Contribution of the scalar unparticle on process e+ e → hh in the randall sundrum model

CONTRIBUTION OF THE SCALAR UNPARTICLECONTRIBUTION OF THE SCALAR UNPARTICLE ON PROCESS e e+ − → hh IN THE RANDALL IN THE RANDALL IN THE RANDALL----SUNDRUM MODEL SUNDRUM MODEL SUNDRUM MOD

CONTRIBUTION OF THE SCALAR UNPARTICLE

CONTRIBUTION OF THE SCALAR UNPARTICLE

ON PROCESS e e+ − → hh IN THE RANDALL IN THE RANDALL IN THE RANDALL SUNDRUM MODEL SUNDRUM MODEL SUNDRUM MODEL

Bui Thi Ha Giang 1 , Dao Thi Le Thuy 1 , Dang Van Soa 2

1 Hanoi National University of Education 2

Hanoi Metropolitan University

Abstract: The pair production of Higgs is studied with the contribution of the scalar

unparticle in the e e+ − collision in the Randall-Sundrum model in detail We evaluate the observable cross-section which depends on the collision energy s and the scaling dimension of the unparticle operator d U The total cross-section with the unparticle contribution is compared to that without the unparticle

Keywords: Higgs, scalar unparticle, cross section , Randall-Sundrum model

Email: giangbth@hnue.edu.vn

Received 15 July 2017

Accepted for publication 10 September 2017

1 INTRODUCTION

The Standard model (SM) of particle is successful in describing the elementary particle picture In the Lagrangian of the SM, the scale invariance is broken at or above the electroweak scale [1, 2] Because of no particle states with a definite nonzero mass, there are no particles with a nonzero mass in a scale invariant sector in four space-time dimensions [1, 3] Georgi has suggested that if the scale invariance exists, it is made of unparticles Based on the Banks-Zaks theory [4], unparticle stuff with nontrivial scaling dimension is considered to exist in our world The invariant Banks-Zaks field can be connected to the SM particles Recently, the evidence of the unparticle has been studied with CMS detector at the LHC [5, 6]

Although the SM describes successfully almost all existing experimental data, the model suffers from many theoretical drawbacks One of many attempts to extend the SM and solve the hierarchy problem, one of theoretical drawbacks of SM [7], is the

Randall-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 (φ ), corresponding to the quantum fluctuations of the distance between the two 3-branes [8] In 2012, Higgs signal at 125 GeV is discovered by the ATLAS and CMS collaborations [9, 10]

However, the unparticle effects on the collisions have not been concerned in the RS model In this paper, we study the Higgs couple production, which has been proposed as an

option of e e+ − collisions The layout of this paper is as follows The unparticle and effective interactions are reviewed in Section 2 mostly cited on [1, 2, 3] Section 3 is

devoted to the creation of Higgs couple in e e+ −collision Finally, we summarize our results and make conclusions in Section 4

2 THE UNPARTICLE AND EFFECTIVE INTERACTIONS

The derivation of the virtual unparticle propagator is based on the scale invariance [2] The unparticle propagators for scalar, vector and tensor operators are given by [2], respectively

( 2) 2,

2sin( π)

−

∆ = d U − d U

scalar

U

iA

q

( 2) 2 ,

2sin( ) πµν π

−

∆ = d U − d U

vector

U

iA

q

2 2

,

2sin( π) µν ρσ

−

∆ = d U − d U

tensor

U

iA

q

where d U is the noninteger scaling dimension of the unparticle operator,

2 2

1

, ( 1) (2 ) (2 )

π π π

Γ + 

=

Γ − Γ

U

d A

(4)

2

2 2

2

| | for s-channel process, is positive, ( )

| | for u-, t-channel process, is negative,

π

− −

−

−





U

U

d

d

q

2

µ ν

µν µν

π q = −g +q q

, 1 2

( ) ( ) ( ) ( ) ( ) ( )

µν ρσ = πµρ πνσ +πµσ πνρ − πµν πρσ 

The effective interactions for the scalar, vector and tensor unparticle operators are given by, respectively

5

λ − γ Ο λ − γ γ Ο

i µ νD νDµ µν G Gµα να µν

(10) where λi (i = 0, 1, 2) stand for the scalar, vector and tensor unparticle operators, respectively '

a

Dµ = ∂ +µ igτ Wµ +ig Bµ

is the covariant derivative, B, i

W are gauge fields,

,

2

a

Y τ

correspond to the standard generators of U(1)Y and SU(2)L The corresponding coupling constants are denoted by g, g’ f stands for a standard model fermion, ψ stands

for a standard model fermion doublet or singlet Gαβ denotes the gauge field strength

