Probing anomalous off-shell electroweak dipole moment of the top quark

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1 EPJ Web of Conferences 18, 42 (17) QFTHEP 17 DOI: 1.11/epjconf/ Probing anomalos off-shell elecroweak dipole momen of he op qark Edward Boos 1,2, Vyacheslav Bnichev 1, Lev Ddko 1, and Georgii Voronikov 1 1 Skobelsyn Insie of Nclear Physics M.V. Lomonosov Moscow Sae Universiy, Moscow , Rssian Federaion 2 Facly of Physics M.V.Lomonosov Moscow Sae Universiy Leninskie Gory, Moscow , Rssian Federaion Absrac. A possibiliy o search for anomalos Wb ineracion µ W µ ( f L W P L + f R W P R) is considered for he firs ime. Despie sch coplings do no conribe o boh pair op qark prodcion or hree main elecroweak prodcion modes, hey cold provide non-zero conribions o associaed single op qark prodcion wih W or bosons or in associaion wih wo forward ligh jes via elecroweak fsion diagrams. 1 Inrodcion The Sandard Model () is a heory, which is now esed and proved in a hndreds of differen experimens. However, obliviosly is no a final heory, b a very sccessfl effecive heory wihin he elecroweak energy scale. One of he primary goal of he Large Hadron Collider is o search for physics beyond he Sandard Model (B). A new physics may manifes iself hrogh differen ways. Many B heories predic new paricles if he energy of collision is greaer han he prodcion hreshold (E collision > E hreshold ). However, even in opposie scenario, when (E collision < E hreshold ) B physics cold prove iself hrogh anomalos coplings originaing from higher dimensional gage invarian operaors or inerference erms of new resonances wih he paricles, ha leads o deviaion from predicion in prodcion cross secions and/or kinemaic disribions. The op qark secor of owing o is niqe properies sch as large mass, small lifeime, spin correlaions and very small mixing o he ligh qark generaions, cold be a window o B physics. The effecive Lagrangian approach is common sed in experimenal physics for model-independen descripion possible effecs of B physics. Ths, lowes-dimension Lagrangian [1] for he Wb verex sally wrien as: L = g γ ( µ fv L P L + fv R P ) R W µ g σµν ν W µ ( f L 2 2 M T P L + ft R P ) R + h.c., (1) W where P L,R = (1 γ )/2, σ µν = i(γ µ γ ν γ ν γ µ )/2, g is he copling consan of he weak ineracion, he consan fv L represens he lef-handed vecor copling, presened in, f V R is he anomalos righ-handed vecor copling and ft L ( f T R ) represens he anomalos lef-handed (righ-handed) ensor copling. Sch anomalos coplings nowadays are relaively well sdied boh heoreically [2]-[] and experimenally [6]-[8]. In his paper we discss addiional anomalos coplings which were no considered ye from phenomenology poin of view. The Ahors, pblished by EDP Sciences. This is an open access aricle disribed nder he erms of he Creaive Commons Aribion License 4. (hp://creaivecommons.org/licenses/by/4./).

