- Email: [email protected]
Heavy quark pair production background to the Higgs signal in linearly polarized photon–photon collisions
Nuclear Instruments and Methods in Physics Research A 472 (2001) 155–159
Heavy quark pair production background to the Higgs signal in linearly polarized photon–photon collisions G. Jikiaa,*, A. Tkabladzeb,1 a
Albert-Ludwig-Fakultat fur Physik, Universita.t Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany b DESY Zeuthen, D-15738 Zeuthen, Germany
Abstract We review the next-to-leading-order cross-sections of the heavy quark–antiquark pair production in linearly polarized photon–photon collision. Implications for the signal of Higgs particles are discussed. r 2001 Elsevier Science B.V. All rights reserved. Keywords: Higgs boson; Photon collider
1. Introduction The experimental discovery of the Higgs boson is crucial for the understanding of the mechanism of electroweak symmetry breaking. The search for Higgs particles is one of the main goals for the LEP2 and Tevatron experiments and is one of the major motivations for the future Large Hadron Collider (LHC) and Linear eþ e Collider (LC). Once the Higgs boson is discovered, it will be of primary importance to determine in a model independent way its tree-level and one-loop induced couplings, spin, parity, CP-nature, and its total width. In this respect the gg Compton Collider [1] option of the LC offers a unique opportunity to produce both Standard Model ðSM) Higgs boson and neutral Higgs states h,
*Corresponding author. E-mail address: [email protected] (G. Jikia). 1 On leave of absence from IHEP, 142284 Protvino, Moscow Region, Russian Federation.
H, A of the Minimal Supersymmetric Standard Model ðMSSMÞ or general two Higgs Doublet Model ð2HDMÞ [2] as s-channel resonance decaying into bb% ; WW * ; ZZ or t%t: gg-h0 ; H0 ; A0 -bb% ; WW * ; ZZ; t%t: The ability to control the polarizations of backscattered photons [1] provides a powerful means for exploring the CP properties of any single neutral Higgs boson that can be produced with reasonable rate at the Photon Linear Collider [3]. CP-even Higgs 0þþ bosons h0 ; H0 couple to the combination 1 ~ e1 ~ e2 ¼ ð1 þ l1 l2 Þ ð1Þ 2 while a CP-odd 0þ Higgs boson A0 couples to og e2 k~g ¼ il1 ð1 þ l1 l2 Þ; ð2Þ ½~ e1 ~ 2 where ~ ei and li ¼ 71 are photon polarization vectors and helicities. The first of these structures couples to linearly polarized photons with the maximal strength if the polarizations are parallel,
0168-9002/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 1 7 5 - 5
156
G. Jikia, A. Tkabladze / Nuclear Instruments and Methods in Physics Research A 472 (2001) 155–159
the letter if the polarizations are perpendicular. Moreover, if the Higgs boson is a mixture of CPeven and CP-odd states, as can occur e.g. in a general 2HDM with CP-violating neutral sector, the interference of these two terms gives rise to CP-violating asymmetries [3]. Since MSSM Higgs particles h0 ; H0 ; A0 decay predominantly into bb% or t%t quark pairs depending on the mass of the Higgs boson, the heavy quark pair background in gg collisions has been studied in great detail. One-loop QCD corrections were calculated for the photon helicity states corresponding to projection of total angular momentum on beam axes Jz ¼ 0 and Jz ¼ 72 [5,6]. Virtual one-loop QCD corrections for Jz ¼ 0 were found to be especially large due to the double-logarithmic enhancement factor [5]. In order to solve this theoretical problem leading QCD corrections for Jz ¼ 0 have been calculated at the two-loop level [7] and recently these leading double-logarithmic QCD corrections were resummed to all orders [8]. However, for the direct measurements of the parity of states of Higgs bosons (1)–(2) linear polarization of photon beams is needed [3]. In this talk we review the QCD corrections to heavy quark–antiquark pair production in photon–photon collision for linearly polarized photon–photon collisions [9].
