No 1 l_Mar 2019|S6 11- Thang 3 nam 20l9|p 57-62
T A P CHI K H O A HOC DAI HOC T A N T R A O ISSN 2 3 5 4 - 1431
http //tckh daihoctantrao edu vn/
Qua trinh ra h-^Zy trong mo hinh inter Zee
Trinh Th] Hdng" , Tnrong Tin Thanh", Le Tho Hue , Nguyen Thuy Nga'^
nghi J'lelNam 'Difi hoc An Giang
'li|(i Vgtly. Vi?n Khoa hgc vd Cdng 'TntmgDai hgc Tdn Trao 'Enia\t: tthong(Siagii.edii.vn Thong tin bai viet
}lgayiihgnbai:
26/02/2019 }igiiv duy?l dang:
m/2019 Tir khoa:
MHiggs: Bo dinh bdc 1 vong: Inter Zee
Tom tat
Bang each them vao cac phd hat mdi cua cac lepton, md hinh inter Zee duac gidi thieu gan day da giai thich tot cac dQ lieu thuc nghiem ve khoi lucmg neuQino va vat chat tdi Chung ldi se chi ra rdng md hinh nay hQa hen du doan cac lin hieu mdi Clia Higgs boson, ra /j —> Z/ ma da bi chan Qong cac md hinh trudc Ddng gdp bac mdt vdng sg dupc tinh trong chuan unitary Dua tren so heu quan sat thuc nghiem, chung tdi Um ty le ra nhanh ciia qua trinh ra h—> Z/ Gia tn be rdng ra nlianh thu duoc ed thl ndm Qong khoang gia In mong doi, cac vung khdng gian tham so phu ho]i thda man dQ heu ihuc nghiem cung se duoc chi ra
1. GiiVi thicu
Hal vd hudng Higgs dupc CPI la manli ghep cudi Cling va ddng vai tro rat quan trong trong md hinh chuan (Standard Mndd-SM) Nd duoc dua ra nham sinh khoi luong cho cac hat co ban thdng qua co che Htggs Nam 2012 thuc nghiem da khdng dinh su tdn tai Clia hat Higgs nay vdi kliPi Iirong cd 125 GeV [! ] Day lai la met Ihanh cdng nQa cua ly ihuyet SM Tuy nluen.
mo hinli nay khdng Ihl giai thich duoc mdt so kit qua Ihyc nghiem dupc cdng bo gan day [ 1 . 4 ] Vi vay SM can diroc mo rdng thanli cac md hinh mdi (Beyond the SM-BSM) dl cd tlil giai thich duoc cac van dl tlnrc nghiem noi Qen Trong sd dd, mdt top cac md hinh don gian dupc xay dung nhdm giai thich hop ly hai van de Ion, sir smh khoi lupng Majprana - dao ddng ciia neutnno thdng qua co che bo dinh bac mdt vdng va vat chat toi moi dupc gidi thilu gan day do la md hinh inter Zee [3, 8, 9] Md hinh duoc xay dung dua tren md hinh Zee, trong dd them vao 2 fermipn la dem tuyin ciia nhom SU(2)L va ludng tuyin cua nhdm S U ( 2 ) L va 2 vd Iiirong Mo hinh nay da dupc khao sat trong mdt sd cong bo gan day [3, 8, 9], tuy nhien phdn ra cua Higgs van chua duoc khao sat Dac biel kenh ra h-^ Zy
dang duoc thuc nghiem tich cue lim kiem gan day va da duoc SM du doan cung bac gia Ui vdi kenh ra
^ .-^ yy [5o d(=)_ CO SU ddng gdp cua cac hat mdi trong md hinh va ty le ra nhanh cua qua Qinh ra ndi tren se bi Ihay doi so vdi SM Trong nghien cuu nay chiing tdi se tim hilu cu thl ddng gdp ciia cac hat mdi dd la higgs va cac hat leplon mdi duoc Ihem vao md hinh vao cudng dd ra nhanh jizy
2. Mo hinh inter Zee
Md hinh inter Zee (IZM) la md hinh md rdng md hinh Zee [4. 5] bdng each them vao cac fermion. la don tuyin, S11{2\-E va ludng luyen cua
SIH2) - T = {N,Ef , va 2 vd hudng la don tuyen Clia ,S7/(2)^-.S' va ludng luyln Clia SV(2),-H, [3,
Y i 9] Toan tu dien tich cua md hinh (^ ^ 7', -f— Chi liet cac hat mdi duoc cho Irong bang 1 [9]
£
'-V
Spin V,
•A
.V(;(3),,,.ST/(2),,(/(!),.Z,
(1,1,-2.-) (1,2,-1.-)
T.THong eial No 1 l_Mar 201y|p 57-62
H,
s-
0 0
(1,2,1.-) (1,1,-2,-)
2V2 UV2
,i..,=(*.^) ™' 275 2V2
T"! (6)
(7) Bang 1: Cdc hai mdi nong mo hinh va cac dnc linh [rong do (rang thai neng khoi lugng E^ va C ; xac ijcH <?di CHfJ chiing Iheo nhom doi xi'nig
SUQ\. « i ' f / ( 2 ) i ® f / ( l ) , » Z ,
Lagrangian bfit bien cua mo hinli duoc viet theo [3]
Azw = ^ w + ^ F "*"^'*"M "1" A ' (1) trong do Cj,., JC^.C^.C^ bao gom
'C^:DI^j''D^'¥,+i£^f"D^£^+iN^f''D„N^+iE„y''D^E,. nip, =-{m^+m^+,j{m.^-m^)' +2y v).
