Searcharxiv⌕ Search

arXiv subjects

Michael Luke

Publications and source records attributed to Michael Luke.

At least 37 records · Page 2Linked to original sources
arXiv2001

Comment on studying the corrections to factorization in B -> D(*) X

We propose studying the mechanism of factorization in exclusive decays of the form B->D(*)X by examining the differential decay rate as a function of the invariant mass of the light hadronic state X. If factorization works primarily due to the large N_c limit then its accuracy is not expected to decrease as the X invariant mass increases. However, if factorization is mostly a consequence of perturbative QCD then the corrections should grow with the X invariant mass. Combining data for hadronic tau decays and semileptonic B decays allows tests of factorization to be made for a variety of final states. We discuss the examples of B->D^*π^+π^-π^-π^0 and B->D^*ωπ^-. The mode B->D^*ωπ^- will allow a precision study of the dependence of the corrections to factorization on the invariant mass of the light hadronic state.

hep-ph↗
arXiv2001

Light-cone distribution functions for B decays at subleading order in 1/mb

We construct the higher twist structure functions that describe inclusive b hadron decays in regions of phase space where the hadronic decay products carry high energy but have low invariant mass. We show that, for B meson decays, there are four new non-vanishing matrix elements of non-local operators. We show that to subleading twist these decays are parametrized in terms of four functions. We compute the tree-level matching for a general heavy-to-light current and apply it to B -> X_s gamma. Using a simple model for these functions we estimate the subleading twist contributions to this decay.

hep-ph↗
arXiv2001

Determining $|V_{ub}|$ from the $\bar B\to X_u\ell\barν$ dilepton invariant mass spectrum

The invariant mass spectrum of the lepton pair in inclusive semileptonic $\bar B\to X_u \ell\barν$ decay yields a model independent determination of $|V_{ub}|$. Unlike the lepton energy and hadronic invariant mass spectra, nonperturbative effects are only important in the resonance region, and play a parametrically suppressed role when $dΓ/ dq^2$ is integrated over $q^2 > (m_B-m_D)^2$, which is required to eliminate the $\bar B\to X_c \ell\barν$ background. We discuss these backgrounds for $q^2$ slightly below $(m_B-m_D)^2$, and point out that instead of $q^2 > (m_B-m_D)^2 = 11.6 GeV^2$, the cut can be lowered to $q^2 \gtrsim 10.5 GeV^2$. This is important experimentally, particularly when effects of a finite neutrino reconstruction resolution are included.

hep-ph↗
arXiv2000

On |V_{ub}| from the B -> X_u l νdilepton invariant mass spectrum

The invariant mass spectrum of the lepton pair in inclusive semileptonic $\bar B\to X_u \ell\barν$ decay yields a model independent determination of $|V_{ub}|$. Unlike the lepton energy and hadronic invariant mass spectra, nonperturbative effects are only important in the resonance region, and play a parametrically suppressed role when $dΓ/ dq^2$ is integrated over $q^2 > (m_B-m_D)^2$, which is required to eliminate the $\bar B\to X_c \ell\barν$ background. We discuss these backgrounds for $q^2$ slightly below $(m_B-m_D)^2$, and point out that instead of $q^2 > (m_B-m_D)^2 = 11.6 GeV^2$, the cut can be lowered to $q^2 \gtrsim 10.5 GeV^2$. This is important experimentally, particularly when effects of a finite neutrino reconstruction resolution are included.

hep-ph↗
arXiv2000

A Model Independent Determination of |V_{ub}|

It is shown that measuring the lepton invariant mass spectrum in inclusive semileptonic B -> X_u l nu decay yields a model independent determination of |V_{ub}|. Unlike the lepton energy and hadronic invariant mass spectra, nonperturbative effects are only important in the resonance region, and play a parametrically suppressed role when dΓ/dq^2 is integrated over q^2 > (m_B-m_D)^2, which is required to eliminate the charm background. Perturbative and nonperturbative corrections are presented to order α_s^2β_0 and Λ_{QCD}^2/m_b^2, and the Λ_{QCD}^3/m_b^3 corrections are used to estimate the uncertainty in our results. The utility of the B -> X_s l^+ l^- decay rate above the ψ(2S) resonance is discussed.

hep-ph↗
arXiv1999

Phenomenology of V_ub from Ratios of Inclusive B Decay Rates

We explore the theoretical feasibility of extracting V_ub from two ratios built from B meson inclusive partial decays, R_1 = Gamma(b-> u cbar s)/3Gamma(b -> c l nu), and R_2 = [Gamma(b -> c X) - Gamma(b -> cbar X)]/Gamma(b -> c ubar d). We discuss contributions to these quantities from perturbative and nonperturbative physics, and show that they can be computed with overall uncertainties at the level of 10%.