2. Cross-sections The cross-section of heavy quark–antiquark pair production in polarized photon–photon collision % ðp4 Þ gðp1 Þ þ gðp2 Þ-Qðp3 Þ þ Q
ð3Þ
can be written in the most general form using the Stokes parameters which describe the polarizations of initial photons. The covariant density matrix of polarized photon with arbitrary polarization can be written in the following form: xð1;2Þ 1 x x y y 1 rð1;2Þ ðe ðex ey þ eym exn Þ ¼ e þ e e Þ7 mn m n 2 m n 2 m n xð1;2Þ ixð1;2Þ 8 2 ðexm eyn eym exn Þ þ 3 ðexm exn eym eyn Þ: 2 2 ð4Þ
are three Stokes parameters describing Here xð1;2Þ i polarization of the photon with momentum p1;2 and ex and ey denote ort vectors in x and y directions. The first order QCD corrections to the crosssection are determined by the interference between the tree level and one-loop diagrams. In the basis of the Stokes parameters the one-loop corrections have the form %Þ dsðgg-QQ ð2Þ ¼ M0 þ xð1Þ 1 x1 M11 dt ð2Þ ð1Þ ð2Þ þ iðxð1Þ 1 x2 þ x2 x1 ÞM12 ð2Þ ð1Þ ð2Þ þ xð1Þ 2 x2 M22 þ x3 x3 M33 ð2Þ þ ðxð1Þ 3 þ x3 ÞM03 :
ð5Þ
In addition to the Born level expression, there is the new term proportional to the non-diagonal ð2Þ ð1Þ ð2Þ product ðxð1Þ 1 x2 þ x2 x1 Þ; which corresponds to the scattering of linearly polarized photon on the circularly polarized one.
3. Results and discussion We consider two cases of linear polarizations of initial photons, when Dg ¼ 0 and p=2; where Dg is the angle between the directions of polarization vectors of the photons. The Dg ¼ 0; p=2 correspond to the collision of linearly polarized photons with parallel and perpendicular polarizations, respectively. For the measurements of the Higgs boson parity it is necessary to consider collisions of linearly polarized photons in order to measure the polarization asymmetry [3] s> sjj A¼ : ð6Þ s> þ sjj In fact if inclusive two-jet final states are studied then after averaging over azimuthal angles and spins of the final particles only three independent cross-sections remain for arbitrary polarization states of initial photons. These independent crosssections can be taken as stot ; sðJz ¼ 0Þ sðJz ¼ 2Þ and s> sjj [1]. For the study of the Higgs boson signal in photon–photon collisions [4–6] it was essential that the background from bb% quark production is
G. Jikia, A. Tkabladze / Nuclear Instruments and Methods in Physics Research A 472 (2001) 155–159
suppressed by a factor of m2b =s for Jz ¼ 0 at the Born level. However at the next-to-leading order the cross-section of the bb% g production for Jz ¼ 0 is not suppressed any more. Therefore experimental cuts selecting only two-jet final states were important to suppress the bb% g background [4–6]. In this section we show, that the difference of s> sjj is suppressed by a factor of m2Q =s even at the next-to-leading order. The cross-section for heavy quark pair production in polarized gg collisions can be cast in the form, which was suggested for the unpolarized case in [10]: a2 Q4 Nc ð0Þ 4 as ð1Þ sgg-QQ% ðgÞ ¼ fgg þ f ; ð7Þ 3 p gg s ð0;1Þ depend on the dimenwhere the functions fjj;> sionless variable s=ð4m2Q Þ only. The numerical ð0;1Þ values of the functions fjj;> are presented in the Fig. 1. Because of the Sommerfeld rescattering ð1Þ correction, the function f> is nonzero at the threshold. In the both cases, Dg ¼ 0 and Dg ¼ p=2; the functions corresponding to QCD corrections are positive and rising at high energies. Taking the average of values of these two functions one
ð0;1Þ Fig. 1. f>;jj versus s=ð4m2Q Þ:
157