C,.(D,H,)\D,H,)^^i4V'l«,y-j(»l»,f*<-0.'<f"'.'^1 Sau khi phi v 8 d6i Nirng dien yiu cac higgs CP chta -/tIS'S)- i(,s'sy fj«^ ujc l„ggs CP ic A° va 2 trang thai vat ly ctia
higgs mang dien h , j [3], +A^(SISXH;H,:)+^(S^SXHIH,)+ / ; £ ^ [ H ; H ^ S + H C ],
- A - 1,t,H,£* « ? » , = , + y1>ff,e+ /;'D,*S*+H c.
dmh bdi
C; ;)
2a =
•C:
^.. =
-s„
c
yv^/2(m,..-
I
m,)'
(2) < . , . = / ' " • l - - ( ^ + ' l . ± ' l s ) v = , ^jj 'Ol f|2 = 1 Hal luong tuyen higgs H^,H,
r
W . = 1 Jl (H,+ iA.)
^ ^ 1 =
V5 (h + v)
K , =T{mJ,..+ m ; . + [ ( % ; - 1 1 1 ' , . ) ' * 2 / ' ' ^ ' l " " l .
trong do m'^ = fJ^ + -Z,v^ va w^. = ^ J + - . ^ v ^
^ Goc tron cua cac tmong vo huong ip duoc xac dinh vtVi h ]a Higgs boson duoc dong nhat voi higgs
trong SM va V = 2 4 6 G e K , Cac gauge bosons ciia be" s i n 2(9 = s , ^ = (%/2/iv) / ( m j . - m ^ . ), Lien he mo hinh giong nim trong mo hinh Zee [4, 5) va SM g,i,j, ^ j ^ i^^„^ i|,j, j j „ ,,^| ^ j ; , , „ „ g ihi, vat lv
""IS] " C;]<::S;-
3. Qua (rinh ri h~>Zy trong mo hinh IZM ^^ n^h dinh /?// la Ihay / / , , / / , vao trong (5), Trong phan nay, chiing tdi quan tam den dinh tuong chi cd sd hang sau cho ddng gdp vao dinh dang xet tac hen quan din cac higgs mang dien va lepton mdi
(9)
duac them vao Cac dinh kliac duoc lay Que tiep nhu - - . , - v 4 ' / / , e r3_i'T .
