arXiv subjects

Iain W. Stewart

Publications and source records attributed to Iain W. Stewart.

At least 163 records · Page 9Linked to original sources

arXiv2002

Soft-Collinear Factorization in Effective Field Theory

The factorization of soft and ultrasoft gluons from collinear particles is shown at the level of operators in an effective field theory. Exclusive hadronic factorization and inclusive partonic factorization follow as special cases. The leading order Lagrangian is derived using power counting and gauge invariance in the effective theory. Several species of gluons are required, and softer gluons appear as background fields to gluons with harder momenta. Two examples are given: the factorization of soft gluons in B->D pi, and the soft-collinear convolution for the B->Xs gamma spectrum.

hep-ph↗

arXiv2002

Threshold Top Quark Production

Predictions for the total cross section for e+e- -> t tbar near threshold are reviewed. The renormalization group improved results at NNLL order have improved convergence and reduced scale dependence relative to fixed order results at NNLO. Prospects for measurements of the top-quark mass, width, and Yukawa coupling are discussed.

hep-ph↗

arXiv2001

A proof of factorization for B -> D pi

We prove that the matrix elements of four fermion operators mediating the decay B^0 -> D^+ π^- and B^- -> D^0 π^- factor into the product of a form factor describing the B -> D transition and a convolution of a short distance coefficient with the nonperturbative pion light-cone wave function. This is shown to all orders in alpha_s, up to corrections suppressed by factors of 1/mb, 1/mc, and 1/E_pi. It is not necessary to assume that the pion state is dominated by the q-qbar Fock state.

hep-ph↗

arXiv2001

Invariant Operators in Collinear Effective Theory

We consider processes which produce final state hadrons whose energy is much greater than their mass. In this limit interactions involving collinear fermions and gluons are constrained by a symmetry, and we give a general set of rules for constructing leading and subleading invariant operators. Wilson coefficients C(mu,P) are functions of a label operator P, and do not commute with collinear fields. The symmetry is used to reproduce a two-loop result for factorization in B -> D pi in a simple way.

hep-ph↗

arXiv2001

An effective field theory for collinear and soft gluons: heavy to light decays

We construct the Lagrangian for an effective theory of highly energetic quarks with energy Q, interacting with collinear and soft gluons. This theory has two low energy scales, the transverse momentum of the collinear particles, p_perp, and the scale p_perp^2/Q. The heavy to light currents are matched onto operators in the effective theory at one-loop and the renormalization group equations for the corresponding Wilson coefficients are solved. This running is used to sum Sudakov logarithms in inclusive B -> X_s gamma and B -> X_u \ell nu decays. We also show that the interactions with collinear gluons preserve the relations for the soft part of the form factor for heavy to light decays found by Charles et al., establishing these relations in the large energy limit of QCD.

hep-ph↗

arXiv2001

The Running Coulomb Potential and Lamb Shift in QCD

The QCD beta-function and the anomalous dimensions for the Coulomb potential and the static potential first differ at three loop order. We evaluate the three loop ultrasoft anomalous dimension for the Coulomb potential and give the complete three loop running. Using this result, we calculate the leading logarithmic Lamb shift for a heavy quark-antiquark bound state, which includes all contributions to the binding energies of the form mα_s^4(α_s lnα_s)^k, k\ge 0.

hep-ph↗

arXiv2001

Running of the heavy quark production current and 1/k potential in QCD

The 1/k contribution to the heavy quark potential is first generated at one loop order in QCD. We compute the two loop anomalous dimension for this potential, and find that the renormalization group running is significant. The next-to-leading-log coefficient for the heavy quark production current near threshold is determined. The velocity renormalization group result includes the alpha_s^3 ln^2(alpha_s) ``non-renormalization group logarithms'' of Kniehl and Penin.