obtains the corresponding function for the unpolarized cross-section. As in the case of Born ð0Þ ; in the asymptotic level functions fjjð0Þ and f> ð1Þ regime the difference between fjjð1Þ and f> vanishes and each of the function tends to the unpolarized 1 one, funpol : Such an asymptotic behavior of the corrections can be understood considering the helicity amplitudes for massless quarks. The difference of the cross-sections with parallel and orthogonal polarized photons can be expressed via the interference term of the following helicity amplitudes % Þ ¼ s> sjj Dsðgg-QQ X Born % ÞM oneloop * ðgg-QQ %Þ CRe Mþþ ðgg-QQ X oneloop % ÞM Born * ðgg-QQ %Þ ðgg-QQ þ Re Mþþ X Born % gÞM Born * ðgg-QQ % gÞ ð8Þ þ Re Mþþ ðgg-QQ here the sum over the helicities of the final state % ðgÞ is implied. The Born amplitude of particles QQ % the QQ pair production in the photon–photon collisions is known to vanish like m2Q =s for equal photon helicities and massless quarks [11,5,6]. Therefore first two terms in the Eq. (8) vanish in the high energy limit. In addition, helicity ampli% pair tudes for the process of massless QQ production with the additional gluon emission % g identically vanish for photon and gluon gg-QQ helicities l1 ¼ l2 ¼ lg ¼ 71 and arbitrary quark helicities [11]. Consequently, in the third term of Born % gÞ and the Eq. (8) amplitudes Mþþ ðgg-QQ Born % gÞ are nonzero only in the case M2 ðgg-QQ when emitted gluons have different polarizations. Therefore there is no interferention between corresponding amplitudes and third term of Eq. (8) term also vanishes at high energies. As % Þresult, the difference of the cross-sections for ðQQ % Þ is suppressed by a pair production, Dsðgg-QQ factor of Oðm2Q =sÞ: For bb% production the relative difference of the cross-section for parallel and orthogonal polarized photons is less than 1% for pffiffi sX200 GeV; i.e. in the whole range of the PLC energies. On the other hand, for top–antitop production there is no strong suppression pffiffi of Ds by the mass of quark at energies sC500– 800 GeV: The production cross-sections for t%t-pair production are illustrated in the Fig. 2 for different
158
G. Jikia, A. Tkabladze / Nuclear Instruments and Methods in Physics Research A 472 (2001) 155–159
Fig. 2. The tt% production cross-section for parallel and orthogonal polarized photon collisions versus c.m.s. energy of photons; the solid lines correspond to the Born cross-section and the dashed lines to the cross-sections with QCD corrections.
helicity states of initial photons. The usual cut for suppression the Higgs background is imposed, jcos yjo0:7: The solid lines correspond to the Born level cross-sections and the dashed lines to the QCD corrected ones. As one can see from Fig. 2 the corrections are large near the threshold and decrease very rapidly with increasing the photon– photon c.m.s energy, Wgg : In the Fig. 3a the difference of two crosssections, Dsðgg-t%tÞ; is shown. The correction to the Ds are rather large near the threshold, up to Wgg C400 GeV; and decreases rapidly. However, the asymmetry, ðs> sjj Þ=ðs> þ sjj Þ gets only small corrections in the whole range of energies.
Fig. 3. The difference of top–antitop production cross-section, Dsðgg-t%tÞ; (a) the absolute value of Ds; (b) the relative value of Ds: The definition of lines is the same as in the previous figure.
4. Conclusion The difference of the cross-sections of heavy quark pair production for parallel and perpendicular polarized photon collisions is suppressed by factor m2Q =s: We show that the QCD correction for the bb% production asymmetry is less than 1% in the
whole energy range of the PLC and practically does not change the background for the measurement of CP parity of Higgs boson. At the same time, there is no such suppression for top–antitop production due to the large mass of top quark. The QCD corrections are large near the threshold
G. Jikia, A. Tkabladze / Nuclear Instruments and Methods in Physics Research A 472 (2001) 155–159
and decrease rapidly with increasing the c.m.s energy of colliding photons. [4]
Acknowledgements We would like to thank J.I. Illana for useful discussions.
