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Photoproduction of selectrons in linear e+e− colliders
Volume 129B, number 3,4
PHYSICS LETTERS
22 September 1983
PHOTOPRODUCTION OF SELECTRONS IN LINEAR e+e - COLLIDERS
M. GLUCK Institut jT~rPhysik, UniversiRtt Dortmund, 4600 Dortmund 50, Fed. Rep. Germany Recewed 16 June 1983
It is suggested to observe photoproduced selectrons in linear e+e- colliders. The energetic photons are provided by an intense laser photon beam colliding with the electron beam. The observability of selectrons is then essentially limited by phase space, i.e. by m~" + m~. <~~ .
The production o f the supersymmetric partners o f the electron, the "selectrons" (~'), has attracted much theoretical interest [ 1 - 4 ] . The simplest process [1] e+e - ~ ~'+~"- is limited essentially by the beam energy E, i.e. by m~- ~
ders one can, in fact, obtain intense '),-beams by backward Compton scattering o f laser fight which is focussed on the electron beams o f these accelerators [6]. The 3'e collisions thus obtained have approximately the same energies and luminosities as the e+e collisions. It is interesting therefore to fred the cross section for 7e ~ 7"e. The differential cross section is given by*l do" = (2n.a2/s2) dt X ((m 2 - u)/s + (t - m 2) (t + U2)/(t - / a 2 ) 2 - [(t - / ~ 2 ) (s - 2A) + F~s - 2 A 2 ] / s ( t - l a 2 ) ) ,
(1)
where/~ --- m?- (the two selectrons are taken to be mass degenerate), m - m~., I2 -=/a 2 + m 2 , A -/~2 _ m 2 and t is the squared momentum transfer between the photon and the selectron. From this one obtains for the total cross section * 1 o = 0ra2/s){r/(1 + 7A/s) - (4A/s)(1 + A/s)
×in([n+s(l+n)]/[,a+s(1-n)])),
(2)
where 772 = 1 - (2Z/s) + (A/s) 2 . For m = 0 this simplifies to o = (rra2/s) [(1 - 1~2/s) (1 + 7/a2/s) - (4//2/s) (1 + la2/s) In (s///2)] ,
(3)
,1 This is consistent with corresponding results in ref. [7]. 255
Volume 129B, number 3,4
PHYSICS LETTERS
In the equations above we have assumed E, t = x/s'/2. For softer laser-induced photons, one just replaces s b y 2ETx/~" everywhere. The improvement over the bremsstrahlung photoproduction [4] is illustrated b y comparing R -O[Opoint for, say, m~[E = 1.5 and m~- = 0. For the direct photoproduction here considered R ~- 10% as compared to [4] R -~ 0.15% for the bremsstrahlung photoproduction process. The actual bounds for observability are now indeed very near the kinematical threshold m ~ + m~- ~ 2 E . The observed electrons coming from the selectron decay are now also much harder than before [4] and thus easier to detect. In other words reasonable energy and angular cuts for the detected electron now diminish the observed number o f evens by a much smaller amount. I am grateful to E. Reya for some helpful comment s.
256
22 September 1983
References [1] [2] [3] [4]
G.R. Farrar and P. Fayet, Phys. Lett. 89B (1980) 191. P. Fayet, Phys. Lett. l17B (1982) 460. J. Ellis and J.S. Hagelin, Phys. Lett. 122B (1983) 303. M~K.Gaillard, L. Hall and I. Hinehliffe, Phys. Lett. 116B (1982) 279. [5] E. Ma and J. Okada, Phys. Rev. Lett. 41 (1978) 287, Phys. Rev. D18 (1978) 4219, KJ .F. Gaemers, R. Gastmans and F.M. Renard, Phys. Rev. D19 (1979) 1605. [6] I.F. Ginzburg, G.L. Kotkin, V.G. Serbo and V.I. Telnov, Eksp. Teor. Ftz. Pis'ma 34 (1981) 514,preprint INP 8150, 81-102 (Novosibtrsk, 1981), G. Akerlof, preprint Um HE 81-59 (Ann Arbor, 1981). [7] P.R. Harrison and C.H. Llewellyn Smith, Nuel. Phys. B213 (1983) 223, S.K. Jones and C.H. Llewellyn Smith, Nucl. Phys. B217 (1983) 145.
