Probing Anomalous WW γ and WWZ Couplings with Polarized Electron Beam at the LHeC and FCC-Ep Collider

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1 Intrnational Journal of Chmical, Molcular, Nuclar, Matrials and Mtallurgical Enginring Vol:9, No:, 25 Probing Anomalous WW γ and WW Couplings with Polarizd Elctron Bam at th LHC and FCC-Ep Collidr I. Turk Cakir, A. Snol, A. T. Tasci, O. Cakir Intrnational Scinc Indx, Physical and Mathmatical Scincs Vol:9, No:, 25 wast.org/publication/99 Abstract W study th anomalous WW and WW couplings by calculating total cross sctions of two procsss at th LHC with lctron bam nrgy E=4 GV and th proton bam nrgy Ep=7 TV, and at th FCC-p collidr with th polarizd lctron bam nrgy E=8 GV and th proton bam nrgy Ep=5 TV. At th LHC with lctron bam polarization, w obtain th rsults for th diffrnc of uppr and lowr bounds as (.975,.8) and (.285,.9) for th anomalous (, ) and (z, z) couplings, rspctivly. As for FCC-p collidr, ths bounds ar obtaind as (.,.65) and (.32,.2) at an intgratd luminosity of L int = fb -. Kywords Anomalous Couplings, Futur Circular Collidr, Larg Hadron lctron Collidr, W-boson and -boson. I. INTRODUCTION HE SU(2) U() gaug symmtry of th Standard Modl T(SM) rsults in th tripl gaug boson intractions. A prcis dtrmination of th trilinar gaug boson couplings is ncssary to tst th validity of th SM and th prsnc of nw physics up to a high nrgy scal. Sinc th tr-lvl couplings of th WWγ and WW vrtics ar fixd by th SM, any dviations from thir SM valus would indicat th nw physics byond th SM. Th photoproduction of th W and bosons through tripl gaug boson intractions in th lptonhadron collidrs HERA+LC and in th Larg Hadron lctron Collidr (LHC) has bn studid thortically in th paprs []-[3] and [4], rspctivly. An invstigation of th potntial of th LHC to prob anomalous WWγ coupling has bn prsntd in [5], [6]. Th prsnt bounds on th anomalous WWγ and WW couplings ar providd by th LEP [7], Tvatron [8], [9] and LHC [], [] xprimnts. Rcntly, th ATLAS [], [] and CMS [2], [3] Collaborations havstablishd updatd constraints on th anomalous WWγ and WW couplings from th γw() and W + W - production procsss. Th rsults from ATLAS and I. Turk Cakir is with th Istanbul Aydin Univrsity, Applications and Rsarch Cntr for Advancd Studis 34295, Sfakoy, Istanbul, Turky (phon: ; fax: /2226; -mail: A. Snol and A. T. Tasci ar with Kastamonu Univrsity, Dpartmnt of Physics, 37, Kuzyknt, Kastamonu, Turky (-mail: asnol@kastamonu.du.tr, atasci@kastamonu.du.tr). O. Cakir is with Istanbul Aydin Univrsity, Applications and Rsarch Cntr for Advancd Studis 34295, Sfakoy, Istanbul, Turky and Ankara Univrsity, Dpartmnt of Physics, 6, Tandogan, Ankara, Turky (mail: ocakir@scinc.ankara.du.tr). CMS xprimnts basd on two-paramtr analysis of th anomalous couplings ar givn in Tabl I. In this work, w invstigat thp ν qγx and p ν qx procsss with anomalous WWγ and WW couplings at th high nrgy lctron-proton collidr LHC and FCC-p (Futur Circular Collidr-lctron proton) collidr [4]. LHC is considrd to b ralisd by acclrating lctrons 4 GV and colliding thm with th 7 TV protons. W tak into account thnrgis of th FCC-p as 8 GV for lctron bam and 5 TV for proton bam. W also considr th possibility of thlctron bam