2 EPJ Web of Conferences 18, 42 (17) QFTHEP 17 DOI: 1.11/epjconf/ Relevan processes As was menioned in he paper [1] here is an addiional conribion o he effecive Lagrangian in case of off-shell W boson: µ W µ P L. Sch an ineracion which one can call off-shell elecroweak dipole momen (osedm) appears in he effecive elecroweak non-linear chiral Lagrangian approach [9]. Phenomenological sdy of his ineracion erm has significan difficlies. The ineracion erm is oally vanish for an on-shell W boson or in he case W coples o massless on-shell fermions. Therefore, he anomalos osedm coplings do no conribe o he main op qark prodcion processes, boh pair or any of hree elecroweak prodcion -, s-, W-channels. Despie sch coplings do no conribe o sal op qark prodcion processes hey cold provide non-zero conribions o associaed single op qark prodcion wih W or bosons or in associaion wih wo forward ligh jes via elecroweak fsion diagrams. The represenaive Feynman diagrams wih non-zero osedm conribion are shown in Fig. 1. In his paper we consider more simple 2 processes of associaed prodcion op qark and elecroweak gage bosons. ū W ū d ū Figre 1. Feynman diagrams of he processes, which cold be sed o search for he anomalos off-shell W boson coplings. The effecive Lagrangian sed in he analysis has he following form: L ef f. = g 2 v Λ 2 µ W µ ( f L W P L + f R W P R) + h.c.. (2) Here v corresponds o naral dimensional facor of he anomalos operaors, v = 246 GeV is Λ 2 vacm expecaion vale, Λ is he scale of a new physics and consans fw L and f W R are he srenghs of lef and righ anomalos coplings. In he prpose of CP conserving, we consider he case of a prely imaginary fw L and f W R vales [9]. For sdying processes wih anomalos osedm he CompHEP 4..2 package [1] was sed o model kinemaic disribions of he osedm and conribions inclding heir inerference. The Feynman rles for he Wb verex were generaed wih he LanHEP package [11], and implemened ino CompHEP. The complee se of elecroweak diagrams for he associaed b prodcion is shown in Fig. 2. The firs hree diagrams give non-zero conribion wih considered anomalos copling while he las wo conain only conribions. The second process bw also conains non-zero osedm conribions from he diagrams like he firs diagram in Fig 1. However, in his case here are diagrams corresponding o op qark pair prodcion and associaed W single op prodcion wih 2

3 EPJ Web of Conferences 18, 42 (17) QFTHEP 17 DOI: 1.11/epjconf/ cross secions significanly larger han possible anomalos conribions. Moreover, in case of Wb final sae here is conribion from glon - glon collision wih hge rae and zero osedm conribion. a) b) d c) d) b e) Figre 2. All relevan Feynman diagrams of he process of associaed prodcion of a op qark wih boson. Kinemaic disribion and exracing poenial Since anomalos osedm ineracions are direcly proporional o he momenm of he W boson, i gives approximaely linear grow of sensiiviy o he coplings wih he energy of he colliding proons. Ths, for sch projecs as High Energy LHC or Fre Circlar Collider, efficiency of he searches for osedm coplings will be increasing -1 imes compare o crren energies a he LHC. The anomalos ineracions cold manifes iself no only in cross secion raes, b also in differen kinemaics of he process. For example, on Fig. one can see disribion of a ransverse momenm of he boson in he process of is associaed prodcion wih op qark. In he case of anomalos conribions, he momenm, in average, is mch higher han for prodcion, and is peaking a abo 16 GeV insead of GeV for. The same siaion is observed for he ransverse momena of he and b qarks. The difference in ransverse momenm disribions of he final sae paricles is provided mosly by heir space bearings, as one can see on he Fig. 4. The asymmery beween he negaive and posiive pars of he plos is provided by choose of iniial sae qarks (), which gives symmeric picre wih a complemenary iniial sae. The anglar disribions (Fig. ) are also shown differen behavior of and osedm prodcion. The anomalos ineracions are characerized by more smooh disribion boh for or b angle. However, one cold see here are pre lef and righ osedm ineracions are oally indisingishable on he Fig. -. The way o see he difference beween he coplings is in heir inerference wih he par. The righ anomalos ineracion has a negaive inerference erm wih, while he lef copling has a small, b posiive one (Fig. 6). Since here are no experimenal limis on osedm coplings we ake sch vales for he coplings o ge visible deviaions from. Anoher disincion beween he copling is he cross secion rae for sea massive qarks in he iniial sae (Fig. 7). The difference is provided by diagrams a) and b) on he Fig 2, where qarks of differen flavors are aken ino accon for propagaors of he iniial viral qark exchange. 4 Conclsion The possible anomalos osedm ineracions are phenomenologically sdied for he firs ime. Sch coplings do no conribe o boh pair op qark prodcion or hree main elecroweak prodcion processes. However, here are several processes considered in his aricle which have non zero

