### The LHC Era

My visit to the University of Warwick in September naturally made me regret my ignorance of the LHCb experiment. Very little time remains for theorists to get off their asses (yours truly included) and make some decent predictions.

The LHCb experiment will study bottom quark physics. It consists of a vertex detector, track reconstruction capabilities, and two Cherenkov detectors for velocity measurements and particle identification, which will separate pions and kaons.

In particular, LHCb will further study the beyond the standard model CDF result for the CP violation parameter $2 \beta_{s}$ in decays of the meson $B_{s}^{0}$. The definition of this parameter is

$2 \beta_{s} = 2 \textrm{arg} \frac{V_{ts} V_{tb}^{*}}{V_{cs} V_{cb}^{*}}$

in terms of the usual CKM matrix parameters. As CDF points out (cheers, Tommaso):

The LHCb experiment will study bottom quark physics. It consists of a vertex detector, track reconstruction capabilities, and two Cherenkov detectors for velocity measurements and particle identification, which will separate pions and kaons.

In particular, LHCb will further study the beyond the standard model CDF result for the CP violation parameter $2 \beta_{s}$ in decays of the meson $B_{s}^{0}$. The definition of this parameter is

$2 \beta_{s} = 2 \textrm{arg} \frac{V_{ts} V_{tb}^{*}}{V_{cs} V_{cb}^{*}}$

in terms of the usual CKM matrix parameters. As CDF points out (cheers, Tommaso):

The presence of physics beyond the standard model could contribute additional processes and modify the magnitudeThe Standard Model predicts $2 \beta_{s} = 0.04$, in contrast to the observation that $2 \beta_{s}$ lies in the interval $[0.32,2.82]$, with $68%$ confidence. The D0 experiment also reports on this decay.

or the phase of the mixing amplitude.

## 9 Comments:

Aw, come on Carl. When I use your values for the CKM phases I get beta_s = 3.501286, which is way too large, it seems.

But then I did use a dodgy online calculator and my old fingers have probably made some mistakes ... let's check.

Okay, I hope I understand this. I'm looking for

2 arg( Vts Vtb* / Vcs Vcb* ) =

2 arg( Vts Vtb* Vcs* Vcb ),

where "*" means complex conjugacy.

Before multiplying by two, and using the numbers from the CKM fit on my webpage (which is not original with me, except as to the peculiar choice of phases so as to make the matrix magic) I get the following angles:

89.33 - 13.06 + 0.25 + 257.90 = 334.42 = -25.58 degrees.

Twice this is -51.15 which is -0.8928 radians.

However, all this stuff is subject to complex conjugacy so it's equivalent to +0.8928 radians, compatible with experiment. In fact, it's dead center. But that's to be expected since the CKM fit on my website was chosen to be compatible with CKM measurements (according to that paper I referenced).

That sounds better. Let's see ...

What I haven't yet found is why the standard model has beta_s = close to zero. Any links?

The CDF paper in the post refers to this paper for the low value.

Er, Carl ... now I get a value of

0.9822629

which is closer to the centre of obs than your number.

Hmmm. The paper referenced doesn't have Vts Vtb&* / Vcs* Vcb in it, though it does have some similar stuff associated with the unitarity triangle.

Yes, it is a bit of a mystery. Tommaso, could you explain this?

Update: checked again May '10 with a decent algebra package ... and found 0.04 in agreement with the SM fits.

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