Tevatron Wij anomaly for a model with two different mechanisms for mass generation of gauge fields

Transcription

1 Hgh Energy and Partcle Physcs September Tevatron Wj anomaly for a model wth two dfferent mechansms for mass generaton of gauge felds E.Koorambas 8A hatzkosta 1151 Ampelokp Athens Greece E-mal:elas.koor@gmal.com Abstract. The latest ollder Detector at Fermlab (DF) anomaly the excess of djet events n the nvarant-mass wndow GeV n assocated producton wth a W boson can be explaned by a new neutral vector -boson of mass (145 GeV) that s predcted by the Wu mechansms for mass generaton of gauge feld. The Standard Model (SM) W Z-bosons normally get ts masses through the couplng wth the SM Hggs of mass GeV. Here the boson has neglgble couplngs to leptons and so s not affected by the dlepton constrants. PAS Numbers: 1.15-y q z 1.10-g Keywords: ollder Detector Fermlab electroweak nteractons gauge feld symmetry breakng ontents 1. Introducton... The Lagrangan of the model. 3. The masses of gauge felds The Phenomenology of the mode 9 5. oncluson References 10 Ths work s lcensed under the reatve ommons Attrbuton 3.0 Unported Lcense. To vew a copy of ths lcense vst or send a letter to reatve ommons 444 astro Street Sute 900 Mountan Vew alforna USA.

2 Hgh Energy and Partcle Physcs September Introducton The latest surprse presented by the Fermlab s ollder Detector (DF) experment s an excess n the nvarant-mass wndow of GeV n the djet system of the assocated producton of a W- boson wth jets [1] [] [3][4]. We shall denote t by Wjj producton. The hypothess behnd Fermlab's DF experment [1] [] [3] [4] predcted that the number of the events producng a W boson and a par of jets would fall off as the mass of the jet par ncreased. The DF expermental data however showed somethng strange (see []): a bump n the number of events when the mass of the jet par was about 145 GeV. The excess of events n the wndow M jj GeV appears to be a resonance. It s reportedly at 4.8 sgma tantalzngly close to fve-sgma certanty [] [3]. However DZero (D0) [7] have cross-checked the observaton wth ther own ndependent data and analyss tools and have found no evdence of a new partcle. The detectors are somewhat dfferent n desgn and n the selecton crtera used to analyze events. It s certanly possble for DF to see somethng that DZero has mssed. From the dstrbuton of the events n the DF experment we can see that the wdth of the resonance appears to be slghtly wder than the SM Z- boson. The canddate partcle may not belong to the standard model of partcle physcs. Instead as some argue [5] [6] [7] t mght be the frst hnt of a new force of nature termed techncolour. Ths force would resolve some problems such as the naturalness problem [8] wth the standard model but predcts the exstence of many lght partcles that should have been detected by now [8]. Most workers agree that the mysterous partcle produced by the DF experment s not the long-sought Hggs boson [ ] beleved by many to endow partcles wth mass. If t were the bump n the expermental data would be 300 tmes smaller. What's more a Hggs partcle would probably decay nto bottom quarks whch seem to be absent from the Fermlab data [1] [] [3] [4]. In ths paper we nvestgate the nature of ths mysterous partcle and propose a model wth two dfferent mechansms for mass generaton of gauge felds. The Tevatron Wj anomaly s explaned by a new neutral vector -boson of mass (145 GeV) as predcted by the Wu mechansms for mass generaton of gauge felds [16] [17] [18] [19]. The SM W Z-bosons normally acqure ther masses through ther couplng wth the SM Hggs boson mass GeV [0] [1] [] [3]. The boson has neglgble couplngs to leptons and so s not affected by the dlepton constrants.. The Lagrangan of the model Suppose that the gauge symmetry of the theory s SU( N) U() group whch s wrtten specfcally as follows: G SU( N) U() (1) where SU ( N ) s the specal untary group of N-dmensons ( x) s a N-component vector n the fundamental representatve space of SU ( N) group and T ( 1... N 1) denotes the representatve matrces of the generators of SU ( N ) group. The latter are Hermt and traceless. They satsfy the condton: E.Koorambas: Tevatron Wj anomaly

3 Hgh Energy and Partcle Physcs September [ T T ] f T Tr( TT ) K () j jk k j j where fjk are structure constants of the SU ( N ) group and K s a constant ndependent of the ndces and j but dependent on the representaton of the group. The representatve matrx of a general element of the SU ( N) group s expressed as: T U (3) e wth beng the real group parameters. In global gauge transformatons all are ndependent of space-tme coordnates whle n local gauge transformatons are functons of space-tme coordnates. U s a untary N N matrx. In order to ntroduce the mass term of gauge felds wthout volatng local gauge symmetry at energy scale close to TeV two knds of gauge felds are requred: a ( x) and b ( x). a ( x) and b ( x) are vectors n the canoncal representatve space of SU ( N ) group. They can be expressed as lnear combnatons of generators as follows a( x) a( x) T (4) b( x) b( x) T (5) where a ( x) and b ( x) are component felds of the gauge felds a ( x) and b ( x) respectvely. orrespondng to these two knds of gauge felds there are two knds of gauge covarant dervatves: D D ga (6) cgb (7) b The strengths of gauge felds a ( x) and b ( x) are defned as 1 a [ D D ] a a g[ a a ] g (8) 1 b [ Db Db ] b b cg [ b b ] (9) cg respectvely. Smlarly a ( x) and b ( x) can also be expressed as lnear combnatons of generators: a a T (10) b b T (11) Usng relatons () and (8) (9) we obtan E.Koorambas: Tevatron Wj anomaly 3

4 Hgh Energy and Partcle Physcs September jk j k a a a gf a a (1) jk j k b b b cgf b b (13) The Lagrangan densty of the model s 1 1 Wu ( D m) Tr( a a ) Tr( b b ) 4K 4K Tr[( a cb )( a cb )] K(1 c ) ([16]) (14) where c s a constant. The space-tme metrc s selected as dag( 1111)( 013). Accordng to relaton () the above Lagrangan densty L can be rewrtten as: 1 1 Wu [( ga T ) m] a a b b 4 4 ( a cb )( a cb ) (1 c ) ([16]) (15) In equaton (1) the gauge group U() SUL() U(1) Y s the known SM of electroweak (EW) nteractons [0] [1] [] [3]. The generators of SU L() correspond to the three components of weak sospn T ( ( 13). The U (1) Y generator corresponds to the weak T3 hyperchargey. These are related to the electrc charge by Q Y. The SU () U(1) nvarant Lagrangan s gven as follows L Y [ g EW g A B ] er [ gb ] er F F B B (16) 4 4 wth the feld strength tensors a a F A A g A A (17) B B B (18) for the three non-abelan felds of SU () L and the sngle Abelan gauge feld assocated wth U (1) Y respectvely. The covarant dervatve s 1 1 D ga T gb (19) E.Koorambas: Tevatron Wj anomaly 4

5 Hgh Energy and Partcle Physcs September wth gg beng the SU () L and U (1) Y the couplng strength respectvely. Ths Lagrangan SU () L and U (1) Y s nvarant under the nfntesmal local gauge transformatons for ndependently. Beng n the adjont representaton the SU () L massless gauge felds form a weak sospn trplet wth the charged felds beng defned by 1 W ( A A )/ The neutral component of states Z A 3 cos B sn w 3 cosw w (0) 3 A mxes wth the Abelan gauge feld B to form the physcal A B A sn () g where tan w s the weak mxng angle. g w (1) Based on the gauge group SU( N) U() follows the fnal Lagrangan of the model s gven as 1 g [ g A B ] [( gat ) m] e [ gb ] e F F B B a a b b Model R R ( a cb )( a cb ) (1 c ) (3) where c s a constant. 3. The masses of gauge felds Obvous characterstcs of the Wu Lagrangan equaton (15) s that the mass term of the gauge felds s ntroduced nto the Lagrangan and that ths term does not affect the symmetry of the Lagrangan. It has been proved that the above Lagrangan has strct local gauge symmetry [16]. Because both vector felds a and b are standard gauge felds ths model s a gauge feld model whch descrbes gauge nteractons between gauge felds and matter felds [16]. The mass term of gauge felds can be wrtten as follows [16]: a ( a b ) M b (4) where M s the mass matrx: E.Koorambas: Tevatron Wj anomaly 5

6 Hgh Energy and Partcle Physcs September c M 1 c c c. (5) Physcal partcles generated from gauge nteractons are egenvectors of mass matrx and the correspondng masses of these partcles are egenvalues of mass matrx. The mass matrx M has two egenvalues m 1 m 0. (6) The correspondng egenvectors are cos sn sn cos (7) where cos 1 1 c sn c 1 c (8) We defne cosa sn b F sna cosb (9) and F are egenstates of mass matrx: they descrbe the partcles generated from gauge nteractons. The nverse transformatons of (9) are a cos sn F b sn cosf (30) Takng equatons (9) and (30) nto account the Wu Lagrangan densty L gven by (15) changes nto: (0) ( I ) Wu Wu Wu (31) where (0) Wu ( m) K K 4 4 (3) E.Koorambas: Tevatron Wj anomaly 6

