scholarly journals Sum rule for the Compton amplitude and implications for the proton–neutron mass difference

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
J. Gasser ◽  
H. Leutwyler ◽  
A. Rusetsky
Keyword(s):  
Asymptotic Behaviour ◽  
Electromagnetic Interaction ◽  
Mass Difference ◽  
Sum Rule ◽  
Dispersive Representation ◽  
Compton Amplitude

AbstractThe Cottingham formula expresses the leading contribution of the electromagnetic interaction to the proton-neutron mass difference as an integral over the forward Compton amplitude. Since quarks and gluons reggeize, the dispersive representation of this amplitude requires a subtraction. We assume that the asymptotic behaviour is dominated by Reggeon exchange. This leads to a sum rule that expresses the subtraction function in terms of measurable quantities. The evaluation of this sum rule leads to $$m_{\mathrm{QED}}^{p-n}=0.58\pm 0.16\,\text {MeV}$$ m QED p - n = 0.58 ± 0.16 MeV .

CHARGE SYMMETRY BREAKING IN pn → dπ0

2011 ◽  
Vol 26 (03n04) ◽  
pp. 592-594
Author(s):  
ARSENIY A. FILIN
Keyword(s):  
Symmetry Breaking ◽  
Cross Section ◽  
Mass Difference ◽  
Leading Order ◽  
Charge Symmetry Breaking ◽  
Chiral Perturbation ◽  
Charge Symmetry ◽  
Sum Rule ◽  
Proton Mass ◽  
Complete Calculation

We study charge symmetry breaking (CSB) in the reaction pn → dπ0. CSB manifests itself in a forward-backward asymmetry of the differential cross section measured recently at TRIUMF. A complete calculation of CSB effects at leading order in chiral perturbation theory is performed. A new leading-order operator is included. This allows us to extract the strong contribution to the neutron-proton mass difference from the analysis. The value obtained is consistent with the result of Gasser and Leutwyler based on the Cottingham sum rule and with an extraction from lattice QCD.

scholarly journals The magnetic moment of $$P_{c}(4312)$$ as a $$\bar{D}\Sigma _{c}$$ molecular state

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Yong-Jiang Xu ◽  
Yong-Lu Liu ◽  
Ming-Qiu Huang
Keyword(s):  
Electromagnetic Field ◽  
Magnetic Moment ◽  
Linear Response ◽  
Electromagnetic Interaction ◽  
External Electromagnetic Field ◽  
Molecular State ◽  
Sum Rule ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Rule Method

AbstractIn this paper, we tentatively assign the $$P_{c}(4312)$$ P c ( 4312 ) to be a $$\bar{D}\Sigma _{c}$$ D ¯ Σ c molecular state with quantum number $$J^{P}=\frac{1}{2}^{-}$$ J P = 1 2 - , and calculate its magnetic moment using the QCD sum rule method in external weak electromagnetic field. Starting with the two-point correlation function in external electromagnetic field and expanding it in power of the electromagnetic interaction Hamiltonian, we extract the magnetic moment from the linear response to the external electromagnetic field. The numerical value of the magnetic moment of $$P_{c}(4312)$$ P c ( 4312 ) is $$\mu _{P_{c}}=1.75^{+0.15}_{-0.11}$$ μ P c = 1 . 75 - 0.11 + 0.15 .

scholarly journals Sum rule measurements of the spin-dependent compton amplitude (nucleon spin structure at Q{sup 2} = 0)

1995 ◽  
Author(s):  
D. Babusci ◽  
G. Giordano ◽  
H. Baghaei ◽  
A. Cichocki ◽  
M. Blecher ◽  
...  
Keyword(s):  
Spin Structure ◽  
Nucleon Spin ◽  
Sum Rule ◽  
Nucleon Spin Structure ◽  
Compton Amplitude

Water, Water, Here and There

2018 ◽  
Author(s):  
Steven E. Vigdor
Keyword(s):  
Quark Mass ◽  
Mass Difference ◽  
Baryon Number ◽  
Electroweak Phase Transition ◽  
Hydrogen Burning ◽  
Quark Masses ◽  
Grand Unified Theories ◽  
Down Quark ◽  
Unified Theories ◽  
The Stability

Chapter 4 deals with the stability of the proton, hence of hydrogen, and how to reconcile that stability with the baryon number nonconservation (or baryon conservation) needed to establish a matter–antimatter imbalance in the infant universe. Sakharov’s three conditions for establishing a matter–antimatter imbalance are presented. Grand unified theories and experimental searches for proton decay are described. The concept of spontaneous symmetry breaking is introduced in describing the electroweak phase transition in the infant universe. That transition is treated as the potential site for introducing the imbalance between quarks and antiquarks, via either baryogenesis or leptogenesis models. The up–down quark mass difference is presented as essential for providing the stability of hydrogen and of the deuteron, which serves as a crucial stepping stone in stellar hydrogen-burning reactions that generate the energy and elements needed for life. Constraints on quark masses from lattice QCD calculations and violations of chiral symmetry are discussed.

Asymptotic behaviour of sample weighted circuits representing recurrent Markov chains

1990 ◽  
Vol 27 (03) ◽  
pp. 545-556 ◽  
Author(s):  
S. Kalpazidou
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Asymptotic Behaviour ◽  
Probabilistic Interpretation ◽  
Stationary Markov Chain

The asymptotic behaviour of the sequence (𝒞 n (ω), wc,n (ω)/n), is studied where 𝒞 n (ω) is the class of all cycles c occurring along the trajectory ωof a recurrent strictly stationary Markov chain (ξ n ) until time n and wc,n (ω) is the number of occurrences of the cycle c until time n. The previous sequence of sample weighted classes converges almost surely to a class of directed weighted cycles (𝒞∞, ω c ) which represents uniquely the chain (ξ n ) as a circuit chain, and ω c is given a probabilistic interpretation.

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