PHYSICS LETTERS
22 September 1983
PHOTOPRODUCTION OF SELECTRONS IN LINEAR e+e - COLLIDERS
M. GLUCK Institut jT~rPhysik, UniversiRtt Dortmund, 4600 Dortmund 50, Fed. Rep. Germany Recewed 16 June 1983
It is suggested to observe photoproduced selectrons in linear e+e- colliders. The energetic photons are provided by an intense laser photon beam colliding with the electron beam. The observability of selectrons is then essentially limited by phase space, i.e. by m~" + m~. <~~ .
The production o f the supersymmetric partners o f the electron, the "selectrons" (~'), has attracted much theoretical interest [ 1 - 4 ] . The simplest process [1] e+e - ~ ~'+~"- is limited essentially by the beam energy E, i.e. by m~- ~
ders one can, in fact, obtain intense '),-beams by backward Compton scattering o f laser fight which is focussed on the electron beams o f these accelerators [6]. The 3'e collisions thus obtained have approximately the same energies and luminosities as the e+e collisions. It is interesting therefore to fred the cross section for 7e ~ 7"e. The differential cross section is given by*l do" = (2n.a2/s2) dt X ((m 2 - u)/s + (t - m 2) (t + U2)/(t - / a 2 ) 2 - [(t - / ~ 2 ) (s - 2A) + F~s - 2 A 2 ] / s ( t - l a 2 ) ) ,
(1)
where/~ --- m?- (the two selectrons are taken to be mass degenerate), m - m~., I2 -=/a 2 + m 2 , A -/~2 _ m 2 and t is the squared momentum transfer between the photon and the selectron. From this one obtains for the total cross section * 1 o = 0ra2/s){r/(1 + 7A/s) - (4A/s)(1 + A/s)
×in([n+s(l+n)]/[,a+s(1-n)])),
(2)
where 772 = 1 - (2Z/s) + (A/s) 2 . For m = 0 this simplifies to o = (rra2/s) [(1 - 1~2/s) (1 + 7/a2/s) - (4//2/s) (1 + la2/s) In (s///2)] ,
(3)
,1 This is consistent with corresponding results in ref. [7]. 255
Volume 129B, number 3,4
PHYSICS LETTERS
In the equations above we have assumed E, t = x/s'/2. For softer laser-induced photons, one just replaces s b y 2ETx/~" everywhere. The improvement over the bremsstrahlung photoproduction [4] is illustrated b y comparing R -O[Opoint for, say, m~[E = 1.5 and m~- = 0. For the direct photoproduction here considered R ~- 10% as compared to [4] R -~ 0.15% for the bremsstrahlung photoproduction process. The actual bounds for observability are now indeed very near the kinematical threshold m ~ + m~- ~ 2 E . The observed electrons coming from the selectron decay are now also much harder than before [4] and thus easier to detect. In other words reasonable energy and angular cuts for the detected electron now diminish the observed number o f evens by a much smaller amount. I am grateful to E. Reya for some helpful comment s.
256
22 September 1983
References [1] [2] [3] [4]
G.R. Farrar and P. Fayet, Phys. Lett. 89B (1980) 191. P. Fayet, Phys. Lett. l17B (1982) 460. J. Ellis and J.S. Hagelin, Phys. Lett. 122B (1983) 303. M~K.Gaillard, L. Hall and I. Hinehliffe, Phys. Lett. 116B (1982) 279. [5] E. Ma and J. Okada, Phys. Rev. Lett. 41 (1978) 287, Phys. Rev. D18 (1978) 4219, KJ .F. Gaemers, R. Gastmans and F.M. Renard, Phys. Rev. D19 (1979) 1605. [6] I.F. Ginzburg, G.L. Kotkin, V.G. Serbo and V.I. Telnov, Eksp. Teor. Ftz. Pis'ma 34 (1981) 514,preprint INP 8150, 81-102 (Novosibtrsk, 1981), G. Akerlof, preprint Um HE 81-59 (Ann Arbor, 1981). [7] P.R. Harrison and C.H. Llewellyn Smith, Nuel. Phys. B213 (1983) 223, S.K. Jones and C.H. Llewellyn Smith, Nucl. Phys. B217 (1983) 145.