the first moment with respect to (1-x), which can be used to measure \barΛand lambda_1. It is shown that there are some two loop corrections which are just as large as the alpha_s^2 beta_0 term, which are usually expected to dominate. We conclude that, for the present energy cut, the threshold logs do not form a dominant sub-series and therefore their resummation is unnecessary. Thus, the prospects for predicting the rate for B -> X_s gamma accurately, given the present energy cut, are promising.

hep-ph↗

arXiv1998

QCD analysis of inclusive B decay into charmonium

We compute the decay rates and $H$-energy distributions of $B$ mesons into the final state $H+X$, where $H$ can be any one of the $S$-wave or $P$-wave charmonia, at next-to-leading order in the strong coupling. We find that a significant fraction of the observed $J/ψ$, $ψ'$ and $χ_c$ must be produced through $c\bar{c}$ pairs in a colour octet state and should therefore be accompanied by more than one light hadron. At the same time we obtain stringent constraints on some of the long-distance parameters for colour octet production.

hep-ph↗

arXiv1997

The Phenomenology of Inclusive Heavy-to-Light Sum Rules

By calculating the O(α_s) corrections to inclusive heavy-to-light sum rules we find model independent upper and lower bounds on form factors for B to pi and B to rho. We use the bounds to rule out model predictions. Some models violate the bounds only for certain ranges of sum rule input parameters \bar{lambda} \simeq m_B-m_b and lambda_1, or for certain choices of model parameters, while others obey or violate the bounds irrespective of the inputs. We discuss the reliability and convergence of the bounds, point out their utility for extracting V_{ub}, and derive from them a new form factor scaling relation.

hep-ph↗

arXiv1997

Kinematic Enhancement of Non-Perturbative Corrections to Quarkonium Production

In this letter we address issues involved in quarkonium production near the boundaries of phase space. It is shown that higher-order non-perturbative contributions are enhanced in this kinematic region and lead to a breakdown of the non-relativistic (NRQCD) expansion. This breakdown is a consequence of sensitivity to the kinematics of soft gluon radiation and to the difference between partonic and hadronic phase space. We show how these large corrections can be resummed giving the dominant contribution to the cross section. The resummation leads to the introduction of non-perturbative, universal distribution functions. We discuss the importance of these shape functions for several observables, in particular the energy distribution of photo-produced $J/ψ$ close to the endpoint.

hep-ph↗

arXiv1997

Bounds on Long-Lived Relics from Diffuse Gamma Ray Observations

We place bounds on long-lived primordial relics using measurements of the diffuse gamma ray spectrum from EGRET and COMPTEL. Bounds are derived for both radiative and hadronic decays with stronger bounds applying for the latter decay mode. We present an exclusion plot in the relic density-lifetime plane that shows nontrivial dependence on the mass of the relic. The violations of scaling with mass are a consequence of the different possible scattering processes which lead to differing electromagnetic showering profiles. The tightest bounds for shorter lifetimes come from COMPTEL observations of the low energy part of the spectrum, while for longer lifetimes the highest observable energy at EGRET gives the tightest bounds. We discuss the implications of the bounds for dark matter candidates as well as relics that have a mass density substantially below the critical density. These bounds can be utilized to eliminate models that contain relics with lifetimes longer than $10^{-4}$ times the age of the universe.

hep-ph↗

arXiv1996

Errors in Lattice Extractions of alpha_s Due to Use of Unphysical Pion Masses

We investigate the errors due to the use of unphysical values of light quark masses in lattice extractions of $α_s$. A functional form for the pion mass dependence of the quarkonium mass splittings ($Δm$) is given as an expansion in $m_π/(4πf_π)$ and $m_πr_B$, where $r_B$ is the quarkonium Bohr radius. We find that, to lowest order,$Δm\simeq A+B m_π^2$, where the scale of $B$ is given by $f_π^2 r_B^3$. To order $m_π^4$ there are four unknown coefficients, however, utilizing multipole and operator product expansions, symmetry arguments eliminate one of the four unknowns. Using the central values for the lattice spacings which were extracted using two different, unphysical values for the pion mass, we find that the errors introduced by extrapolating to the physical regime are comparable to the errors quoted due to other sources. Extrapolation to physical values of the pion mass {\it increases} the value of $α_s(M_Z)$, bringing its value closer to the high energy extractions.

hep-ph↗

arXiv1996

The Extraction of $V_{ub}$ from Inclusive B Decays and the Resummation of End Point Logs

In this paper we discuss the theoretical difficulties in extracting $V_{ub}$ using the data from inclusive B decays. Specifically, we address the issue of the end point singularities. We perform the resummation of both the leading and next to leading end point logs and include the leading corrections to the hard scattering amplitude. We find that the resummation is a $20\%-50\%$ effect in the end point region where the resummation is valid. Furthermore, the resummed sub-leading logs dominate the resummed double logs. The consequences of this result for a model independent extraction of the mixing angle $V_{ub}$ are explored.

hep-ph↗

arXiv1996

Hadro-production of Quarkonia in Fixed Target Experiments

We analyze charmonium and bottomonium production at fixed target experiments. We find that inclusion of color octet production channels removes large discrepancies between experiment and the predictions of the color singlet model for the total production cross section. Furthermore, including octet contributions accounts for the observed direct to total $J/ψ$ production ratio. As found earlier for photo-production of quarkonia, a fit to fixed target data requires smaller color octet matrix elements than those extracted from high-$p_t$ production at the Tevatron. We argue that this difference can be explained by systematic differences in the velocity expansion for collider and fixed-target predictions. While the color octet mechanism thus appears to be an essential part of a satisfactory description of fixed target data, important discrepancies remain for the $χ_{c1}/χ_{c2}$ production ratio and $J/ψ$ ($ψ'$) polarization. These discrepancies, as well as, the differences between pion and proton induced collisions emphasize the need for including higher twist effects in addition to the color octet mechanism.

hep-ph↗

arXiv1995

$ψ'$ Polarization as a test of colour octet quarkonium production

We calculate the $α_s$ corrections to the transverse polarization fraction of $ψ^\prime$'s produced at the Tevatron. If the `$ψ^\prime$-anomaly' is explained by gluon fragmentation into a colour octet Fock component of the $ψ^\prime$, the $ψ^\prime$'s should be $100\%$ transversely polarized at leading order in $α_s$, up to spin symmetry breaking long-distance corrections. We find that the short-distance correction to the transverse polarization fraction is a few percent, so that a polarization measurement would provide a reliable test of the colour octet mechanism.

hep-ph↗

arXiv1994

Bounds on Dirac Neutrino Masses from Nucleosynthesis

We derive new bounds on the Dirac mass of the tau and muonic neutrinos. By solving the kinetic equation for the rate of energy deposition due to helicity flipping processes and imposing the constraint that the number of effective species contributing to the energy density at the time of nucleosynthesis be $Δk_ν<~0.3$, we find the bounds $m_{ν_μ} < ~150$ KeV and $m_{ν_τ} < ~190$ KeV for $T_{\rm QCD}= 200$ MeV. The constraint $Δk_ν~<0.1~$ leads to the much stronger bound $m_ν<10$ KeV for both species of neutrinos.

hep-ph↗

arXiv1994

Eikonal Wave Functions and Model Independent Exclusive B Decays

In this letter we investigate the proper normalization for the B meson eikonal valence wave function used in exclusive B decays. The normalization appropriate for a hard scattering process renormalized at the scale $μ$ is determined by calculating the short distance contribution to the purely leptonic decay.

hep-ph↗