Endpoint Region Research Articles

The Mainz Neutrino Mass Experiment

Abstract The Mainz neutrino mass experiment is investigating the endpoint region of the tritium β decay spectrum to determine the mass of the electron antineutrino. With its recently improved setup data were taken over more than 7 month in 1998 and 1999. For these measurements two different analyses are presented leading to mv2 = +0.6±2.8±2.1 eV2/c4and mv2 = −1.6 ± 2.5 ± 2.1 eV2/c4, from which upper limits of mv

Shape function effects inB→Xcℓν¯ℓ

Owing to the fact that m_c^2 ~ m_b \Lambda_QCD, the endpoint region of the charged lepton energy spectrum in the inclusive decay B -> X_c l \nu_l is affected by the Fermi motion of the initial-state b quark bound in the B meson. This effect is described in QCD by shape functions. Including the mass of the final-state quark, we find that a different set of operators as employed in Ref. hep-ph/0205150 is needed for a consistent matching, when incorporating the subleading contributions in B -> X_q l \nu_l for both q = u and q = c. In addition, we modify the usual twist expansion in such a way that it yields a description of the lepton energy spectrum which is not just valid in the endpoint region, but over the entire phase space.

Subleading Shape Functions in Inclusive B Decays

The contributions of subleading shape functions to inclusive decay distributions of B mesons are derived from a systematic two-step matching of QCD current correlators onto soft-collinear and heavy-quark effective theory. At tree-level, the results can be expressed in terms of forward matrix elements of bi-local light-cone operators. Four-quark operators, which arise at O(g^2), are included. Their effects can be absorbed entirely into a redefinition of other shape functions. Our results are in disagreement with some previous studies of subleading shape-function effects in the literature. A numerical analysis of B->X_u+l+nu decay distributions suggests that power corrections are small, with the possible exception of the endpoint region of the charged-lepton energy spectrum.

Gluon content of theηandη′mesons and theηγ,η′γelectromagnetic transition form factors

We compute power-suppressed corrections to the \eta\gamma and \eta^{\prime}\gamma transition form factors Q^2F_{\eta(\eta^{\prime})\gamma}(Q^2) arising from the end point regions x \to 0,1 by employing the infrared-renormalon approach. The contribution to the form factors from the quark and gluon content of the \eta,\eta^{\prime} mesons is taken into account using for the \eta-\eta^{\prime} mixing the SU_f(3) singlet \eta_1 and octet \eta_8 basis. The theoretical predictions obtained this way are compared with the corresponding CLEO data and restrictions on the input parameters (Gegenbauer coefficients) B_2^q(\eta_1), B_2^g(\eta_1), and B_2^q(\eta_8) in the distribution amplitudes for the \eta_1,\eta_8 states with one nonasymptotic term are deduced. Comparison is made with the results from QCD perturbation theory.

LIFETIME DIFFERENCE AND ENDPOINT EFFECT IN THE INCLUSIVE BOTTOM HADRON DECAYS

The lifetime differences of bottom hadrons are known to be properly explained within the framework of heavy quark effective field theory (HQEFT) of QCD via the inverse expansion of the dressed heavy quark mass. In general, the spectrum around the endpoint region is not well behaved due to the invalidity of 1/mQ expansion near the endpoint. The curve fitting method is adopted to treat the endpoint behavior. It turns out that the endpoint effects are truly small and the explanation on the lifetime differences in the HQEFT of QCD is then well justified. The inclusion of the endpoint effects makes the prediction on the lifetime differences and the extraction on the CKM matrix element |Vcb| more reliable.

Shape function effects inB→XsγandB→Xulν¯decays

We calculate the decay distributions for inclusive $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}\ensuremath{\gamma}$ and $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{u}\mathcal{l}\overline{\ensuremath{\nu}}$ decays in the endpoint region, where radiative corrections are large. The computation is done using effective field theory methods. The matching coefficients are computed to $\mathcal{O}({\ensuremath{\alpha}}_{s})$ and the anomalous dimensions to next-to-leading order. The final expressions for the differential decay spectra include the complete $\mathcal{O}({\ensuremath{\alpha}}_{s})$ corrections and sum the leading and next-to-leading Sudakov series. We present results for regions of phase space where the shape function can be expanded in local operators and give the matching coefficients of the resulting enhanced non-perturbative effects to order ${\ensuremath{\alpha}}_{s}.$ We show that moments of the shape function are not given by moments of local operators once perturbative effects are included, explain why the shape function and its moments satisfy different renormalization group equations, and contrast this with the situation for deep inelastic scattering. We show that there are large perturbative corrections in the usual definition of the shape function. This renders incorrect previous prescriptions for combining radiative corrections with the shape function.

