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M. R. Pennington

Publications and source records attributed to M. R. Pennington.

At least 55 records · Page 3Linked to original sources
arXiv2007

Extracting the ${\bar q}q$ condensate for light quarks beyond the chiral limit in models of QCD

It has recently been suggested \cite{Chang:2006bm} that a reliable and unambiguous definition of the non-perturbative massive quark condensate could be provided by considering a non positive-definite class of solutions to the Schwinger Dyson Equation for the quark propagator. In this paper we show that this definition is incomplete without considering a third class of solutions. Indeed, studying these three classes reveals a degeneracy of possible condensate definitions leading to a whole range of values. However, we show that the {\it physical} condensate may in fact be extracted by simple fitting to the Operator Product Expansion, a procedure which is stabilised by considering the three classes of solution together. We find that for current quark masses in the range from zero to 25 MeV or so (defined at a scale of 2 GeV in the $\bar{MS}$ scheme), the dynamically generated condensate increases from the chiral limit in a wide range of phenomenologically successful models of the confining QCD interaction. Lastly, the role of a fourth class of noded solutions is briefly discussed.

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arXiv2007

Quark Condensates: Flavour Dependence

We determine the q-bar q condensate for quark masses from zero up to that of the strange quark within a phenomenologically successful modelling of continuum QCD by solving the quark Schwinger-Dyson equation. The existence of multiple solutions to this equation is the key to an accurate and reliable extraction of this condensate using the operator product expansion. We explain why alternative definitions fail to give the physical condensate.

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arXiv2007

Can experiment distinguish tetraquark scalars, molecules and $\qq$ mesons?

Scalar mesons are a key expression of the strong coupling regime of QCD. How those with $I_3=0$ couple to two photons supplies important information about which is transiently ${\bar q}q$ or ${\bar {qq}} qq$ or multi-meson molecule or largely glue, provided (i) we know the location of the corresponding poles in the complex energy plane, and (ii) we have reliable predictions from strong coupling QCD of the radiative widths for these compositions. Number (i) is being supplied by careful analyses of high statistics data particularly that coming from $B$, $D$, $J/ψ$ and $ϕ$ decays. Number (ii) is still required, before we can answer the question in the title.

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arXiv2007

Aspects of quark mass generation on a torus

In this talk we report on recent results for the quark propagator on a compact manifold. The corresponding Dyson-Schwinger equations on a torus are solved on volumes similar to the ones used in lattice calculations. The quark-gluon interaction is fixed such that the lattice results are reproduced. We discuss both the effects in the infinite volume/continuum limit as well as effects when the volume is small.

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arXiv2006

${\bar {q}}q$ condensate for light quarks beyond the chiral limit

We determine the ${\bar{q}}q$ condensate for quark masses from zero up to that of the strange quark within a phenomenologically successful modelling of continuum QCD by solving the quark Schwinger-Dyson equation. The existence of multiple solutions to this equation is the key to an accurate and reliable extraction of this condensate using the operator product expansion. We explain why alternative definitions fail to give the physical condensate.

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arXiv2006

Dalitz Analyses: A Tool for Physics within and Beyond the Standard Model

Dalitz analyses are introduced as the method for studying hadronic decays. An accurate description of hadron final states is critical not only to an understanding of the strong coupling regime of QCD, but also to the precision extraction of CKM matrix elements. The relation of such final state interactions to scattering processes is discussed.

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arXiv2006

Checking the transverse Ward-Takahashi relation at one loop order in 4-dimensions

Some time ago Takahashi derived so called {\it transverse} relations relating Green's functions of different orders to complement the well-known Ward-Green-Takahashi identities of gauge theories by considering wedge rather than inner products. These transverse relations have the potential to determine the full fermion-boson vertex in terms of the renormalization functions of the fermion propagator. He & Yu have given an indicative proof at one-loop level in 4-dimensions. However, their construct involves the 4th rank Levi-Civita tensor defined only unambiguously in 4-dimensions exactly where the loop integrals diverge. Consequently, here we explicitly check the proposed transverse Ward-Takahashi relation holds at one loop order in $d$-dimensions, with $d=4+ε$.

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arXiv2006

Crouching Sigma, Hidden Scalar in $γγ\toπ^0π^0$

There has long been speculation about the nature of the $σ$-resonance. For three decades Jaffe has argued for a tetraquark composition, while others have claimed it is largely a glueball. A key pointer to its nature is its coupling to two photons. Consequently, there have been recent proposals to observe this important scalar hiding in $γγ\toπ^0π^0$. We show here that the $σ$ is already crouching in this cross-section exactly as measured twenty years ago. What is new is that precise knowledge of the position of the $σ$-pole, provided by the analysis of the Roy equations, now allows its two photon coupling to be accurately fixed. Its two photon width is found to be $(4.1 \pm 0.3)$ keV, a value far too large for a gluonic, or even a tetraquark, state.

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arXiv2006

Finite volume effects in a quenched lattice-QCD quark propagator

We investigate finite volume effects in the pattern of chiral symmetry breaking. To this end we employ a formulation of the Schwinger-Dyson equations on a torus which reproduces results from the corresponding lattice simulations of staggered quarks and from the overlap action. Studying the volume dependence of the quark propagator we find quantitative differences with the infinite volume result at small momenta and small quark masses. We estimate the minimal box length L below which chiral perturbation theory cannot be applied to be L \simeq 1.6 fm. In the infinite volume limit we find a chiral condensate of |<\bar{q}q>|_{\bar{MS}}^{2 GeV} = (253 \pm 5.0 MeV)^3, an up/down quark mass of m_{\bar{MS}}^{2 GeV} = 4.1 \pm 0.3 MeV and a pion decay constant which is only ten percent smaller than the experimental value.

