398 research outputs found

### A momentum subtraction scheme for two--nucleon effective field theory

We introduce a momentum subtraction scheme which obeys the power counting of
Kaplan, Savage, and Wise (KSW), developed for systems with large scattering
lengths, $a$. Unlike the power divergence subtraction scheme, coupling
constants in this scheme obey the KSW scaling for all $\mu_R > 1/a$. We comment
on the low-energy theorems derived by Cohen and Hansen. We conclude that there
is no obstruction to using perturbative pions for momenta $p>m_\pi$.Comment: 12 pages, 3 fig

### Jet Vetoes Interfering with H->WW

Far off-shell Higgs production in $H \rightarrow WW,ZZ$, is a particularly
powerful probe of Higgs properties, allowing one to disentangle Higgs width and
coupling information unavailable in on-shell rate measurements. These
measurements require an understanding of the cross section in the far off-shell
region in the presence of realistic experimental cuts. We analytically study
the effect of a $p_T$ jet veto on far off-shell cross sections, including
signal-background interference, by utilizing hard functions in the soft
collinear effective theory that are differential in the decay products of the
$W/Z$. Summing large logarithms of $\sqrt{\hat s}/p_T^{veto}$, we find that the
jet veto induces a strong dependence on the partonic centre of mass energy,
$\sqrt{\hat s}$, and modifies distributions in $\sqrt{\hat s}$ or $M_T$. The
example of $gg\rightarrow H \rightarrow WW$ is used to demonstrate these
effects at next to leading log order. We also discuss the importance of jet
vetoes and jet binning for the recent program to extract Higgs couplings and
widths from far off-shell cross sections.Comment: 31 pages, 8 figures. v2: Journal Versio

### 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

### 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

### Fragmentation inside an identified jet

Using Soft-Collinear Effective Theory we derive factorization formulae for
semi-inclusive processes where a light hadron h fragments from a jet whose
invariant mass is measured. Our analysis yields a novel "fragmenting jet
function" G_i^h(s,z) that depends on the jet invariant mass \sqrt{s}, and on
the fraction z of the large light-cone momentum components of the hadron and
the parent parton i. We show that G_i^h(s,z) 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). Our analysis
yields a simple replacement rule that allows any factorization theorem
depending on a jet function J_i to be converted to a semi-inclusive process
with a fragmenting hadron h.Comment: 3 pages; presented at "Quark Confinement and the Hadron Spectrum IX -
QCHS IX" (30 August - 3 September 2010, Madrid, Spain), to appear in the
proceeding

### Stability for a class of equilibrium solutions to the coagulation-fragmentation equation

We consider the behaviour of solutions to the continuous constant-rate coagulation-fragmentation equation in the vicinity of an equilibrium solution. Semigroup methods are used to show that the governing linear equation for a perturbation epsilon(x,t) has a unique globally defined solution for suitable initial conditions. In addition, Laplace transforms and the method of characteristics lead to an explicit formula for epsilon. The long-term behavior of epsilon is also discussed

- â€¦