3 THE HIGGS PRODUCTION

In this section, we consider the e e+ − →hh collision process

e ( )− p +e+(p )→h k( )+h k( ), (11) Here p k i, i(i = 1,2) stand for the momentums There are three Feynman diagrams contributing to reaction (11), representing the s, u, t-channels exchange depicted in Fig.1

We obtain the scattering amplitude in the s, u, t-channels, respectively

2 2

2sin( )

π

−

−

U

A

2

2 2 ( )(ˆ ) ( )

−

eeh

g

2

2 2 ( )(ˆ ) ( )

−

eeh

g

where g eehare given by [11], q s=p1+p2= +k1 k2, q u =p1−k2= −k1 p2, q t =p1− =k1 k2−p2 The expressions of the differential cross-section [12]

2

1 | |

| | , (cos ) 64 | | fi

M

σ

ψ = π

r

where|M fi| 2 = |M s| 2 + |M u| 2 + |M t| 2 + 2 Re(M M s+ u+M M s+ t+M M u+ t).

We give some estimates for the cross-sections as follows

i) In Fig.2, we evaluate the dependence of the total cross-section on the collision energy s with the various dU We choose λ0= Λ =1, U 1000GeV[2] In case of the scalar unparticle, 1<d U < [13] The total cross-sections decrease when the collision energy 2 s

increases

Figure 2 Total cross-sections for e e+ −→hh versus s with the various d U

ii) The proportion of the total cross-sections with the unparticle contribution σU to that without the unparticle σ0 in Ref.14 is calculated in Table 1 The results show that the unparticle contribution is significant

s

0

/

U

σ σ

1.1

U

d = d = U 1.2 d = U 1.3 d = U 1.5 d = U 1.7 d = U 1.9

300 4.3743 1.2514 0.3655 0.0353 0.0048 0.0022

500 6.9403 2.4403 0.8731 0.1265 0.0261 0.0178

800 9.2157 3.8971 1.6887 0.3578 0.1066 0.1063

1000 10.4242 4.8242 2.2788 0.5751 0.2055 0.2454

1500 13.2143 7.1753 3.9935 1.3961 0.6883 1.1396

2000 16.0221 9.8011 6.1105 2.6851 1.6685 3.4696

2500 19.5210 13.0539 8.8922 4.6706 3.4730 8.6227

3000 23.9716 17.2340 12.6950 7.7305 6.6383 19.078

4 CONCLUSION

In this paper, the total cross-sections for the process e e+ −→hh with the unparticle

contribution are evaluated The results indicate that the cross-sections depend on the parameter d Uand the collision energy s They are larger in case of the small d U and decrease when sincreases When s =3000GeV and d = U 1.1, the cross-section with the unparticle contribution is about 24 times as large as that without the unparticle

Acknowledgement: The work is supported in part by Hanoi National university of

Education project under Grant No SPHN-16-05

REFERENCES

1 H Georgi (2007), Phys Rev Lett 98 p.221601

2 K Cheung, W-Y Keung and T-C Yuan, Phys Rev D76 p.055003

3 S-L Chen, X-G He (2007), Phys Rev D76 p.091702

4 T Banks and A Zaks (1982), Nucl Phys B196, p.189

5 CMS Collaboration (2015), Eur Phys J C75 p.235

6 CMS Collaboration (2016), Phys Rev D93 p.052011

7 L Randall and R Sundrum (1999), Phys Rev Lett 83 p.3370

8 L Randall and R Sundrum (1999), Phys Rev Lett 83 p.4690

9 M Frank, K Huitu, U Maitra, M Patra (2016), Phys Rev D94 p.055016

13 M E Peskin and D V Schroeder (1995), “An Introduction to Quantum Field Theory”,

Addision-Wesley Publishing

14 A Friedland, M Giannotti, M Graesser (2009), Phys Lett B678 pp.149-155

15 B T H Giang and D T L Thuy (2016), Journal of science of HNUE, Vol 61, No 7, pp.58-64

ĐÓNG GÓP CỦA PHI HẠT VÔ HƯỚNG VÀO QUÁ TRÌNH

e e+ −→hh TRONG MÔ HÌNH RANDALL-SUNDRUM

Tóm tắt

Tóm tắt: Sự tạo cặp của Higgs trong mô hình Randall-Sundrum từ va chạm e e+ −với sự ñóng góp của U-hạt vô hướng ñược nghiên cứu chi tiết Chúng tôi ñánh giá tiết diện quan sát phụ thuộc vào năng lượng va chạm và số chiều toán tử U-hạt Tiết diện toàn phần có ñóng góp của U-hạt ñược so sánh với trường hợp không có ñóng góp của U-hạt

Từ khóa

Từ khóa: Tạo Higgs, U-hạt vô hướng, tiết diện, mẫu Randall-Sundrum