Neutrino masses and mixings in non-factorizable geometry
Yuval Grossman,Matthias Neubert +1 more
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In this paper, it was shown that if the fermion mass is larger than half the curvature of the compact dimension, the zero mode can be localized on the hidden 3-brane in the Randall-Sundrum model.About:
This article is published in Physics Letters B.The article was published on 2000-02-17 and is currently open access. It has received 856 citations till now. The article focuses on the topics: Neutrino & Randall–Sundrum model.read more
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The Minimal Composite Higgs Model
TL;DR: In this article, the authors proposed a composite Higgs in the framework of a five-dimensional AdS theory, where electroweak symmetry is broken dynamically via top loop effects, all flavour problems are solved, and contributions to electroweak precision observables are below experimental bounds.
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Fermion Masses, Mixings and Proton Decay in a Randall-Sundrum Model
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TL;DR: In this paper, the authors consider a Randall-Sundrum model in which the Standard Model fermions and gauge bosons correspond to bulk fields and show how the observed charged fermion masses and CKM mixings can be explained, without introducing hierarchical Yukawa couplings.
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The Physics of the B Factories
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Lindsay,Luca Lista,C. Liu,F. Liu,Hung-wen Liu,H. M. Liu,Jiurong Liu,R. Liu,T. Liu,Yueh-Feng Liu,Z. Q. Liu,D. Liventsev,M. Lo Vetere,Christopher Locke,W. S. Lockman,F. Di Lodovico,V. Lombardo,G. W. London,D. Lopes Pegna,L. Lopez,N. Lopez-March,J. Lory,Jm Losecco,X. C. Lou,R. Louvot,A. Lu,C. Lu,M. Lu,Rong-Shyang Lu,T. Lueck,S. Luitz,P. Lukin,P. Lukin,P. Lund,Eleonora Luppi,A. M. Lutz,O. Lutz,G. Lynch,H. L. Lynch,A. J. Lyon,V. R. Lyubinsky,D. B. MacFarlane,Catherine Kirsty Mackay,J. MacNaughton,M. Macri,S. Madani,Wolfgang Mader,Stephanie Majewski,G. Majumder,Yasuhiro Makida,B. Malaescu,Roberto Malaguti,Julie Malcles,U. Mallik,E. Maly,H. Mamada,A. Manabe,G. Mancinelli,M. Mandelkern,F. Mandl,P.F. Manfredi,D. Mangeol,Elisa Manoni,Z. P. Mao,M. Margoni,C.E. Marker,G. Markey,J. Marks,D. Marlow,V. Marques,H. Marsiske,S. Martellotti,E. Martin,J. P. Martin,L. Martin,A. J. Martinez,Moreno Marzolla,A. Mass,Mika Masuzawa,A. Mathieu,P. Matricon,Takahiko Matsubara,T. Matsuda,H. Matsumoto,S. Matsumoto,T. Matsumoto,H. Matsuo,T. S. Mattison,D. Matvienko,D. Matvienko,A. Matyja,B. Mayer,M. Mazur,M.A. Mazzoni,Malcolm