398 research outputs found

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

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    We introduce a momentum subtraction scheme which obeys the power counting of Kaplan, Savage, and Wise (KSW), developed for systems with large scattering lengths, aa. Unlike the power divergence subtraction scheme, coupling constants in this scheme obey the KSW scaling for all μR>1/a\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>mπp>m_\pi.Comment: 12 pages, 3 fig

    Jet Vetoes Interfering with H->WW

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    Far off-shell Higgs production in HWW,ZZH \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 pTp_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/ZW/Z. Summing large logarithms of s^/pTveto\sqrt{\hat s}/p_T^{veto}, we find that the jet veto induces a strong dependence on the partonic centre of mass energy, s^\sqrt{\hat s}, and modifies distributions in s^\sqrt{\hat s} or MTM_T. The example of ggHWWgg\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

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    The quasi parton distribution is a spatial correlation of quarks or gluons along the zz 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 MS\overline{\text{MS}} scheme. Here we carry out a direct matching from the RI/MOM scheme for the quasi-PDF to the MS\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 PzP^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

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    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

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    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

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    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
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