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Đ A I H O C Q U Ố C CilA IIÀ N Ộ I —- O0 — - f ) ê l : ỨNG DỤNG C Á C NHÓM ĐỐI XỨNG MỎ RỘNG TRONG NGHIÊN cứu VẬT LÝ HẠT c M a so : ọ »0.08 C h ù n h i ệ m (10 tai : I S IIÌI 11uy Bmiiịí ' THUNG*;MTHL'ir '•*# • ữĩ I 0 Ĩ L _ _ I — -1 BẢN ĐẠI HỌC QUỐC' GIA HÀ NỘI A - HÁO CÁO TÓM TẢT TÌNII 1IÌNII VÀ KKI QUA I IIỊÍC HIKN t)KTÀI NĂM 2000 T ê n (tê t i : ÚNG DỤNG CÁC NHĨM ĐƠÌ XÚNG MỞ RỘNG T R O N G N M I I K N Cl'il I VẬT I V H Ạ T c HẤN Mã số : QT OO.OK C h ủ n h iệ m d ề t i : TS I I luy Hằnti C c c n b ộ th a m gia: IJ( Ì S IS I l o n u N u ụ c 1.01112 TS N u II y e n A n h K ỳ , TS Đ ặ n Sỉ V ã n Soa ThS c'ao Tlìị Vi Ha, ThS t)ặiiL! Oìnli ’lơi, IS Nuuyéii Mạn ('h unu M ục tit'll Iiội thing Iighien cứu : N uhiên cứu hệ I|ii;i vậl lý cùa m õ hình ly ihul mớ rộnu mâu LÌuiiín đ ợ c x â y c lựnu 11ơn c s ứ cát' n h ó m d ố i x ú n u Otiii kêl luận càn ihiêi cho ill ục nuhiệm nil Am pliál hạl mơi il ưực lion iliián III lý llniycl T ì n h liình th ự c liiẹn (lê tai : Xiìy ilựnu lý ihiiyêì uronu lác nội limit: cú a Vill ly ciíc hạl C1Í bá n M u diiiiỊÍn c ú a c;k' UKíim l ác d i ệ n lu y ê u tlòi tlúnli ilau 1111)1 I m o v IHMKII II'OIIU v ậl lý v d ã rát ( h n h CỎI1U VC p h iu r n u ili ệ n lliụv n u h i c m T u \ n h i c n 111) vãn k l i ò n t i Ilá lời (.lươc i n õ l s ỏ v ã n l i e l ý i l u i ỵ ẽ i q u a i l t IOI1 u VÌI i l o i l l ) c n i l ụ v m r òni i C c m ẩ u c l n i a n m rộ liu uà n d ã y d ợ c x â y cl ụnu l i ê n c s s i ê u d o i XIÍI1U h ó a m ill! c l u i â i i d a n li i l u o v c c n h v ặ l lý I |i i a n l ã m n u h i è n c ứ u s ì c o n h i ê u LI LI điếm đáim cluí ý Đi ilieo hướne million cứu d u i n u lõi dã dạl clươc kóI C| sail dày: - Tính lốn liốl diện tán xạ vi phàn trình đưa (.lánh uiá số c ũ n u n h điều kiện 111 ực n u h i ộ m c ầ n ihiốl g i ú p c h o v iệ c l ì m k i ê m c c hai a x i o n i r on ti m ầ u c h u â n c c hạ! Sc| Liaik II'OIIU m ầ u cliLiân si ê u d ố i \ i h m lõi i h i c u ( M S S M ) - Nuhiõn cứu vi pliam iloi \ ứ n u ( l J ironu máu cluiân siêu dõi \IÍI !Ì loi ihiổii dua cách xác định troim ihiim sô cúa mãn nà) Câu trúc nên mộl m ầu 331 siêu đôi xứng với neutrino xoắn pliái nghiổn cứu sector Higgs Irong mẫu 331 tối thiếu G ần dây biốn d ạng lượng lử t ủ a đại số Lie dã xâm nháp vào nhiều lĩnh vực vật lý dặc biệt lý ilmì trường lượng lử hạl hán Trong đề tài c h ú n g la đưa liên hệ biên dạng lổng q u t'v i đ ộ chuyên dời mẫu chu ấn có dối xứng phái trái, xây dựng nơn dại số siêu đơi xứnu biín d ạng N = Iham sô' trở lliành toán tử Đ n h g iá c h u n g : - Đồ lài ihực dúniỊ liên độ dạt chái lượng cao Các kêl I|iiá cú a dồ lài dược cônu hô' a hài báo dăng lạp chí IroniỊ, nụoai nước liên T u yển lặp háo cáo Hội ntiliị vậl lý lý lliuyốl loàn quốc lần lliứ XXVI - Đồ lài dã góp phần lạo học viên cao học, nghiên cứu sinh T ìn h h ìn h s d ụ n g k in h p l ứ c ủ a d ê tài: - Được (.luyộl cấp : 7.000.000 - Đ ã c h o khoán sau : + Chi phí tlniê mướn : 4.400.000 (.lồng + Chi phí hoại đón ụ chun mịn: 1.1 ()().()()() í l ị n u + Cơng lác phí hội Ill’ll ị : 91 ().