hep-ph↗
arXiv1999

The B -> X_s gamma Photon Spectrum

The photon energy spectrum in inclusive weak radiative B -> X_s gamma decay is computed to order alpha_s^2 beta_0. This result is used to extract a value for the HQET parameter $\barΛ$ from the average <1-2E_γ/m_B>, and a value of the parameter $λ_1$ from <(1-2E_γ/m_B)^2>. An accurate measurement of <1-2E_γ/m_B> can determine the size of the nonperturbative contributions to the Upsilon(1S) mass which cannot be absorbed into the b quark pole mass.

hep-ph↗
arXiv1997

Hadronic Spectral Moments in Semileptonic B Decays With a Lepton Energy Cut

We compute the first two moments of the final hadronic invariant mass in inclusive semileptonic B decay, in the presence of a cut on the charged lepton energy. These moments may be measured directly by experiments at the Upsilon(4S) using the neutrino reconstruction technique, which requires such a cut. Measurement of these moments will place constraints on the nonperturbative parameters \barΛand λ_1, which are relevant for extracting the quark masses m_b and m_c, as well as the CKM angle V_cb. We include terms of order α_s^2β_0 and 1/m_b^3 in the operator product expansion, and use the latter to estimate the theoretical uncertainty in the extraction of \barΛand λ_1.

hep-ph↗
arXiv1997

Power Counting in Dimensionally Regularized NRQCD

We present a scheme for calculating in NRQCD with consistent power counting in the heavy quark velocity v. As an example, we perform the systematic matching of an external current onto NRQCD at subleading order in v, a calculation relevant for the process e^+e^- -> hadrons near threshold. Consistent velocity power counting in dimensional regularization is achieved by including two distinct gluon fields, one corresponding to gluon radiation and one corresponding to an instantaneous potential. In this scheme power counting is manifest in any gauge, and also holds for non-gauge interactions. The matching conditions for an external vector current in NRQCD are calculated to O(g^2 v^2) and the cancellation of infrared divergences in the matching conditions is shown to require both gluon fields. Some subtleties arising in the matching conditions at subleading order are addressed.

hep-ph↗
arXiv1996

Bound States and Power Counting in Effective Field Theories

The problem of bound states in effective field theories is studied. A rescaled version of nonrelativistic effective field theory is formulated which makes the velocity power counting of operators manifest. Results obtained using the rescaled theory are compared with known results from NRQCD. The same ideas are then applied to study Yukawa bound states in 1+1 and 3+1 dimensions, and to analyze when the Yukawa potential can be replaced by a delta-function potential. The implications of these results for the study of nucleon-nucleon scattering in chiral perturbation theory is discussed.

hep-ph↗
arXiv1996

Higher Order QCD Corrections to $b\to c\overline{c}s$

We calculate the ${\cal O}(α_s^2 β_0 )$ corrections to the decay rate $b\rightarrow c\bar c s$. For reasonable values of $m_c/m_b$ this term is of the same order as both the one-loop and $\CO(α_s^2 \log^2 m_W/m_b)$ corrections to the decay rate. For $m_c/m_b=0.3$ the $\CO(α_s^2β_0)$ corrections enhance the rate by $\sim 18\%$ . We also discuss the $\CO(α_s^2β_0)$ corrections to $R_τ$, the $B$ semileptonic branching fraction and the charm multiplicity.

hep-ph↗
arXiv1996

Resumming Phase Space Logarithms in Inclusive Semileptonic $B$ Decays

We study logarithms of the form $\ln(m_q/m_b)$ which arise in the inclusive semileptonic decay of a bottom quark to a quark of mass $m_q$. We use the renormalization group to resum the leading radiative corrections to these terms, of the form $m_q^2α_s^n\ln^n(m_q/m_b)$, $m_q^3α_s^{n+1}\ln^n(m_q/m_b)$ and $m_q^4α_s^n\ln^{n+1}(m_q/m_b)$. The first two resummations are trivial, while the latter involves a non-trivial mixing of four-fermi operators in the $1/m_b$ expansion. We illustrate this technique in a toy model in which the semileptonic decay is mediated by a vector interaction, before treating the more complicated case of left-handed decay.