Leading power SCET analysis of [formula omitted

Recently, Belle and BaBar Collaborations observed surprising suppression in the endpoint J/ψ spectrum, which stimulates us to examine the endpoint behaviors of the e+e−→J/ψgg production. We calculate the J/ψ momentum and angular distributions for this process within the framework of the soft-collinear effective theory (SCET). The decreasing spectrum in the endpoint region is obtained by summing the Sudakov logarithms. We also find a large discrepancy between the NRQCD and SCET spectrum in the endpoint region even before the large logarithms are summed, which is probably due to the fact that only the scalar structure of the two-gluon system is picked out in the leading power expansion. A comparison with the process ϒ→γgg is made.

Subprocess size in hard exclusive scattering

The interaction region of hard exclusive hadron scattering can have a large transverse size due to endpoint contributions, where one parton carries most of the hadron momentum. The endpoint region is enhanced and can dominate in processes involving multiple scattering and quark helicity flip. The endpoint Fock states have perturbatively short lifetimes and scatter softly in the target. We give plausible arguments that endpoint contributions can explain the apparent absence of color transparency in fixed angle exclusive scattering and the dimensional scaling of transverse rho photoproduction at high momentum transfer, which requires quark helicity flip. We also present a quantitative estimate of Sudakov effects.

Soft, collinear, and nonrelativistic modes in radiative decays of very heavy quarkonium

We analyze the end-point region of the photon spectrum in semi-inclusive radiative decays of very heavy quarkonium $(m{\ensuremath{\alpha}}_{\mathrm{s}}^{2}\ensuremath{\gg}{\ensuremath{\Lambda}}_{\mathrm{QCD}}).$ We discuss the interplay of the scales arising in the soft-collinear effective theory, m, $m(1\ensuremath{-}{z)}^{1/2},$ and $m(1\ensuremath{-}z)$ for z close to 1, with the scales of heavy quarkonium systems in the weak coupling regime, m, $m{\ensuremath{\alpha}}_{\mathrm{s}},$ and $m{\ensuremath{\alpha}}_{\mathrm{s}}^{2}.$ For $1\ensuremath{-}z\ensuremath{\sim}{\ensuremath{\alpha}}_{\mathrm{s}}^{2}$ only collinear and (ultra)soft modes are seen to be relevant, but the recently discovered soft-collinear modes show up for $1\ensuremath{-}z\ensuremath{\ll}{\ensuremath{\alpha}}_{\mathrm{s}}^{2}.$ The S- and P-wave octet shape functions are calculated. When they are included in the analysis of the photon spectrum of the $\ensuremath{\Upsilon}(1S)$ system, the agreement with data in the end-point region becomes excellent. The nonrelativistic QCD matrix elements $〈{1}^{3}{S}_{1}|{O}_{8}{(}^{1}{S}_{0})|{1}^{3}{S}_{1}〉$ and $〈{1}^{3}{S}_{1}|{O}_{8}{(}^{3}{P}_{J})|{1}^{3}{S}_{1}〉$ are also obtained.

Deep inelastic scattering asx→1using soft-collinear effective theory

Soft-collinear effective theory (SCET) is used to sum Sudakov double-logarithms in the x ->1 endpoint region for the deep inelastic scattering structure function. The calculations are done in both the target rest frame and the Breit frame. The separation of scales in the effective theory implies that the anomalous dimension of the SCET current is linear in ln mu, and the anomalous dimension for the Nth moment of the structure function is linear in ln N, to all orders in perturbation theory. The SCET formulation is shown to be free of Landau pole singularities. Some important differences between the deep inelastic structure function and the shape function in B decay are discussed.

Latest results of the Mainz Neutrino Mass Experimen

The Mainz Neutrino Mass Experiment investigates the endpoint region of the tritium β decay spectrum very precisely to extract the rest mass of the electron antineutrino. The measurements are performed with a MAC-E-Filter, combining agnetic diabatic ollimation and an lectrostatic high pass Filter. After optimal preparation of the apparatus very stable and high quality data have been taken in 2001, which do not show any residual problem. A combined analysis of data from 1998/1999 and 2001 lead to the final value of m ν 2 = –0.7 ± 2.2 stat ± 2.1 sys eV2/c4, leading to an upper limit m ν ≤ 2.3 eV/c2 (95% C.L.). PACS: 14.60.P Neutrinos, mass and mixing – 23.40 β decay

Enhanced nonperturbative effects in jet distributions.

We consider the triple differential distribution d Gamma/dE(J)dm(2)(J)d Omega(J) for two-jet events at center of mass energy M, smeared over the end-point region m(2)(J)<<M2, absolute value 2E(J)-M approximately Delta, Lambda(QCD)<<Delta<<M. The leading nonperturbative correction, suppressed by Lambda(QCD)/Delta, is given by the matrix element of a single operator. A similar analysis is performed for three-jet events, and the generalization to any number of jets is discussed. At order Lambda(QCD)/Delta, nonperturbative effects in four or more jet events are completely determined in terms of two matrix elements which can be measured in two- and three-jet events.

