Scalar and Tensor Sea Contributions to Nucleons M. Batra1* and A. Upadhayay2 SPMS , Thapar University Patiala-147004. *email:
[email protected]
Introduction: The low energy parameters of baryons like spin distribution, magnetic moment, weak decay, coupling constant ratios are still a challenge for particle physicist. In past various models and theories have been suggested to describe the structure of baryons in these context. The experimental investigation for the structure of baryons came into existence from DeepInelastic experiments. Later on EMC [1] at CERN concluded that spin of proton is carried by quark -anti quark pair in addition to valence part. SMC collaboration [2] measured the spin structure g1(x) of proton and neutron at Q2=10 GeV2. Also different models are put forward with perturbative and non perturbative approach to define the quark interactions. For example, Isgur and Karl [3].defined the confining interaction potentials among quarks. Some models explain the low energy properties through presence of οΏ½π·π·1β βͺ = 2
constituent quarks inside the baryon. In order to have reliable information about the various properties of hadrons at low energy, selfconsistent approach should be adopted. Low energy parameters for baryons are computed here by assuming baryons as a composite system of three quarks known as valence part and sea-part as made up of quark-antiquark pair and gluons. The wave-function [4] for valence part of the baryon is denoted by πΏπΏ = π±π±[|ππβͺ|ππβͺ|ππβͺ]|ππβͺwhere each part contributes in such a way so as to make the total wave-function anti-symmetric in nature. Here sea is assumed to be flavorless and in Swave, spin of sea part are chosen to be in 0, 1, 2 οΏ½οΏ½οΏ½οΏ½οΏ½ππ ). The total flavorand color can be (1ππ , 8ππ , 10 spin-color wave function of a spin up baryon which consist of three-valence quarks and sea components can be written as
β β β 1 1 οΏ½12οΏ½β οΏ½1 οΏ½ οΏ½1 οΏ½ 2 [π·π·1 π»π»0 πΊπΊ1 + ππ8 π·π·8 2 π»π»0 πΊπΊ8 + ππ10 π·π·102 π»π»0 πΊπΊ10 οΏ½οΏ½οΏ½οΏ½ + ππ1 οΏ½π·π·1 β¨π»π»1 οΏ½ πΊπΊ1 + ππ 1
β
β
1
3
3
2 2 2 β β + ππ8 οΏ½π·π·82 β¨π»π»1 οΏ½ πΊπΊ8 + ππ10 οΏ½π·π·10 β¨π»π»1 οΏ½ πΊπΊ10 οΏ½οΏ½οΏ½οΏ½ + ππ8 (π·π·8 β¨π»π»1 ) πΊπΊ8 +ππ8 (π·π·8 β¨π»π»2 ) πΊπΊ8 ]
2 2 + ππ12 + ππ82 + ππ10 + ππ82 + ππ82 ππ 2 = 1 + ππ82 + ππ10
Where
Each term in above defined wave-function consists of two parts where π·π· represents contribution from valence part and other contributes to sea. Various combinations contributing to sea take into account antisymmetry of each term in the wave-function. The first three terms in wave-function come from
coupling of spin 1/2 state coupled to scalar sea and other three b1, b8, b10 represents coupling between spin 1/2 and vector Sea. Finally terms with c8 and d8 are due to coupling of spin 3/2 with vector and tensor sea respectively. Various low energy parameters can be calculated by defining a suitable operator for each property of the system.
1 (β) οΏ½ (β) οΏ½ if >ππππ < Ο οΏ½ if >ππππ < Ο οΏ½ if >ππππ < Ο οΏ½Ξ¦1/2 οΏ½ = 2 [ππ βππ < Ξ οΏ½iz >ππβππβ +< Ξ οΏ½iz >ππβππβ + 2 < Ξ οΏ½iz >ππβππβ οΏ½Ξ¦1/2 οΏ½Ξ ππ
οΏ½ if Ξ
ππππ
Ο οΏ½iz
ππβππβ
Ο οΏ½iz
οΏ½ if Ξ
ππβππβ
ππππ
Ο οΏ½iz
οΏ½ if Ξ
ππβππβ
ππππ
Ο οΏ½iz
ππβππβ
+b
> )οΏ½ < > +< > οΏ½ + ππ βππ [< > < > + < > < > β2 < 3 3 οΏ½ if >ππππ ] + πποΏ½βππ ( < Ξ οΏ½ if >ππππ β< Ξ οΏ½ if >ππππ οΏ½ < Ο οΏ½ if >ππππ < Ο οΏ½ if >ππππ +βππ < Ξ οΏ½iz >ππβ2β + 2 βππ < Ξ οΏ½iz >ππβ2β ] ππ[βππ < Ξ Here
i
οΏ½ if Ξ
οΏ½ if >ππππ + < βππ (< Ξ
>ππππ < Ο οΏ½iz >ππβππβ ] +
i
οΏ½ f >ππππ =οΏ½ππ ππ οΏ½Ξππππ οΏ½ππ ππ οΏ½ , < ΟοΏ½ iz >ππβππβ = οΏ½ππ ππβ οΏ½πππ§π§ππ οΏ½ππ ππβ οΏ½, < Ξ οΏ½ f >ππππ = οΏ½ππππ οΏ½Ξππππ οΏ½ππππ οΏ½and < ΟοΏ½ iz >ππβππβ = οΏ½ππ ππβ οΏ½πππ§π§ππ οΏ½ππ ππβ οΏ½