McCulloch,J. McDonald,J. D. McFall,P. McGrath,A. K. McKemey,J. A. McKenna,S. E. Mclachlin,Steve McMahon,T. R. McMahon,S. McOnie,T. Medvedeva,R. Melen,Bruce Mellado,W. Menges,Sven Menke,A. M. Merchant,J. Merkel,R. Messner,S. Metcalfe,Scott D. Metzler,N. Meyer,T. I. Meyer,W. T. Meyer,A.K. Michael,G. Michelon,Shinichiro Michizono,P. Micout,V. Miftakov,A. Mihalyi,Y. Mikami,D. A. Milanes,M. Milek,Toshihiro Mimashi,J. S. Minamora,C. Mindas,S. Minutoli,Lluisa-Maria Mir,K. Mishra,Winfried Mitaroff,H. Miyake,T. S. Miyashita,H. Miyata,Y. Miyazaki,L.C. Moffitt,A. Mohapatra,A. Mohapatra,D. Mohapatra,A. Moll,G. R. Moloney,J. P. Mols,Remigius K. Mommsen,M. R. Monge,D. Monorchio,T. B. Moore,G. F. Moorhead,P. Mora de Freitas,Mauro Morandin,N. Morgan,S. E. Morgan,M. Morganti,S. Morganti,Shigeki Mori,T. Mori,M. Morii,Joseph P. Morris,F. Morsani,G. W. Morton,L. Moss,J. P. Mouly,R. Mount,James Mueller,Ralph Müller-Pfefferkorn,M. Mugge,F. Muheim,A. Muir,E. Mullin,M. Munerato,A. Murakami,T. Murakami,Norihito Muramatsu,P. Musico,I. Nagai,Tadashi Nagamine,Yasushi Nagasaka,Y. Nagashima,S. Nagayama,Maria A. Nagel,M. T. Naisbit,T. Nakadaira,Yu Nakahama,M. Nakajima,T. Nakajima,I. Nakamura,T. Nakamura,T. T. Nakamura,E. Nakano,H. Nakayama,J. W. Nam,S. Narita,I. Narsky,Jordan Nash,Z. Natkaniec,U. Nauenberg,M. Nayak,H. A. Neal,E. Nedelkovska,Matteo Negrini,K. Neichi,D. Nelson,S. Nelson,Nicola Neri,G. Nesom,S. Neubauer,D. Newman-Coburn,C. Ng,X. Nguyen,H. Nicholson,C. Niebuhr,J.Y. Nief,M. Niiyama,M. B. Nikolich,N. K. Nisar,K. Nishimura,Y. Nishio,Osamu Nitoh,R. Nogowski,S. Noguchi,T. Nomura,Martin Nordby,Yuri Nosochkov,A. Novokhatski,S. Nozaki,T. Nozaki,Ian Michael Nugent,C. P. O’Grady,S. W. O'Neale,F. G. O'Neill,B. Oberhof,P. J. Oddone,I. Ofte,A. Ogawa,K. Ogawa,S. Ogawa,Y. Ogawa,R. Ohkubo,Kazuhito Ohmi,Y. Ohnishi,F. Ohno,T. Ohshima,Yasuhiro Ohshima,Norihito Ohuchi,Katsunobu Oide,N. Oishi,T. Okabe,N. Okazaki,T. Okazaki,S. Okuno,Emmanuel Olaiya,A. Olivas,P. Olley,James D. Olsen,S. Ono,G. Onorato,A. P. Onuchin,A. P. Onuchin,A. P. Onuchin,Y. Onuki,T. Ooba,Toyoko Orimoto,T. Oshima,I. L. Osipenkov,W. Ostrowicz,C. Oswald,S. Otto,J. Oyang,A. Oyanguren,H. Ozaki,Veysi Erkcan Ozcan,H. P. Paar,C. Padoan,K. Paick,H. Palka,B. Pan,Y. B. Pan,W. Panduro Vazquez,J.H. Panetta,A. I. Panova,R. S. Panvini,E. Panzenböck,E. Panzenböck,E. Paoloni,P. Paolucci,M. Pappagallo,Sudarshan Paramesvaran,Chawon Park,C. W. Park,H. Park,H. Park,Hyangkyu Park,K. S. Park,W. Park,R. J. Parry,N. Parslow,S. Passaggio,F. Pastore,P.M. Patel,C. Patrignani,P. Patteri,T.J. Pavel,J. Pavlovich,D. J. Payne,L.S. Peak,D. R. Peimer,M. Pelizaeus,R. Pellegrini,Mario Pelliccioni,C. C. Peng,J. C. Peng,K. C. Peng,T. Peng,Y. Penichot,S. Pennazzi,Michael