hep-ph↗

arXiv2000

Nonrelativistic Bound States in Quantum Field Theory

Nonrelativistic bound states are studied using an effective field theory. Large logarithms in the effective theory can be summed using the velocity renormalization group. For QED, one can determine the structure of the leading and next-to-leading order series for the energy, and compute corrections up to order alpha^8 ln^3 alpha, which are relevant for the present comparison between theory and experiment. For QCD, one can compute the velocity renormalization group improved quark potentials. Using these to compute the renormalization group improved t-tbar production cross-section near threshold gives a result with scale uncertainties of 2%, a factor of 10 smaller than existing fixed order calculations.

hep-lat↗

arXiv2000

Bound States in NRQCD/NRQED and the Renormalization Group

The application of renormalization group techniques to bound states in non-relativistic QED and QCD is discussed. For QED bound states like Hydrogen and positronium, the renormalization group allows large logarithms of the velocity, ln v (or equivalently ln alpha's), to be predicted in a universal and simple way. The series of (alpha ln alpha)'s are shown to terminate after a few terms. For QCD one can systematically sum infinite series of the form [alpha_s ln alpha_s]^k$, and answer definitively the question ``alpha_s at what scale?''.

hep-ph↗

arXiv2000

The renormalization group for correlated scales: one-stage versus two-stage running

Nonrelativistic bound states have two low energy scales, a soft scale mu_S of order mv and an ultrasoft scale mu_U of order mv^2. In two-stage running, the soft and ultrasoft scales are lowered from m to mv, and then the ultrasoft scale is lowered from mv to mv^2. In one-stage running, the two scales are lowered in a correlated way using a subtraction velocity. We compare these two methods of summing logarithms and show that only the correlated running in velocity space of the one-stage method correctly reproduces the logarithms in non-relativistic bound states in QED. The argument for one-stage running is general, and should apply to any system with correlated scales.

hep-ph↗

arXiv2000

NNLO Corrections to Nucleon-Nucleon Scattering and Perturbative Pions

The 1S0, 3S1, and 3D1 nucleon-nucleon scattering phase shifts are calculated at next-to-next-to-leading order (NNLO) in an effective field theory. Predictions for the 1P1, 3P0, 3P1, 3P2, 1D2, 3D2, and 3D3 phase shifts at this order are also compared with data. The calculations treat pions perturbatively and include the NNLO contributions from order $Q_r^3$ and $Q_r^4$ radiation pion graphs. In the 3S1, 3D1, 3P0, and 3P2 channels we find large disagreement with the Nijmegen partial wave analysis at NNLO. These spin triplet channels have large corrections from graphs with two potential pion exchange which do not vanish in the chiral limit. We compare our results to calculations within the Weinberg approach, and find that in some spin triplet channels the summation of potential pion diagrams seems to be necessary to reproduce the observed phase shifts. In the spin singlet channels the nonperturbative treatment of potential pions does not afford a significant improvement over the perturbative approach.

nucl-th↗

arXiv2000

The NN scattering 3S1-3D1 mixing angle at NNLO

The 3S1-3D1 mixing angle for nucleon-nucleon scattering, epsilon_1, is calculated to next-to-next-to-leading order in an effective field theory with perturbative pions. Without pions, the low energy theory fits the observed epsilon_1 well for momenta less than $\sim 50$ MeV. Including pions perturbatively significantly improves the agreement with data for momenta up to $\sim 150$ MeV with one less parameter. Furthermore, for these momenta the accuracy of our calculation is similar to an effective field theory calculation in which the pion is treated non-perturbatively. This gives phenomenological support for a perturbative treatment of pions in low energy two-nucleon processes. We explain why it is necessary to perform spin and isospin traces in d dimensions when regulating divergences with dimensional regularization in higher partial wave amplitudes.