7 Hgh Energy and Partcle Physcs September cos sn cos 3 1 sn sn gf K g f K 4 g f f 4cos ( I ) jk k jk k Wu g (cos sn F) gf 0 gf K0 K K jk k jk j k jk lm j k l m 0 sn 0 sn g f f K K K K g tc f jk lm j k lm m jk lm j k lm m sn f K sn jk lm j k l m j k m j k l m g f f ( K K K K K K ) In the above relatons we have used the followng smplfed notatons: 0 0 K F F (33) (34) From equaton (3) t s deduced that the mass of feld s μ and the mass of gauge feld F s zero. That s M g M F 0 (35) where g s the couplng constant of the -boson and v the vacuum expectaton value. Transformatons (9) and (30) are pure algebrac operatons whch do not affect the gauge symmetry of the Lagrangan [16]. They can therefore be regarded as redefntons of gauge felds. The local gauge symmetry of the Lagrangan s stll strctly preserved after feld transformatons. In other words the symmetry of the Lagrangan before transformatons s completely the same as the symmetry of the Lagrangan after transformatons. We do not ntroduce any knd of symmetry breakng at energy scales close to TeV. Felds and F are lnear combnatons of gauge felds a and b so the forms of local gauge transformatons of felds and F are determned by the forms of local gauge transformatons of gauge felds a and b. Because and F consst of gauge felds a and b and transmt gauge nteractons between matter felds for the sake of smplcty we also call them gauge felds just as W and Z are called gauge felds n the electroweak model ([0] [1] [] [3]). Ths gauge feld theory therefore predcts the exstence of two dfferent knds of force transmttng vector felds exst n ths gauge feld theory: one s massve and another s massless. Takng the Hggs mechansm [0-3] nto account n the vacuum energy scale of 179GeV the W and 0 Z become massve whle the photon A remans massless. The symmetry SU ( N ) 0 does not break down snce the gauge bosons and F get ther masses by the Wu mechansms [16] [17] [18] [19] n the vacuum energy scale of TeV. The EW Lagrangan (16) changes nto: EW ( D) ( D ) ( ) 1 1 F F B B 4 4 (36) E.Koorambas: Tevatron Wj anomaly 7

8 Hgh Energy and Partcle Physcs September The covarant dervatves are gven by the equaton (19) whch acts on a complex SU () feld: (37) Let us now ntroduce the vacuum expectaton value of 179 GeV whch volates local gauge symmetry of the Lagrangan. 1 0 (38) 1 0 ( ) U U( ) exp 1 0 U( ) 1 (39) (40) (41) From the above we calculate: EW ( )( ) ( ) ( ) F F B B ( gb ga)( gb ga ) 4 (4) The EW Lagrangan EW can be wrtten as the sum of classcal part a part quadratc n the felds and a part cubc and quadratc n the felds whch gves rse to nteractons. By the defntons of the gauge felds equatons (0) (1) () the masses are gven as follows 1 1 M A 0 MW g MZ g g (43) The gauge felds and masses predcted by ths model are summarzed n Table.1. Table.1. Gauge felds and masses predcted by the present model. Gauge felds Masses (M)-GeV Vacuum (v)-gev Symmetry patter (New) Before -symmetry breakng F (New) Before- symmetry breakng W After -symmetry breakng Z After - symmetry breakng A After- symmetry breakng E.Koorambas: Tevatron Wj anomaly 8

9 Hgh Energy and Partcle Physcs September The Phenomenology of the model The phenomenology of the proposed gauge boson s smlar to the Z-prme a hypothetcal carrer of a new force smlar to the electroweak force [9]. Followng ref [9] the couplng constant g s the SM couplng g /cos w. For our setup g s related to g by g g 5 xw 3 1/ 1/ 0.63 (44) where xw sn w and w s the weak mxng angle. The decay wdth of gauge boson nto fermons s gven by G M F f f c n n ( ff ) N ( M ) M 1 4 x[ u (1 x) a (1 4 x)] (45) 6 where G F s the Ferm couplng constant and Nc 3 or 1 f f s a quark or a lepton respectvely. The term s gven by the followng equaton: 3 s s s M ( ) 1/ / 1.409( / ) 1.77( / ) ( M ) s s (46) s the strong couplng at the scale f M x m / M The wdth s proportonal to λ whch sets the strength of the couplng. For 1the total wdth s / M 0.0 for M m (47) t Ths wdth wll be ncreased somewhat f there are open channels for decay nto the top quark superpartners and other exotc partcles. The boson can be drectly produced at a hadron collder va the qq subprocess for whch the cross secton n the narrow wdth approxmaton s G ˆ FM q q ( qq ) K [( un ) ( an ) ] ( sˆ M ) ([4]) (48) 3 The K-factor represents the enhancement from hgher-order QD processes estmated to be s( M ) 4 4 K ([4]) (49) When mxng s gnored t s q q n n ( u ) ( a ) (0.6) (50) E.Koorambas: Tevatron Wj anomaly 9