R. Pennington,R. C. Penny,A. Penzkofer,A. Perazzo,Alejandro Perez,M. L. Perl,M. Pernicka,Jean-Pierre Perroud,I. M. Peruzzi,R. Pestotnik,K. Peters,M. D. Peters,Brian Petersen,Troels Petersen,E. Petigura,S. Petrak,A. Petrella,M. Petrič,A. Petzold,Maria Grazia Pia,T. Piatenko,Davide Piccolo,M. Piccolo,L. Piemontese,M. Piemontese,Maurizio Pierini,S. Pierson,M. Pioppi,G. Piredda,M. Pivk,Stéphane Plaszczynski,F. Polci,A. Pompili,P. Poropat,M. Posocco,C. T. Potter,R.J.L. Potter,V. Prasad,E.J. Prebys,E. Prencipe,J. Prendki,R. Prepost,M. Prest,M. T. Prim,M. Pripstein,X. Prudent,S. Pruvot,E. M. T. Puccio,Milind Purohit,N. D. Qi,Helen R. Quinn,J. L. Raaf,R. Rabberman,F. Raffaelli,G. Ragghianti,Shahram Rahatlou,A. M. Rahimi,R. Rahmat,A. Rakitin,A. S. Randle-Conde,P. Rankin,Irina Rashevskaya,S. Ratkovsky,G. Raven,Valerio Re,M. Reep,J. J. Regensburger,James J. Reidy,Roberto Reif,B. Reisert,C. Renard,F. Renga,S. Ricciardi,Jeffrey Richman,J. L. Ritchie,M. Ritter,Claudio Rivetta,G. Rizzo,C. Roat,P. Robbe,D. A. Roberts,A. I. Robertson,Enrico Robutti,S. Rodier,Diego Rodriguez,Jorge Luis Rodriguez,R. Rodriguez,N. A. Roe,M. Röhrken,W. Roethel,J. Rolquin,L.V Romanov,A. Romosan,M. T. Ronan,G. Rong,Frederic Jean Ronga,Lydia Roos,N.I. Root,M. Rosen,E. I. Rosenberg,Alessandro Rossi,A. Rostomyan,Marcello Rotondo,E. Roussot,J. Roy,M. Rozanska,Yoram Rozen,A. E. Rubin,W. O. Ruddick,A. M. Ruland,K. Rybicki,A. Ryd,S. Ryu,J. Ryuko,S. Sabik,R. Sacco,Mohammad Alam Saeed,F. Safai Tehrani,H. Sagawa,H. Sahoo,S.K Sahu,M. Saigo,T. Saito,S. Saitoh,K. Sakai,Hiroshi Sakamoto,H. Sakaue,M. Saleem,A. A. Salnikov,E. Salvati,F. Salvatore,A. Samuel,David Sanders,P. Sanders,S. Sandilya,F. Sandrelli,W. Sands,W. R. Sands,M. Sanpei,D. Santel,Luka Santelj,V. Santoro,A. Santroni,T. Sanuki,Tapas Sarangi,S. Saremi,Alessio Sarti,T. Sasaki,N. Sasao,M. Satapathy,N. Sato,Noriaki K. Sato,Y. Sato,N. Satoyama,A. Satpathy,A. Satpathy,V. Savinov,N. Savvas,O. H. Saxton,K. Sayeed,S. F. Schaffner,T. Schalk,S. Schenk,J. R. Schieck,T. Schietinger,T. Schietinger,C. J. Schilling,Rafe Schindler,S. Schmid,R. Schmitz,H. Schmuecker,O. Schneider,G. Schnell,G. Schnell,P. Schonmeier,K. C. Schofield,G. Schott,H. Schröder,M. Schram,J. Schubert,J. Schümann,J. Schultz,Bruce Schumm,Marie Helene Schune,U. Schwanke,Herbert Schwarz,J. Schwiening,R. Schwierz,Roy F Schwitters,C. Sciacca,G. Sciolla,I. J. Scott,J.T. Seeman,Abraham Seiden,R. Seitz,T. Seki,A. Sekiya,Sergey Semenov,D. Semmler,Sercan Sen,K. Senyo,O. Seon,V. V. Serbo,S. I. Serednyakov,S. I. Serednyakov,B. Serfass,M. Serra,J. Serrano,Y. Settai,Rolf Seuster,M. E. Sevior,K. V. Shakhova,L. Shang,M. Shapkin,Vivek Sharma,V.E. Shebalin,V.E. Shebalin,V. G. Shelkov,B. C. Shen,D. Z. Shen,Y.