nucl-th↗

arXiv2000

The QCD heavy-quark potential to order v^2: one loop matching conditions

The one-loop QCD heavy quark potential is computed to order v^2 in the color singlet and octet channels. Several errors in the previous literature are corrected. To be consistent with the velocity power counting, the full dependence on |p' + p|/|p' - p| is kept. The matching conditions for the NRQCD one-loop potential are computed by comparing the QCD calculation with that in the effective theory. The graphs in the effective theory are also compared to terms from the hard, soft, potential, and ultrasoft regimes in the threshold expansion. The issue of off-shell versus on-shell matching and gauge dependence is discussed in detail for the 1/(m k) term in the potential. Matching on-shell gives a 1/(m k) potential that is gauge independent and does not vanish for QED.

hep-ph↗

arXiv2000

Logarithms of alpha in QED bound states from the renormalization group

The velocity renormalization group is used to determine ln(alpha) contributions to QED bound state energies. The leading order anomalous dimension for the potential gives the alpha^5 ln(alpha) Bethe logarithm in the Lamb shift. The next-to-leading order anomalous dimension determines the alpha^6 ln(alpha), alpha^7 ln^2(alpha), and alpha^8 ln^3 (alpha) corrections to the energy. These are used to obtain the alpha^8 ln^3(alpha) Lamb shift and alpha^7 ln^2(alpha) hyperfine splitting for Hydrogen, muonium and positronium, as well as the alpha^2 ln(alpha) and alpha^3 ln^2(alpha) corrections to the ortho- and para-positronium lifetimes.

hep-ph↗

arXiv2000

Conformal Invariance for Non-Relativistic Field Theory

Momentum space Ward identities are derived for the amputated n-point Green's functions in 3+1 dimensional non-relativistic conformal field theory. For n=4 and 6 the implications for scattering amplitudes (i.e. on-shell amputated Green's functions) are considered. Any scale invariant 2-to-2 scattering amplitude is also conformally invariant. However, conformal invariance imposes constraints on off-shell Green's functions and the three particle scattering amplitude which are not automatically satisfied if they are scale invariant. As an explicit example of a conformally invariant theory we consider non-relativistic particles in the infinite scattering length limit.

hep-th↗

arXiv1999

Renormalization group analysis of the QCD quark potential to order v^2

A one-loop renormalization group analysis of the order v^2 relativistic corrections to the static QCD potential is presented. The velocity renormalization group is used to simultaneously sum ln(m/mv) and ln(m/mv^2) terms. The results are compared to previous calculations in the literature.

hep-ph↗

arXiv1999

Radiation pions in two-nucleon effective field theory

For interactions involving two or more nucleons it is useful to divide pions into three classes: potential, radiation, and soft. The momentum threshold for the production of radiation pions is $Q_r = \sqrt{M_N m_π}$. We show that radiation pions can be included systematically with a power counting in $Q_r$. The leading order radiation pion graphs which contribute to NN scattering are evaluated in the PDS and OS renormalization schemes and are found to give a small contribution. The power counting for soft pion contributions is also discussed.

nucl-th↗

arXiv1999

Applications of Chiral Perturbation Theory in Reactions with Heavy Particles

Effective field theory techniques are used to describe the interaction of heavy hadrons in a model independent way. Predictability is obtained by exploiting the symmetries of QCD. Heavy hadron chiral perturbation theory is reviewed and used to describe $D^*$ decays. The phenomenologically important $D^*Dπ$ coupling is extracted from data working to first order in the chiral and heavy quark symmetry breaking parameters. A method is described for determining $|V_{ub}|$ from exclusive semileptonic $B$ and $D$ decays with 10% uncertainty. An effective field theory for two-nucleon systems is then discussed. The large S-wave scattering lengths necessitate expanding around a non-trivial fixed point. A detailed discussion of the interplay between renormalization and the power counting is given. In power counting pion interactions with nucleons it is useful to consider three classes of pion: potential, radiation, and soft. A power counting for massive radiation is developed. Finally, it is shown that the leading terms in the effective theory for nucleon-nucleon interactions are invariant under Wigner's SU(4) spin-isospin symmetry in the infinite scattering length limit.

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