()()() d ỏ n g + Cung ứng vãn phòng: 300.000 dỏng + Chi khác: 2X0.000 Xác Iiliận cúa Iỉam Chù nhiệm Klioii Vậl lý Clui Irì (le lài K 'lM TS H H u y B n g Xác nhận cùa Trường Đại học Khoa học Tụ nhiên V IE T N A M N A T IO N A L U N IV E R SIT Y —- O0 — - Project: THE APPLICATIO NS OF GENERALIZED SYMMETRY GROUPS IN STUDYING ELEMENTARY PARTICLE PHYSICS Code- Q 00.08 D irec to r o f project: Dr I la I III V Bang H a noi 2001 V IE T N A M N A T IO N A L U N IV E R SIT Y REPORT ON THE SITUATION AND THK KKSUIXS OK I N K I’ROJKCT / Title o f the p r o je c t: Ti ll' APPLICATIONS OF GF.NF.RAI.IZI-D SYMMETRY GROUPS IN STUDYING ELEMENTARY PARTICLE PHYSICS Code : QT 00.08 Director o f p r o j e c t : Dr Ha Huy Banu Participants: - Ass h o i Ur I Ioann Niioc Limn Dr Nmiyen Anil Ky, Dr Danu Van S(ta Vki.' ('an Till Vi Ha Msc Danu Dinli 'I’lli, Dr N uuycn.M au Clumu A i m a n d co nt en t o f researchers: Si Lilly inu p h ysic al c o n s c q u c n c e s (>r b e y o n d standard m o d e! based on extended symmetric 1>roups Dcrivinu, conclusions for cxpcricncc.s It) rind new particles Ihill prcilicled Imm theories S c h e m e f o r the project: C o nsuu clin u llic theory 1)1' interactions is main aim (>!' panicle physics, [lie slandaixl model 1)1 llic clcclrowcak inlcralions has been considered ail extremely succcsslul theory from the phenomenological point C)!' view I Imvcvcr, this model contains a larue num her o f unanswered questions and ils u c n c ia l i/ a li o n is n cccssa i) [lie ILXCIII p rop osed m odels based oil Mipersymincll'ic standard model have ihc nicc lea lures and have been obtained mail) allcnlion.N Ill ÍÌIÌ.S d irectio n , n r Ill/ve o b ia in e cl lilt' m ain vcsiths Ơ.V fo llo w s: - ( o m p u l i i m Ihe d ifferen tia l C IONS - s e c t io n s OÍ p r o c e s s e s and u i v i n e the numerical evaluations and some cslimcs lor expcrimenlal conditions lor huiilinu ax ion and squarks in Ihc Minimal Supersym m clric Standard Model I M S S M ) - - Sludyinu llic CP-violaiion ill MSSM and simucsiinu llic method ol cic 1ill ill tị one 1)1 parameters 1)1' ill is model Conslniclinu a version ol 331 supcrsymmclric model willi null-handed nculrinos Investigating in (Jclail the iliu u s sccloi ol'lhc minimal 3-3-1 model Recently, quanlum clclbrmalions of Lie aluchra has been shown to lie deeply moled ill many problems 1) 1' physical inlcicsl, especially ill quanlum field theory and particle physics In this project wc have given the connection between llic ucncrali/.ccl dcloi'inaliun and ilie transition Irom Ihe left-riglil model lo llic standard model, have consliuclcd a ủ - ilelormalion ol llic N = SUSY algebra C on c l us io n: llic schedule 1)1 pmjecl is noud results have been published by s papers in ihc Journals anti ihc reports ol XXVI national conlcrenec ol llieorelical physics of Vietnam Ihc project has played a pari ill the iraininu course o f three graduated sI lkIciHs and three Ph D .students The us in g o f the f u n d : I'olal ÍLind is allowed and obtained: 7.000.000 VND or : + papers : 4.400.000 VND + prinlinu: 2.320.000 V ND + Ice: 280.000 VND THE DIRECTOR OF THE PROJECT V ỊU V '''— Dr H a H u y B a n g 15 CÁC CỔNG TRÌNH KIIOA HỌC CÚA TẢI QT.00.08 P h o lo p r o d u c lio n ol' a x io n s ill a r e s o n a n t e lc c l m in a g n c lic cavity 1C/00/147 (T p c h í c ủ a T r u n g lâm q u ố c lố VỘI lý, Italy) Q u a n t u m g r o u p s and b e y o n d ihc S tan dard M o d e l I I H Bang, c T Vi Ba ironu, T u y ê n lập Báo c o I lội n u h ị vậi lý lý tliuyèt loàn q u ố c 21 / / 0 Đ Lạt V A g e n e r a l i/.iĩd Ọ - d c l o n n c đ H e i s e n b e r g - VVcyl a l g e b r a vvilh c o m p l e x d c lo n r u itio n p a m e lc rs H H Bang D p K hoi, N A Ky Irong T u y ế n lập Lỉiío c o I lội nghị vịil lý