-T. Shen,D. J. Sherwood,T. Shibata,T. A. Shibata,H. Shibuya,Tetsuo Shidara,K. Shimada,M. Shimoyama,S. Shinomiya,J. G. Shiu,H. W. Shorthouse,L. I. Shpilinskaya,A.L. Sibidanov,Etienne Sicard,A. Sidorov,V.A. Sidorov,V. Siegle,M. Sigamani,M. C. Simani,M. Simard,Gabriele Simi,Frank Simon,F. Simonetto,N. B. Sinev,H. Singh,J. Singh,R. Sinha,S. Sitt,Yu I. Skovpen,Yu I. Skovpen,R. J. Sloane,P. Smerkol,A. J.S. Smith,David J. Smith,David J. Smith,David J. Smith,D.S. Smith,J. R. Smith,A. Smol,H. Snoek,Adam Snyder,R. Y. So,Randall Sobie,E. Soderstrom,Aron Soha,Y. S. Sohn,Michael Sokoloff,A. Sokolov,P. Solagna,E. Solovieva,N. Soni,N. Soni,P. Sonnek,Viola Sordini,B. Spaan,Stefan Spanier,E. Spencer,V. Speziali,M. Spitznagel,P. Spradlin,H. Staengle,Rainer Stamen,M. Stanek,S. Stanič,Jan Stark,M. Steder,H. Steininger,M. Steinke,J. Stelzer,E. Stevanato,Achille Stocchi,R. Stock,H. Stoeck,D. P. Stoker,R. Stroili,D. M. Strom,P. Strother,J. Strube,Bjarne Stugu,J. Stypula,D. Su,R. Suda,R. Sugahara,A. Sugi,Takashi Sugimura,A. Sugiyama,S. Suitoh,Michael Sullivan,M. Sumihama,T. Sumiyoshi,Don Summers,L. Sun,L. Sun,S. Sun,J. E. Sundermann,H. F. Sung,Y. Susaki,P. Sutcliffe,A. Suzuki,J. Suzuki,J. I. Suzuki,K. Suzuki,K. Suzuki,S. Suzuki,S. Y. Suzuki,J.E. Swain,Sanjay Kumar Swain,Stephane T'Jampens,Makoto Tabata,Kerstin Tackmann,Hiroyuki Tajima,Osamu Tajima,K. Takahashi,S. Takahashi,T. Takahashi,Fumihiko Takasaki,T. Takayama,M. Takita,K. Tamai,U. Tamponi,N. Tamura,N. Tan,P. Tan,K. Tanabe,T. Tanabe,H. A. Tanaka,Junichi Tanaka,M. Tanaka,Satoshi Tanaka,Y. Tanaka,Kiyoshi Tanida,N. Taniguchi,P. Taras,N. Tasneem,G. Tatishvili,T. Tatomi,Masafumi Tawada,F. E. Taylor,G. N. Taylor,G. Taylor,Valery I. Telnov,Valery I. Telnov,L. Teodorescu,R. Ter-Antonyan,Y. Teramoto,Dmitry Teytelman,G. Therin,Ch Thiebaux,D. Thiessen,E. Thomas,J. M. Thompson,F. Thorne,X. C. Tian,M. J. Tibbetts,I. Tikhomirov,J. S. Tinslay,G. Tiozzo,V. Tisserand,V. Tocut,W. Toki,E. W. Tomassini,Makoto Tomoto,T. Tomura,Ezio Torassa,E. Torrence,S. Tosi,C. Touramanis,J. C. Toussaint,S. N. Tovey,P.P. Trapani,E. Treadwell,G. Triggiani,Sophie Trincaz-Duvoid,William Trischuk,D. Troost,A. Trunov,K. L. Tsai,Y.T. Tsai,Yuichi Tsujita,K. Tsukada,T. Tsukamoto,J. M. Tuggle,A. Tumanov,Y. W. Tung,L. Turnbull,Jill R. Turner,M. Turri,K. Uchida,M. Uchida,Y. Uchida,M. Ueki,K. Ueno,N. Ujiie,Keith Ulmer,Yoshinobu Unno,P. Urquijo,Y. Ushiroda,Yu. V. Usov,Yu. V. Usov,M. Usseglio,Y. Usuki,U. Uwer,J. Va'vra,S. Vahsen,G. Vaitsas,A. Valassi,E. Vallazza,A. Vallereau,P. Vanhoefer,W. C. van Hoek,C. Van Hulse,D. Van Winkle,G. Varner,Erich Varnes,Kevin Varvell,G. Vasileiadis,Yu. S. Velikzhanin,M. Verderi,S. Versille,K. Vervink,B. Viaud,P. B. Vidal,Sara Villa,Pablo