hep-ph↗
arXiv1996

Phenomenology of the $1/m_Q$ Expansion in Inclusive $B$ and $D$ Meson Decays

We apply a recent theoretical analysis of hadronic observables in inclusive semileptonic heavy hadron decays to the phenomenology of $B$ and $D$ mesons. Correlated bounds on the nonperturbative parameters $\barΛ$ and $λ_1$ are derived by considering data from $B$ decays and, independently, data from $D$ decays. The two sets of bounds are found to be consistent with each other. The data from $B$ decays are then are used to extract a lower limit on the CKM matrix element $|V_{cb}|$. We address the issue of the convergence of the perturbative expansions used in the analysis, and compare our bounds on $\barΛ$ and $λ_1$ to lattice and QCD sum rule results. Finally, we argue that a comparison of the analyses of $D$ and $D_s$ decays provides evidence for the applicability of parton-hadron duality in the semileptonic decay of charmed hadrons.

hep-ph↗
arXiv1995

Hadron Spectra for Semileptonic Heavy Quark Decay

We calculate the leading perturbative and power corrections to the hadronic invariant mass and energy spectra in semileptonic heavy hadron decays. We apply our results to the $B$ system. Moments of the invariant mass spectrum, which vanish in the parton model, probe gluon bremsstrahlung and nonperturbative effects. Combining our results with recent data on $B$ meson branching ratios, we obtain a lower bound $\barΛ>410\,{\rm MeV}$ and an upper bound $m_b^{\rm pole}<4.89\,$GeV. The Brodsky-Lepage-Mackenzie scale setting procedure suggests that higher order perturbative corrections are small for bottom decay, and even tractable for charm decay.

hep-ph↗
arXiv1995

Renormalons in Effective Field Theories

We investigate the high-order behavior of perturbative matching conditions in effective field theories. These series are typically badly divergent, and are not Borel summable due to infrared and ultraviolet renormalons which introduce ambiguities in defining the sum of the series. We argue that, when treated consistently, there is no physical significance to these ambiguities. Although nonperturbative matrix elements and matching conditions are in general ambiguous, the ambiguity in any physical observable is always higher order in $1/M$ than the theory has been defined. We discuss the implications for the recently noticed infrared renormalon in the pole mass of a heavy quark. We show that a ratio of form factors in exclusive $Λ_b$ decays (which is related to the pole mass) is free from renormalon ambiguities regardless of the mass used as the expansion parameter of HQET. The renormalon ambiguities also cancel in inclusive heavy hadron decays. Finally, we demonstrate the cancellation of renormalons in a four-Fermi effective theory obtained by integrating out a heavy colored scalar.

hep-ph↗
arXiv1994

Charm Mass Dependence of the $\CO(α_s^2 n_f)$ Correction to Inclusive $B\rightarrow X_c e\barν_e$ Decay

We compute the $α_s^2 n_f$ perturbative QCD contribution to semileptonic B decay, including the finite mass of the charm quark. This result provides an estimate of the size of the two-loop correction, which is found to be about 50\% of the one-loop correction. We use these results to set the scale for the one-loop correction using the scheme of Brodsky, Lepage and Mackenzie and find a BLM scale of $μ_{\rm BLM} = 0.13\, m_b$, when the inclusive semileptonic rate is expressed in terms of the $b$ and $c$ quark pole masses and the \msbar strong coupling. The two loop correction lies roughly midway between that obtained at $m_c=0$ and that obtained in the Shifman-Voloshin limit $m_b, m_c\gg m_b-m_c\ggΛ_{\rm QCD}$ while the corresponding BLM scale is somewhat closer to that obtained in the former case.

hep-ph↗
arXiv1994

Perturbative Strong Interaction Corrections to the Heavy Quark Semileptonic Decay Rate

We calculate the part of the order $α_s^2$ correction to the semileptonic heavy quark decay rate proportional to the number of light quark flavors, and use our result to set the scale for evaluating the strong coupling in the order $α_s$ term according to the scheme of Brodsky, Lepage and Mackenzie. Expressing the decay rate in terms of the heavy quark pole mass $m_Q$, we find the scale for the $\overline{MS}$ strong coupling to be $0.07\, m_Q$. If the decay rate is expressed in terms of the $\overline{MS}$ heavy quark mass $\overline m_Q(m_Q)$ then the scale is $0.12\, m_Q$. We use these results along with the existing calculations for hadronic $τ$ decay to calculate the BLM scale for the nonleptonic decay width and the semileptonic branching ratio. The implications for the value of $|V_{bc}|$ extracted from the inclusive semileptonic $B$ meson decay rate are discussed.

hep-ph↗
arXiv1993

Hadronic Event Shapes in $B$ Decay

We compute the differential momentum correlation function for hadrons produced in the decay of $B$-mesons. This measure of hadronic event shapes tests the free $b$-quark decay picture for nonleptonic and semileptonic decays of $B$-mesons. Our results can also be applied to $B_s$ and $Λ_b$ decay.

hep-ph↗