4 T T EPJ Web of Conferences 18, 42 (17) QFTHEP 17 DOI: 1.11/epjconf/ /σ dσ/d P T P () 1/σ dσ/d P 6 P () /σ dσ/d P 7 6 P (b) 1/σ dσ/d M 4 M(b) M, GeV Figre. Transverse momenm disribions for he ineracion () and pre lef () and righ () osedm in he process of associaed prodcion of a op qark wih boson wih he iniial sae. There are plos for boson (op lef), op qark (op righ) and boom qark (boom lef), and invarian mass for and b (boom righ). The disribions of each copling are normalized o he corresponding cross secions. conribion from sch anomalos coplings. Necessary calclaions of hese processes have been performed. The difference in he shape of he kinemaic disribions owing o he conribion of he osedm coplings are demonsraed in his aricle. The demonsraed difference in he kinemaic disribions is promising for he search and achieving he firs experimenal limis on hese coplings. More accrae esimaion of he sensiiviy o osedm coplings reqires simlaion of he hadronizaion wih deecor response and carefl esimaion of he backgrond conribions. 4

5 EPJ Web of Conferences 18, 42 (17) QFTHEP 17 DOI: 1.11/epjconf/ () 4 4 () (b) Figre 4. Psedorapidiy disribions for he ineracion () and pre lef () and righ () osedm in he process of associaed prodcion of a op qark wih boson wih he iniial sae. There are plos for boson (op lef), op qark (op righ) and boom qark (boom). The disribions of each copling are normalized o he corresponding cross secions cos(,) 4 4 cos(,b) Figre. Anglar disribions for he ineracion () and pre lef () and righ () osedm in he process of associaed prodcion of a op qark wih boson wih he iniial sae. There are plos for cosine of angle beween boson and op qark (lef), and cosine of angle beween op and boom qarks (righ). The disribions of each copling are normalized o he corresponding cross secions.

6 EPJ Web of Conferences 18, 42 (17) QFTHEP 17 DOI: 1.11/epjconf/ /σ dσ/d P T P () () () cos(,b) Figre 6. Disribions for he ineracion (), and lef osedm (+), and and righ anomalos copling (+), inclding inerference, in he process of associaed prodcion of a op qark wih boson wih he iniial sae. There are plos for Transverse momenm of boson (op lef), psedorapidiy of boson (op righ) and op qark (boom lef), and cosine of angle beween op and boom qarks (boom righ). The all disribions are normalized o he cross secion of ineracion. 1/σ dσ/d P T 2 P () 4 cos(,) Figre 7. Disribions for he pre lef () and righ () anomalos coplings, in he process of associaed prodcion of a op qark wih boson wih he c s iniial sae. There are plos for Transverse momenm of op qark (lef), and cosine of angle beween boson and qark (righ). The all disribions are normalized o he cross secion of lef osedm. 6

7 EPJ Web of Conferences 18, 42 (17) QFTHEP 17 DOI: 1.11/epjconf/ Acknowledgemens The work was sppored by gran of Rssian Science Fondaion. References [1] G. L. Kane, G. A. Ladinsky and C. P. Yan, Phys. Rev. D 4 (1992) 124. [2] W. Bchmller and D. Wyler, Ncl. Phys. B 268 (1986) 621. [] K. Whisnan, J. M. Yang, B. L. Yong and X. hang, Phys. Rev. D 6 (1997) 467 [4] E. Boos, M. Dbinin, M. Sachwiz and H. J. Schreiber, Er. Phys. J. C 16 () 269 [] J. A. Agilar-Saavedra, J. Carvalho, N. F. Casro, F. Veloso and A. Onofre, Er. Phys. J. C (7) 19 [6] V. M. Abazov e al. [D Collaboraion], Phys. Le. B 78 (12) 21 [7] V. Khacharyan e al. [CMS Collaboraion], JHEP 11 (1) [8] V. Khacharyan e al. [CMS Collaboraion], JHEP 172 (17) 28 [9] F. Larios and C. P. Yan, Phys. Rev. D (1997) 7218 [1] E. Boos e al. [CompHEP Collaboraion], Ncl. Insrm. Meh. A 4 (4) 2 [11] A. Semenov, Comp. Phys. Commn. 1 (16) 167 7