Villanueva-Perez,E. L. Vinograd,L. Vitale,G. M. Vitug,C. Voß,C. Voci,C. Voena,A. Volk,J.H. von Wimmersperg-Toeller,V. Vorobyev,V. Vorobyev,A. Vossen,G. Vuagnin,Carl Vuosalo,K. Wacker,A. P. Wagner,D. L. Wagner,G. Wagner,M. N. Wagner,S. R. Wagner,D. E. Wagoner,David Walker,Wolfgang Walkowiak,David Wallom,C. C. Wang,C. H. Wang,Jing Wang,J. G. Wang,Kelin Wang,Lianqi Wang,L. Wang,P. Wang,T. J. Wang,Weitao Wang,X. L. Wang,Yanchu Wang,Fr Wappler,M. Watanabe,Alan Watson,J. E. Watson,N. K. Watson,M. Watt,James Weatherall,M. Weaver,Tristan Weber,Robin Wedd,J. T. Wei,A. W. Weidemann,A. J. Weinstein,W. A. Wenzel,Claire A. West,Colin West,T. J. West,E. J. White,Ryan White,J. Wicht,L. Widhalm,J. Wiechczynski,Ulrich Wienands,L. Wilden,M. Wilder,Dc Williams,G. Williams,J. Williams,K. M. Williams,M. I. Williams,Stephane Willocq,J. R. Wilson,M. G. Wilson,Robert Wilson,F. Winklmeier,L. Winstrom,Marc Winter,William J. Wisniewski,M. Wittgen,J. L. Wittlin,W. Wittmer,R. Wixted,A. Woch,B. J. Wogsland,Q. K. Wong,B. C. Wray,A. C. Wren,David Wright,C. H. Wu,Junqiao Wu,Sau Lan Wu,Howard Wells Wulsin,Stefania Xella,Q. L. Xie,Y. Xie,Z. Z. Xu,Ch. Yèche,Y. Yamada,M. Yamaga,A. Yamaguchi,H. Yamaguchi,T. Yamaki,Hitoshi Yamamoto,N. Yamamoto,R. K. Yamamoto,Shimpei Yamamoto,Tomoyuki Yamanaka,H. Yamaoka,J. Yamaoka,Yoshio Yamaoka,Y. Yamashita,M. Yamauchi,D. S. Yan,Y. Yan,H. Yanai,S. Yanaka,Hyun Seok Yang,R. Yang,S. Yang,A. K. Yarritu,S. Yashchenko,J. Yashima,Z. Yasin,Yoshiji Yasu,S. W. Ye,P. Yeh,J. I. Yi,K. Yi,Ming Yi,Z. W. Yin,J. Ying,Gerald Yocky,K. Yokoyama,Masashi Yokoyama,T. Yokoyama,K. Yoshida,M. Yoshida,Yumiko Yoshimura,C. Young,C. X. Yu,Zongfu Yu,C. Z. Yuan,Y. Yuan,Francisco Yumiceva,Y. Yusa,A. N. Yushkov,H. Yuta,V. Zacek,S. B. Zain,A. Zallo,S. Zambito,D. Zander,S. L. Zang,D. Zanin,B. G. Zaslavsky,Q. L. Zeng,Amina Zghiche,B. Zhang,J. Zhang,L.M. Zhang,Lei Zhang,S. Q. Zhang,Zhiqing Zhang,H. W. Zhao,M. Zhao,Zhengguo Zhao,Y. Zheng,Y. H. Zheng,Z. P. Zheng,V. Zhilich,V. Zhilich,P. Zhou,Ren-Yuan Zhu,Y. S. Zhu,Z. M. Zhu,Vladimir Zhulanov,Vladimir Zhulanov,T. Ziegler,V. Ziegler,G. Zioulas,Michael S. Zisman,M. Zito,D. Zurcher,N. Zwahlen,O. Zyukova,O. Zyukova,T. Živko,D. Žontar +2064 more
TL;DR: The physics of the SLAC and KEK B Factories are described in this paper, with a brief description of the detectors, BaBar and Belle, and data taking related issues.
References
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Journal ArticleDOI
Large Mass Hierarchy from a Small Extra Dimension
TL;DR: In this paper, the weak scale is generated from the Planck scale through an exponential hierarchy, but this exponential arises not from gauge interactions but from the background metric, which is a slice of spacetime.