Qong SM Lagrangian Yukawa bicu dien luong tac mdi ~-={h+v) Clia fermion va higgs cd dang [9],
£ 3 vE—7=e-\-H.c,
• V2
+ f^LyS' +H.c}+m^.f'^? + m^ee. \ (5)
I day. L, va e^, la ludng tuyin lepton va dan K c ^ - s ; ) s , „ h E , £ , . (10) tuyin nlwm SU(2),V = {N,Ef. y,ri„p, va / , '^"' '1°' * " ' ' "™I5 ' " gida higgs trang hoa va la hSng s6 tuong tac Yukawa mcii va i la chi sii thi he '''•^ ' ' " ""™'' ^'"^ ^ '^"""'^ '*•= B'*" Z boson va cac
lepton xuat phat tit phuong h-inh (2) Khai tri4n cac s6 hang tir i den 4 trong Lagrangian £^,
S&i;i:i'58
T.THong tial/lia | l_Mar2019|p 57-62
= e,fi,T,ii,d,c.s.b,lE
^^ ''iiw'^iif >'\^',. lan luol la cac ddng | boson chuan W, fermion va cac higgs mang dien, / , / ) / . , ^s,(e,^ig Bjr% ^J-^sy"P,cZ^ trong dd / ^ ^ ^ g.dng nhu SM. Bilu thQc cho ddng gdp
(11) chung Clia cac fennion cd dang nliu sau [6]
Dinh Urang tac duoc vilt d bang 2 Do H, khdng ,. '^^A',,- , chira higgs mang dien nen khi tinli dinh hrong tac giQa , / ^. „ ,
, , . , . . . . . . , . , ^^(^"™-'^/-™+-0(f>^'2)+2(K;.™ + c c ) C „ l , r , , =0.
Z boson va higgs mang dien ta chi can xet Lagrangian
(14) 5^" va
£=(D,HjUD^H,)-H(D^5)^(D^5-), (12) A^,™ ='«,(r„^;, .n„,.;,).it„„, =,«^{r,,j,;,+n,„«;,)
bang each Ihay cac dao ham hiep bien va H-,\zc\ C^) (ll),kltquacho trong bang 2 Tuong tu nhu vay dinh ^'''ong md hinh IZM. X,^ = 7 ^ ^ va nhan gia In
tirang lac giQa SM-hke higgs vdi cae higgs mang dien ,, , : .; t ' - j^^ i/ , / . . , , '^"'^^ '^''" ^e" ^lLja< = K^.RL = "h^'A^L+'^R )- xuat phat lu the higgs £ , trong (2) va khai tnen bang
Ihay cac he so dinli tuong ung Irong bang 2, kll qua each thay cac gia hi cua / / , , Hj IQ (3) Cac kit qua vill lai nhu sau
, , -i^ftAV-"; . r,, .,.._,, , , , 32;r=i.r,, " ' """[[^'i • ' « ; " ' ^ "
cgO, N,ini r, , , ,
— ^ - ^ , ^ c o s a s i i i Q ' (f,: - v : . . i s i i r a cho Irong b
DMl
KK
m
"•K
'•KA,
-"VV
' • » , • * ;
H(,i-1.1, iJ'^K,
'l[v{Af',*il',}-T2>^^.]
-'[v/^A--^l-.^^,-4)^^
-,[.[V.Mci).V3«.^.]
"Ifii/^^iv 1
•^i'U^-li.•.>^^ J
•^^^^1^1^..-..}
DIph 3-VA-:,
n..
^..
1-E.E,
ZS,E,
Z-E,E,
Z-E,E,
Hi >o dliUi
-^(,.„-..„)
-=....
=.,.,.
-t!f>_:v,,(.:-i)
^[i.i-ii<:/i-i|i.^.wl i;[(i-.ii.;«-.i(i.-:if.]
-|;..[('i-''-l'.-".]
fio'ig 2 BoHg cdc /je so dinh lirolig Idc dong gop vao bm do rd h~-> Zya gdn dung bdc I vong Imng chuan utiilary, Imng do e = gs^
Be rpng ra neng phan h - > Z/ du doan tir IZM
% c Viet nhir sau
-v;(i+^os^.)>[ic(<-„+''..+f.) + 4r.]. jl,j
» , - • < , , I , , - , , 1 ™ . - ; . ' ( < „ .
< V * ' M + " . ] (18)
Tuong tu nhu vay eA..
•x4[Q+C,,-l-C„],cac
r'"ih^zy)^j^U-!h.\\F-r\'
(13)'"'•'• {\6,r')
thira sd 4 j = 2 ( j ; ^ j . , ^ _ / l j ^ . , J duoc lict ke trong b i n g 3 v a m ^ = m „ . / c „ - = ^ ^ / ( Z c ^ . ) .