polarization at LHC [5] and FCC-p which xtnds th snsitivity to anomalous tripl gaug boson couplings. TABLE I THE AVAILABLE 95% C.L. TWO-PARAMETER BOUNDS ON ANOMALOUS COUPLINGS (, ) AND ( Κ, ) FROM THE ATLAS AND CMS EXPERIMENTS ATLAS CMS ATLAS (upprlowrlowr) CMS (uppr- -.42, , , , z -.45, , z -.63, , II. ANOMALOUS COUPLINGS Th WWγ and WW intraction vrtics ar dscribd by an ffctiv Lagrangian with th coupling constants g WW and g WW and dimnsionlss paramtr pairs (,) and (z, z) () whr sin and cos. In gnral ths vrtics involv six C and P consrving couplings [6]. Howvr, thlctromagntic gaug invarianc rquirs that. Th anomalous couplings ar dfind as Δ whr V=γ, and Δ. Th W μν, μν and A μν ar th fild strngth tnsors for th W- boson, - boson and photon, rspctivly. Th on-loop corrctions to th WWγ and WW vrtics within th framwork of th SM hav bn studid in [7]- [9]. Ths corrctions to th Δκ V hav bn found to b of th ordr of -2 and -3, rspctivly. Th valus of th Intrnational Scholarly and Scintific Rsarch & Innovation 9() scholar.wast.org/999.2/99

2 Intrnational Journal of Chmical, Molcular, Nuclar, Matrials and Mtallurgical Enginring Vol:9, No:, 25 Intrnational Scinc Indx, Physical and Mathmatical Scincs Vol:9, No:, 25 wast.org/publication/99 couplings κ γ =κ = and λ γ =λ = corrspond to th cas of th SM. Sinc unitarity rstricts th WWγ and WW couplings to thir SM valus at vry high nrgis, th tripl gaug couplings ar modifid as Δκ (q 2 )=Δκ ()/(+q 2 /Λ 2 ) 2 V V and λ (q 2 )=λ ()/(+q 2 /Λ 2 ) 2 V V whr V=γ,. Th q 2 is th squar of momntum transfr into th procss and Λ is th nw physics nrgy scal. Th Δκ () V () ar th valus of th anomalous couplings at q 2 =. W assum th valus of th anomalous couplings rmain approximat constant in th intrstd nrgy scal (Λ 2 >q 2 ). W tak Δκ V as fr paramtrs in th considrd rang and find th bounds on ths couplings ffctivly. For th numrical calculations, w hav implmntd intractions trms in th CalcHEP [2]. Fig. Rprsntativ Fynman diagrams for subprocss q ν γq' Fig. 2 Rprsntativ Fynman diagrams for subprocss q ν q' III. PRODUCTION CROSS SECTIONS FOR LHEC According to thffctiv Lagrangian, th anomalous vrtics for tripl gaug intractions WWγ and WW ar prsntd in th Fynman graphs as shown in Figs. and 2. In ordr to calculat th cross sctions for th procss p ν qγx and p ν qx, w apply th transvrs momntum cut on photon and jt as 5 GV, 2 GV; missing transvrs momntum cut 2 GV, psudorapidity cuts, < 3.5; a con radius cut btwn photons and jts Δ, >.5. Using ths cuts and th parton distribution functions of CTEQ6L [2], th total cross sctions of th procss p ν qγx as a function of anomalous couplings Δκ γ and λ γ for E =4 GV with lctron bam P =±.8 and P = ar prsntd in Figs. 3 and 4. In Figs. 5 and 6, th total cross sctions of thp ν qx procss ar givn for th sam nrgy. It is clar from ths figurs that th polarization (P =.8) nhancs th cross sctions according to th unpolarizd cas P =-.8 P = P = Fig. 3 Th cross sction dpnding on anomalous coupling of th procss p ν qγx at E=4 GV for diffrnt lctron bam b P =-.8 P = P = Fig. 4 Th cross sction dpnding on anomalous coupling of th procss p ν qγx at E=4 GV for diffrnt lctron bam P =-.8 P = P = Fig. 5 Th cross sction dpnding on anomalous Δκ coupling of th procss p ν qx for E =4 GV Intrnational Scholarly and Scintific Rsarch & Innovation 9() scholar.wast.org/999.2/99