lý lliuyốt toàn q u ố c , 21 - /8 /2 0 , Đ Lại T h e l l i g e s se c to r ill ihc m in im a l 3-3-1 M od el with the m o s t g e n e l leplon - n u m b e r c o n s e r v in g potential N T A n h, N A Ky and II.N 1.oim Ini J Mod Phys A 16 No ( 0 ) 541 > Pho to n - a x io n c o n v e rs io n c m s s - s e c lio n s ill an c lcclrom cignelic Held, 1) V Soil II II Bang Ini .1 M od Phys Vol 16 N„ X (2001 ) 1491 S q u a ik s ilccays into w a n d z b o s o n s in ihc M SSM w ilh c o m p le x p a r a m e t e r s D T L T l i u y N c C u o n g a n d H 11 B a n g i r o i i g T u y c n l ậ p IHH>c o I lội liuhi \ 'til Iv lý llniyủi toàn q u ố c lần lliứ 26 Hạ L o n g 0 W a v e f u n c tio n c o r r e c tio n s o f S q u a rk in the M SSM w ith c o m p le x p a m e te rs D T L T h u y , L T T u o n g a n d H H Bang, đ ã đư ợ c n hận đ ã n u tạp c h í K ho a h o c Đ H S P H N ội K T h e ù - đ d o n n c d N = s u p e r s y m m e l r ic a lg e b H H Bang and C’.T V ilia d ợ c n h ậ n đ ã n u C o m 111 in Pliys Available at: h ttp ://w v v ic t r ie s t e i t/ ~ p u b _ off I C /2 0 / 1-J7 United Nations Educational Scientific and C ultural O rganization and International Atomic Energy Agency TH E ABDUS SALAM INTERNATIONAL CENTRE FOR TH EO R ETIC A L PHYSICS P H O T O P R O D U C T I O N O F A X IO N S IN A R E S O N A N T E L E C T R O M A G N E T IC C A V IT Y Dang Van Soa, Hoang Ngoc Long The Abdus Salam International Centre, for Theoretical Physics, Trieste, Italy, Ha Huy Bang Department of Physics, Hanoi National University, Hanoi, Vietnam and Nguyen Mai Hung Hanoi Training College, Hanoi, Vietnam A b s tr a c t Photon - axion conversions in a resonant electromagnetic cavity w ith frequency equal to the axion mass are considered in detail by the Feynman diagram m ethods T he differential cross sections are presented and numerical evaluations are given It is shown th a t there is a reso nant conversion for the considered process From our results, some estim ates for experimental conditions are given MIRAMARE - T R IESTE September 2000 In the 1970’s, it was shown that the strong CP problem can be solved [1] by the introduction of a light pseudoscalar particle, called the axion [2], At present, the axion mass is constrained by laboratory searches [3] and by astrophysical and cosmological considerations [4] to between 10 eV and 10 eV Besides th at, an axino (the fermionic partner of the axion) naturally appears in SUSY models [5,6], which acquires a mass from three - loop Feynman diagrams in a typical range between a few eV up to a maximum of keV [7,8], A particle, if it has a two - photon vertex, may be created by a photon entering an external electromagnetic (EM) field T he axion is one of such particles So far almost all experiments designed to search for light axions make use of the coupling of the axion to photons Conversion of the axions into EM power in a resonant cavity was first suggested by Sikivie [9] He suggested th a t this method can be used to detect the hypothetical galactic axion flux th a t would exist if axions were the dark m atter of the Universe Various terrestrial experiments to detect invisible axions by making use of their coupling to photons have been proposed [10,11], and the new results of such experim ents appeared recently [12,13] An experimental EM detection of axions is briefly described as follows[14]: The initial photon of energy q0 from the laser (maybe