Bang 3 Thira so A,, f ^ .. Trim
' 21 - r ,
•E^™ + Z^t?,./
T.T.Hong eial No I l_Mar 2ul 9|p 57-62
2"'/lV:- --V"'!'-*'
2/H^I« + ;i.,,/(r-
Be rong ra loan phan eo tlie xem 1 ^ — • /, Theo dd dai luong thuc nghiem chung tdi quan lam la cudng dd lin hieu /i^v [2] Qong IZM cd dang sau
-"^,
Br"" [h -> Zy) __ r^^^ (/; ^ Zy) _ \F^
Br"" [h -> Zy) r ^ ' {h -^ Zy) \ F^f \ De chpn duoc viing tham sd thda man thuc nghiem hien nay [2] cho SM-hke Higgs boson h dang xet, chung tdi phai xet den gidi han thuc nghiem hien nay cho rS h^> yy Thuc nghiem cho thdy cac he sd dinh tuong tac hW^W va hff phai nguoc ddu nhau va cd dp ldn rat gan vdi ket qua du doan lu SM Chpn tham so trdn cac Higgs mang dien ip va khoi luong cac Higgs mang dien la cac tham so ddc lap dung de khao sat so. Iham so fj trong he sd tu luong lac hh^h duoc
xac dmh theo he Ihuc / / =
^/2w He sd dinh hh^h chi phu thudc them hai iham so /i, ^, chung toi chon A^ = —A^ sao cho cac hang so luong tac cho ddng gdp vao ra h —> Zy la nhd nhdt va dam bao gidi han tliuc nghiem Vdi cac dilu kien neu tren, cae tham so ddc lap chua biet Qong phan kliao sal nay la' klidi lupng Higgs mang dien m]^^. khdi luong lepton mdi.
gdc Iron <p . he so tu luong tac Xi, Dua theo cac kit qua kiiao sal trong lai lieu [3. 5], cac khoang gidi han Iham sd duoc chon la
IO0G<;I-'<Nj^ <l SxlO'GeK. 0 5<.v^<l, \mGeV <m^ <500Gel' va 0< /[^<AK Cac diam so da bill lu thuc nghiem duac idy Iheo [2] Cac hdng sd khac duoc tinh nhu sau e = -J^ce^^^^g = Itn,^. Iv
Do S^—.S^= C, = 0 ihira sd chua /I, trong ddng gdp hcso A^ ^ 22 \'a lliua sd chua A;;i^. = iu'_ - ;ij'. = 0
trong 4 , JJ diu bdng 0 Chung ldi \ e t Qudng hup dac biel vdi 5 = I / V 2 trong tdt ea cac khao sat sau day
Hinh f: Dd thi hieu dien //^y ^"^ ^f^2-''^^° ^^"' Clia khat lirang htggs mang diin
Do Ihl ben hen cua hinh I bieu dien / / ^ l^'^^" '''^"^
cua khoi luong Higgs mang diln 777^ vdi cac gia Qi khac nhau cua A^ , Am^, = 0 va do thi dudi bilu diln
^Mzr hroTig ling TQ bieu thuc giai hch va giai so cho thay ddng gdp cua higgs mang dien cung dau vdi cac hat trong SM Do dd, dd dd ihi cho thdy cudng dd tin hieu deu rdt I m Irong khoang khdi luong nhd cua cac Higgs mang dien va dd ldn ciia /t, nhan gia Qi ldn, Trong khi do thuc nghiem hien nay chi la duoc/./2r ^ ^ 6 '''C'l do tin cay 95% (95%CL) [7] Vi vay trong thai gian ldi. niu thuc nghiem xac dmh duoc gia in cu thl / ^ J > I md hinh IZM cd ihl giai thich duoc gia tn nay / 4 f ^ = ^ , J , thong qua ddng gdp clia cac hat Higgs boson mang dien
T.T.Hong elal/Vio !l_Mai 2U|y|pS7.A2
-
?
s
V ! -
: r ? : ^ ^ ^ = ^
" s - T O " " • tfieVl
_;;^';-|
Hinh 2- Dd thi bieu dien //^v '"^ '^Azv'^'^° ^''^'"
ciifl Widi tirang lepton mdi mang dien
Do thl ben tren ciia hinh 2 bieu dien p.-^ ^^^° ^^m Clia khoi tucmg lepton mang dien mdi m^ vdi cae gia In khac nhau ciia A , , m^ = ' " £ + 4 0 0 G t ; F v a do Ih) dirdi bieu diln A//^^ hrong Qng Ddng gdp cua 2 lepton mang dien mdi nguoc nhau ve dau, long cua chiing Cling ddu hay nguac dau vdi cac ddng gdp eua SM phu thupc vao hieu klipi lupng cua 2 hat mdi nay Cu the, tu do Ihi cho thdy cudng do tin hieu thay doi nho khi gia hi ciia khoi luong m^ thay doi va cudng dg tin hieu ciing phu thudc vao Aj Cac ddng gdp eua 2 lepton mdi vao kenh ra tren la nhd, nen md hinh IZM du doan kenh ra nay gan nhu tning vdi SM khi xet ddng gop Clia cac hat E^
4. Ket luan
Bang viec hnh cac ddng gdp cua higgs mang dien va lepton mdi. chiing tdi da tinh duoc be rpng ra neng phan va ti le rS nhanh cua qua Qinh ra h—>Zy trong 110 hinh IZM Du doan v l U lc ra nhanh trong md hinh 'ZM la tin hieu de phan biet SM va mo hinh IZM klu Uiirc nghiem do dupc kenh ra nay Cudng dd lin hieu
nhan gia tri ldn Qong vung thda mSn dong Uidi cae dilu kien sau Khoi luong cac Higg mang dien nlid, hdng so hr tuong tac A^ phai ldn. s^ nhan gia hi phu hop hong khoang tu [0 5, 1] Gia tn cac iham sd eua md hinh cd thl lam lang cudng hoac khu cac ddng gdp iQ SM lam cho gia tr) cudng do lin hieu cd thl nhd hon I hoac ldn hon I rat nhieu Thuc nghiem trong thai gian tdi tiep tuc uln gan ldi gia Iri / / ^ > 1 Vi vay gia Iq / ^ > 0 rdt d l dupc xac nhan Qong tuong lai gan Cac ddng gdp cua cac leplon mdi dupc them vao md hinh vao kenh ra /i —> Zy\k nhd khdng dang k l va md hinh du doan kenh ra nay gan nhu tning vdi du doan cua SM
TAI LIfU THAM KHAO
I. ATLAS collaboration (2012), Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at Ihe LHC, Phys Lett B 716,1-29
2 ATLAS and CMS Coilaboralions (2016).
Measurements of the Higgs boson production and decay rales and constraints on Us couplings from a combined ATLAS and CMS analysis of Ihe LHC pp collision data al \s = 7 and8 TeV, .mV.P 1608,045 3. A Gavma, R Longas and 6 Zapala (2018), Charged leplon flavor violation and electric dipole moments in llie men Zee model, J\\¥JP 1810, 188 4 A Zee {\9W), A iheoiy of Leplon Number Violation.
Neutrino Majorana .Mass, and Oscillation, Phys Lett B 93,389
5 J Herrero-Gaicia. T Ohlsson. S Riadand.1 Wiren (2017). Full parameter scan of the Zee model:
exploring Higgs lepton flavor violation. .IHEP 1704, 130
6 L T Hue. A B Arbuzov. T T Hong, T Phong Nguyen, D T Si. H N hon%{2i)\?'). General one-loop formulas fo, decay h - Zy. EUROPEAN PHYSICAL
.lOURNAL C 78, 885
7 M Aaboud eial (2017), .Se«rc/?<?,5>r//)e Zy decay mode of Ihe Higgs boson and for new high-mass resonances m pp collisions al VA^ = 1 3 Tev with the ATL4Sdetector. Jl-KV mn, U2
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8 S Kanemura, T. Shmdou. and H Sugiyama (2015), R-Panty Conserving Supersymmelnc Extension of the Zee Model, Phys Rev D92, 11500 i
9 R Longas, D Portiho, D ResQepo, and 0 Zapata (2016), The Inert Zee Model, .IHEP 03, 162
10 Particle Data Group (2016), Review of Particle Physics, Chmsese Physics C 40,100001
Decay of SM-Iike Higgs boson h ->Zy inn inter Zee model
Tnnh Thl Hong. Truong Tm Thanh, Le Tho Hue, Nguyen Thuy Nga
Recieved- 26/02/2019 Accepled- 10/3/2019
Keywords:
Higgs decay.
One-loop conection. Inter Zee.
Abstract
By adding new particle spectra of the leptons, the recently inQoduced inter Zee model well explained the cuiTcnt experimental data of neutnno mass and dark matter We will show that Qiis model promises lo predict the new Higgs boson signals that have been blocked in previous models One-loop contnbution to these decay amplitudes is introduced in the unitary gauge Based on the current expenmental data, we find the branching ratio of the decay ' . The obtained branch width value can be within the expected range, the parameter space that matches the expenmental data will
