Charmonium Physics at LHCb

Such a sys­tem, i.e., an atom, can decrease its energy by the tran­si­tion of the
elec­tron into an ener­get­i­cally lower orbit. Since such a tran­si­tion is a pure quan­tum mechan­i­cal process, each, in this sense, quan­tum mechan­i­cally not for­bid­den but "allowed" tran­si­tion causes the emis­sion of radi­a­tion energy in the form of pho­tons of a cer­tain fre­quency and energy.

Thus, the spec­tra of an atom are very char­ac­ter­is­tic for that par­tic­u­lar atom.

The c quarks of the char­mo­nium sys­tem are bound together by means of the strong force. The rel­a­tive motion of the bound quarks gives rise to the orbital angu­lar momen­tum, mea­sured in whole-​number mul­ti­ples of Planck’s con­stant h, which con­tributes to the total energy of the sys­tem. The quarks, like the pro­ton and elec­tron, also pos­sess some intrin­sic angu­lar momen­tum called spin. Quan­ti­za­tion of these angu­lar momenta results in a unique set of allowed energy lev­els for the char­mo­nium sys­tem in anal­ogy to those of an atomic sys­tem.

In this con­text, a char­mo­nium state is often referred to as "hydro­gen atom of strong inter­ac­tion".
All Char­mo­nium states are heav­ier than a hydro­gen atom which has a mass of roughly 0.94 GeV/​c² or 1.67 •10^-27kg.
The charm quark c, dis­cov­ered in 1974, has a mass of approx­i­mately 1.3 GeV/​c² or 2.6 • 10^-27 kg. The light­est char­mo­nium state, the η_c  meson, has a mass of 2.98 GeV/​c².

Unlike the hydro­gen atom or other sta­ble mat­ter, the J/​ψ meson and all

char­mo­nium states are unsta­ble par­ti­cles and decay. That means that even a char­mo­nium ground state is not sta­ble whereas a hydro­gen atom in its ground state should exit for­ever.
The J/​ψ meson, for instance, has a mean life­time on the order of 10^-21 s.

All cha­mo­nium states, can, in prin­ci­ple, decay into

• other hadrons via the strong inter­ac­tion

• into lep­tons via the elec­tro­mag­netic inter­ac­tion

Although the char­mo­nium states pre­dom­i­nantly decay via the strong inter­ac­tion into hadrons, addi­tion­ally the excited char­mo­nium states can decay into lower energy states by the emis­sion of a pho­ton, just as in atomic physics.

Thanks to this result, the LHCb col­lab­o­ra­tion opens a new avenue to pre­ci­sion mea­sure­ments of char­mo­nium par­ti­cles at hadron col­lid­ers, that was unex­pected by the physics com­mu­nity. - Gio­vanni Pas­sal­eva, Spokesper­son for the LHCb col­lab­o­ra­tion

Anal­o­gous to the hydro­gen atom, a c-​quark c-​antiquark pair (cc) in a bound state must occupy dis­crete energy lev­els as well. The η_c meson rep­re­sents the char­mo­nium ground state with spin 0 (zero). Each of its con­stituents, the c-​quark and the c-​antiquark are par­ti­cles with spin ½. There­fore, the low­est energy state cor­re­sponds to an antipar­al­lel spin-​vector ori­en­ta­tion which results in a spin mag­ni­tude of 0 for the com­pos­ite par­ti­cle sys­tem.
In its first excited state, the spin-​vectors of both c quarks are aligned par­al­lel so that their mag­ni­tudes sum up to spin 1. The first excited state of a char­mo­nium is called a J/​ψ (J/​psi) meson which is a spin 1 par­ti­cle state.

To reach ener­get­i­cally higher states, the sys­tem, i.e., the J/​ψ meson has to be excited again, which means the sys­tem must absorb energy which is stored as poten­tial energy of the two quarks occu­py­ing 'higher' orbits. Two of those excited states are rep­re­sented by the χ_c1 and  χ_c2 mesons.

The plot shows a part of the spec­trum of pho­ton ener­gies observed when in an excited J/​ψ meson one of the excited energy states relaxes to lower-​energy lev­els. As we see here, the mass of the c quark- c anti­quark pair in an excited ψ state is higher than the sum of masses of its con­stituents which means that the sys­tem has stored bind­ing energy. This stored energy has a mass equiv­a­lent, because of E/​c² = m.

The LHCb exper­i­ment stud­ied, for its first time, the par­tic­u­lar trans­for­ma­tion of χ_c1 and χ_c2 mesons decay­ing into a J/​ψ par­ti­cle and a pair of muons in order to deter­mine some of their prop­er­ties very pre­cisely. Pre­vi­ous stud­ies of χ_c1 and χ_c2 at par­ti­cle col­lid­ers have exploited another type of decay of these par­ti­cles fea­tur­ing a pho­ton in the final state instead of a pair of muons.

How­ever, mea­sur­ing the energy of a pho­ton is very chal­leng­ing exper­i­men­tally in the harsh envi­ron­ment of a hadron col­lider. This new mea­sure­ment opens a new avenue to pre­ci­sion stud­ies of the prop­er­ties of χ_c mesons at the LHC, more than 40 years after the Novem­ber Rev­o­lu­tion took place.

As Gio­vanni Pas­sal­eva stated:

“Not only are we no longer obliged to resort to purpose-​built exper­i­ments for such stud­ies, but also, in the near future, we will be able to think about apply­ing a sim­i­lar approach for the study of a sim­i­lar class of par­ti­cles, known as bot­tomo­nium, where charm quarks are replaced with beauty quarks.”

For an easy intro­duc­tion into par­ti­cle physics and the stan­dard model, check out also our lat­est e-​book edi­tion: "The Mys­tery Of The Higgs Boson".