~/Physics

"The noblest pleasure is the joy of understanding." ~ Leonardo da Vinci
"...one of the strongest motives that lead men to art and science is escape from everyday life with its painful crudity and hopeless dreariness, from the fetters of one's own ever-shifting desires. A finely tempered nature longs to escape from the personal life into the world of objective perception and thought." ~ Albert Eistein
"He who has Art and Science also has religion, But those who do not have them better have religion." ~Johann Wolfgang von Goethe
“古之欲明德于天下者，先治其国。欲治其国者，先齐其家，欲齐其家者， 先修其身。欲修其身者，先正其心。欲正其心者，先诚其意。欲诚其意者， 先致其知。致知在格物。”~《大学》
“天地有大美而不言， 四时有明法而不议， 万物有成理而不说。圣人者， 原天地之美而达万物之理。”~《庄子外篇·知北游》

Effective (field) theories

It is possible to understand, at least phenomenologically, a good amount of (19th-centuray) chemistry without much detailed knowledge of quantum mechanics andvirtually nothing of QCD, even the existence of it. By similar philosophy, making useful and nontrivial preditions for many physical systems often do not require a detailed understanding of its "fundamental"/"under-laying" theory, sometimes not even the existence of it. An effective (field) theory is often an implementation of this idea for a specific physical system of interest in order to describe its dynamics in terms of relavent degrees of freedom, and to make phenomenological predictions with relavent accuracy. This is often achieved by leveraging the separation of scales present in the physical system, so the leading order effects can be extracted.

Research Projects


The Effects of charged charm mesons on the line shapes of the X(3872)

The Effects of Charged Charm Mesons on the Line Shapes of the X(3872), with Eric Braaten, arXiv:0710.5482v1 [hep-ph]

The quantum numbers J^PC = 1++ of the X(3872) and the proximity of its mass to the D*0 anti-D0 threshold imply that it is either a loosely-bound hadronic molecule whose constituents are a superposition of D*0 anti-D0 and D0 anti-D*0 or it is a virtual state of charm mesons. The line shapes of the X(3872) can discriminate between these two possibilities. At energies within a few MeV of the D*0 anti-D0 threshold, the lines shapes of the X produced in B -> K transitions are determined by its binding energy and its width. Their normalizations are determined by a short-distance constant that is different for B+ -> K+ and B0 -> K0. At energies comparable to the 8 MeV splitting between the D*0 anti-D0 and D*+ D- thresholds, the charged meson channels D*+ D- and D+ D*- have a significant effect on the line shapes of the X. We calculate the line shapes taking into account the resonant coupling between the charged and neutral 1++ channels. The line shapes and their normalizations depend on one additional scattering parameter and two additional short-distance constants associated with the B -> K transitions. The line shapes of the X resonance depend on its decay channel; they are different for J/psi pi+ pi-, J/psi pi+ pi- pi0, and D0 anti-D0 pi0. The line shapes are also different for X produced in B+ decays and in B0 decays. Some conceptual errors in previous work on this problem are pointed out.

Line shapes of the X(3872)

Line Shapes of the X(3872), with Eric Braaten, arXiv:0709.2697v1 [hep-ph]

If the quantum numbers of the X(3872) are J^{PC}=1^{++}, the measurement of its mass implies that it is either a loosely-bound hadronic molecule whose constituents are a superposition of the charm mesons pairs D^{*0} Dbar^0 and D^0 Dbar^{*0} or else it is a virtual state of these charm mesons. Its binding energy is small enough that the decay width of a constituent D^{*0} or Dbar^{*0} has a significant effect on the line shapes of the X resonance. We develop a simple approximation to the line shapes that takes into account the effect of the D^{*0} width as well as inelastic scattering channels of the charm mesons. We carry out a simultaneous fit to the line shapes in the J/psi pi^+ pi^- and D^0 Dbar^0 pi^0 channels measured in the decays B^+ to K^+ + X by the Belle Collaboration. The best fit corresponds to the X(3872) being a bound state just below the D^{*0} Dbar^0 threshold, but a virtual state just above the D^{*0} D-ar^0 threshold is not excluded.

Weakly-bound Hadronic Molecule near a 3-body Threshold

Weakly-bound Hadronic Molecule near a 3-body Threshold, with Eric Braaten and Jungil Lee, arXiv:hep-ph/0702128v1

Systematic treatment in "Scalar Meson Model" of its light-meson exchange interaction and 3-body threshold effect. Calculation of observables to NLO in the pion exchange coupling constant. Renormalization to treat ultraviolet divergences appearing in various observables. Resummation to deal with infrared divergences associated with the pathological behavior of normal perturbation theory at $D_1D_2$ threshold.

Operator Product Expansion in the Production and Decay of the X(3872)

Operator Product Expansion in the Production and Decay of the X(3872), with Eric Braaten, arXiv:hep-ph/0606115v1

Develop a framework based on operator product expansion formalism to facilitate a systematic treatment of the problem. Derive factorization formulas for observables in effective field theories without pion interactions. Explicit derivation carried out for:

One-dimensional Dirac equation with double-well potential

The Extended Wronskian determinant approach and the iterative solutions of one-dimensional Dirac equation, with Ying Xu, Ru-Keng Su, arXiv:nucl-th/0306010v1

Physics References

Physics Books, a collection of physics books.

My collection research papers at CiteULike.com.

Physics Notes

(Migrated into my personal wiki.)