MATSIN WUTAR GLUON, BAYAN SHEKARU ASHIRIN

Gluon ne ke haɗa quark wuri ɗaya, su ne masu ɗauke da ƙaƙƙarfan ƙarfi (strong force). Idan aka dumama abu sosai, wannan haɗin yana sakewa: gluon suna yawo a sake cikin plasma. Don nazarin wannan yanayi ba tare da sarƙaƙiya da yawa ba, masana kimiyyar lissafi kan bar quark su riƙe gluon kawai — ka’idar da ake kira tsantsar Yang-Mills (pure Yang-Mills). Tana riƙe da muhimman siffofin ainihin ƙaƙƙarfan ƙarfi, in ji marubutan, kuma a lokaci guda tana da sauƙi isasshe da za a iya kwaikwayon ta daidai sosai a kwamfutoci.

Wata muhimmiyar tambaya game da wannan plasma: wane matsi take yi a wani matakin zafi?

Amsar da aka gina mataki-mataki

A zafi mai tsanani sosai, ƙarfin da ke tsakanin gluon yana raunana, kuma ana auna shi da wata ƙaramar lamba g, wato haɗin kai (coupling). Sannan za a iya rubuta matsin a matsayin jeri: babban ɓangare, sannan gyare-gyare masu daidaito da g², g³, g⁴, da sauransu, kowanne ƙasa da na baya. Babban ɓangaren shi ne matsin gluon da ke sake, wanda ake kira iyakar Stefan-Boltzmann.

Marubutan suna bin tarihin. An gano ɓangaren g⁴ mai logarithm a 1982; cikakken ɓangaren g⁴ sai a 1994, saboda lissafin da’ira uku yana da wuya sosai; ɓangaren g⁵ ba da daɗewa ba bayan haka. A mataki na gaba, g⁶, abubuwa sun ƙara wuya. Wani ɓangarensa yana fitowa ne daga sauye-sauyen maganadisu masu jinkiri a cikin plasma waɗanda ba za a iya lissafa su da irin wannan faɗaɗawar ko kaɗan ba. Wata dabara da ke raba plasma zuwa ma’auni daban-daban — mai sauri, mai ɗan jinkiri, mafi jinkiri — ta kula da wannan ɓangaren, kuma kwaikwayon kwamfuta na wani sauƙaƙaƙƙen sigar mai girma uku ya samar da ƙimarsa.

Hakan ya bar yanki ɗaya: gudummawar ma’auni mafi sauri, wanda ke buƙatar a haɗa kowane zanen vacuum mai da’ira huɗu. “An daɗe ana ganin ba za a iya warware shi ba,” ƙungiyar ta rubuta, “wannan matsalar ta kasance a buɗe sama da shekaru ashirin.”

Zane-zane 65, awoyi miliyan ɗaya

Keijo Kajantie, Pablo Navarrete, Risto Paatelainen, Leon Sandbote, York Schröder, Kaapo Seppänen da Aleksi Vuorinen — daga Jami’o’in Helsinki da Turku, Jami’ar Bío-Bío a Chile da Jami’ar Bern — sun ɗauki nauyin aikin.

• Akwai zane-zane 65 masu da’ira huɗu na gluon (da ƙwayoyin “fatalwa” (ghost) masu taimako).
• Warware lissafin aljabarsu ya samar da kusan haɗakai 100,000, waɗanda suke raguwa zuwa siffofi na ƙa’ida 21. Goma ba za a iya raba su zuwa guntaye mafiya sauƙi ba, kuma tara daga cikinsu ba a taɓa lissafa su ba.
• Don ƙididdige su, ƙungiyar ta yi amfani da wata hanya da ake kira thermal loop-tree duality, tare da sababbin hanyoyin cire marasa iyaka da ke bayyana a manya-manyan da ƙananan-ƙananan momentum. Abin da ya rage yana da iyaka kuma an iya haɗa shi da lissafin lambobi ta hanyar ɗaukar samfura bazuwar: kusan awoyin CPU miliyan ɗaya a kan manyan kwamfutoci.

A matsayin tantancewa, dogaro kan wani zaɓi na ganin dama a cikin lissafin (gauge parameter) ya soke kansa, kamar yadda dole ne. Marasa iyaka daga ma’auni daban-daban su ma sun soke juna daidai, kamar yadda ka’idar ta buƙata.

Lambar da ta ɓace

Muhimmin sabon ma’aunin lissafi (coefficient) ya fito a 6236 ± 40. Wani ƙiyasi na baya, wanda aka fitar a kaikaice daga kwaikwayo, ya ba da 6000 ± 600 — ya yi daidai, amma ƙasa da daidaito sau goma sha biyar. A cikin rubutun da marubutan suka saba amfani da shi, cikakken ma’aunin g⁶ na matsin ga SU(3) — sigar da ke da “launuka” uku, wadda ake kwaikwayo a kan lattice — shi ne −3591.2, da rashin tabbas na ±16.9 daga wannan lissafin da ±250 daga ɓangaren maganadisu da aka lissafa a kan lattice.

Ka’ida ta haɗu da kwaikwayo

Ribar tana bayyana idan aka kwatanta jerin da kwaikwayon lattice mai girma huɗu, waɗanda suka lissafa wannan matsin har zuwa ninki dubu na zafin da gluon ke ƙwacewa (kusan 260 MeV). Ƙananan matakai suna yin rashin kyau: sakamakon g³ da g⁴ sun wuce iyakar gluon da ke sake, kuma g⁵ ya faɗi ƙasa sosai da kwaikwayon. Da aka haɗa da ɓangaren g⁶, ta amfani da wata hanyar ƙa’ida ta sake tsara jerin, ka’idar ta zo daidai da bayanan lattice a ƙididdige har zuwa ninki kaɗan na wannan zafi mai muhimmanci.

A cewar marubutan, wannan shi ne karo na biyu kawai da aka warware yanayin zafi (thermodynamics) na wata ka’idar filin quantum mai zafi har zuwa wannan mataki, kuma na farko a cikin wata ka’idar gauge ta zahiri. Yayin da suke kammalawa, sun samu labarin cewa wata ƙungiya mai zaman kanta a Jami’ar Granada tana ƙoƙarin yin lissafi iri ɗaya; ƙungiyoyin biyu sun tabbatar cewa babban sakamakonsu ya yi daidai.

Abin da ke gaba a jerinsu: ɓangaren g⁷, da cikakken ƙaƙƙarfan ƙarfi tare da quark da yawan quark da ba sifili ba. Hakan zai kai ga yanayoyin da suka wuce kwaikwayon lattice na yau, masu muhimmanci, in ji marubutan, ga haɗewar taurarin neutron.