3 Intrnational Journal of Chmical, Molcular, Nuclar, Matrials and Mtallurgical Enginring Vol:9, No:, P =-.8 P = P = /fb /fb Intrnational Scinc Indx, Physical and Mathmatical Scincs Vol:9, No:, 25 wast.org/publication/ Fig. 6 Th cross sction dpnding on anomalous λ coupling of th procss p ν qx for E =4 GV IV. ANALYSIS FOR LHEC In ordr to stimat th snsitivity to th anomalous WWγ and WW couplings, w us th χ 2 function: Δ,, (2) whr Δ. with. / and N =σ. SM SM L. In our calculations, w considr that two of th couplings (Δκ,λ) ar assumd to dviat from thir SM valu. Wstimat th snsitivity to th anomalous couplings at 95 C.L. at th LHC for th intgratd luminositis of fb - and fb -. Th contour plots of anomalous couplings in Δκ γ - λ γ plan for th intgratd luminositis of fb - and fb - at lctron bam nrgis E =4 GV ar givn in Fig. 7. Th contour plots of anomalous couplings in Δκ -λ plan for th intgratd luminositis of fb - and fb - at lctron bam nrgis of E =4 GV ar shown in Fig /fb /fb Fig. 7 Two dimnsional 95% C.L contour plot anomalous couplings in th λ Δκ plan for th intgratd luminosity of fb - and γ γ fb - at lctron bam nrgy E =4 GV with polarization P = Fig. 8 Two-dimnsional 95% C.L contour plot of anomalous couplings in th - plan for th intgratd luminosity of fb - and fb - at lctron bam nrgy E =4 GV with polarization P=-.8 Th diffrnc of th uppr and lowr bounds on th (whr V=γ, ) can b writtn as Δ Δ Δ, λ λ (3) Th currnt limits on anomalous couplings and th diffrnc of th uppr and lowr bounds for lctron bam nrgis of 4 GV with intgratd luminositis L = int fb - and fb - at LHC with th unpolarizd (polarizd) lctron bam ar givn in Tabl II. W hav obtaind two-paramtr limits on δδκ γ and δλ γ which can b compard to th ATLAS and CMS rsults. Howvr, th limits on δλ is found to b much mor snsitiv than th currnt limits. TABLE II THE 95% C.L. CURRENT LIMITS ON THE ANOMALOUS COUPLINGS AND THE DIFFERENCE OF THE UPPER AND LOWER BOUNDS FOR ELECTRON BEAM ENERGY OF E E =4 GEV WITH L INT = FB - FOR POLARIED AND UNPOLARIED ELECTRON BEAM P , , , , , , P z z z z , , , , , ,..4 V. PRODUCTION CROSS SECTIONS FOR FCC-EP For calculat th cross sctions for th procss p ν qγx and p ν qx, w apply th transvrs momntum cut on photon and jt as 2 GV, 2 GV; missing transvrs momntum cut 2 GV, psudorapidity cuts, th rang of btwn -5 and ; Using ths cuts and th parton distribution functions of CTEQ6M [4], th total cross sctions of th procss p νγqx as a function of anomalous couplings Δκ γ and λ γ for E =8 GV with (P =±.8) and Intrnational Scholarly and Scintific Rsarch & Innovation 9() scholar.wast.org/999.2/99

4 Intrnational Journal of Chmical, Molcular, Nuclar, Matrials and Mtallurgical Enginring Vol:9, No:, 25 without (P =) lctron bam polarization ar prsntd in Figs. 9 and. It is clar from ths figurs that th polarization (P =.8) nhancs th cross sctions according to and without (P =) lctron bam polarization ar prsntd in Figs. and 2. th unpolarizd cas P =-.8 P = P = Intrnational Scinc Indx, Physical and Mathmatical Scincs Vol:9, No:, 25 wast.org/publication/ Fig. 9 Th cross sction dpnding on anomalous coupling Δκ of th γ procss p ν qγx at E =8 