Searcharxiv⌕ Search

arXiv subjects

Ben D. Pecjak

Publications and source records attributed to Ben D. Pecjak.

27 records · Page 2Linked to original sources
arXiv2009

Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories

The infrared divergences of QCD scattering amplitudes can be derived from an anomalous dimension Γ, which is a matrix in color space and depends on the momenta and masses of the external partons. It has recently been shown that in cases where there are at least two massive partons involved in the scattering process, starting at two-loop order Γreceives contributions involving color and momentum correlations between three (and more) partons. The three-parton correlations can be described by two universal functions F_1 and f_2. In this paper these functions are calculated at two-loop order in closed analytic form and their properties are studied in detail. Both functions are found to be suppressed like O(m^4/s^2) in the limit of small parton masses, in accordance with mass factorization theorems proposed in the literature. On the other hand, both functions are O(1) and even diverge logarithmically near the threshold for pair production of two heavy particles. As an application, we calculate the infrared poles in the q qbar --> t tbar and g g --> t tbar scattering amplitudes at two-loop order.

hep-ph↗
arXiv2009

Two-loop divergences of scattering amplitudes with massive partons

We complete the study of two-loop infrared singularities of scattering amplitudes with an arbitrary number of massive and massless partons in non-abelian gauge theories. To this end, we calculate the universal functions F_1 and f_2, which completely specify the structure of three-parton correlations in the soft anomalous-dimension matrix, at two-loop order in closed analytic form. Both functions are found to be suppressed like O(m^4/s^2) in the limit of small parton masses, in accordance with mass factorization theorems proposed in the literature. On the other hand, they are unsuppressed and diverge logarithmically near the threshold for pair production of two heavy particles. As an application, we calculate the two-loop anomalous-dimension matrix for q q_bar --> t t_bar near threshold and show that it is not diagonal in the s-channel singlet-octet basis.

hep-ph↗
arXiv2008

NNLO corrections to B --> X_u l nu and the determination of |V_ub|

The calculation of partial decay rates in B --> X_u l nu decays at next-to-next-to-leading order (NNLO) in alpha_s and to leading order in 1/m_b is described. New results for the hard function are combined with known results for the jet function and shape-function moments in a numerical analysis which explores the impact of the NNLO corrections on partial decay rates and the determination of |V_{ub}|.

hep-ph↗
arXiv2008

Towards $B \to V γ$ Decays at NNLO in SCET

We compute NNLO (${\cal O}(α_s^2)$) corrections to the hard-scattering kernels entering the QCD factorization formula for $B\to Vγ$ decays, where $V$ is a light vector meson. We give complete NNLO results for the dipole operators $Q_7$ and $Q_8$, and partial results for $Q_1$ valid in the large-$β_0$ limit and neglecting the NNLO correction from hard spectator scattering. Large perturbative logarithms in the hard-scattering kernels are identified and resummed using soft-collinear effective theory. We use our results to estimate the branching fractions for $B\to K^*γ$ and $B_s\to ϕγ$ decays at NNLO and compare them with the current experimental data.

hep-ph↗
arXiv2006

Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering

Renormalization-group methods in soft-collinear effective theory are used to perform the resummation of large perturbative logarithms for deep-inelastic scattering in the threshold region x->1. The factorization theorem for the structure function F_2(x,Q^2) for x->1 is rederived in the effective theory, whereby contributions from the hard scale Q^2 and the jet scale Q^2(1-x) are encoded in Wilson coefficients of effective-theory operators. Resummation is achieved by solving the evolution equations for these operators. Simple analytic results for the resummed expressions are obtained directly in momentum space, and are free of the Landau-pole singularities inherent to the traditional moment-space results. We show analytically that the two methods are nonetheless equivalent order by order in the perturbative expansion, and perform a numerical comparison up to next-to-next-to-leading order in renormalization-group improved perturbation theory.

hep-ph↗
arXiv2005

Non-factorizable contributions to deep inelastic scattering at large x

We use soft-collinear effective theory (SCET) to study the factorization properties of deep inelastic scattering in the region of phase space where 1-x = O(Lambda_{QCD/Q}). By applying a regions analysis to loop diagrams in the Breit frame, we show that the appropriate version of SCET includes anti-hard-collinear, collinear, and soft-collinear fields. We find that the effects of the soft-collinear fields spoil perturbative factorization even at leading order in the 1/Q expansion.

hep-ph↗
arXiv2002

Higher-Order Corrections to QCD Factorization in B->pi K,pi pi Decays

The renormalon calculus is used to calculate the terms of order $β_0^{n-1}α_s^n$ in the perturbative expansions of the Wilson coefficients and hard-scattering kernels entering the QCD factorization formula for hadronic B-meson decays into two light pseudoscalar mesons. The asymptotic behavior of the expansions is analyzed, and a minimal model of power corrections arising from soft ``non-factorizable'' gluon exchange to the B->pi K,pi pi decay amplitudes is obtained, which takes into account the structure of the leading and subleading infrared renormalon singularities. Whereas the resulting power corrections are generally very small, some of the strong-interaction phases of the hard-scattering kernels receive sizeable two-loop corrections. The implications of these findings on CP asymmetries and branching ratios are investigated.

hep-ph↗
arXiv2001

Asymptotics of QCD Factorization in Exclusive Hadronic Decays of B Mesons

Using the renormalon calculus, we study the asymptotic behavior of the perturbative expansion of the hard-scattering kernels entering the QCD factorization formula for the nonleptonic weak decays B->D M, where M is a light meson. In the ``large-beta_0 limit'', the kernels are infrared finite and free of endpoint singularities to all orders of perturbation theory. The leading infrared renormalon singularity corresponding to a power correction of order Lambda/m_b vanishes if the light meson has a symmetric light-cone distribution amplitude. We calculate the Borel transforms and the corresponding momentum distribution functions of the hard-scattering kernels, and resum the series of O(beta_0^{n-1} alpha_s^n) corrections to explore the numerical significance of higher-order perturbative and power corrections. We also derive explicit expressions for the O(beta_0 alpha_s^2) contributions to the kernels, and for the renormalon singularities corresponding to power corrections of order (Lambda/m_b)^2. Finally, we study the limit m_c->0 relevant to charmless hadronic decays such as B->pi pi.

hep-ph↗