32115869
Factorization theorem for high-energy scattering near the end point.
A consistent factorization theorem is presented in the framework of effective field theories. Conventional factorization suffers from infrared divergences in the soft and collinear parts. We present a factorization theorem in which the infrared divergences appear only in the parton distribution functions by carefully reorganizing collinear and soft parts. The central idea is extracting the soft contributions from the collinear part to avoid double counting. Combining it with the original soft part, an infrared-finite kernel is obtained. This factorization procedure can be applied to various high-energy scattering processes.
18725095
Consequences of symmetries in renormalizing collinear effective theory
We consider effects of symmetries on renormalization properties of the collinear effective theory. We investigate which types of operators are possible in the effective theory satisfying gauge invariance, reparameterization invariance and residual energy invariance. Each symmetry puts a constraint on the possible structure of the theory, and there can appear only specific combinations of operators in the effective Lagrangian satisfying all the symmetry requirements. And the final effective Lagrangian is not renormalized to all orders in alpha_s as long as no other nonlocal operators are induced at higher order. We explicitly prove this at one loop by renormalizing one-gluon vertices and discuss their features.
119217158
Factorization and resummation for single color-octet scalar production at the LHC
Heavy colored scalar particles appear in a variety of new physics (NP) models and could be produced at the Large Hadron Collider. Knowing the total production cross section is important for searching for these states and establishing bounds on their masses and couplings. Using soft-collinear effective theory, we derive a factorization theorem for the process $pp\ensuremath{\rightarrow}SX$, where $S$ is a color-octet scalar, that is applicable to any NP model provided the dominant production mechanism is gluon-gluon fusion. The factorized result for the inclusive cross section is similar to that for the standard model Higgs production; however, differences arise due to color exchange between initial and final states. We provide formulas for the total cross section with large (partonic) threshold logarithms resummed to next-to-leading logarithm accuracy. The resulting $K$ factors are similar to those found in Higgs production. We apply our formalism to the Manohar-Wise model and find that the next-to-leading logarithm cross section is roughly 2 times (3 times) as large as the leading order cross section for a color-octet scalar of mass of 500 GeV (3 TeV). A similar enhancement should appear in any NP model with color-octet scalars.
8812146
Rare radiative exclusive B decays in soft-collinear effective theory
We consider rare radiative B decays such as $\overline{B}\ensuremath{\rightarrow}{K}^{*}\ensuremath{\gamma}$ or $\overline{B}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\gamma}$ in soft-collinear effective theory (SCET) and show that the decay amplitudes are factorized to all orders in ${\ensuremath{\alpha}}_{s}$ and at leading order in ${\ensuremath{\Lambda}}_{\mathrm{QCD}}{/m}_{b}.$ By employing two-step matching, we classify the operators for radiative B decays in powers of a small parameter $\ensuremath{\lambda}(\ensuremath{\sim}\sqrt{{\ensuremath{\Lambda}}_{\mathrm{QCD}}{/m}_{b}})$ and obtain the relevant operators to order $\ensuremath{\lambda}$ in ${\mathrm{SCET}}_{\mathrm{I}}.$ These operators are constructed with or without spectator quarks including the four-quark operators contributing to annihilation and W-exchange channels. And we employ ${\mathrm{SCET}}_{\mathrm{II}}$ where the small parameter becomes of order ${\ensuremath{\Lambda}}_{\mathrm{QCD}}{/m}_{b},$ and evolve the operators in order to compute the decay amplitudes for rare radiative decays in soft-collinear effective theory. We show explicitly that the contributions from the annihilation channels and the W-exchange channels vanish at leading order in SCET. We present the factorized result for the decay amplitudes in rare radiative B decays at leading order in SCET and at next-to-leading order in ${\ensuremath{\alpha}}_{s}.$
117566763
Gauge-invariant Lagrangian of the soft-collinear effective theory and its application to soft-collinear currents
We construct the soft-collinear effective Lagrangian which is manifestly gauge invariant order by order. Field redefinitions of collinear gauge fields and a proper decomposition of quark fields are necessary to make the Lagrangian gauge invariant. We can obtain the effective Lagrangian order by order in SCET_I and SCET_II by adopting appropriate power counting methods. Various types of current operators can be investigated using this formalism, and we choose the soft-collinear current as a specific example to present explicit radiative corrections. The hard-collinear, collinear, and ultrasoft modes in SCET_I and the collinear and soft modes in SCET_II reproduce the infrared divergences of the full theory and the matching can be performed. We show our results explicitly using two types of regularization schemes. The first scheme is the dimensional regularization both for the ultraviolet and the infrared divergences with on-shell particles, and the second scheme is regulating the infrared divergence with the off-shellness of external particles. We discuss other types of operators in terms of the two-step matching.
119340841
Collinear effective theory at subleading order and its application to heavy - light currents
We consider a collinear effective theory of highly energetic quarks with energy E, interacting with collinear and soft gluons by integrating out collinear degrees of freedom to subleading order. The collinear effective theory offers a systematic expansion in power series of a small parameter lambda ~ p_{\perp}/E, where p_{\perp} is the transverse momentum of a collinear particle. We construct the effective Lagrangian to first order in $\lambda$, and discuss its features including additional symmetries such as collinear gauge invariance and reparameterization invariance. Heavy-light currents can be matched from the full theory onto the operators in the collinear effective theory at one loop and to order lambda. We obtain heavy-light current operators in the effective theory, calculate their Wilson coefficients at this order, and the renormalization group equations for the Wilson coefficients are solved. As an application, we calculate the form factors for decays of B mesons to light energetic mesons to order lambda and at leading-logarithmic order in alpha_s.
120458097
A Study of the Azimuthal Decorrelation between Jets with Large Rapidity Separation