Quark Fragmentation within an Identified Jet

We derive a factorization theorem that describes an energetic hadron h fragmenting from a jet produced by a parton i, where the jet invariant mass is measured. The analysis yields a "fragmenting jet function" G_i^h(s,z) that depends on the jet invariant mass s, and on the energy fraction z of the fragmentation hadron. We show that G^h_i can be computed in terms of perturbatively calculable coefficients, J_{ij}(s,z/x), integrated against standard non-perturbative fragmentation functions, D_j^{h}(x). We also show that the sum over h of the integral over z of z G_i^h(s,z) is given by the standard inclusive jet function J_i(s) which is perturbatively calculable in QCD. We use Soft-Collinear Effective Theory and for simplicity carry out our derivation for a process with a single jet, B -> X h l nu, with invariant mass m_{X h}^2 >> Lambda_QCD^2. Our analysis yields a simple replacement rule that allows any factorization theorem depending on an inclusive jet function J_i to be converted to a semi-inclusive process with a fragmenting hadron h. We apply this rule to derive factorization theorems for B -> X K gamma which is the fragmentation to a Kaon in b -> s gamma, and for e^+e^- -> (dijets)+h with measured hemisphere dijet invariant masses.Comment: 26 pages, 2 figures; v3: small correction to eq.(72

Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme

The quasi parton distribution is a spatial correlation of quarks or gluons along the $z$ direction in a moving nucleon which enables direct lattice calculations of parton distribution functions. It can be defined with a nonperturbative renormalization in a regularization independent momentum subtraction scheme (RI/MOM), which can then be perturbatively related to the collinear parton distribution in the $\overline{\text{MS}}$ scheme. Here we carry out a direct matching from the RI/MOM scheme for the quasi-PDF to the $\overline{\text{MS}}$ PDF, determining the non-singlet quark matching coefficient at next-to-leading order in perturbation theory. We find that the RI/MOM matching coefficient is insensitive to the ultraviolet region of convolution integral, exhibits improved perturbative convergence when converting between the quasi-PDF and PDF, and is consistent with a quasi-PDF that vanishes in the unphysical region as the proton momentum $P^z\to \infty$, unlike other schemes. This direct approach therefore has the potential to improve the accuracy for converting quasi-distribution lattice calculations to collinear distributions.Comment: 18 pages, 6 figure

An application of semigroup theory to a fragmentation equation

The process of fragmentation arises in many physical situations, including polymer degradation, droplet breakage and rock crushing and grinding. Under suitable assumptions, the evolution of the size distribution c(x, t), where x represents particle size and t is time, may be described by the linear integro-differential equation

Semileptonic Lambda_b decay to excited Lambda_c baryons at order Lambda_{QCD}/m_Q

Exclusive semileptonic Lambda_b decays to excited charmed Lambda_c baryons are investigated at order Lambda_{QCD}/m_Q in the heavy quark effective theory. The differential decay rates are analyzed for the J^\pi=1/2^- Lambda_c(2593) and the J^\pi=3/2^- \Lambda_c(2625). They receive 1/m_{c,b} corrections at zero recoil that are determined by mass splittings and the leading order Isgur-Wise function. With some assumptions, we find that the branching fraction for Lambda_b decays to these states is 2.5-3.3%. The decay rate to the helicity \pm 3/2 states, which vanishes for m_Q \to \infty, remains small at order Lambda_{QCD}/m_Q since 1/m_c corrections do not contribute. Matrix elements of weak currents between a Lambda_b and other excited Lambda_c states are analyzed at zero-recoil to order Lambda_{QCD}/m_Q. Applications to baryonic heavy quark sum-rules are explored.Comment: 27 pages, 1 fig., minor changes, version to appear in Phys.Rev.

Building Blocks for Subleading Helicity Operators

On-shell helicity methods provide powerful tools for determining scattering amplitudes, which have a one-to-one correspondence with leading power helicity operators in the Soft-Collinear Effective Theory (SCET) away from singular regions of phase space. We show that helicity based operators are also useful for enumerating power suppressed SCET operators, which encode subleading amplitude information about singular limits. In particular, we present a complete set of scalar helicity building blocks that are valid for constructing operators at any order in the SCET power expansion. We also describe an interesting angular momentum selection rule that restricts how these building blocks can be assembled.Comment: 22 pages without references, 2 figures v2. Updated minor typo in Table