GV for diffrnt lctron bam Fig. Th cross sction dpnding on anomalous λ coupling of th γ procss p ν qγx for E =8 GV Fig. Th cross sction dpnding on anomalous Δκ coupling of th procss p ν qx for E =8 GV Th cross sctions dpnding on anomalous couplings Δκ and λ of th procss p ν qx for E =8 GV with P =±.8 Fig. 2 Th cross sction dpnding on anomalous λ coupling of th procss p ν qx for E =8 GV VI. ANALYSIS FOR FCC-EP Th contour plots of anomalous couplings in Δκ γ - λ γ plan for th intgratd luminositis of fb - and fb - at lctron bam nrgis E =8 GV ar givn in Fig. 3. For th procss p ν qx, w mak analysis of th signal and backgrounds whn dcays lptonically, l + l whr l=, μ. Th contour plots of anomalous couplings in Δκ -λ plan for th intgratd luminositis of fb - and fb - at lctron bam nrgis of E =8 GV ar prsntd in Fig. 4. Th diffrnc of th uppr and lowr bounds on th (whr V=γ, ) can b writtn as Δ Δ Δ, λ λ (4) Th currnt limits on anomalous couplings and th diffrnc of th uppr and lowr bounds for lctron bam nrgis of E =8 GV with intgratd luminositis fb - at FCC-p with th unpolarizd (polarizd) lctron bam ar givn in Tabl III. W hav obtaind two-paramtr limits on δδκ γ and δλ γ which can b compard to th ATLAS and CMS rsults. Howvr, th currnt limits on δλ is found to b much mor snsitiv at th FCC-p. TABLE III THE 95% C.L. CURRENT LIMITS ON THE ANOMALOUS COUPLINGS AND THE DIFFERENCE OF THE UPPER AND LOWER BOUNDS FOR ELECTRON BEAM ENERGY OF E E =8 GEV WITH L INT = FB - FOR POLARIED ELECTRON BEAM P : : P z z z z : :.2.23 Intrnational Scholarly and Scintific Rsarch & Innovation 9() scholar.wast.org/999.2/99

5 Intrnational Journal of Chmical, Molcular, Nuclar, Matrials and Mtallurgical Enginring Vol:9, No:, 25 ACKNOWLEDGMENT Th work of O.C. is partially supportd by Stat Planning Organisation (DPT) - Ministry of Dvlopmnt undr th grant No. DPT26K-247. A.S. would lik to thank Abant Izzt Baysal Univrsity Dpartmnt of Physics whr of part this study was carrid out for thir hospitality Intrnational Scinc Indx, Physical and Mathmatical Scincs Vol:9, No:, 25 wast.org/publication/99 Fig. 3 Two dimnsional 95% C.L contour plot anomalous couplings in th λ Δκ plan for th intgratd luminosity of fb - and γ γ fb - at lctron bam nrgy E =8 GV with polarization P =.8 Fig. 4 Two-dimnsional 95% C.L contour plot of anomalous couplings in th λ Δκ plan for th intgratd luminosity of fb - and fb - at lctron bam nrgy E =8 GV with polarization VII. CONCLUSION Th WWγ and WW anomalous intractions through th procsss p ν qγx and p ν qx can b studid indpndntly at th LHC and FCC-p. W obtain twoparamtr accssibl rangs of tripl gaug boson anomalous couplings at LHC and FCC-p with th polarizd lctron bam at thnrgis E =4 GV and E p =7 TV, and E =8 GV and E p =5 TV, rspctivly. Our limits compar with th rsults from two-paramtr analysis givn by ATLAS and CMS Collaborations []-[3]. W find that th snsitivitis to (V=γ, ) will b of th ordr of -, which is an ordr of magnitud largr than th SM loop lvl snsitivity of -2, howvr a masurmnt of ths couplings abov -2 would offr a possibl nw physics signal. W conclud that th anomalous couplings λ γ and λ can b wll constraind with th snsitivity of th ordr of -2 and -3 at th FCC-p with polarizd lctron bam. Th LHC and FCC-p