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arXiv2005

Scalars in the hadron world: the Higgs sector of the strong interaction

Scalar mesons are a key expression of the strong physics regime of QCD and the role condensates, particularly $ $, play in breaking chiral symmetry. What new insights have been provided by recent experiments on $D, D_s$ and $J/ψ$ decays to light hadrons is discussed. We need to establish whether all the claimed scalars $σ$, $κ$, $f_0(1370)$, etc., really exist and with what parameters before we can meaningfully speculate further about which is transiently ${\bar q}q$, ${\bar{qq}} qq$, multi-meson molecule or largely glue.

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arXiv2005

Estimating the I=3/2 K pi interaction in D decay

Heavy flavour decay to light hadrons is the key to understanding many aspects of the SM from CP violation to strong dynamics. It is often presumed in line with the simple quark spectator model of D decay to Kpipi that the Kpi system has only I=1/2. E791 have recently presented an analysis of their results on D+ to (K-pi+)pi+ using a generalised isobar picture of two body interactions. While higher Kpi waves are described by sums of known resonances, the S-wave amplitude and phase are determined bin-by-bin in Kpi mass. The phase variation is found not to be that of K-pi+ elastic scattering. This hints at a different mixture of I=1/2 and I=3/2 S-wave interactions than in elastic scattering. Applying Watson's theorem to this generalised isobar model allows us to estimate the I=3/2 Kpi S-wave component. We indeed find that this is larger than in hadronic scattering or semileptonic processes.

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arXiv2005

Swimming with Quarks

These six lectures, given at the XI Mexican School of Particles and Fields held at Xalapa in August 2004, are on the subject of strong coupling QCD. How this colours and shapes the hadron world in terms of (i) the hadron spectrum, (ii) chiral symmetry breaking, (iii) dynamical mass generation and (iv) confinement, are the topics discussed.

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arXiv2004

QCD Down Under: Building Bridges

The strong coupling regime of QCD is responsible for 99% of hadronic phenomena. Though considerable progress has been made in solving QCD in this non-perturbative region, we nevertheless have to rely on a disparate range of models and approximations. If we are to gain an understanding of the underlying physics and not just have numerical answers from computing `` black'' boxes, we must build bridges between the parameter space where models and approximations are valid to the regime describing experiment, and between the different modellings of strong dynamics. We describe here how the Schwinger-Dyson/Bethe-Salpeter approach provides just such a bridge, linking physics, the lattice and experiment.

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arXiv2003

Light by light scattering at a low energy $e^+e^-$ collider -or- What to do while waiting for that rare kaon decay event

Two photon processes are a wonderful by-product of an $e^+e^-$ collider at any energy. Two photon reactions probe the very structure of matter. A machine operating below 2 GeV has the potential to reveal the Higgs sector of the strong interaction -- the scalars with vacuum quantum numbers that reflect dynamical mass generation from the breakdown of chiral symmetry. One of the many $e^+e^-$ machines around the globe must have a dedicated $γγ$ facility.

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arXiv2003

In the debris of hadron interactions lies the beauty of QCD (part II)

Recent progress in understanding the strong physics regime of QCD is described. The role played by condensates, particularly $ $, in breaking chiral symmetry and generating constituent masses for $u$ and $d$ quarks is reviewed. The influence this has on hadrons with vacuum quantum numbers is emphasised. What we know of this sector from recent experiments on $ϕ$-radiative decays and from $D$ decays to light hadrons is discussed. How we may gain a more complete understanding of this vacuum sector is outlined.

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arXiv2003

In the debris of hadron interactions lies the beauty of QCD

Recent progress in understanding the strong physics regime of QCD is described. The role played by condensates, particularly $q{\bar q}$, in breaking chiral symmetry and generating constituent masses for $u$ and $d$ quarks is reviewed. The influence this has on hadrons with vacuum quantum numbers is emphasised. What we know of this sector from recent data on $ϕ$-radiative decays and from $D$ decays to light hadrons is discussed. The key to further understanding is comprehensive analyses of such data, including that planned for Hall D at Jefferson Laboratory.

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arXiv2003

Towards a model independent determination of the phi -> f_0 - gamma coupling

A guide to the composition of the enigmatic f_0(980) and a_0(980) states is their formation in phi-radiative decays. Precision data are becoming available from the KLOE experiment at the DAPHNE machine at Frascati, as well as results from SND and CMD-2 at VEPP-2M at Novosibirsk. We show how the coupling of the f_0(980) to this channel can be extracted from these, independently of the background provided by sigma production. To do this we use the fact that the behaviour of both the f_0(980) and sigma cannot be determined by these data alone, but is strongly constrained by experimental results from other hadronic processes as required by unitarity. We find that the resulting coupling for the phi -> gamma f_0(980) is about 10^{-4} GeV with a background that is quite unlike that assumed if unitarity is neglected. This provides an object lesson in how unitarity teaches us to add resonances. Not surprisingly the result is crucially dependent on the pole position of the f_0(980), for which there are still sizeable uncertainties. At present this leads to an uncertainty in the phi -> f_0 gamma branching ratio which can only be fixed by further precision data on the f_0(980).

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