[5]
References
[6]
[1] I.F. Ginzburg, G.L. Kotkin, V.G. Serbo, V.I. Telnov, Pis’ma ZhETF 34 (1981) 514; Nucl. Instr. and Methods 205 (1983) 47; I.F. Ginzburg, G.L. Kotkin, S.L. Panfil, V.G. Serbo, V.I. Telnov, Nucl. Instr. and Methods 219 (1984) 5. [2] J.F. Gunion, H.E. Haber, G. Kane, S. Dawson, The Higgs Hunter’s Guide, Addison-Wesley, Reading, MA, 1990. [3] B. Grzadkowski, J.F. Gunion, Phys. Lett. B 294 (1992) 261; J.F. Gunion, J. Kelly, Phys. Lett. B 333 (1994) 110; V. Barger, K. Cheung, A. Djouadi, B.A. Kniehl, P.M. Zerwas, Phys. Rev. D 49 (1994) 79;
[7] [8]
[9] [10] [11]
159
M. Kr.amer, J. Ku. n, M.I. Stong, P.M. Zerwas, Z. Phys. C 64 (1994) 21; G.J. Gounaris, G.P. Tsirigoti, Phys. Rev. D 56 (1997) 3030. D.L. Borden, D.A. Bauer, D.O. Caldwell, Phys. Rev. D 48, (1993) 4018; D.L. Borden, V.A. Khoze, W.J. Stirling, J. Ohnemus, Phys. Rev. D 50 (1994) 4499. G. Jikia, A. Tkabladze, Proc. of the Workshop on Gamma–Gamma Colliders, March 28–31, 1994, Lawrence Berkeley Laboratory, Nucl. Instr. and Meth. A 355 (1995) 81–83; Phys. Rev. D 54 (1996) 2030. B. Kamal, Z. Merebashvili, A.P. Contogouris, Phys. Rev. D 51 (1995) 4808. V.S. Fadin, V.A. Khoze, A.D. Martin, Phys. Rev. D 56 (1997) 484. M. Melles, W.J. Stirling, Phys. Rev. D 59 (1999) 94009; Eur. Phys. J. C 9 (1999) 101; M. Melles, W.J. Stirling, V.A. Khoze, Phys. Rev. D 61 (2000) 54015. G. Jikia, A. Tkabladze, DESY-00-057, Apr 2000, hepph=0004068. J.H. Ku. hn, E. Mirkes, J. Steegborn, Z. Phys. C 57 (1993) 615. R. Gastmans, Tai Tsun Wu, The Ubiquitous Photon: Helicity method for QED and QCD, Clarendon, Oxford, 1990.
Heavy quark pair production background to the Higgs signal in linearly polarized photon–photon collisions G. Jikiaa,*, A. Tkabladzeb,1 a
Albert-Ludwig-Fakultat fur Physik, Universita.t Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany b DESY Zeuthen, D-15738 Zeuthen, Germany
Abstract We review the next-to-leading-order cross-sections of the heavy quark–antiquark pair production in linearly polarized photon–photon collision. Implications for the signal of Higgs particles are discussed. r 2001 Elsevier Science B.V. All rights reserved. Keywords: Higgs boson; Photon collider
1. Introduction The experimental discovery of the Higgs boson is crucial for the understanding of the mechanism of electroweak symmetry breaking. The search for Higgs particles is one of the main goals for the LEP2 and Tevatron experiments and is one of the major motivations for the future Large Hadron Collider (LHC) and Linear eþ e Collider (LC). Once the Higgs boson is discovered, it will be of primary importance to determine in a model independent way its tree-level and one-loop induced couplings, spin, parity, CP-nature, and its total width. In this respect the gg Compton Collider [1] option of the LC offers a unique opportunity to produce both Standard Model ðSM) Higgs boson and neutral Higgs states h,
*Corresponding author. E-mail address: [email protected] (G. Jikia). 1 On leave of absence from IHEP, 142284 Protvino, Moscow Region, Russian Federation.
H, A of the Minimal Supersymmetric Standard Model ðMSSMÞ or general two Higgs Doublet Model ð2HDMÞ [2] as s-channel resonance decaying into bb% ; WW * ; ZZ or t%t: gg-h0 ; H0 ; A0 -bb% ; WW * ; ZZ; t%t: The ability to control the polarizations of backscattered photons [1] provides a powerful means for exploring the CP properties of any single neutral Higgs boson that can be produced with reasonable rate at the Photon Linear Collider [3]. CP-even Higgs 0þþ bosons h0 ; H0 couple to the combination 1 ~ e1 ~ e2 ¼ ð1 þ l1 l2 Þ ð1Þ 2 while a CP-odd 0þ Higgs boson A0 couples to og e2 k~g ¼ il1 ð1 þ l1 l2 Þ; ð2Þ ½~ e1 ~ 2 where ~ ei and li ¼ 71 are photon polarization vectors and helicities. The first of these structures couples to linearly polarized photons with the maximal strength if the polarizations are parallel,
0168-9002/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 1 7 5 - 5
156
G. Jikia, A. Tkabladze / Nuclear Instruments and Methods in Physics Research A 472 (2001) 155–159
the letter if the polarizations are perpendicular. Moreover, if the Higgs boson is a mixture of CPeven and CP-odd states, as can occur e.g. in a general 2HDM with CP-violating neutral sector, the interference of these two terms gives rise to CP-violating asymmetries [3]. Since MSSM Higgs particles h0 ; H0 ; A0 decay predominantly into bb% or t%t quark pairs depending on the mass of the Higgs boson, the heavy quark pair background in gg collisions has been studied in great detail. One-loop QCD corrections were calculated for the photon helicity states corresponding to projection of total angular momentum on beam axes Jz ¼ 0 and Jz ¼ 72 [5,6]. Virtual one-loop QCD corrections for Jz ¼ 0 were found to be especially large due to the double-logarithmic enhancement factor [5]. In order to solve this theoretical problem leading QCD corrections for Jz ¼ 0 have been calculated at the two-loop level [7] and recently these leading double-logarithmic QCD corrections were resummed to all orders [8]. However, for the direct measurements of the parity of states of Higgs bosons (1)–(2) linear polarization of photon beams is needed [3]. In this talk we review the QCD corrections to heavy quark–antiquark pair production in photon–photon collision for linearly polarized photon–photon collisions [9].
2. Cross-sections The cross-section of heavy quark–antiquark pair production in polarized photon–photon collision % ðp4 Þ gðp1 Þ þ gðp2 Þ-Qðp3 Þ þ Q
ð3Þ
can be written in the most general form using the Stokes parameters which describe the polarizations of initial photons. The covariant density matrix of polarized photon with arbitrary polarization can be written in the following form: xð1;2Þ 1 x x y y 1 rð1;2Þ ðe ðex ey þ eym exn Þ ¼ e þ e e Þ7 mn m n 2 m n 2 m n xð1;2Þ ixð1;2Þ 8 2 ðexm eyn eym exn Þ þ 3 ðexm exn eym eyn Þ: 2 2 ð4Þ
are three Stokes parameters describing Here xð1;2Þ i polarization of the photon with momentum p1;2 and ex and ey denote ort vectors in x and y directions. The first order QCD corrections to the crosssection are determined by the interference between the tree level and one-loop diagrams. In the basis of the Stokes parameters the one-loop corrections have the form %Þ dsðgg-QQ ð2Þ ¼ M0 þ xð1Þ 1 x1 M11 dt ð2Þ ð1Þ ð2Þ þ iðxð1Þ 1 x2 þ x2 x1 ÞM12 ð2Þ ð1Þ ð2Þ þ xð1Þ 2 x2 M22 þ x3 x3 M33 ð2Þ þ ðxð1Þ 3 þ x3 ÞM03 :
ð5Þ
In addition to the Born level expression, there is the new term proportional to the non-diagonal ð2Þ ð1Þ ð2Þ product ðxð1Þ 1 x2 þ x2 x1 Þ; which corresponds to the scattering of linearly polarized photon on the circularly polarized one.