could giv complmntary information about anomalous couplings compard to Tvatron and LHC. REFERENCES [] U. Baur, t al., Masuring th WWγ Vrtx in Singl W Production at p Collidrs, Nucl. Phys. B, vol.325, 989, pp [2] C.S. Kim, t al., Photoproduction of massiv gaug bosons in highnrgy lctron - proton collisions,. Phys. C, vol. 53, 992, pp [3] S. Atag, t al., Anomalous WW gamma vrtx in gamma p collision, Phys. Rv. D, vol. 63, 2, pp [4] C. Brnnr Mariotto, t al., Analysis of th photoproduction of massiv gaug bosons at th LHC, Phys. Rv. D, vol. 86, 22, pp [5] S. Sudhansu Biswal, t al., Anomalous Tripl Gaug Vrtics at th Larg Hadron-Elctron Collidr, arxiv: (hp-ph), 24, pp.. [6] I.T. Cakir, t al., Sarch for Anomalous WWγ and WW couplings with polarizd -bam at th LHC, Acta. Phys. Pol. B, vol. 45, 24, pp [7] S. Schal, t al., ALEPH and DELPHI and L3 and OPAL and LEP Elctrowak Collaborations, Elctrowak Masurmnts in Elctron- Positron Collisions at W-Boson-Pair Enrgis at LEP, Phys. Rpt., vol. 532, 23, pp [8] T. Aaltonn, t al., CDF Collaboration, Masurmnt of th W+W- Production Cross Sction and Sarch for Anomalous WWγ and WW Couplings in pp Collisions, Phys. Rv. Ltt., vol. 4, 2, pp. 28. [9] V.M. Abazov, t al., D Collaboration, Limits on anomalous trilinar gaug boson couplings from WW, W and Wγ production in pp collisions at s=.96 TV, Phys. Ltt. B, vol. 78, 22, pp [] G. Aad, t al., ATLAS Collaboration, Masurmnt of W+W production in pp collisions at s=7tv with th ATLAS dtctor and limits on anomalous WW and WWγ couplings, Phys. Rv. D, vol. 87, pp. 2, 23. Erratum-ibid. D, vol. 88, 23, pp [] G. Aad, t al., ATLAS Collaboration, Masurmnts of Wγ and γ production in pp collisions at s=7tv with th ATLAS dtctor at th LHC, Phys. Rv. D, vol. 87, 23, pp. 23. [2] S. Chatrchyan, t al., CMS Collaboration, Masurmnt of th W+W Cross sction in pp Collisions at s=7 TV and Limits on Anomalous WWγ and WW couplings, Eur. Phys. J. C, vol. 73, 23, pp. 26. [3] S. Chatrchyan, t al., CMS Collaboration, Masurmnt of th W gamma and gamma inclusiv cross sctions in pp collisions at s = 7 TV and limits on anomalous tripl gaug boson couplings, Phys. Rv. D, vol. 89, 24, pp [4] FCC Collaboration, Futur Circular Collidr Study Kickoff Mting, 24. [5] J. L. Abllira Frnandz, t al., LHC Study Group Collaboration, A Larg Hadron Elctron Collidr at CERN: Rport on th Physics and Dsign Concpts for Machin and Dtctor, J. Phys. G, vol. 39, 22, pp. 75. [6] K. Hagiwara, t al., Probing th Wak Boson Sctor in + --> W+ W, Nucl. Phys. B, vol. 282, 987, pp [7] E. N. Argyrs, t al. On loop corrctions to thr vctor boson vrtics in th Standard Modl, Nucl. Phys. B, vol. 39, 993, pp. 23. [8] P. Kalyniak, t al. Extracting W boson couplings from th+ - production of four lptons, Phys. Rv. D, vol. 48, 993, pp [9] G. Coutur, t al. Anomalous Magntic and Quadrupol Momnts of th W Boson in th Two Higgs Doublt Modl, Phys. Rv. D, vol. 36, 987, pp [2] A. Blyav, t al., CalcHEP 3.4 for collidr physics within and byond th Standard Modl, Comput. Phys. Commun., vol. 84, 23, pp [2] J. Pumplin, t al., Nw gnration of parton distributions with uncrtaintis from global QCD analysis, JHEP, vol. 27, 22, pp. 2. Intrnational Scholarly and Scintific Rsarch & Innovation 9() scholar.wast.org/999.2/99