better from X ray) interacts with a virtual photon from the EM field to produce the axion of energy p0 and m om entum : p = y/pQ —m ị The photon beam is then blocked to elim inate everything except the axions, which penetrate the wall because of their extremely weak interaction with ordinary m atter (Such shielding is straightforward for a low-energy laser beam.) The axion then interacts with another virtual photon in the second EM field to produce a real photon of energy (j'0, whose detection is the signal for the product ion of the axion Recently, a photon regeneration experim ent using RF photons was described in Ref.[15], This experim ent consists of two cavities which are placed at a small distance apart A more or less homogeneous magnetic field exists in b oth cavities T he first, or emiting cavity, is excited by incoming RF radiation Depending on the axion-photon coupling constant, a certain am ount of RF energy will be deposited in the second, or receiving cavity However, the author studied the problem by using the classical m ethod T he purpose of this paper is to consider conversions of photons into axions in a resonant EM cavity with frequency equal to the axion mass using the Feynman diagram methods For the axion- photon system a suitable Lagrangian density is given by [4,9] L = - ~ F ln, F ^ + 47T J a + ị d ^ ộ a z - ị m j2 l [ l Hr ( ộ ị / v 2)}, z (1) w h e re 4>a is t h e a x io n field, m a is i ts m ass, Fpv = ỊịEijvpơ F pơ, a n d f a is t h e a x io n d e c a y c o n s t a n t and is defined ill term s of the axion mass m a by [9,12]: f a = f 7Tm n ự m umđ[ĩiia{rllu + rnd)}~ • Interaction of axions to the photons arieses from the triangle loop diagram, in which two vertices are interactions of the photon to electrically charged feinion and an another vertex is coupling of the axion with fermion T his coupling is model dependent and is given by: !h = ( w- - - ^ + ^ t ) where N = T ^Q p q Q Ĩo Io t) alld N e = Q p q Q 'L Tr represents the sume over all left - handed Weyl fermions QPQ, Qem, and Qculor are respectively the PecceiQ uinn charge, the electric charge, and one of the generators of SU {3)c In particular in the Dine- Fischler - Srednicki - Zhitnitskii model [16]: 97(D FSZ)~ 0.36, and in the Kim- ShifinanVainshtein- Zakharov mode] [17] (where the axions not couple to light quarks and leptons) : 57 (K SV Z)~ -0.97 Now we consider the conversion of the photon w ith momentum (] into the axion II with momentum p in an external electromagnetic field For the abovementioned process, the relevant coupling is the seconrl term in (1) Using the Feynman rules we get the following expression for the m atrix element 121 where k = q - p, the momentum transfer to the EM field, gal = (J1 - j - = + ’7id)(7r/^mTy m v r i^ ) -1 and £^(q,ơ) represents the polarization vector of the photon Ex pression (2) is valid for an arbitrary externa] EM field In the following we shall use it for conversions in the resonant EM cavity of the T M n o mode with frequency equal to the axion mass Here we use the following notations: q = |l — m ’-;)1/ and is the angle between p and q T he nontrivial solution of the T M n o mode is given by [18] 1ĨX \ 16ĨT nil / 7XX \ f Try here the propagation of the EM wave is ill the z - direction Substitution of (3) to (2) gives us the following expression for the m atrix element (p\M\q) = — (27T)VP0
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