Latest results from the Mainz Neutrino Mass experiment

The Mainz Neutrino Mass experiment investigates the endpoint region of tritium β decay spectrum very precisely to extract the rest mass of the electron antineutrino. The measurements are performed with a MAC-E-Filyer, combining M agnetic A diabatic C ollimation and an E lectrostatic high pass Filter. After an optimal preparation very stable and high quality data have been taken in 2001, which do not show any residual problem.

The photon spectrum inΥdecays

We present a theoretical prediction for the photon spectrum in radiative Upsilon decay. Parts of the spectrum have already been understood, but an understanding of the endpoint region has remained elusive. In this paper we provide the missing piece, and resolve a controversy in the literature. We treat the endpoint region of Upsilon -> X gamma decay within the framework of the soft-collinear effective theory (SCET). Within this approach the Upsilon structure function arises naturally, and kinematic logarithms are summed by running operators using renormalization group equations. In a previous paper we studied the color-octet contribution to the decay. Here we treat the color-singlet contribution. We combine our result with previous results to obtain the Upsilon -> X gamma spectrum. We find that resumming the color-singlet contribution in the endpoint gives a result that is in much better agreement with the data than the leading order prediction.

Subleading shape functions and the determination of Vub

The endpoint region of the inclusive lepton energy spectrum in B → X ul v can be used for a determination of V ub by comparing it to the endpoint region of the inclusive photon spectrum of B → X s γ. We consider the subleading twist contributions to this V ub determination.

Resummed photon spectrum in radiative upsilon decays.

We present a theoretical prediction for the photon spectrum in radiative upsilon decay including the effects of resumming the end point region, E(gamma)-->M(upsilon)/2. Our approach is based on nonrelativistic QCD (NRQCD) and the soft-collinear effective theory. We find that our results give much better agreement with data than the leading order NRQCD prediction.

Interference of conversion and bremsstrahlung amplitudes in the decay KL→μ+μ−γ

In the region of large μ+μ− invariant mass, the decay spectrum of KL→μ+μ−γ deviates from the Dalitz pair spectrum, as a result of interference between conversion (KL→γ∗γ→μ+μ−γ) and bremsstrahlung amplitudes. The latter is proportional to the KL→μ+μ− matrix element, whose 2γ-absorptive part appears to dominate the observed KL→μ+μ− decay rate. We examine the extent to which a scrutiny of the KL→μ+μ−γ spectrum in the end-point region could provide evidence on the real part of the KL→μ+μ− amplitude. As a by-product, we obtain the absorptive part of the KL→γ∗γ form factor, using data on the KL→π+π−γ spectrum.

Threshold resummation for exclusiveBmeson decays

We argue that double logarithmic corrections $\alpha_s\ln^2 x$ need to be resumed in perturbative QCD factorization theorem for exclusive $B$ meson decays, when the end-point region with a momentum fraction $x\to 0$ is important. These double logarithms, being of the collinear origin, are absorbed into a quark jet function, which is defined by a matrix element of a quark field attached by a Wilson line. The factorization of the jet function from the decay $B\to\gamma l\bar\nu$ is proved to all orders. Threshold resummation for the jet function leads to a universal, {\it i.e.}, process-independent, Sudakov factor, whose qualitative behavior is analyzed and found to smear the end-point singularities in heavy-to-light transition form factors.

Subleading shape functions and the determination of |Vub|

It is argued that the dominant subleading shape-function contributions to the endpoint region of the charged-lepton energy spectrum in B→Xulν decays can be related in a model-independent way to an integral over the B→Xsγ photon spectrum. The square root of the fraction of B→Xulν events with charged-lepton energy above E0=2.2 GeV can be calculated with a residual theoretical uncertainty from subleading shape-function effects that is safely below the 10% level. These effects have therefore a minor impact on the determination of |Vub|.

Enhanced subleading structure functions in semileptonic B decay

The charged lepton spectrum in semileptonic B→X uℓ ν ̄ decay near maximal lepton energy receives important corrections from subleading structure functions that are formally suppressed by powers of Λ QCD/ m b but are enhanced by numerical factors. We investigate the series of higher order terms which smear over a region of width ΔE ℓ∼ Λ QCD near the endpoint the contributions proportional to δ( E ℓ− m b /2) times (i) the matrix element of the chromomagnetic operator, and (ii) four-quark operators. These contribute to the total rate at the few percent level, but affect the endpoint region much more significantly. Implications for the determination of | V ub | are discussed.