Production of higgs in two photon collision

1. Introduction The Standard model (SM) of particles can be used to describe the elementary particle picture. However, some theoretical drawbacks in SM have been motivation for the construction of new physical theories. Extra dimensional theory is one of many attempts to extend the SM and solve the hierarchy problem. Although the first idea, the Kaluza Klein (KK) theory, has difficulty in phenomenology, the KK idea is used as a base of the following modern theories. The Randall-Sundrum (RS) model is one of many attempts to extend the SM and solve the hierarchy problem, one of theoretical drawbacks of SM [1]. The RS setup involves two three-branes bounding a slice of 5D compact anti-de Sitter space taken to be on an S Z / 2 orbifold. Gravity is localized UV brane, while the Standard Model (SM) fields are supposed to be localized IR brane. The separation between the two 3-branes leads directly to the existence of an additional scalar called the radion ( ), corresponding to the quantum fluctuations of the distance between the two 3-branes [2]. The radion mass is considered in the range of  (10 GeV) ≤ m ≤ (TeV) [3]. The common origin of the radion and KaluzaKlein gravitons means a sensitivity to brane curvature terms. The radion couples with the matter via the trace of the energy momentum tensor. Therefore, the structure of the coupling of the radion with the SM fields is similar to that of the Higgs boson. The mixing of Higgs with another particle will change the Higgs production or decay patterns. General covariance allows a possibility of mixing between the radion and the Higgs boson.

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89 JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1059.2017-0035 Mathematical and Physical Sci. 2017, Vol. 62, Iss. 8, pp. 89-95 This paper is available online at PRODUCTION OF HIGGS IN TWO PHOTON COLLISION Bui Thi Ha Giang and Dao Thi Le Thuy Faculty of Physics, Hanoi National University of Education Abstract. The Higgs production was studied using the Randall-Sundrum model from photon- photon collision. The independent parameters in the Randall-Sundrum model: the vacuum expectation value of the radionfield  , the radion mass m , the Higgs mass hm and  must be specified to fix the state mixing parameters. The total cross-section has been evaluated as the function of the parameters ,  , the collision energy s and the result shows the advantageous direction to observe the Higgs boson. Keywords: Higgs production, photon collision, Randall-Sundrum model. 1. Introduction The Standard model (SM) of particles can be used to describe the elementary particle picture. However, some theoretical drawbacks in SM have been motivation for the construction of new physical theories. Extra dimensional theory is one of many attempts to extend the SM and solve the hierarchy problem. Although the first idea, the Kaluza Klein (KK) theory, has difficulty in phenomenology, the KK idea is used as a base of the following modern theories. The Randall-Sundrum (RS) model is one of many attempts to extend the SM and solve the hierarchy problem, one of theoretical drawbacks of SM [1]. The RS setup involves two three-branes bounding a slice of 5D compact anti-de Sitter space taken to be on an 1 2/S Z orbifold. Gravity is localized UV brane, while the Standard Model (SM) fields are supposed to be localized IR brane. The separation between the two 3-branes leads directly to the existence of an additional scalar called the radion ( ), corresponding to the quantum fluctuations of the distance between the two 3-branes [2]. The radion mass is considered in the range of  (10 GeV) ≤ m ≤ (TeV) [3]. The common origin of the radion and Kaluza- Klein gravitons means a sensitivity to brane curvature terms. The radion couples with the matter via the trace of the energy momentum tensor. Therefore, the structure of the coupling of the radion with the SM fields is similar to that of the Higgs boson. The mixing of Higgs with another particle will change the Higgs production or decay patterns. General covariance allows a possibility of mixing between the radion and the Higgs boson. Received July 17, 2017. Accepted August 20, 2017. Contact Dao Thi Le Thuy, e-mail: thuydtl@hnue.edu.vn Bui Thi Ha Giang and Dao Thi Le Thuy 90 The mixing of radion with Higgs will modify the Higgs and radion phenomenology significantly [4]. In Ref [5], the authors show that the Higgs-dominated state at 125 GeV, in which the Higgs signal is discovered by the ATLAS and CMS collaborations [6, 7], is preferred to the radion-dominated state at 125 GeV. Additionally, the associated production of Higgs bosons with the radion was also studied in Ref [8–12]. 