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An Alternative to compactification
TL;DR: In this paper, a single 3-brane embedded in five dimensions was shown to reproduce four-dimensional Newtonian and general relativistic gravity to more than adequate precision, even without a gap in the Kaluza-Klein spectrum.
Quantum Fields in Curved Space
N. D. Birrell,Paul Davies +1 more
TL;DR: A comprehensive review of the subject of gravitational effects in quantum field theory can be found in this paper, where special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe.
Journal ArticleDOI
Evidence for oscillation of atmospheric neutrinos
Y. Fukuda,T. Hayakawa,E. Ichihara,Kunio Inoue,K. Ishihara,H. Ishino,Yoshitaka Itow,Takaaki Kajita,J. Kameda,S. Kasuga,Ken-ichiro Kobayashi,Yohei Kobayashi,Yusuke Koshio,M. Miura,Masayuki Nakahata,S. Nakayama,A. Okada,Ko Okumura,N. Sakurai,Masato Shiozawa,Yoshihiro Suzuki,Y. Takeuchi,Y. Totsuka,Shinya Yamada,M. Earl,Alec Habig,E. Kearns,M. D. Messier,Kate Scholberg,J. L. Stone,Lawrence Sulak,C. W. Walter,M. Goldhaber,T. Barszczxak,D. Casper,W. Gajewski,P. G. Halverson,J. Hsu,W. R. Kropp,L. R. Price,Frederick Reines,Michael B. Smy,Henry W. Sobel,Mark R. Vagins,K. S. Ganezer,W. E. Keig,R. W. Ellsworth,S. Tasaka,J. W. Flanagan,A. Kibayashi,John G. Learned,S. Matsuno,V. J. Stenger,D. Takemori,T. Ishii,Junichi Kanzaki,T. Kobayashi,S. Mine,K. Nakamura,K. Nishikawa,Yuichi Oyama,A. Sakai,Makoto Sakuda,Osamu Sasaki,S. Echigo,M. Kohama,A. T. Suzuki,Todd Haines,Todd Haines,E. Blaufuss,B. K. Kim,R. Sanford,R. Svoboda,M. L. Chen,Z. Conner,Z. Conner,J. A. Goodman,G. W. Sullivan,J. Hill,C. K. Jung,K. Martens,C. Mauger,C. McGrew,E. Sharkey,B. Viren,C. Yanagisawa,W. Doki,Kazumasa Miyano,H. Okazawa,C. Saji,M. Takahata,Y. Nagashima,M. Takita,Takashi Yamaguchi,Minoru Yoshida,Soo-Bong Kim,M. Etoh,K. Fujita,Akira Hasegawa,Takehisa Hasegawa,S. Hatakeyama,T. Iwamoto,M. Koga,Tomoyuki Maruyama,Hiroshi Ogawa,J. Shirai,A. Suzuki,F. Tsushima,Masatoshi Koshiba,M. Nemoto,Kyoshi Nishijima,T. Futagami,Y. Hayato,Y. Kanaya,K. Kaneyuki,Y. Watanabe,D. Kielczewska,D. Kielczewska,R. A. Doyle,J. S. George,A. L. Stachyra,L. Wai,L. Wai,R. J. Wilkes,K. K. Young +124 more
Abstract: We present an analysis of atmospheric neutrino data from a 33.0 kton yr (535-day) exposure of the Super-Kamiokande detector. The data exhibit a zenith angle dependent deficit of muon neutrinos which is inconsistent with expectations based on calculations of the atmospheric neutrino flux. Experimental biases and uncertainties in the prediction of neutrino fluxes and cross sections are unable to explain our observation. The data are consistent, however, with two-flavor ${\ensuremath{
u}}_{\ensuremath{\mu}}\ensuremath{\leftrightarrow}{\ensuremath{
u}}_{\ensuremath{\tau}}$ oscillations with ${sin}^{2}2\ensuremath{\theta}g0.82$ and $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}l\ensuremath{\Delta}{m}^{2}l6\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3}\mathrm{eV}{}^{2}$ at 90% confidence level.
Journal ArticleDOI
Solitons with Fermion Number 1/2
Roman Jackiw,C. Rebbi +1 more
TL;DR: In this article, it was shown that the existence of a non-degenerate, isolated, zero-energy, $c$-number solution of the Dirac equation implies that the soliton is a degenerate doublet with Fermi number.