Rho meson

In particle physics, a rho meson is a short-lived hadronic particle that is an isospin triplet whose three states are denoted as ρ+, ρ0 and ρ−. After the pions and kaons, the rho mesons are the lightest strongly interacting particle with a mass of roughly 6990123367589499000♠770 MeV for all three states. There should be a small mass difference between the ρ+ and the ρ0 that can be attributed to the electromagnetic self-energy of the particle as well as a small effect due to isospin breaking arising from the light quark masses; however, the current experimental limit is that this mass difference is less than 6987112152354090000♠0.7 MeV.

The rho mesons have a very short lifetime and their decay width is about 6989232315590615000♠145 MeV with the peculiar feature that the decay widths are not described by a Breit-Wigner form. The principal decay route of the rho mesons is to a pair of pions with a branching rate of 99.9%. Neutral rho mesons can decay to a pair of electrons or muons which occurs with a branching ratio of 6995500000000000000♠5×10⁻⁵. This decay of the neutral rho to leptons can be interpreted as a mixing between the photon and rho. In principle the charged rho mesons mix with the weak vector bosons and can lead to decay to an electron or muon plus a neutrino; however, this has never been observed.

Rho

Rho (/ˈroʊ/; uppercase Ρ, lowercase ρ or ϱ; Greek: ῥῶ) is the 17th letter of the Greek alphabet. In the system of Greek numerals, it has a value of 100. It is derived from Phoenician letter res . Its uppercase form is not to be confused with the Latin letter P, although both types use the same glyph; P.

Uses

Greek

Rho is classed as a liquid consonant (together with lambda and sometimes the nasals mu and nu), which has important implications for morphology. In both Ancient and Modern Greek, it represents a trilled or tapped r.

In polytonic orthography a rho at the beginning of a word is written with a rough breathing (equivalent to h) — ῥ rh — and a double rho within a word is written with a smooth breathing over the first rho and a rough breathing over the second — ῤῥ rrh — apparently reflecting an aspirated or voiceless pronunciation in Ancient Greek, hence the various Greek-derived English words that start with rh or contain rrh.

The name of the letter is written in Greek as ῥῶ (polytonic) or ρω/ρο (monotonic).

Greeks (finance)

In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters (as are some other finance measures). Collectively these have also been called the risk sensitivities,risk measures or hedge parameters.

Use of the Greeks

The Greeks are vital tools in risk management. Each Greek measures the sensitivity of the value of a portfolio to a small change in a given underlying parameter, so that component risks may be treated in isolation, and the portfolio rebalanced accordingly to achieve a desired exposure; see for example delta hedging.

The Greeks in the Black–Scholes model are relatively easy to calculate, a desirable property of financial models, and are very useful for derivatives traders, especially those who seek to hedge their portfolios from adverse changes in market conditions. For this reason, those Greeks which are particularly useful for hedging—such as delta, theta, and vega—are well-defined for measuring changes in Price, Time and Volatility. Although rho is a primary input into the Black–Scholes model, the overall impact on the value of an option corresponding to changes in the risk-free interest rate is generally insignificant and therefore higher-order derivatives involving the risk-free interest rate are not common.

Rho GTPase

Rho GTPase may refer to: