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Michael Luke

Publications and source records attributed to Michael Luke.

At least 19 recordsLinked to original sources
arXiv2022

Factorization at subleading power in deep inelastic scattering in the $x\rightarrow 1$ limit

We examine the endpoint region of inclusive deep inelastic scattering at next-to-leading power (NLP). Using a soft-collinear effective theory approach with no explicit soft or collinear modes, we discuss the factorization of the cross section at NLP and show that the overlap subtraction procedure introduced to eliminate double counting of degrees of freedom at leading power ensures that spurious endpoint divergences in the rate cancel at NLP at one loop. For this cancellation to occur at all renormalization scales a nontrivial relation between the anomalous dimensions of the leading and subleading operators is required, which is demonstrated to hold at one loop.

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arXiv2021

Theoretical predictions for inclusive $B\to X_u \tau \bar\nu$ decay

With the expected large increase in data sets, previously not measured decays will be studied at Belle II. We derive standard model predictions for the $B\to X_u \tau\bar\nu$ decay rate and distributions. The region in the lepton energy spectrum where higher-dimension operators in the local OPE need to be resummed into the $b$-quark light-cone distribution function is a significantly greater fraction of the phase space than for massless leptons. The finite $\tau$ mass has the novel effect of shifting and squeezing how the distribution function enters the lepton energy spectrum. We also derive new predictions for the $\tau$ polarization.

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arXiv2021

Factorization of Power Corrections in the Drell-Yan Process in EFT

We examine the quark-induced Drell-Yan process at next-to-leading power (NLP) in Soft-Collinear Effective Theory. Using an approach with no explicit soft or collinear modes, we discuss the factorization of the differential cross section in the small-$q_T$ hierarchy with $q^2\gg q_T^2\gg\Lambda_{\mathrm{QCD}}^2$. We show that the cross section may be written in terms of matrix elements of power-suppressed operators $T_{(i,j)}$, which contribute to $O(q_T^2/q^2)$ coefficients of the usual parton distribution functions. We derive a factorization for this observable at NLP which allows the large logarithms in each of the relevant factors to be resummed. We discuss the cancellation of rapidity divergences and the overlap subtractions required to eliminate double counting at next-to-leading power.

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arXiv2020

Rapidity Logarithms in SCET Without Modes

We re-examine observables with rapidity divergences in the context of a formulation of Soft-Collinear Effective Theory in which infrared degrees of freedom are not explicitly separated into modes. We consider the Sudakov form factor with a massive vector boson and Drell-Yan production of lepton pairs at small transverse momentum as demonstrative examples. In this formalism, rapidity divergences introduce a scheme dependence into the effective theory and are associated with large logarithms appearing in the soft matching conditions. This scheme dependence may be used to derive the corresponding rapidity renormalization group equations, and rates naturally factorize into hard, soft and jet contributions without the introduction of explicit modes.

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arXiv2017

Power Counting and Modes in SCET

We present a formulation of soft-collinear effective theory (SCET) in the two-jet sector as a theory of decoupled sectors of QCD coupled to Wilson lines. The formulation is manifestly boost-invariant, does not require the introduction of ultrasoft modes at the hard matching scale Q, and has manifest power counting in inverse powers of Q. The spurious infrared divergences which arise in SCET when ultrasoft modes are not included in loops disappear when the overlap between the sectors is correctly subtracted, in a manner similar to the familiar zero-bin subtraction of SCET. We illustrate this approach by analyzing deep inelastic scattering in the endpoint region in SCET and comment on other applications.

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arXiv2011

SCET, QCD and Wilson Lines

Soft Collinear Effective Theory (SCET) is an effective field theory which describes the interactions of low invariant mass jets which are highly boosted with respect to one another. In the standard formulation of SCET, the effective Lagrangian for collinear fields is expanded in inverse powers of the energy. At leading order this leads to manifest decoupling of soft and collinear degrees of freedom; however, subleading terms in the effective Lagrangian violate this manifest decoupling. In this paper we point out that the collinear expansion in the SCET Lagrangian is unnecessary, and that the SCET Lagrangian may instead be written as multiple decoupled copies of QCD. The interactions between the sectors in full QCD are reproduced in the effective theory by an external current consisting of QCD fields coupled to Wilson lines. We illustrate this picture with two examples: dijet production and B->X_s + gamma.

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arXiv2010

Constraining weak annihilation using semileptonic D decays

The recently measured semileptonic D_s decay rate can be used to constrain weak annihilation (WA) effects in semileptonic D and B decays. We revisit the theoretical predictions for inclusive semileptonic D_{(s)} decays using a variety of quark mass schemes. The most reliable results are obtained if the fits to B decay distributions are used to eliminate the charm quark mass dependence, without using any specific charm mass scheme. Our fit to the available data shows that WA is smaller than commonly assumed. There is no indication that the WA octet contribution (which is better constrained than the singlet contribution) dominates. The results constrain an important source of uncertainty in the extraction of |Vub| from inclusive semileptonic B decays.

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arXiv2009

Phase Space and Jet Definitions in SCET

We discuss consistent power counting for integrating soft and collinear degrees of freedom over arbitrary regions of phase space in the soft-collinear effective theory (SCET), and illustrate our results at one loop with several jet algorithms: JADE, Sterman-Weinberg and k_T. Consistently applying SCET power-counting in phase space, along with non-trivial zero-bin subtractions, prevents double-counting of final states. The resulting phase-space integrals over soft and collinear regions are individually ultraviolet divergent, but the phase-space ultraviolet divergences cancel in the sum. Whether the soft and collinear contributions are individually infrared safe depends on the jet definition. We show that while this is true at one loop for JADE and Sterman-Weinberg, the k_T algorithm does not factorize into individually infrared safe soft and collinear pieces in dimensional regularization. We point out that this statement depends on the ultraviolet regulator, and that in a cutoff scheme the soft functions are infrared safe.

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arXiv2009

High order perturbative corrections to the determination of |Vub| from the P+ spectrum in B -> Xu l nu

We investigate the behaviour of the perturbative relation between the photon energy spectrum in B -> Xs gamma and the hadronic P+ spectrum in semileptonic B -> Xu l nu decay at high orders in perturbation theory in the "large-beta_0" limit, in which only terms of order alpha_s^n beta_0^(n-1) are retained. The leading renormalon in the weight function W(Delta,P_gamma) relating the two spectra is confirmed to be at u=1/2, corresponding to nonperturbative corrections at O(Lambda_QCD/m_b). We show that the P_gamma dependent pieces of the weight function have no infrared renormalons in this limit, and so the factorial growth in perturbation theory arises solely from the constant terms. We find no numerical enhancement of leading logarithms, suggesting that fixed-order perturbation theory is more appropriate than a leading-log resummation for the extraction of |Vub|. The importance of various terms in the expansion of the weight function is studied using a model for the B -> Xs gamma photon spectrum. Our analysis suggests that higher order perturbative corrections do not introduce a significant uncertainty in the extraction of |Vub|.

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arXiv2005

Perturbative corrections to the determination of Vub from the P+ spectrum in B->X_u l nu

We investigate the relation between the E_gamma spectrum in B->X_s gamma decay and the P+ spectrum in semileptonic B->X_u l nu decay (P+ is the hadronic energy minus the absolute value of the hadronic three-momentum), which provides in principle the theoretically simplest determination of Vub from any of the "shape function regions" of B->X_u l nu spectra. We calculate analytically the P+ spectrum to order alpha_s^2 beta_0, and study its relation to the B->X_s gamma photon spectrum to eliminate the leading dependence on nonperturbative effects. We compare the result of fixed order perturbation theory to the next-to-leading log renormalization group improved calculation, and argue that fixed order perturbation theory is likely to be a more appropriate expansion. Implications for the perturbative uncertainties in the determination of Vub from the P+ spectrum are discussed.

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arXiv2004

Global analysis of inclusive B decays

In light of the large amount of new experimental data, we revisit the determination of V_{cb} and m_b from inclusive semileptonic and radiative B decays. We study shape variables to order lqcd^3/m_b^3 and alpha_s^2β_0, and include the order alpha_s, lqcd/m_b correction to the hadron mass spectrum in semileptonic decay, which improves the agreement with the data. We focus on the 1S and kinetic mass schemes for the b quark, with and without expanding m_b-m_c in HQET. We perform fits to all available data from BABAR, BELLE, CDF, CLEO, and DELPHI, discuss the theoretical uncertainties, and compare with earlier results. We find V_{cb} = (41.4 +- 0.6 +- 0.1) x 10^{-3} and m_b^{1S} = 4.68 +- 0.03 GeV, including our estimate of the theoretical uncertainty in the fit.

hep-ph↗
arXiv2003

B decay shape variables and the precision determination of |Vcb| and mb

We present expressions for shape variables of B decay distributions in several different mass schemes, to order $α_s^2β_0$ and (Lambda_{QCD}/mb)^3. Such observables are sensitive to the b quark mass and matrix elements in the heavy quark effective theory, and recent measurements allow precision determinations of some of these parameters. We perform a combined fit to recent experimental results from CLEO, BABAR, and DELPHI, and discuss the theoretical uncertainties due to nonperturbative and perturbative effects. We discuss the possible discrepancy between the OPE prediction, recent BABAR results and the measured branching fraction to D and D* states. We find |Vcb| = (40.8 +- 0.9) x 10^{-3} and mb^{1S} = 4.74 +- 0.10 GeV, where the errors are dominated by experimental uncertainties.

hep-ph↗
arXiv2002

The Mass of the b Quark

We review the current status of determinations of the b-quark mass, m_b. We describe the theoretical tools required for determining m_b, with particular emphasis on effective field theories both in the continuum and on the lattice. We present several definitions of m_b and highlight their advantages and disadvantages. Finally, we discuss the determinations of m_b from b-bar b systems, b-flavored hadrons, and high-energy processes, with careful attention to the corresponding theoretical uncertainties.

hep-ph↗
arXiv2002

Subleading shape functions in B -> X_u l \nu and the determination of |Vub|

We calculate the subleading twist contributions to the endpoint of the inclusive lepton energy spectrum in B -> X_u l \nu. We show that the same two subleading twist functions that appear in the decay B -> X_s \gamma govern the subleading effects in this decay. Using these results we find large O(Lambda/mB) corrections to the determination of |Vub| from the endpoint of the charged lepton spectrum. Using a simple model for the relevant subleading shape functions, we estimate the uncertainty in |Vub| from Lambda/mb corrections to be at the ~ 15% level for a lower lepton energy cut of 2.2 GeV.

hep-ph↗
arXiv2001

Precision determination of Vub

We review how to determine |Vub| from inclusive semileptonic B decay using combined cuts on the leptonic and hadronic invariant masses to eliminate the b -> c background. This leads to a determination of |Vub| with theoretical uncertainty at the 5 -10% level.

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arXiv2001

Precision determination of |V_{ub}| from inclusive decays

We propose determining |V_{ub}| from inclusive semileptonic B decay using combined cuts on the leptonic and hadronic invariant masses to eliminate the b->c background. Compared to a pure dilepton invariant mass cut, the uncertainty from unknown order (\Lambda_{QCD}/m_b)^3 terms in the OPE is significantly reduced and the fraction of b->u events is roughly doubled. Compared to a pure hadronic invariant mass cut, the uncertainty from the unknown light-cone distribution function of the b quark is significantly reduced. We find that |V_{ub}| can be determined with theoretical uncertainty at the 5-10% level.

hep-ph↗
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^*\pi^+\pi^-\pi^-\pi^0 and B->D^*\omega\pi^-. The mode B->D^*\omega\pi^- will allow a precision study of the dependence of the corrections to factorization on the invariant mass of the light hadronic state.

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