3. Results and discussion We consider two cases of linear polarizations of initial photons, when Dg ¼ 0 and p=2; where Dg is the angle between the directions of polarization vectors of the photons. The Dg ¼ 0; p=2 correspond to the collision of linearly polarized photons with parallel and perpendicular polarizations, respectively. For the measurements of the Higgs boson parity it is necessary to consider collisions of linearly polarized photons in order to measure the polarization asymmetry [3] s> sjj A¼ : ð6Þ s> þ sjj In fact if inclusive two-jet final states are studied then after averaging over azimuthal angles and spins of the final particles only three independent cross-sections remain for arbitrary polarization states of initial photons. These independent crosssections can be taken as stot ; sðJz ¼ 0Þ sðJz ¼ 2Þ and s> sjj [1]. For the study of the Higgs boson signal in photon–photon collisions [4–6] it was essential that the background from bb% quark production is
G. Jikia, A. Tkabladze / Nuclear Instruments and Methods in Physics Research A 472 (2001) 155–159
suppressed by a factor of m2b =s for Jz ¼ 0 at the Born level. However at the next-to-leading order the cross-section of the bb% g production for Jz ¼ 0 is not suppressed any more. Therefore experimental cuts selecting only two-jet final states were important to suppress the bb% g background [4–6]. In this section we show, that the difference of s> sjj is suppressed by a factor of m2Q =s even at the next-to-leading order. The cross-section for heavy quark pair production in polarized gg collisions can be cast in the form, which was suggested for the unpolarized case in [10]: a2 Q4 Nc ð0Þ 4 as ð1Þ sgg-QQ% ðgÞ ¼ fgg þ f ; ð7Þ 3 p gg s ð0;1Þ depend on the dimenwhere the functions fjj;> sionless variable s=ð4m2Q Þ only. The numerical ð0;1Þ values of the functions fjj;> are presented in the Fig. 1. Because of the Sommerfeld rescattering ð1Þ correction, the function f> is nonzero at the threshold. In the both cases, Dg ¼ 0 and Dg ¼ p=2; the functions corresponding to QCD corrections are positive and rising at high energies. Taking the average of values of these two functions one
ð0;1Þ Fig. 1. f>;jj versus s=ð4m2Q Þ:
157
obtains the corresponding function for the unpolarized cross-section. As in the case of Born ð0Þ ; in the asymptotic level functions fjjð0Þ and f> ð1Þ regime the difference between fjjð1Þ and f> vanishes and each of the function tends to the unpolarized 1 one, funpol : Such an asymptotic behavior of the corrections can be understood considering the helicity amplitudes for massless quarks. The difference of the cross-sections with parallel and orthogonal polarized photons can be expressed via the interference term of the following helicity amplitudes % Þ ¼ s> sjj Dsðgg-QQ X Born % ÞM oneloop * ðgg-QQ %Þ CRe Mþþ ðgg-QQ X oneloop % ÞM Born * ðgg-QQ %Þ ðgg-QQ þ Re Mþþ X Born % gÞM Born * ðgg-QQ % gÞ ð8Þ þ Re Mþþ ðgg-QQ here the sum over the helicities of the final state % ðgÞ is implied. The Born amplitude of particles QQ % the QQ pair production in the photon–photon collisions is known to vanish like m2Q =s for equal photon helicities and massless quarks [11,5,6]. Therefore first two terms in the Eq. (8) vanish in the high energy limit. In addition, helicity ampli% pair tudes for the process of massless QQ production with the additional gluon emission % g identically vanish for photon and gluon gg-QQ helicities l1 ¼ l2 ¼ lg ¼ 71 and arbitrary quark helicities [11]. Consequently, in the third term of Born % gÞ and the Eq. (8) amplitudes Mþþ ðgg-QQ Born % gÞ are nonzero only in the case M2 ðgg-QQ when emitted gluons have different polarizations. Therefore there is no interferention between corresponding amplitudes and third term of Eq. (8) term also vanishes at high energies. As % Þresult, the difference of the cross-sections for ðQQ % Þ is suppressed by a pair production, Dsðgg-QQ factor of Oðm2Q =sÞ: For bb% production the relative difference of the cross-section for parallel and orthogonal polarized photons is less than 1% for pffiffi sX200 GeV; i.e. in the whole range of the PLC energies. On the other hand, for top–antitop production there is no strong suppression pffiffi of Ds by the mass of quark at energies sC500– 800 GeV: The production cross-sections for t%t-pair production are illustrated in the Fig. 2 for different
158
G. Jikia, A. Tkabladze / Nuclear Instruments and Methods in Physics Research A 472 (2001) 155–159
Fig. 2. The tt% production cross-section for parallel and orthogonal polarized photon collisions versus c.m.s. energy of photons; the solid lines correspond to the Born cross-section and the dashed lines to the cross-sections with QCD corrections.
helicity states of initial photons. The usual cut for suppression the Higgs background is imposed, jcos yjo0:7: The solid lines correspond to the Born level cross-sections and the dashed lines to the QCD corrected ones. As one can see from Fig. 2 the corrections are large near the threshold and decrease very rapidly with increasing the photon– photon c.m.s energy, Wgg : In the Fig. 3a the difference of two crosssections, Dsðgg-t%tÞ; is shown. The correction to the Ds are rather large near the threshold, up to Wgg C400 GeV; and decreases rapidly. However, the asymmetry, ðs> sjj Þ=ðs> þ sjj Þ gets only small corrections in the whole range of energies.
Fig. 3. The difference of top–antitop production cross-section, Dsðgg-t%tÞ; (a) the absolute value of Ds; (b) the relative value of Ds: The definition of lines is the same as in the previous figure.
4. Conclusion The difference of the cross-sections of heavy quark pair production for parallel and perpendicular polarized photon collisions is suppressed by factor m2Q =s: We show that the QCD correction for the bb% production asymmetry is less than 1% in the
whole energy range of the PLC and practically does not change the background for the measurement of CP parity of Higgs boson. At the same time, there is no such suppression for top–antitop production due to the large mass of top quark. The QCD corrections are large near the threshold
G. Jikia, A. Tkabladze / Nuclear Instruments and Methods in Physics Research A 472 (2001) 155–159
and decrease rapidly with increasing the c.m.s energy of colliding photons. [4]
Acknowledgements We would like to thank J.I. Illana for useful discussions.
[5]
References
[6]
[1] I.F. Ginzburg, G.L. Kotkin, V.G. Serbo, V.I. Telnov, Pis’ma ZhETF 34 (1981) 514; Nucl. Instr. and Methods 205 (1983) 47; I.F. Ginzburg, G.L. Kotkin, S.L. Panfil, V.G. Serbo, V.I. Telnov, Nucl. Instr. and Methods 219 (1984) 5. [2] J.F. Gunion, H.E. Haber, G. Kane, S. Dawson, The Higgs Hunter’s Guide, Addison-Wesley, Reading, MA, 1990. [3] B. Grzadkowski, J.F. Gunion, Phys. Lett. B 294 (1992) 261; J.F. Gunion, J. Kelly, Phys. Lett. B 333 (1994) 110; V. Barger, K. Cheung, A. Djouadi, B.A. Kniehl, P.M. Zerwas, Phys. Rev. D 49 (1994) 79;
[7] [8]
[9] [10] [11]
159
M. Kr.amer, J. Ku. n, M.I. Stong, P.M. Zerwas, Z. Phys. C 64 (1994) 21; G.J. Gounaris, G.P. Tsirigoti, Phys. Rev. D 56 (1997) 3030. D.L. Borden, D.A. Bauer, D.O. Caldwell, Phys. Rev. D 48, (1993) 4018; D.L. Borden, V.A. Khoze, W.J. Stirling, J. Ohnemus, Phys. Rev. D 50 (1994) 4499. G. Jikia, A. Tkabladze, Proc. of the Workshop on Gamma–Gamma Colliders, March 28–31, 1994, Lawrence Berkeley Laboratory, Nucl. Instr. and Meth. A 355 (1995) 81–83; Phys. Rev. D 54 (1996) 2030. B. Kamal, Z. Merebashvili, A.P. Contogouris, Phys. Rev. D 51 (1995) 4808. V.S. Fadin, V.A. Khoze, A.D. Martin, Phys. Rev. D 56 (1997) 484. M. Melles, W.J. Stirling, Phys. Rev. D 59 (1999) 94009; Eur. Phys. J. C 9 (1999) 101; M. Melles, W.J. Stirling, V.A. Khoze, Phys. Rev. D 61 (2000) 54015. G. Jikia, A. Tkabladze, DESY-00-057, Apr 2000, hepph=0004068. J.H. Ku. hn, E. Mirkes, J. Steegborn, Z. Phys. C 57 (1993) 615. R. Gastmans, Tai Tsun Wu, The Ubiquitous Photon: Helicity method for QED and QCD, Clarendon, Oxford, 1990.