2. Content 2.1. A review of Randall - Sundrum model The RS model is based on a 5D spacetime with non - factorizable geometry [1]. The single extra dimension is compactified on an 1 2/S Z orbifold of which two fixed points accommodate two three-branes (4D hyper-surfaces): the UV brane and the IR brane. 1S is a sphere in one dimension and 2Z is the multiplicative group {-1, 1}. The background metric reads: 2 | |2 2 2 ,c kr cds e dx dx r d              (1) with ( 0,1,2,3)x   the coordinates on the 4D hyper-surfaces of constant c, r the compactification radius and k the bulk curvature. The four dimensional effective action is obtained by integrating out the extra dimension. The Higgs action can be shown as    2 2 4 ,c kr HS d x D H D H H H e               (2) where is a mass parameter, the Higgs field .c kr H e H  The gravity-scalar mixing is described by the following action 4 ˆ ˆ ( ) ,vis visS d x g R g H H    (3) where  is the mixing parameter [13–16], ( )visR g is the Ricci scalar for the metric 2 ( )( )vis bg x h       induced on the visible brane,   01ckrb x e           is the warp factor, 0 is the canonically normalized massless radion field, Hˆ is the Higgs field in the 5D context before rescaling to canonical normalization on the brane. With 0  , there is neither a pure Higgs boson nor pure radion mass eigenstate. This  term mixes the 0h and 0 into the mass eigenstates h and  as given by [12] 0 0 1 6 / cos sin , 0 1/ sin cos h Z h d c h Z b a                                       (4) where  2 2 2 21 6 1 6 36 Z          is the coefficient of the radion kinetic term after undoing the kinetic mixing , /v    , 246  GeV. The mixing angle  is Production of Higgs in two photon collision 91   0 0 0 2 2 2 2 2 2 tan 2 12 36 h h m Z m Z m        , (5) where 0h m and 0 m are the Higgs and radion masses before mixing. The new physical fields h and in (4) are Higgs-dominated state and radion, respectively [18]  0 0 0 0 0 02 2 2 2 2 2 2 2 2, 2 1 [ ] 4 2 h h h hm m m m m Z m m Z          . (6) Therefore, there are four independent parameters , , , ,hm m   that must be specified to fix the state mixing parameters. For the massless gauge bosons such as photon and gluon, there are no large couplings to Higgs (or radion) because there are no brane-localized mass terms. However, these couplings may come from the loop effects of the gauge bosons. We lay out the necessary Higgs - photon coupling 1 2 h hc hF F    L , (7) with    2 2( ) , 2 i h i c i i Y i c d b e N F b b b                  (8) where 2 19 / 6, 41/ 6Yb b   [12]. The auxiliary functions of the h are given by  1/2 ( ) 2 1 1 ,F f         (9)  1( ) 2 3 3 2 ,F f       (10) with   2 2 1 arcsin ( 1) , 1 1 1 ln ( 1) 4 1 1 f i                                 (11) 2 2 4 .ii h m m   (12) im is the mass of the internal loop particle (including quarks, leptons and W boson). Here, 2 2 W W2 2 4 , 4 f f h h m m m m    denote the squares of fermion and W gauge boson mass ratios, respectively. Bui Thi Ha Giang and Dao Thi Le Thuy 92 2.2. The creation of Higgs in the two photon collision In this section, we consider the photon collision process 1 2 1 2( ) ( ) ( ) ( ),p p h k h k    (13) Here ,i ip k (i = 1,2) stand for the momentums. There are three Feynman diagrams contributing to reaction (13), representing the s, u, t-channels exchange depicted in Fig.1. Figure.1. Feynman diagrams for hh  collision We obtain the scattering amplitude in the s, u, t-channels, respectively 1 1 2 1 2 22 2 2 2 ( ) ( ) ( ), hh hhh s h s s h g g M C C p p p p p p q m