10 Hgh Energy and Partcle Physcs September and the above cross secton s ndependent of the parameter γ as long as V A 1. Note that all the current and prevous djet-mass searches at the Tevatron are lmted to M 00GeV. These energy levels are not applcable to the present wth M 145GeV. jj The relevant djet data are from the UA collaboraton wth collson energy at s 630GeV. The UA ollaboraton [5] has detected the W + Z sgnal n the djet mass rage 48 GeV m( jj) 138GeV and has placed the upper bound of B ( jj ) over the range 80 GeV m( jj) 30GeV. The assocated producton of wth a W- boson goes through the t- and u-channel exchange of quarks whle the s-channel boson exchange s hghly suppressed because of the neglgble mxng angle between the SM Z -boson and the. onsequently we expect smlar or even larger cross sectons for M M Z than the SM WZ producton n whch there s a delcate gauge cancellaton among the t- u- and s-channel dagrams. We have ncluded a K-factor ( K 1.3 to approxmate next-to-leadng order QD contrbutons [6]. We can see that at around GeV the cross secton s rght at the order of 4 pb whch s requred to explan the excess n the DF Wjj anomaly []. 5. oncluson We have shown that a new neutral vector - boson of mass (145GeV) predcted by the Wu mechansms for mass generaton of gauge feld can explan the excess n the nvarant-mass wndow GeV n the djet system of Wjj producton. In ths model the Standard Model (SM) WZ-bosons acqure ther masses through the couplng wth the SM Hggs of mass GeV. The -boson has neglgble couplngs to leptons and so s not affected by the dlepton constrants. References [1]. T. Aaltonen et al. [DF ollaboraton] 008 Preprnt hep-ex/ []. T. Aaltonen et al. [DF ollaboraton] 011 Preprnt hep-ex/ [3]. V. M. Abazov et al. [D ollaboraton] 008 Preprnt hep-ex/ [4]. T. Aaltonen et al. [DF ollaboraton] 011 Preprnt hep-ex / [5]. B. Holdom 1981 Phys. Rev. D [6]. T. W. Appelqust D. Karabal and L.. R. Wjewardhana 1986 Phys. Rev. Lett [7]. K. Yamawak M. Bando and K.-. Matumoto 1986 Phys. Rev. Lett [8]. T. Akba and T. Yanagda 1986 Phys. Lett. B [9]. J. Goldstone 1961 Nov. m [10]. Y Nambu G.Jona-Lasno 1961 Phys.Rev. 134 [11]. J.Goldstone A.Salam S.Wenberg Phys.Rev.17 E.Koorambas: Tevatron Wj anomaly 10

11 Hgh Energy and Partcle Physcs September [1]. P.W.Hggs 1964 Phys.Lett [13]. F.Englert R.Brout 1964 Phys.Rev.Lett [14]. G.S.Guralnk.R.Hagen T.W.B.Kbble 1964 Phys.Rev.Lett 585 [15]. P.W.Hggs 1966 Phys.Rev [16]. Nng Wu 000 Preprnt hep-ph/ [17]. Nng Wu 1998 Preprnt hep-ph/98036 [18]. Nng Wu 1998 Preprnt hep-ph/98037 [19]. Nng Wu 1998 Preprnt hep-ph/ [0]. S. Wenberg 1967 Phys. Rev. Lett [1]. S. Wenberg 197 Phys. Rev. D []. A. Salam 1968 In Elementary Partcle Theory: Relatvstc Groups and Analytcty (Nobel Symposum No. 8 ed. N. Svartholm (Almqvst and Wksell Stockholm) [3]. S. Glashow 1961 Nucl. Phys. 579 [4]. V. Barger and R.J.N. Phllps 1987 ollder Physcs (Addson-Wesley) [5]. J. Altt et al. [UA ollaboraton] 1991 Z. Phys [6] J. Ohnemus 1993 Phys. Rev. D [7].V.M. Abazov et al. [D0 ollaboraton] 011 Preprnt hep-ex / [8]. Graham G. Ross 001 Structure beyond the Standard Model Phl. Trans. R. Soc. Lond. A [9]. Kngman. Jeonghyeon.S 011 Preprnt hep-ph/ E.Koorambas: Tevatron Wj anomaly 11