Mestvirishvili, M

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C E R N LIBRARIES, G E N E V A CM-P00100667 INSTITUTE OF HIGH-ENERGY PHYSICS, SERPUKHOV Report IHEP-STF-70-46 VECTOR DOMINANCE AND THE REDUCTION OF THE DIFFERENTIAL CROSS-SECTION OF LEPTON PAIR PRODUCTION AT HIGH ENERGIES AT LARGE ANGLES M. Mestvirishvili Serpukhov, 1970 Translated at CERN by A. Sanders Revised by N. Mouravieff (Original: Russian) (CERN Trans. 71-14) Geneva March 1971 The present paper shows that on the basis of the hypothesis of vector dominance1,2), the differential cross-section of lepton pair production dσ/(dq2 d cos θ dØ) in the region of large angles θ and Ø  decreases as the energy increases. Let us consider the process when the lepton pair l+,l- is produced by a hadron collision: a + b → * + A. γ ↓ ↓ l+ l -Here, a and b are strongly interacting particles, and A is a hadron group which is produced at the end of the reaction. It can be shown2) that in α = e2/4π the approximation in the centre¬ of-mass system ( = 0) is: dσ = α2 π(q2) σ'(s, q 2 ) , (1) dq2 2π q2 where q = P l + + Pl- is the four-momentum of the virtual gamma quantum π(q 2) = q2 + 2me2 √ q 2 - 4 m e 2 , 6πq 2 q2 and σ'(s,q2) = 1 ∫δ(Pa + Pb - q-Σ ki) Π × √(P a•P b) 2-P a 2P b 2 iЄA 2qo(2π)3iЄA 2kio(2π)3 × <P aP b||q,k 1... ><q, k 1...|S|P a,P b>. By virtue of the hypothesis of vector dominance σ'(s,q)2 can be written in the form: - 2 -σ'(S,C2) = 1 ( m20 ) 2 σρ(s)+ 1 ( m2ω ) 2 σ ω ( s ) + f2ρ q 2 - m2ρ f2ω m2ω - q2 + 1 ( m 2 Ø ) σ Ø(s) f2Ø q 2 - m2Ø (2) plus interference terms, and here σi(s) i = p,ω,Ø are the total cross¬ sections of the processes a + b → i + Α, i = ρ,ω,Ø. Ignoring the interference terms in (2), from (1) we find dσ = α2 π ( q 2 ) [ 1 ( m2ρ ) 2 σ ρ ( s ) + dq2 2π q2 f20 q 2 - m2ρ + 1 ( m2ω )2 σω(s) + 1 ( m2Ø ) 2 σ Ø ( S ) ] . f2ω q2 -m2ω f2Ø q 2 - m 2 Ø (3) It is well-known that when s → ∞ σ i(s), i = ρ,ω,Ø are limited from above by the expression (π/m2π) ln2 P(s): where P(s) is a certain s polynomial. Therefore in the region s → ∞ and q2 → ∞ from (3) we obtain dσ < α2 ln 2 Ρ (s) ( m4ρ + m4ω + m4Ø ). dq2 12π mπ2q6 f2ρ f2ω f2Ø Let us designate by Θ the angle of flight of the particles ρ, ω, and Ø in relation to the direction of the relative momentum = = - , and by Ø, the angle between the planes passing through vectors , and , , where is the momentum of a certain fixed particle from A. - 3 -Then, as was shown elsewhere3), using unitarity and analyticity, according to the variables cos Θ and e one can establish the limita­tion for fixed Θ and Ø namely: dσi(s) | Θ ≠ 0, π ≤ const ln12(s/s0) , i = ρ, ω, Ø. (4) dcosΘdØ s sin 5Θ sin8Ø Ø ≠ 0, π S → ∞ By substituting (4) in (3) we find dσ | Θ ≠ ο, π ≤ const £n12(s/so) • (5) dq2dcosΘ dØ q6s sin5Θ sin 8Ø Ø ≠ 0 , π s2 → ∞ q → ∞ This latter inequality shows that as the energy increases, the differential cross-section of the production of the pair (l+, l-) for large θ and Ø decreases. Finally, let us note that for the value of the angles Θ = Ο, π and Ø = 0,π, one can obtain more accurate estimates than (5) 3): dσ | Θ = Ø = 0,π ≤ coast s l n 4 ( s / s 0 ) , d cos Θ dØ dq2 q2 → ∞ q6 S → ∞ dσ | Ø = ο, π ≤ const 1 s7/6 ln13/3 (s/s 0) • dq2dcosΘ dØ. q6 sin2/3Θ cos1/3Θ Θ ≠ 0, π S → ∞ q2 → ∞ In conclusion, the writer wishes to express his warmest thanks to G.G. Volkov, S.S. Gerstein, V.V. Ezhela, A.A. Logunov, V.A. Matveev and R.M. Muradyan for fruitful discussions. - 4 -REFERENCES 1) J.J. Sakurai, Currents and mesons (University of Chicago Press, Chicago, 111., 1969). J.J. Sakurai, Phys. Rev. Letters 22, 981 (1969). CF. Cho and G.J. Gounaris, Phys. Rev. 186, 1619 (1969). 2) V.A. Matveev, R.M. Muradyan, A.N. Tavkhelidze, Preprint E2 4968, Dubna, 1970. 3) V.V. Ezhela, A.A. Logunov, M.A. Mestvirishvili, Preprint IHEP 70-43, Serpukhov, 1970. 

Vector dominance and the reduction of the differential cross-section of lepton pair production at high energies at large angles

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