q m                          (14) 2 2 2 2 1 1 12 1 ( ) ( ) ( ) ( ),u h u u u u u M iC p q p q p p q p q p q                      (15) 2 1 1 1 2 2 22 1 ( ) ( ) ( ) ( ),t h t t t t t M iC p q p q p p q p q p q                      (16) where C , hC , hhg , hhhg are given by [12], 1 2 1 2 ,sq p p k k    1 2 1 2 ,uq p k k p    1 1 2 2tq p k k p    . The expressions of the differential cross-section [18] 21 | | | | , (cos ) 32 | | fi d k M d s p     (17) where 1/2 2| | , | | , 4 2 h s s k m p         2 2 2 2| | | | | | | | 2Re( ).fi s u t s u s t u tM M M M M M M M M M         We evaluate the dependence of the differential cross-section on cos ( 1 1( , )p k  the angle between momenta of the initial photon and the final Higgs) and the dependence of the total cross- section on the collision energy s , VEV of the radion  and . We give some estimates or the cross-sections in the process hh  as follows i) In Fig.2, we choose 125hm GeV (CMS), 5TeV  , 1/ 6, 110m GeV   [2]. We plot the differential cross-section as the function of cos at the fixed collision energy, 3s TeV (CLIC). The result shows that the differential cross- section reaches maximum value when cos is about 0. Therefore, the advantageous direction to collect Higgs is perpendicular direction to the initial photon beam. In Ref [19], we worked the radion production in high energy photon collisions. The Production of Higgs in two photon collision 93 cross-section in hh  is about 6 times as large as that in   in the same condition. Figure 2. The differential cross-section in hh  as a function of cos with 125hm GeV , 5TeV  , 1 / 6, 110m GeV   , 3s TeV ii) We plot the total cross-section as a function of the collision energy s in Fig.3. The parameters are chosen as Fig.2. The total cross-section achieves the minimum value 0.0268 fbar at 1380s GeV and increases in the high energy region. In the region 3 5 ,TeV s TeV  the cross-section is as a linear function of the collision energy. Figure 3. The total cross-section in hh  as a function of the collision energy s with 125hm GeV , 5TeV  , 1 / 6, 110m GeV   iii) In Table 1, we give the dependence of the total cross-section on  . The range  is chosen as 1 5TeV TeV   . We choose 125hm GeV (CMS), 110m GeV  , 1/ 6  , 3 .s TeV The total cross-section has a maximum value at 1TeV  . Table 1. The total cross-section in hh  as a function of  .  (TeV) 1 2 3 4 5 ( )fbar 21.0198 1.1807 0.2649 0.0961 0.0475 Bui Thi Ha Giang and Dao Thi Le Thuy 94 iv) To have 2 0,Z  must lie in the region 2 2 1 4 1 4 1 1 1 1 12 12                        . We choose 125hm GeV (CMS), 110 ,m GeV  3 ,s TeV 5TeV  corresponding to the range 3.31 3.47   . We plot the dependence of the total cross-section on  in Fig.4. The result shows that the total cross-section decreases in the region 3.31 0   and increases in the region 0 3.47  . We also give some of the total cross-section value in Table 2. The total cross-section achieves the minimum value ( 0.004608fbar ) in case of 0.1146  . Figure 4. The total cross-section in hh  as a function of  with 125hm GeV , 5TeV  , 110 ,m GeV  3s TeV . Table 2. The total cross-section in hh  as a function of .  -3 -2 -1 -1/6 0 1/6 1 2 3 ( )fbar 4495 2 421.66 2 5.650 1 0.005 2 0.009 4 0.047 5 6.24 9 597.98 7 14882 6 3. Conclusion In this paper, we have studied the Higgs production in two photon collision in high energy. The ability of search the Higgs boson is the perpendicular direction to the initial photon beam. We have evaluated the dependence of the total cross-section on the parameters , ,s   . Numerical evaluation gives observable cross-section in the future colliders. Acknowledgement: The work is supported in part by Hanoi National University of Education project under Grant No. SPHN-16-05. Production of Higgs in two photon collision 95 REFERENCES [1] L. Randall and R. Sundrum, 1999. Phys. Rev. Lett. 83 3370. L. Randall and R. Sundrum, 1999, Phys. Rev. Lett. 83 4690. [2] M. Frank, K. Huitu, U. Maitra, M. Patra, 2016. Phys. Rev. D94, 055016. [3] G.D. Kribs, 2001. Conf C010630 P317. [4] M. Chaichian, A. Datta, K. Huitu and Z. 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